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Economic model predictive control for building energy systems

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Economic model predictive control for building energy systems

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Content ECONOMIC MODEL PREDICTIVE CONTROL FOR
BUILDING ENERGY SYSTEMS
by
Jingran Ma
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CHEMICAL ENGINEERING)
December 2012
Copyright 2012 Jingran Ma
ii
Dedication
To my parents, my wife and children.
iii
Acknowledgments
Pursuing a PhD degree is not an easy task. Along the four-and-a-half
year journey, I owe so many people so many things. In fact, there is no way
that I can complete this dissertation without these people who help me in
every way that one can be helped.
First of all, I would like to devote my deepest gratitude to my advi-
sor, Prof. S. Joe Qin. It is my greatest honor to study and work under his
guidance. I learned from him not only how to become a good researcher, but
also more importantly, how to become a good person. His kind support, se-
rious attitude, insightful view and always-positive personality inspire me
significantly. He offered a very free environment to conduct research, and
added my skill set with how to communicate with people effectively, which
I believe is very important for my career development in the future.
I am grateful for having such an honorable dissertation committee.
Deep thanks go to Prof. Katherine Shing and Prof. Qiang Huang for their
constructive comments. I would also thank Prof. Fred Aminzadeh, Prof.
Michael Safonov, and Prof. Pin Wang for their suggestions to my research.
I feel very fortunate to have the opportunity to study and work in the
Qin Research Group. The atmosphere here in the group is so enjoyable that I
iv
always feel like living in a warm family. When I just joined the group, Quan,
Carlos, Yamin and Bo helped me settle down smoothly. I would also like to
thank the current group members, including Alan, Yingying, Hu, Yu, Tao,
Johnny, Yining, Dr. Liu and Zhaohui, for their friendship and consistent
help. All the moments of studying and living in the group are pleasant and
will be kept forever in my memory.
In particular I am grateful to Dr. Tim Salsbury for his suggestions
from industry point of view that always ensure my research is on a correct
track. I cannot go that far to implement my idea in practice without his
big effort in making the field tests happen. It has been my great fortune to
have such interesting internship experiences. I would like to thank Dr. John
Seem, Dr. John House, Youngchoon Park, Gary Gavin and other colleges in
Johnson Controls. I appreciate Dr. Fang Yang and Dr. Guoxiao Guo for their
outstanding mentorship during my internships in ABB Corporate Research
and Western Digital, respectively.
I would like to acknowledge Johnson Controls Inc., Texas-Wisconsin-
California Control Consortium (TWCCC) and Center for Interactive Smart
Oilfield Technologies (Cisoft) for the financial supports they offered during
my graduate studies.
Finally, I owe huge to my parents and my wife Fang for their invalu-
able encouragement, patience and support. Thanks to my daughter Iris for
bringing endless happiness to my life.
v
Table of Contents
Dedication ii
Acknowledgments iii
ListofTables viii
ListofFigures ix
Abstract xii
Chapter1. Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Chapter2. BuildingEnergyModeling 18
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.2 Modeling in EnergyPlus . . . . . . . . . . . . . . . . . . . . . . 19
2.2.1 Step response tests . . . . . . . . . . . . . . . . . . . . . . 20
2.3 System Identification . . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.1 Excitation experiments . . . . . . . . . . . . . . . . . . . 21
2.3.2 ARX models . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Chapter3. BalancedModelReduction 32
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.2 Overview of Model Reduction . . . . . . . . . . . . . . . . . . . 34
3.2.1 Balanced model reduction for linear systems . . . . . . . 34
3.2.2 Nonlinear model reduction . . . . . . . . . . . . . . . . . 37
3.2.3 Balanced model reduction for buildings . . . . . . . . . . 38
vi
3.2.3.1 Balanced realization . . . . . . . . . . . . . . . . 39
3.2.3.2 Hankel singular value sequence . . . . . . . . . 39
3.2.3.3 Reduced states determination . . . . . . . . . . . 39
3.2.3.4 Truncation or residualization . . . . . . . . . . . 39
3.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Chapter4. EconomicMPCforBuildings 44
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.2 Existing Control Strategies . . . . . . . . . . . . . . . . . . . . . 45
4.3 Economic MPC Formulation . . . . . . . . . . . . . . . . . . . . 46
4.3.1 Economic Objective function . . . . . . . . . . . . . . . . 47
4.3.2 Linear programming . . . . . . . . . . . . . . . . . . . . . 47
4.3.2.1 Objective Function . . . . . . . . . . . . . . . . . 48
4.3.2.2 Constraints . . . . . . . . . . . . . . . . . . . . . 49
4.4 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.4.1 Real-time simulation environment . . . . . . . . . . . . . 51
4.4.2 Electricity price structure . . . . . . . . . . . . . . . . . . 53
4.4.3 Simulation scenario selection . . . . . . . . . . . . . . . . 54
4.4.4 Simulation results . . . . . . . . . . . . . . . . . . . . . . 57
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Chapter5. FieldTests 70
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2 Field Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2.1 Building information . . . . . . . . . . . . . . . . . . . . 72
5.2.2 Test environment . . . . . . . . . . . . . . . . . . . . . . . 73
5.2.3 Test procedure . . . . . . . . . . . . . . . . . . . . . . . . 74
5.2.4 Test results . . . . . . . . . . . . . . . . . . . . . . . . . . 75
5.2.4.1 Model performance . . . . . . . . . . . . . . . . . 75
5.2.4.2 Control strategy tests . . . . . . . . . . . . . . . . 76
5.2.4.3 Result analysis . . . . . . . . . . . . . . . . . . . 77
5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Chapter6. EconomicMPCinMicrogrids 86
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
vii
6.2 System Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.3 MPC Problem Formulation . . . . . . . . . . . . . . . . . . . . . 89
6.3.1 Objective Function . . . . . . . . . . . . . . . . . . . . . . 89
6.3.2 Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6.3.2.1 Real power balance . . . . . . . . . . . . . . . . . 91
6.3.2.2 Physical capacity . . . . . . . . . . . . . . . . . . 91
6.3.2.3 Power flow equations . . . . . . . . . . . . . . . 92
6.3.2.4 Voltage limit . . . . . . . . . . . . . . . . . . . . . 94
6.4 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.4.1 OpenDSS Simulator . . . . . . . . . . . . . . . . . . . . . 94
6.4.1.1 IEEE 13 node system . . . . . . . . . . . . . . . . 95
6.4.1.2 Distributed generators . . . . . . . . . . . . . . . 95
6.4.1.3 Energy storage . . . . . . . . . . . . . . . . . . . 96
6.4.1.4 Load schedule . . . . . . . . . . . . . . . . . . . . 97
6.4.2 Simulation Results . . . . . . . . . . . . . . . . . . . . . . 97
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Chapter7. Conclusions 105
Bibliography 109
viii
List of Tables
Table 2.1 Major building features modeled in EnergyPlus . . . . . . . 20
Table 4.1 TOU-GS-3 energy charge rate . . . . . . . . . . . . . . . . . . 54
Table 4.2 Ambient temperature of the simulation week (

C) . . . . . . 57
Table 4.3 Weekly cost savings compared to the baseline . . . . . . . . . 59
Table 5.1 Time-of-use electricity rates[107] . . . . . . . . . . . . . . . . 73
Table 5.2 Weather conditions for the testing days . . . . . . . . . . . . 78
ix
List of Figures
Figure 2.1 The user interface of Dymola . . . . . . . . . . . . . . . . . . 27
Figure 2.2 Zones division and input-output configuration in the En-
ergyPlus model . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Figure 2.3 Weekday schedule of the building internal loads: occu-
pant (top), lighting (middle) and equipment (bottom) . . . . 28
Figure 2.4 Step response tests of EnergyPlus model . . . . . . . . . . . 29
Figure 2.5 Input-output data of an excited zone for model identification 29
Figure 2.6 Temperature model prediction . . . . . . . . . . . . . . . . . 30
Figure 2.7 Power model prediction . . . . . . . . . . . . . . . . . . . . 30
Figure 2.8 Approximation of power by calculatingmT . . . . . . . . 31
Figure 3.1 Building model reduction for MPC . . . . . . . . . . . . . . 42
Figure 3.2 Model step responses . . . . . . . . . . . . . . . . . . . . . . 43
Figure 3.3 Trajectory tracking under random inputs . . . . . . . . . . . 43
Figure 4.1 Basic concept of MPC (Adapted from [6]) . . . . . . . . . . 61
Figure 4.2 Pro-programmed (Open-loop) control strategies . . . . . . 62
Figure 4.3 Framework of the building energy simulation system . . . 63
Figure 4.4 System diagram that enables Matlab and EnergyPlus ex-
change data in real-time on BCVTB . . . . . . . . . . . . . . 64
x
Figure 4.5 Graphic interface of running Matlab and EnergyPlus co-
simulation on BCVTB . . . . . . . . . . . . . . . . . . . . . . 64
Figure 4.6 Time period division in MPC simulation . . . . . . . . . . . 65
Figure 4.7 Weekly electrical costs vs. varyingt
1
, (t
3
=t
4
= 12) . . . . . 66
Figure 4.8 Weekly electrical costs vs. varyingt
3
, (t
1
= 2,t
4
= 12) . . . . 66
Figure 4.9 Zone temperature and power profiles in the weekly simu-
lation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Figure 4.10 Zone temperature profile (one day) . . . . . . . . . . . . . . 68
Figure 4.11 Power profile (one day) . . . . . . . . . . . . . . . . . . . . . 69
Figure 5.1 Floor map of the testing area . . . . . . . . . . . . . . . . . . 80
Figure 5.2 Remote HVAC setpoints control via internet . . . . . . . . . 81
Figure 5.3 Excitation data (one day one zone) . . . . . . . . . . . . . . 81
Figure 5.4 Temperature model prediction . . . . . . . . . . . . . . . . . 82
Figure 5.5 Power model prediction . . . . . . . . . . . . . . . . . . . . 82
Figure 5.6 Temperature and power profiles for a baseline testing day
(08.29.2012) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Figure 5.7 Temperature and power profiles for an EMPC testing day
(08.30.2012) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Figure 5.8 Ratio of power consumed in peak hours over non-peak
hours . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Figure 6.1 Schematic diagram of a typical MicroGrid . . . . . . . . . . 100
Figure 6.2 Project block diagram . . . . . . . . . . . . . . . . . . . . . . 100
xi
Figure 6.3 Load level daily schedule . . . . . . . . . . . . . . . . . . . . 101
Figure 6.4 Modified IEEE 13 node test feeder . . . . . . . . . . . . . . . 101
Figure 6.5 Generation output profiles under MPC . . . . . . . . . . . . 102
Figure 6.6 Generation cost comparison between ordinary control s-
trategy and MPC . . . . . . . . . . . . . . . . . . . . . . . . . 102
Figure 6.7 Bus voltage distribution measured after convergence of
each power flow calculation . . . . . . . . . . . . . . . . . . 103
Figure 6.8 Comparison between the EMPC application in buildings
and Microgrids . . . . . . . . . . . . . . . . . . . . . . . . . . 104
xii
Abstract
In the United States, buildings account for nearly three quarters of
electricity consumption and about 40% of greenhouse gas emissions. The
heating, ventilation and air-conditioning (HVAC) systems are responsible
for approximately one third of the energy usage in commercial buildings.
The inefficiency in operation and control of HVAC systems in most of the
current buildings places significant energy saving potentials. Even more
importantly, under advanced electricity rate structures in the nowadays u-
tility market with demand response, the energy cost for building HVAC
systems can be very high due to the high peak power demand associated
with the ordinary control strategies.
In this dissertation, we present a cost-effective supervisory control
strategy for the building HVAC systems. The goal of this work is to propose
and demonstrate an advanced control solution to optimize building energy
cost under the time-of-use rate structure, while maintaining the thermal
comfort level and indoor air quality. Model Predictive Control (MPC) is
the core methodologies investigated in this work, which is carried out in
two stages.
In the first stage, we develop a simulation framework, in which a
xiii
commercial building model crated in EnergyPlus acts as the building to be
controlled. Since the simulation model is not suitable to be directly used
in MPC, system identification is performed to obtain the empirical models,
which relate the thermostat setpoints to the zone temperature as well as
power consumption. Balanced model reduction technique is then applied
to lower the model order, while the major input-output dynamic relation is
captured.
The MPC problem is formulated utilizing the identified models with
reduced-order. Due to the slow building thermal dynamics, an economic
objective is combined with the underlying dynamic models, which forms
the Economic MPC (EMPC). The optimization in terms of building energy
cost has a min-max objective function to account for the combination of en-
ergy and demand charges, and a number of constraints to represent allowed
temperature range and model relation. The optimization is converted to a
linear programming and solved effectively in each time step, giving the op-
timal zone temperature setpoints.
The effectiveness of EMPC is demonstrated by a weekly simulation.
Substantial cost savings are brought by EMPC over the baseline and other
open-looped strategies. The simulation system established in this work can
also be used as a test-bed for other control algorithms.
In the second stage of this work, the proposed EMPC method is im-
plemented in a large office building located in Milwaukee, WI. The EMPC
xiv
controller is located at USC and connected to the building automation sys-
tem (BAS) via the Internet. Field tests results show that the EMPC strategy
is capable of shifting significant portion of power consumption out of peak
hours, therefore brings cost savings to the building.
In addition, another application of EMPC to the power dispatch
problem in Microgrid is described. It shows the potential of EMPC in
the area of renewable energy integration. A Microgrid with renewable
generation resources and controllable energy storages is considered.
Simulation-based EMPC structure is formulated to minimize the overall
power generation cost within the Microgrid.
1
Chapter 1
Introduction
1.1 Background
According to a report by the U.S. Department of Energy in 2009 [41],
73% of the nation’s electricity consumption and 40% of greenhouse gas e-
missions occur in buildings. Buildings account for 39% of total energy con-
sumption among all sectors, costing $350 billion per year [15]. Heating, ven-
tilation and air conditioning (HVAC) systems are responsible for one third
of building energy usage [41], which places significant saving potentials.
It is recognized that most existing buildings are not operated as effi-
ciently as they could be. In general, there are two approaches to achieve en-
ergy savings from consumption management by building automation sys-
tems (BAS): reducing consumption and shifting consumption [106]. The for-
mer can be realized by installing more energy efficient equipment in build-
ings, which usually faces into the resistance from building managers be-
cause additional investment is required for the system upgrade. The latter
approach on the other hand, aims at optimizing the operation of HVAC sys-
tems with existing equipment. It is seen that significant energy savings can
be brought up by simply changing control settings with advanced control
2
strategies [13].
In addition to reducing overall energy consumption, another impor-
tant need for building controls is to lower the peak power demand. Owing
to the fact that buildings especially commercial buildings tend to consume
energy simultaneously during peak hours, the peak-average-ratio (PAR) in
the electricity grid can be high [68]. Both electricity suppliers and customers
are concerned with the peak demand due to economic and environmental
challenges. New power plants are built every year merely to cope with the
rapidly increasing peak demand, which reduces efficiency in off-peak hours
and leads to higher energy costs [98]. Moreover, uncontrolled high peak de-
mand also makes it difficult to integrate renewable and distributed energy
resources. Therefore, it is of great interest to develop advanced technologies
to flatten the peak demand relative to base loads.
Although demand response (DR) is a relatively new term in the elec-
tricity market, it has received extensive attentions in buildings as a promis-
ing means to lower the peak demand. DR is an approach to encourag-
ing end users to change their electric usages from regular patterns, in re-
sponse to incentives of electricity price [1, 88]. Advanced electricity pricing
is increasingly applied by utilities, which includes time-of-use (TOU) rates,
critical-peak-pricing (CPP) and real-time pricing (RTP). It is demonstrated
that under these time varying price structures, the end-users are capable of
3
reducing energy costs by taking certain DR actions [100, 75, 83]. The cost-
effective strategy for building HVAC control is to shift the energy usage
away from the peak hours while all the normal operations, such as thermal
comfort level and indoor air quality are maintained [111].
Most of the current buildings are operated with the night-setback (N-
S) strategy, in which the HVAC is turned on when the occupied period starts
and turned off when it ends. The setpoints of thermostat are usually set as
constants during the entire occupied period. This strategy is really simple
and reliable, but far away from optimal in the sense of energy efficiency or
cost-effectiveness [10]. Previous attempts in [110, 50] developed some alter-
native strategies showing that significant peak reduction can be achieved by
doing pre-cooling (or pre-heating) in unoccupied period and adjusting set-
points during peak hours. These strategies take advantage of the building
thermal mass to shift the power demand. However, the setpoints schedules
are pre-determined, meaning that these open-looped strategies are not able
to response to the ever-changing indoor and outdoor conditions as well as
the states of HVAC systems. Therefore, there is still a large potential for
energy or cost savings with advanced HVAC control, as the building au-
tomation system (BAS) becomes an effective tool to manage resources and
data all over the buildings.
In this dissertation, we develop a set of advance control solution for
4
HVAC systems in commercial buildings based on Economic Model Predic-
tive Control (EMPC). The basic motivation of applying EMPC in energy ef-
ficient buildings is to give the controller the ability to anticipate the upcom-
ing peak hours, and to make right decisions such as pre-cooling in advance
automatically and optimally. Some features of the presented work are listed
below:
The presented methodologies make use of existing building automa-
tion systems. No additional equipment or sensor is needed.
The proposed control solution is cost-effective, which is determined
by the economic objective function. Significant economic benefits can
be realized from the proposed building control strategies.
The control algorithm is model-based. The dynamic models are ob-
tained by performing system identification on simulation models or
real buildings.
The disturbances such as internal loads and weather conditions are
modeled in a building energy simulator, e.g. EnergyPlus.
The demand response actions, such as pre-cooling is triggered auto-
matically and optimally. The time-of-use electricity price structure in
incorporated into the controller design.
5
The proposed control strategy is easy to implement in real buildings
by replacing the existing controller because it only overwrites the tem-
perature setpoints.
The indoor comfort level is maintained by appropriate configuration
of temperature constraints in the MPC design. The solutions given by
the controller should be always feasible.
1.2 Literature review
Building HVAC control systems can be divided into two hierarchical
layers, i.e., local controls and supervisory controls [106]. Local controls are
designed to ensure proper operations of equipment, such as chillers, cooling
coils, fans and dampers in air handling units (AHU). The controller types
used in local control loops include proportional-integral-derivative (PID)
control, On/Off control, step control and modulating control. They have
been developed maturely in theory and implemented effectively in prac-
tice. Typical objectives of local controls are reference tracking and system
stability. The local actuators are able to work effectively by proper controller
settings, however, these settings may not be optimal when the whole build-
ing is of concern. Therefore, supervisory controls in the upper layer aim
at optimizing the overall system performance (such as energy consumption
or cost) by determining optimal setpoints for local controllers. Supervisory
6
controls also need to provide satisfied indoor comfort and healthy envi-
ronment, while taking in to account the constantly changing internal and
external disturbances.
The idea of using advanced supervisory control technologies to im-
prove building energy efficiency has been evolving for decades. At the ear-
ly stages, although the energy conservation potential was observed, it was
hard to make substantial progress due to the limited computational capa-
bility [99, 69, 39]. Thanks to the advancements in modeling, simulation and
optimization techniques [59], advanced control in buildings received exten-
sive attentions in the past decade, and has been applied to various types
of systems by building researchers. Well developed building simulation
tools are often employed as online building computation models [112]. Ad-
vanced control techniques for demand response and building energy effi-
ciency constantly emerge, facilitating the level of DR from manual to semi-
automated and fully-automated [43].
Depending on wether certain types of models are needed, supervi-
sory controls can be divided into model-free and model-based categories.
Krarti gave an outstanding review on artificial intelligence-based methods
for building energy systems [46]. Most of them are model-free, yet they
usually require large amounts of data from specific buildings, meaning that
even though the apporaches have been tested successfully in a particular
7
building, same performance is not guaranteed in other buildings, or even
for the same building but under different operation conditions. In other
words, the model-free methods require additional effort to develop into
generalized technologies.
Ben-Nakhi and Mahmoud developed an optimal temperature set-
back strategy using general regression neural networks [7]. The work in
[74] and [73] used Genetic Algorithm (GA) to solve optimization problems
formulated in terms of energy consumption and thermal comfort in multi-
zone buildings. The work in [65] used Particle Swarm Optimization to ex-
tract operation rules for mixed-mode buildings. Lin and Henze proposed
an reinforcement learning method for building HVAC control, in which the
controller attempts to learn from previous operations to improve itself [55].
The learning period can be unacceptably long and the control performance
is sensitive to many parameters, which makes it not very attractive to im-
plement in practice.
With more and more modeling approaches available and the as-
sistance of various modeling packages, accurate modeling for large scale
buildings is not a bottle-neck any more [38, 19, 116]. In building energy
system control, the models are utilized to predict the system thermal
and/or energy behavior as well as the system response to changes of
control settings. Model-based building control can be implemented either
8
off-line or on-line. In off-line implementations, the optimization formulated
in terms of energy consumption or other objectives is independent with
current building operations. The open-loop optimal control actions are
passed back and applied in the building after the optimization is finished.
By contrast, on-line implementation refers to the scheme coupling both
building and controllers. The optimization is formulated with current and
future information and generates actual operations in every time interval.
Apparently the on-line model-based control is more powerful yet more
complicated, and requires a close coupling with the BAS [23].
A number of model-based control methods have been developed and
tested for optimizing the operation of HVAC systems [36]. Applications
include supervisory control of building power plants, central chilled water
system [64], vapor compression cycle (VCC)[103], air handling units [105],
thermal energy storage [84] and ventilation [117], etc. However, there has
not been much work on direct optimization of thermostat setpoints, which
is the main scope in this dissertation.
Modeling plays a crucial role in building energy control. According
to the knowledge utilized in the modeling phase, models can be labeled as
white-box, black-box or grey-box. White-box models are established from
the system physical description, so that the model parameters have physical
meanings. Differential equations are the typical form to describe fundamen-
9
tal conservation laws of energy, mass, heat transfer, momentum, etc. For ex-
ample, the analogy of R-C circuit network is often used in modeling zonal
heat transfer in buildings [63, 8]. In general, white-box models have good
prediction performance as long as the they are working in allowed ranges,
and they need less training data to build. However, these physical model-
s are usually structurally complicated, which may result in limitations for
online applications.
High-end building energy simulation programs such as EnergyPlus
[77] and Modelica [81] allow for the immersive representation of building
thermal dynamics. However, incorporating a simulation model directly to
the optimal control design, i.e. simulation-based control design [11], is often
a tedious task because the simulator may be called a large number of times
in the iterations searching for optimal solutions [76] and local optima are
often encountered with non-gradient based searching algorithms [40]. Be-
sides, Calibration is needed for the simulation model of existing buildings
to ensure qualified fidelity [82, 115].
Black-box models do not need to have any prior knowledge of the
system, and usually their parameters have no physical significance. They
are developed to relate input variables to output variables directly in math-
ematics, based on the empirical behaviors of the system. The models can
be either linear or nonlinear, and used to describe system behavior in tran-
10
sient process or steady-state. System identification is an effective method
to estimate model parameters, when there are adequate training data avail-
able. There are two major challenges in model identification for building
HVAC systems [85, 4]. 1) Extensive excitation is often not applicable be-
cause buildings are required to operate within certain range (For example,
indoor temperature is forced in the comfort region during occupied hours).
A corresponding solution is to crate simulation models for the building, and
then perform model reduction on the simulation model [29, 27, 21]. 2) The
model with time-invariant parameters may not be able to simulate building
behavior very well since buildings are operated in a constantly changing en-
vironment. For example, the model estimated from data in summer season
should not have good prediction performance in winter.
Gray-box models are seen as a hybrid combination of white-box and
black-box models. They contain both physically significant and insignifi-
cant parameters. A typical approach of creating gray-box models is to add
a black-box component on top of the white-box model in order to represent
or correct the features that can not be captured by the physical model [36].
When there are accurate dynamic models to be used for control,
Model Predictive Control (MPC) is a good approach. MPC has been shown
as a successful approach by numerous industrial applications [86]. How-
ever, there has been little attempt of using MPC to minimize the energy
11
and demand costs in buildings. MPC is essentially an optimization based
strategy in which an explicit model is employed to predict the behavior of
the controlled plants over a receding horizon [66, 89]. In each time step, an
open-loop optimal control problem is formulated and solved, and only the
control action of the current time step is implemented on the plant. This
routine is iterated at subsequent intervals with new measurements and
updated plant information.
The advantages of the MPC method in building energy control are in
three folds: 1) There is a systematic procedure to create a dynamic building
thermal model for the purpose of predictive control; 2) Various constraints
from physical, environmental and safety perspectives can be explicitly in-
corporated into the optimal control calculations; 3) The impact of distur-
bances, such as ambient temperature and solar radiations, can be handled
in real-time by the ability of MPC in uncertainty estimations.
Recently, MPC has received increasing effort in research and devel-
opment in building area [92]. Although MPC is a rather mature method
in process industry, its applications in buildings usually need some special
treatments. For commercial buildings, the operations have daily cycles. The
indoor temperature needs to be regulated in occupied period only, which is
an important knowledge that should be carried by the prediction model-
s [33, 16]. Building system is so complicated that it is unrealistic to try to
12
formulate a global optimization problem for the entire building. Instead,
it is wise to break down the models, measurements and optimization into
smaller pieces and handle them separately. Morosan et. al. developed a
distributed MPC scheme for building temperature regulation, in which the
distributed controller takes the advantages of both pure centralized control
and pure decentralized control [72].
Other than energy consumption, another important control objective
in buildings is thermal comfort, which as a abstract concept can be defined
quantitatively by various indices [24]. In a majority of MPC designs, ther-
mal comfort requirement is set as constraints on zone temperature. Freire
et. al. formulated a multi-objective optimization in MPC to find the optimal
solution in the trade-off between thermal comfort and energy consumption
[26]. Kolokotsa et. al. applied MPC in a building energy management sys-
tem (BEMS) on the optimization of indoor environmental conditions [45].
Lee and Braun developed a demand limiting strategy based on M-
PC, in which a target demand for peak hours is determined by off-line op-
timizations [51]. Pre-cooling is started before occupied periods and lasts
until peak hours. The setpoints for pre-cooling are fixed at the lower bound
of the thermal comfort range. During peak hours (demand limiting peri-
ods), MPC adjusts the temperature setpoints to ensure the power demand
will not exceed the target threshold. It is found that the setpoints trajecto-
13
ries under demand limiting have the logarithmic shape [52, 53]. Coffey et.
al. supported this finding and developed a software framework for MPC
applications, in which a modified genetic algorithm was used to solve the
optimization problems in MPC [17]. The demand limiting method is able
to give near-optimal solutions that ensure the peak demand is lower than
target, however it is not able to handle disturbances like building internal
loads and weather conditions.
Building thermal mass has been recognized as an important asset to
shift energy consumption, and there have been a number of simulation and
experimental studies on reducing the peak demand by taking advantage
of the it. Braun and Rabl exploited the possibility of shifting cooling load-
s from daytime to nighttime to reduce the peak demand, and meanwhile
mixing the ventilation at night with mechanical cooling to saving energy
[9, 87]. The basic idea is to save cooling into the building thermal mass
during unoccupied hour, when the electricity is cheaper and outside tem-
perature is lower, and release the stored cooling in peak hours. The ability
of demand shifting strongly depends on several factors including the level
of building thermal capacitance, electricity rate structure, occupancy sched-
ule and weather conditions. In those buildings that have active thermal
storage installed, for example cold water tanks or ice storage, optimal con-
trol strategies are designed to operate the buildings in a demand responsive
14
fashion [44, 34]. Ma et. al. carried out studies on predictive control in build-
ings with thermal storage [62]. Yin et. al. developed a simulation tool to
assess the automated demand response and optimal pre-cooling strategies
for buildings in the California climate zone [113].
Buildings are operated in a constantly changing environment. Exter-
nal disturbances, such as weather conditions, solar radiations can affect the
control performance significantly. Hong and Jiang developed a stochastic
weather model and incorporated it to the building HVAC control algorithm-
s [37]. Florita and Henze compared various short-term weather forecasting
methods, such as time series analysis and Neural Networks, and evaluated
their applicability in MPC schemes [25]. The OptiControl Project conduct-
ed in ETH [71] took advantage of archived weather forecast provided by a
public service, and a crated disturbance model to account for the prediction
uncertainty [79, 78].
The occupancy is a major internal load in buildings. Thanks to the
availability of occupancy sensors and information fusion technologies, the
number of people in each zone can be monitored and occupancy distribu-
tion can be estimated [104, 54], which gives more useful information to su-
pervisory controllers.
While many studies focus on reducing the energy consumption and
peak demand, there has been less work on reducing the energy and de-
mand costs of build energy systems. Daryanian and Norford investigated
15
the minimum-cost control under real-time prices [20]. Henze et.al. consid-
ered both energy and demand charges in a two-loop optimization of build-
ing thermal mass control [35]. A target demand limit as in [51] is deter-
mined in the outer loop. The inner loop works in a batch mode, and decision
variables in each planning horizon (48 hours) only contain temperature set-
points in pre-cooling and post-cooling periods as well as the time constant
of exponential trajectory for controlled release of storage in demand limit-
ing periods. The optimization is solved by Nelder-Mead simplex searching
algorithm and the obtained solutions have a clear pattern [14]. The major
limitation of this work is that the simplified selection of decision variables
sacrifices a large portion of space in searching for optimal setpoints trajec-
tories. Besides, the batch mode is not able to response to unexpected distur-
bance changing in real-time.
1.3 Outline
The following parts of this dissertation are organized as follows.
In Chapter 2, we start with the studies on building energy modeling.
The models are used to predict the building thermal and energy behavior,
with temperature setpoints for HVAC systems as model inputs and actual
zone temperature and power consumption as outputs. Different state-of-
the-art building energy modeling simulators are reviewed and compared.
EnergyPlus is selected as the primary tool for simulating a single-floor,
16
multi-zone commercial building. System identification methods is then
applied to obtain a empirical model from excitation data.
Chapter 3 investigates the balanced model reduction method for the
high-order models obtained from system identification in Chapter 2. It is
seen that by transforming the system into a balance realization using sys-
tem Gramins, the major input and output relation can be captured. Simu-
lation shows the order of the model can be significantly reduced without
sacrificing much of prediction accuracy.
In Chapter 4, an Economic MPC scheme is formulated. The differ-
ences of Economic MPC from traditional MPC are described. Current con-
trol strategies in existing literature is reviewed for comparison with the M-
PC method proposed in this work. An economic objective function is de-
signed to represent the total power cost of building HVAC systems. By in-
troducing an intermediate variable to account for the peak demand, the op-
timization is converted to a linear programming. Building dynamic models
are explicitly incorporated to the equality constraints. A real-time simula-
tion system is built to form a close-looped simulation environment, where
EnergyPlus acts as the building to be controlled and the controller is de-
veloped in Matlab. The data exchange between EnergyPlus and Matlab
directed by a middleware software is described. Simulation results shows
that the proposed economic MPC method can bring substantial cost savings
17
over the baseline and other ordinary control strategies.
As a subsequent demonstrating work, in Chapter 5, the implemen-
tation of the proposed MPC method in a real building is presented. A
network-based remote control system is established, in which the controller
locates remotely and overwrites optimal setpoints schedules to the server,
and the building automation system reads the setpoints in each time
step and applies to the zones. The test results are shown and analysis is
followed.
Chapter 6 presents another application based on the proposed eco-
nomic MPC method, which is the power dispatch problem in a Microgrid.
The system structure is illustrated, showing the similarity of this problem
and the building HVAC control project. An optimization scheme, including
objective functions and constraints is designed to minimize the overall gen-
eration cost in the Microgrid, in the presence of renewable energy resources,
distributed generations and energy storages. Simulation-based MPC is ap-
plied based on a distribution network simulation model. Simulation results
show that MPC can reduce generation cost while satisfying all the loads and
operation constraints.
Chapter 7 concludes the dissertation and suggests future directions
of this research.
18
Chapter 2
Building Energy Modeling
2.1 Introduction
Thanks to the development of modeling and simulation technolo-
gies, a number of building energy simulation programs have been devel-
oped and enhanced. A good review in terms of evaluations of different
building energy simulation programs is given in [18]. EnergyPlus, eQuest
and Modelica are among the most popular programs for building energy
simulation. EnergyPlus is a modular program inherited from BLAST and
DOE-2 [77]. It describes the building features in an input file and carries
thermal simulation with an embedded engine. The package of eQuest al-
lows users to crate the building models using a wizard, and carry out mul-
tiple simulations and view the alternative results with graphical plots[18].
Modelica is an object-oriented modeling language for complex systms[101].
A library particularly for buildings is available, allowing users to simulate
building thermal behavior with first-principle models. Modelica is a stand-
alone language that requires a simulation environment to run, such as Dy-
mola [81], whose interface is shown as 2.1.
In this work, we start with crating a model using a simulator. En-
19
ergyPlus is selected as the major tool to simulate buildings, even though it
does not have an user interface, because using input/output files in sim-
ulation is more convenience for applying system identification and close
looped control. The utilization of weather files in EnergyPlus allows one to
handle the ambient disturbance separately. In the simulation studies, the
model in Energyplus is acting as the real building to control, and the pre-
diction models in MPC are obtained through system identification.
2.2 Modeling in EnergyPlus
A single story commercial building located in Chicago, Illinois with
a simple layout is modeled in EnergyPlus. Shown in Fig. 2.2, the building
is divided into five conditioned zones which include one interior and four
exterior. A set of VAV boxes with controllable actuators and temperature
sensors is installed in each zone. The position of dampers is determined in-
ternally by EnergyPlus and no control can be directly imposed on it. Other
major properties of the modeled building are listed in Table 2.1.
The impact of building cooling loads such as occupants, lighting and
electrical equipment is included in the EnergyPlus model. Fig. 2.3 shows
the internal load schedules in normal weekdays where the factors represent
the ratios between actual and full loads. 60% of the occupants are assumed
to go outside the building during lunch breaks. The schedule of lighting
is consistent with the occupancy schedule. The higher load of equipment
20
Table 2.1: Major building features modeled in EnergyPlus
Floor area 5000ft
2
Orientation 30

east of north
Window to wall ratio 0.29
Internal loads
Occupant 1 occupant / 100ft
2
Lighting 16.18 watts /ft
2
Equipment 10.79 watts /ft
2
Occupied hours 7:00 18:00
Cooling system VAV direct expansion (DX)
Heating system N/A
Natural ventilation N/A
in afternoon indicates that more equipment needs to be turned on in this
period, and this is one of the reasons why this period is usually counted as
on-peak. Note that different schedules of internal loads are used in week-
days and weekends.
Energyplus is also capable of simulating the external disturbances.
A TMY2 weather file that contains historical measurements of ambient tem-
perature, relative humidity and various types of solar radiation is used.
2.2.1 Step response tests
Step responses of the EnergyPlus model are firstly conducted to test
the building thermal capacity. Fig. 2.4 depicts two tests in which all zones
are being deeply cooled at a very low temperature (18

C) until shutting
down the HVAC at noon. The tests on weekend and weekday both show
21
that the cooling stored in the building can naturally release out in about
4 hours. This result provides a prior knowledge to the subsequent MPC
controller design.
2.3 System Identication
The building thermal and energy behavior can be simulated by En-
ergyPlus very well, however, mathematical input-output relations are stil-
l required to implement model-based controllers. System identification is
therefore performed on the EnergyPlus simulation model to obtain math-
ematical models that can be used to predict building thermal and power
behavior.
Autoregressive exogenous (ARX) models are used here where their
inputs are zone temperature setpoints of the cooling system and their out-
puts are actual zone temperature and power measurements. The task of
model identification is challenging due to non-linearity and disturbances
[93]. Experiment are designed to identify the models while the cooling sys-
tem is being operated over normal conditions.
2.3.1 Excitation experiments
A pseudorandom binary sequence (PRBS) is generated as the excita-
tion input. The binary levels of the PRBS are the lower and upper bounds
of the thermal comfort region, which in this work are set as 21 and 25

C.
22
For the considered single-floor,five-zone building,each zone is excited sep-
arately in order to reduce the interactive effects among the HVAC control
actions of different zones. In other words, when one zone is excited with
PRBS, the cooling of the other four zones is maintained in action as much as
possible. This is done by altering the zone setpoint of the excited zone with
lowered setpoint values during PRBS tests. The cooling setpoints are set as
(2.1). The EnergyPlus model is fully excited over an one month period and
the input-output data of occupied hours is used for system identification,
which is shown in Fig. 2.5.
T
sp;i
(k) =
8
<
:
21; excited zone, PRBS = 0
25; excited zone, PRBS = 1
25; non-excited zones
(2.1)
2.3.2 ARX models
Linear ARX model is chosen as the model structure. Suppose the
number of zones is , the input-output relation is represented as the form
of difference equations. The MISO power prediction modelF
P
is described
as
A
P
(q)y
P
(k) =B
P
(q)u(k) +e(k) (2.2)
where
y
P
(k) =P (k) (2.3)
23
is the model output, and
u(k) =
2
6
6
6
4
T
sp1
(k)
T
sp2
(k)
.
.
.
T
sp
(k)
3
7
7
7
5
(2.4)
is the model input.P (k) is the power consumption in thekth time interval,
T
spi
(k) is the temperature setpoint for theith zone.
A
P
(q) andB
P
(q) are polynomials in terms of the time shifting oper-
atorq.
A
P
(q) = 1 +
No
X
i=1
a
P
i
q
i
(2.5)
B
P
(q) = [B
P 1
(q);:::;B
P
(q)] (2.6)
B
Pj
(q) =
No
X
i=1
b
P
ji
q
i
; j = 1::: (2.7)
In (2.5) and (2.7),N
o
is the model order, which is initially determined
by the Matlab System Identification Toolbox. a
P
i
andb
P
i
are the parameters
to be identified for the power prediction model.
The prediction model for temperature F
T
has actual zone tempera-
ture as multiple outputs, sharing the same inputu(k) with the power model.
24
y
T
(k) =
2
6
6
6
4
T
z1
(k)
T
z2
(k)
.
.
.
T
z
(k)
3
7
7
7
5
(2.8)
The temperature model is MIMO, which is described as
A
T
(q)y
T
(k) =B
T
(q)u(k) +e(k) (2.9)
A
T
(q) andB
T
(q) are model parameters to be identified
A
T
(q) = [A
T 1
(q);:::;A
T
(q)] (2.10)
B
T
(q) = [B
T 1
(q);:::;B
T
(q)] (2.11)
A
Tj
(q) = 1 +
No
X
i=1
a
T
ji
q
i
; j = 1::: (2.12)
B
Tj
(q) =
No
X
i=1
b
T
ji
q
i
; j = 1::: (2.13)
2.4 Simulation Results
The input-output data are collected from excitation experiments, and
then the offest is removed from data to obtain zero-mean. Invalid data due
to saturation of HVAC are also eliminated from the training data set. Pre-
diction models for temperature and power are obtained through system i-
dentification in Matlab Toolbox [57].
25
Fig. 2.6 and Fig. 2.7 show the prediction performance of models. A
separate testing data set is used to validate the model outputs. The nor-
malized root mean square (NRMSE) measure is calculated to indicate the
goodness of the fit. Orders for both the temperature and power models are
determined as 20. It can be seen from the plots that the models have good fit
with the original EnergyPlus model. Therefore, the obtained ARX models
can be used in MPC design to predict the thermal and power behavior for
the zones.
It is noted that the direct power measurements in the EnergyPlus
simulation may not be available in the world. Most buildings only have
measurements for the whole building. On the other hand, the model in En-
ergyPlus is created using first principle and treated as a black-box, the pow-
er should calculated from thermal balance equation as (2.14) and affected
by other complicated factors.
Q =mC
p
T (2.14)
where, Q is the power consumption, m is the cooling air flow rate, C
p
is
specific heat and T is the temperature deviation caused by the cooling.
Fig. 2.8 shows the approximation of power consumption.
26
2.5 Summary
Building modeling is presented in this section. We start from a build-
ing model created in EnergyPlus, and obtain the mathematical models by
system identification. The models represent the relation between zone set-
points and actual zone temperature and power. The predictions made by
the models will be utilized in the following MPC development.
27
Figure 2.1: The user interface of Dymola
Figure 2.2: Zones division and input-output configuration in the Energy-
Plus model
28
0
0.5
1
Occupant factor
0
0.5
1
Lighting factor
0 4 8 12 16 20 24
0
0.5
1
Time of day (hr)
Equipment factor
Figure 2.3: Weekday schedule of the building internal loads: occupant (top),
lighting (middle) and equipment (bottom)
29
Figure 2.4: Step response tests of EnergyPlus model
17
19
21
23
25
27
Temperature (
°
C )

T
sp
T
z
8 9 10 11 12 13 14 15 16 17 18
0
5
10
15
20
25
Time of day ( hr )
Power ( kw )
Figure 2.5: Input-output data of an excited zone for model identification
30
7700 7800 7900 8000 8100 8200
68
69
70
71
72
73
74
75
Tz4. (sim)
Time Step
Tz4 (F)

Measured
Model Tz4; fit: 76.95%
Figure 2.6: Temperature model prediction
7700 7800 7900 8000 8100 8200
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
P
cooling
. (sim)
Time step
P
cooling
(W)

Data P
Test
; measured
Model P; fit: 67.02%
Figure 2.7: Power model prediction
31
0 48 96 144 192 240 288 336 384 432 480
0
5
10
15
20
mΔT
0 48 96 144 192 240 288 336 384 432 480
0
2000
4000
6000
8000
Cooling Power [W]
Timestep
Figure 2.8: Approximation of power by calculatingmT
32
Chapter 3
Balanced Model Reduction
3.1 Introduction
The ultimate goal of the work presented in this dissertation is to ap-
ply MPC for optimizing the operation of HVAC system in buildings and
thus reducing energy cost. The performance of MPC strongly relies on the
models that are used to relate control signals to zone temperatures and pow-
er consumptions. Thanks to the development in modeling and simulation
techniques, it is possible to simulate a building by establishing highly ac-
curate and reliable models in dynamic simulators, and it is noticed that
newly designed and constructed buildings are often associated with sim-
ulation models [18]. However, using a rigorous model directly in designing
a model-based controller is arduous because of the difficulty in formulating
the optimization problem and heavy computational burden brought by the
complexity and nonlinearity of the models [36]. Thus it is necessary apply
model reduction techniques to achieve a trade-off between prediction ac-
curacy and model complexity. In this section the evolution process from a
building model build in a simulator (EnergyPlus) to a reduced-order model
for control is described, as shown in Fig. 3.1.
33
A method based on Markov chains is proposed in [21] to reduce
building thermal models, which are originally built by aggregation of
blocks of RC-networks. This method preserves the electrical analogy
interpretation, however, the scaling of RC-network models grows steeply
with the increasing building structure complexity. In [27], a first-principles
dynamic model is created by a combination of a linear-time-invariant (LTI)
and a nonlinear component, and model reduction is performed by first
applying standard balanced realization to the LTI part, and then truncating
states in the transformed coordinates.
A simulation-based scheme is developed in [76] using the Energy-
Plus simulator as a black-box model as well as the actual building to be
controlled, which means the exact thermal dynamics of the building is as-
sumed to be known. When solving the optimization in MPC, the prediction
model built inside the simulator needs to be called a great number of time
in each iteration, which leads to unacceptable computational cost.
Unlike [76], model reduction and system identification are employed
in our work to obtain models to be used in MPC [60]. The identification
often needs input-output data generated in real occupied buildings, but
qualified data is hard to obtain due to the requirements of thermal com-
fort [33]. Therefore in this work, we perform model reduction on simu-
lation models to obtain state-space models. The model reduction method
34
applied is based on balanced realization theory. Because the most signifi-
cant portion of input-output relations is captured by the presented model
reduction method, MPC equipped with reduced-order models can achieve
as good performance as using identified models directly in the sense of cost
savings, however, the computational cost is significantly lowered.
3.2 Overview of Model Reduction
There have been extensive literatures focusing on the model reduc-
tion and the methods for linear models are well studied [70, 91, 5]. In gen-
eral the balanced model reduction method consists of two steps [31, 29]. 1)
Find a linear coordinate transformation to balance the controllability and
observability gramians; 2) Perform a projection to the states corresponding
to the largest eigenvalues of the balanced gramians.
3.2.1 Balanced model reduction for linear systems
Consider annth order LTI system
x(k + 1) =Ax(k) +Bu(k) (3.1)
y(k) =Cx(k) +Du(k)
Suppose the system is open-loop stable, the system is controllable
if its controllability gramianW
c
has full rank and observable if its observ-
ability gramian W
o
has full rank. These gramians are determined by the
35
Lyapunov equations
W
c
=
R
1
0
e
At
BB
T
e
A
T
t
dt (3.2)
W
o
=
R
1
0
e
A
T
t
C
T
Ce
At
dt
AW
c
+W
c
A
T
+BB
T
= 0 (3.3)
A
T
W
o
+W
o
A +C
T
C = 0
A system realization (A,B,C,D) is called balanced if its controllability
and observability gramians are identical and diagonal. It is shown that there
exists an invertible state-space transformationT2R
nn
x =Tx (3.4)
such that the transformed system
x(k + 1) = TAT
1
x(k) +TBu(k) =

A x(k) +

Bu(k) (3.5)
y(k) = CT
1
x(k) +Du(k) =

C x(k) +Du(k)
is in balanced form [70]. In balanced realization, the gramians are trans-
formed as

W
c
=TW
c
T
T
(3.6)

W
o
= (T
1
)
T
W
o
T
1
36
such that

W
c
=

W
o
= = diag (
1
;
2
;:::;
n
) (3.7)

1

2

n
0 (3.8)
where
i
’s are the Hankel singular values, which are indices to represent
the importance of the states. The state corresponding to the largest singu-
lar value (
1
) has the most influence on the input-output behavior of the
system. It is known that the Hankel singular values are independent to the
selection ofT [47].
The central idea of the balanced model reduction is to remove those
states that are unimportant in affecting the input-output behavior, i.e., the
states corresponding to zero and small singular values. For the system in
balanced form as in (3.5), the state vector x can be partitioned into more
important states ( x
1
2R
r
) and less important states ( x
2
2R
nr
) by setting a
threshold for singular values.

x
1
(k + 1)
x
2
(k + 1)

=

A
11

A
12

A
21

A
22

x
1
(k)
x
2
(k)

+

B
1

B
2

u(k)
y(k) =

C
1

C
2

x
1
(k)
x
2
(k)

+Du(k) (3.9)
Simply eliminating the state vector x
2
, an rth order system is ob-
tained as shown in (4.3).
x
1
(k + 1) =

A
11
x
1
(k) +

B
1
u(k) (3.10)
y(k) =

C
1
x
1
(k) +Du(k)
37
It is noted that although the reduced-order model by simply trun-
cating of x
2
approximates most of the system behavior, the steady-state re-
sponse is altered. In circumstances where this matters, a modification can
be made to enforce matching the steady-state response, which is referred as
residualization in [31]. The reduced system represented in (4.4) is better than
in (4.3) is the sense of maintaining steady-state behavior of the full-order
system.
x
1
(k + 1) =

A
11

A
12

A
1
22

A
21

x
1
(k) +

B
1

A
12

A
1
22

B
2

u(k) (3.11)
y =

C
1

C
2

A
1
22

A
21

x
1
(k) +

D

C
22

A
1
22

B
2

u(k)
Balanced model reduction is intuitively straightforward and easy to
implement. It is especially favorable for problems where the reduced-order
model will be used for controller design, because the input-output behavior
is retained at the maximum extent.
3.2.2 Nonlinear model reduction
Model reduction for nonlinear systems is much less developed.
Scherpen proposes a balancing method by defining the controllability and
observability energy functions [97], which are related to the gramians.
These energy functions however are difficult to compute and the method is
only working for control-affine systems.
Lall et al. use the defined empirical gramians to determine the impor-
38
tance of particular subspace, in terms of its contribution to the input-output
behavior [47]. These empirical gramians are calculated by simulation or ex-
perimental data generated within the system’s expected operating region,
in which some of the nonlinear behavior is captured by resulted gramians.
Hahn and Edgar propose a hybrid method by introducing controllability
and observability covariance matrices [30], which can be computed from
data along system trajectories. The covariance matrices outperform empiri-
cal gramians because it accepts data generated by various input shape. The
balanced truncation method is further extended in [94, 95] by introducing
the so-called extended gramians to improve error bounds and enforce struc-
tural constraints.
The model reduction methods for nonlinear system is not an empha-
size in this work, since the model reduction is carried out on basis of the LTI
identified models.
3.2.3 Balanced model reduction for buildings
The order of identified modelsn is determined in the Matlab toolbox.
It is initially set to be high to ensure that significant portion of building dy-
namic behavior is captured. It is suggested in [21] that the number of states
steeply grows with the increasing of building complexity. Even for minimal
realizations in which all states are both controllable and observable, there is
still potential to further reduce the model order without seriously affecting
39
the input-output relation. The balanced method is employed to eliminate
the states that contribute none or little to the system input-output behavior.
The model reduction for the temperature modelF
T
is carried out by
following steps:
3.2.3.1 Balanced realization
Take linear coordinate transformation as (3.5) with matrixT2R
nn
which is constructed by the method described in [70].
3.2.3.2 Hankel singular value sequence
Calculate transformed gramians with (3.6) to obtain the sorted Han-
kel singular values.
3.2.3.3 Reduced states determination
Suppose the reduced model has the order ofr, (r n). r is decided
by
minr s:t:
r
X
i=1

i
.
n
X
i=1

i
(3.12)
where2 (0; 1). It is known that twice the sum of truncated Hankel singu-
lar values gives anH
1
error bound [30].
3.2.3.4 Truncation or residualization
Partition the transformed state vector. The reduced model is ob-
tained by truncation as (4.3) or by residualization as (4.4). The resultingrth
40
order modelF
T;r
is realized as (A
T;r
;fB
T;r;u
;B
T;r;v
g);C
T;r
;fD
T;u
;D
T;v
g).
The above routine can also be done forF
P
if necessary, which results
in the reduced power modelF
P;r
.
3.3 Simulation Results
The original temperature model F
T
has the order of 20. By setting
= 0:9 in (4.7), its order can be reduced to 4. Both balanced truncation and
residualization algorithms are implemented to obtain reduced models.
Fig. 3.2 shows the model step responses under the setpoints of 23

C
and Fig. 3.3 shows the tracking performance for random integer setpoints
within the thermal comfort region. It can be seen that system identification
is successful because the outputs of identified model much well with the
validated data from EnergyPlus, and the dominant input-output behavior
is captured by the reduced models. The residualized model outperforms
the truncated one since it does not carry offest, therefore it is used as the
prediction model in MPC.
3.4 Summary
This chapter presents a balanced method for model reduction
of building energy systems. Since rigorous building models built by
simulators like EnergyPlus are not suitable to be used in MPC directly,
system identification is carried out to give high-order state-space models.
41
The order of the models is then reduced by balance truncation and/or
residualization. Shown by simulation, the presented model reduction
method works well in capturing the input-output behavior.
While MPC is popularly known as an effective control strategy in
practice, one of its inherent limitations compared to simpler methods (e.g.
PID) is the high computational costs involved. The complexity and accura-
cy of prediction models both play important roles for the success of MPC.
It should be noted although currently the model complexity is not a big
concern because the time interval of 10 minutes allows high computation
costs associated with high order, the incentive of performing model reduc-
tion is to investigate if the dominant input-output relations can be captured
by lower ordered models.
42
EnergyPlus
Model
High-order state-space
(A,B,C,D)
Reduced-order model
(Ar,Br,Cr, D)
System
identification
Model reduction
Model predictive control
Temperature
Power
Cost
Figure 3.1: Building model reduction for MPC
43
4 8 12 16 20 24 28 32 36 40
19
20
21
22
23
Temperature (
°
C)
Time step

Identified
Truncated
Residualized
Validated
Figure 3.2: Model step responses
4 8 12 16 20 24 28 32 36 40
18
20
22
24
26
Temperature (
°
C)
Time step

Identified
Truncated
Residualized
Validated
Figure 3.3: Trajectory tracking under random inputs
44
Chapter 4
Economic MPC for Buildings
4.1 Introduction
MPC has been proven as a successful approach by numerous indus-
trial applications [86]. It is essentially an optimization based strategy in
which an explicit model is employed to predict the behavior of the con-
trolled plants over a receding horizon [66, 89]. In each time step, an open-
loop optimal control problem is formulated and solved, and only the con-
trol action of the current time step will be implemented on the plant. This
routine is iterated at subsequent intervals with new measurements and up-
dated plant information. Fig. 4.1 illustrates the basic principle of MPC.
For complex industrial plants, the control system is usually designed
in hierarchical layers. In upper layers, supervisory control strategies such
as MPC are responsible to generate the optimal setpoints in steady-states.
Economic Model Predictive Control (EMPC) refers to the strategy where the
setpoints in steady-states reflects economic criterion[2, 90]. It combines the
functions of Real Time Optimization (RTO) and dynamic MPC into one lay-
er, where the objective is economic and the underlying model is dynamic.
EMPC is applicable when
45
The time scales of the layers are very close.
The operations rarely reach steady state.
The operations go through frequent start-ups and shut-downs or in-
termittent mode changes.
In this chapter, EMPC design for building HVAC systems is present-
ed. The prediction models in EMPC are obtained from system identification
and balanced model reduction in the previous chapters.
4.2 Existing Control Strategies
Several open-looped control strategies for building HVAC systems
are proposed in [111], which are described in Fig. 4.2. These strategies
are simple since the setpoints are pre-programmed to the controller (Open-
looped control).
The baseline night-setup strategy is applied in most of the current
regular buildings, in which the temperature set-points are set as the lower
bound of comfort region during entire occupied hours and cooling is shut
off for the rest of the day. Therefore, the building thermal mass always plays
the role of resistance rather than assistance. In the step-up strategy, the cool-
ing set-points are lifted to a higher value when the on-peak period comes
so that the cooling stored in building thermal mass can be discharged. The
46
linear-up strategy is a compromise of the previous two. Reference [111] al-
so suggests extending the pre-cooling period to unoccupied hours to store
more cooling.
There still exists large potential to lower peak loads, and then reduce
costs on time-of-use pricing structure, by wisely pre-designing the cooling
set-point schedules. However, performing an efficient open-looped strate-
gy requires significant amount of knowledge and effort from building op-
erators, and it is hard to generally evaluate how good a strategy is unless a
particular building is targeted. Another limitation of open-looped strategies
is that the controller is incapable of adjusting in accordance with changing
disturbances inside and outside the buildings.
In this work these open-looped strategies are introduced as compar-
isons to the proposed EMPC approach.
4.3 Economic MPC Formulation
MPC is essentially an optimization-based method. The objectives in
standard MPC are usually set as trajectory tracking or disturbance rejection.
Instead of using a quadratic criterion as in standard MPC [89], an economic
objective function is designed as follows to account for the building energy
costs. Constraints in both equalities and inequalities are followed to ensure
the feasibility of obtained solutions.
47
4.3.1 Economic Objective function
The economic objective function as (4.1) is a combination of energy
and demand costs under a time-of-use rate structure.
min J = C
e
+C
d
(4.1)
=
P
N
k=1
[E
c
(k)P (k)T
s
] +D
c
(k) maxfP (k)g
In (4.1),C
e
is energy charge andC
d
is demand charge.T
s
is the length
of time intervals, which in the simulation study is set as 15 minutes. There-
fore the total number of time steps in a day isN = 96. At the time stepk, the
prediction horizon is formed from the current to the end of this day, which
makes the length of prediction horizon shrink over time, i.e.N
p
=Nk.
It can also be seen in (4.1) that the charge ratesE
c
(k) andD
c
(k) de-
pend on time-of-use. The rate structure is designed by utilities toward vari-
ous types of customers. For certain rate plans, customers also have flexibil-
ities in some detailed configurations such as peak periods so that they can
save costs by achieving demand response operations [107].
The function to be minimized at the time stepk is formulated as
min
e
J(k) =
N
X
t=k+1
[E
c
(t)P (t)T
s
] +D
c
(t
d
) max
1tN
fP (t)g (4.2)
4.3.2 Linear programming
Equation (4.2) shows a min-max optimization problem. By the fol-
lowing routine, it can be converted to a linear programming.
48
A standard linear programming has the form of
min
x
f
T
x s:t:
8
<
:
Axb
A
eq
x =b
eq
lbxub
(4.3)
For the ease of implementation, it is hoped to convert the min-max
optimization as (4.2) into the exact form as (4.3), so as to be conveniently
solved by the Matlab build-in function linprog.
4.3.2.1 Objective Function
Define a new variablez to represent the peak power demand for the
current day
z(k) = max
1tN
fP (t)g (4.4)
Note the power terms up to a given time stepk, are recorded history
datafP (1);:::;P (k)g. The future termsfP (k + 1);:::;P (N)g are generated
from model predictions.
The decision variable x in (4.3) is formulated as a long vector, con-
taining both the inputs and outputs in the prediction horizon.
x(k) =
h
z(k) P
Np
k
T
Np
z;k
T
Np
sp;k
i
T
(4.5)
where
P
Np
k
= [P (k + 1);:::;P (k +N
p
)] (4.6)
T
Np
z;k
=
h
T
Np
z1;k
::: T
Np
z;k
i
(4.7)
49
T
Np
sp;k
=
h
T
Np
sp1;k
::: T
Np
sp;k
)
i
(4.8)
Fori = 1::: in (4.7) and (4.8),
T
Np
zi;k
= [T
zi
(k + 1);:::;T
zi
(k +N
p
)] (4.9)
T
Np
spi;k
= [T
spi
(k);:::;T
spi
(k +N
p
1)] (4.10)
The dimension of x is equal to 1 +N
p
(1 + 2) and it changes over
time. The corresponding linear coefficient vectorf in the objective function
(4.3) is
f(k) =
h
D
c
(t
d
) E
Np
c;k
0
1Np
0
1Np
i
(4.11)
where
E
Np
c;k
= [E
c
(k + 1);:::;E
c
(k +N
p
)] (4.12)
4.3.2.2 Constraints
Equations (4.13) and (4.14) specify the lower and upper bounds for
zone temperature and setpoints respectively. For occupied hours, the zone
temperature must be regulated within the thermal comfort region [70 75]F .
For unoccupied hours, the temperature constraints can be relax for purpos-
es such as pre-cooling.
lb(k) =
h
0 0
1Np
T
Np
z;min;k
T
Np
sp;min;k
i
(4.13)
50
ub(k) =
h
1 1
1Np
T
Np
z;max;k
T
Np
sp;max;k
i
(4.14)
The inequality constraints in (4.3) are constructed by (4.15) and (4.16),
which are brought by the definition ofz(k) in (4.4), i.e. the peak term needs
to be not smaller than any of the history measurements as well as power
predictions.
A(k) =

1 0
1Np
0
1Np
0
1Np
1
Np1
I
Np
0
NpNp
0
NpNp

(4.15)
b(k) =

max
i=1:::k
P (i)
0
Np1

(4.16)
The equality constraintA
eq
x = b
eq
represents input-output relations
in prediction modelsfA
P
;B
P
g andfA
T
;B
T
g. The elements in A
PA
eq
, A
PB
eq
and b
P
eq
in (4.17) and (4.18) can be derived from the ARX prediction form
by substituting (3.2) (3.6) into (3.1). The terms A
TA
eq
, A
TB
eq
and b
T
eq
can be
obtained similarly from temperature model coefficients.
A
eq
=

0
Np1
A
PA
eq
0
NpNp
A
PB
eq
0
Np1
0
NpNp
A
TA
eq
A
TB
eq

(4.17)
b
eq
=

b
P
eq
b
T
eq

(4.18)
The linear programming is formed by substituting (4.4) (4.18) to
(4.3). Only the current temperature setpoints (T
spi
(k) in (4.10)) are imple-
51
mented to the building zones. The optimization is reformulated in each
time step with updated data.
4.4 Simulation Studies
4.4.1 Real-time simulation environment
The framework of the building energy simulation system is de-
scribed in Fig. 4.3. The simulation environment is set up with the following
steps.
1. Modify on basis of one of benchmark files that come along with the
EnergyPlus version 6.0 package, and obtain a virtual model of a com-
mercial building with moderate thermal mass (as described in Section
2.2);
2. Design an input sequence and excite the EnergyPlus model to gener-
ate corresponding output signals;
3. Identify mathematical models for temperature and power consump-
tion in the Matlab Systen Identification Toolbox with the input and
output data [57] (as described in Section 2.3);
4. Employ the identified models and develop MPC algorithm that gives
control actions of temperature setpoints for the building HVAC sys-
tem;
52
5. Implement the MPC controller to the original EnergyPlus building
model;
6. Obtain and report the actual zone temperature, power and demand
profiles.
EnergyPlus is one of the most comprehensive simulation tools devel-
oped for building energy analysis. However, one limitation of EnergyPlus
is the lack of a friendly graphical user interface. It carries out simulation
by reading input data files (idf-files), which contain all of the pre-defined
information regarding the building to be simulated including the simula-
tion period, building dimension, layout and material, HVAC schedules and
so on. This means that once a simulation is started, it cannot be paused
to wait for data updates. As a result, it can only run in batch mode giv-
en pre-determined HVAC schedules but closed-loop controllers cannot be
implemented.
In order to solve this problem, the Building Controls Virtual Test Bed
(BCVTB) is employed as a middleware. BCVTB [108] is an open-source soft-
ware developed in Ptolemy II environment [12]. It allows users to couple
different programs and conduct synchronized simulations. Shown as Fig.
4.4, Matlab and EnergyPlus both play the role of clients connected to BCVT-
B. As soon as the simulation starts, there is a socket connection established
from the middleware to each client. In each time step, which is 15 minutes
53
in simulation time, both clients send and receive data to and from the sock-
et. The socket moves back and forth between the two programs directed
by the middleware and data exchange is realized inside the middleware.
This co-simulation process keeps running until a termination signal is de-
tected. As shown in Fig. 4.5, the command windows of both programs can
be monitored at the same time.
4.4.2 Electricity price structure
The rate plan of TOU-GS-3 (Time of use - General service - 3) from
Southern California Edison [96] is used in the simulation conducted in this
work. Medium-sized commercial and industrial customers such as 24-hour
service stations, restaurants, motels and so on may benefit from choosing
this plan. End users can save electric bill if they are able to use a majority
of energy during, or shift a significant amount of energy use to, the mid-
and/or off-peak hours. The electricity price is comprised of energy charge,
demand charge and customer charge. The energy charge is depicted in
Table 4.1. The demand charge is $9:83 per monthly maximum kW. Since
customer charge is fixed, it is not included in the optimization scheme in
this work.
54
Table 4.1: TOU-GS-3 energy charge rate
Energy charge
($ / kWh)
On-peak
0.31176 12:00 18:00
Summer weekdays except holidays
season Mid-peak
0.14200 Jun. 1 8:00 12:00, 18:00 23:00
Oct. 1 weekdays except holidays
Off-peak
0.06866 23:00 08:00, weekdays and
all day on weekends and holidays
Mid-peak
0.10468 Winter 8:00 21:00
season weekdays except holidays
Oct. 1 Off-peak
0.07151 Jun. 1 21:00 8:00, weekdays and
all day on weekends and holidays
4.4.3 Simulation scenario selection
In the MPC simulation, the zone temperature is regulated by real-
time constraints [T
z;min
;T
z;max
]. In this work one day is divided into five pe-
riods as described in Fig. 4.6, which is similar to the approach described in
[35]. However, the time periods are determined in a way that zone temper-
ature level in each period can be maintained within an appropriate range,
rather than at a constant temperature setpoint as in [35].
1. Period 1 (t
1
t
2
): The building can be pre-cooled at as low as 18

C
from the early morning until the occupied period starts. Cooling is
expected to be stored in the building thermal mass and released later
55
when necessary.
2. Period 2 (t
2
t
3
): During the off-peak and mid-peak occupied hours,
zone temperature is maintained in lower half of the thermal comfort
range 21

C 23

C with the hope that the stored cooling can be saved
for utilizing in on-peak period.
3. Period 3 (t
3
t
4
): Zone temperature is free as long as within the
comfort range. The stored cooling in building envelope can be either
supplied or released.
4. Period 4 (t
4
t
5
): Maintain zone temperature in 23

C 25

C with
the contribution of stored cooling.
5. Period 5 (t
5
t
1
of the next day): Shut down the cooling system to
avoid needless energy consumption.
Since t
2
and t
5
are fixed to the beginning and end of the occupied
hours, there are three parameters (t
1
,t
3
andt
4
) that can be adjusted to reach
a good simulation scenario. Manipulatingt
3
andt
4
can be interpreted from
Fig. 4.6 as cutting off the areas of A and B from the thermal comfort re-
gion. Note that changing t
4
should not affect the control results a lot be-
cause the MPC controller tends to adjust the zone temperature trajectories
to approach the upper bound of comfort region during the on-peak period
56
so that cooling stored in the building thermal mass can be released to reduce
the demand cost.
Theoretically, the constraints should be overlapped with the thermal
comfort region all the occupied hours to have the controller search for the
optimal solution over the whole feasible space. Changing the shape of the
thermal comfort region is to take advantage of the beforehand knowledge
of the solution patterns, and counterbalance the impact of model mismatch
[14].
Weekly simulations were performed to investigate effect oft
1
andt
3
in the MPC configuration. The results are shown as Fig. 4.7 and Fig. 4.8.
The weather temperature condition of the testing week in July is listed in
Table 4.2.
A trade-off can be observed from Fig. 4.7 that starting pre-cooling
earlier can lead to lower demand cost but higher energy cost, and a balanced
point oft
1
is found around 2 a.m. This is consistent with the result of step
response tests on the EnergyPlus model in Section 2.2.1, which suggests that
it takes 4 hours to fully pre-cool the considered building. Fig. 4.8 indicates
that setting t
3
as late as possible in the non-peak period can reduce both
energy and demand costs.
Consequently, the best scenario is selected to bet
1
= 2,t
3
= 12 and
t
4
= 12, and this selection is not affected by the weather conditions. How-
ever, it is expected that the selection of these parameters is dependent on
57
Table 4.2: Ambient temperature of the simulation week (

C)
Sun. Mon. Tue. Wed. Thu. Fri. Sat.
July 1 2 3 4 5 6 7
Ave. 24.0 26.8 28.9 22.4 19.8 21.7 25.6
Hi. 31.7 31.1 34.4 26.1 25.0 27.8 32.2
Lo. 14.7 19.4 23.3 17.2 13.3 11.7 16.7
the building attributes, especially the level of building thermal mass.
4.4.4 Simulation results
With the optimally selectedt
1
andt
3
, the simulation is run with the
EMPC controller for a whole week. Simulation results of zone temperature
and power profiles are shown as Fig. 4.9. Fig. 4.10 and Fig. 4.11 show
the detailed daily temperature and power behavior. The results are gener-
ated out of the upgraded simulation by adapting to the newer EnergyPlus
version 6:0.
The effect of ambient temperature on overall energy consumption
level can be indicated clearly in Fig. 4.9 [61]. For example, the power spike
at about 3 a.m. on Tuesday is caused by the relatively warm night that
makes the building thermal mass more difficult to be pre-cooled. Less pow-
er was consumed over weekend than weekdays due to the different sched-
ules of internal loads (occupants).
Fig. 4.10 shows the intelligent actions of EMPC for the sake of opti-
58
mizing energy costs. The precooling automatically starts at 2 am. The room
temperature is controlled to the thermal comfort region when at the begin-
ning of occupied periods, and always maintained within. During morning,
the temperature setpoints are kept in the lower part of the comfort region
to keep the stored cooling until the peak hours. As soon as the peak hours
start, the setpoints are lifted to the upper limit without recharge the cool-
ing, therefore the power demand in afternoon is minimized. After occupied
period, the setpoints are set high to make the cooling turn off. It can be ob-
served from Fig. 4.11 that the peak loads have been shifted away from the
on-peak period and the on-peak power profile has been flattened.
The cost savings brought by EMPC over the baseline is compared
with other pre-programmed control strategies in Tabel 4.3. As described in
Section 4.2, the baseline night-setup strategy (BL) is applied in many build-
ings, in which the temperature setpoints are simply set to the lower bound
of comfort region during entire occupied hours and cooling is shut down for
all unoccupied hours. Therefore, the building thermal mass always plays
the role of resistance rather than assistance. Linear-up and Step-up are sim-
ple alterative strategies to reduce power demand during peak hours.
MPC with reduced order models brings cost savings of 26:78% for the
studied week. In contrast with the saving of 28:52% using original identified
models, the usage of reduced models does not significantly affect the MPC
59
Table 4.3: Weekly cost savings compared to the baseline
Strategy Cost saving (%)
Linear-up 17.42
Step-up 24.35
MPC 28.52
performance.
The simulation is carried out on a computer with a Quad-core
1:81GHz processor and 3Gb RAM. In terms of the computation time, MPC
with full-order models takes 50 minutes for a weekly simulation. That
time is cut to 28 minutes when the reduced-order models are used. As
indicated in [76], most of the time in the simulation is spent by EnergyPlus
simulator even though in this work it is only called once in a time step.
The computation efficiency brought by reduced-order models is more
significant when connecting MPC to the control system real buildings.
4.5 Summary
In this chapter, a simulation-based work on demand reduction in
building energy systems via EMPC is presented. The Building Controls Vir-
tual Test Bed software was employed as a middleware to link Energyplus
and Matlab and the real-time data exchange between the two programs en-
abled implementation of closed-loop controllers. In the proposed model
predictive control algorithm, the min-max optimization problem with an e-
60
conomic objective, a shrinking prediction horizon and several constraints
was transformed into a linear programming and solved at each time step.
The proposed method aims at minimizing the costs on the daily basis (with-
in each calendar day), which is why the shrinking horizon is chosen. This
shrinking horizon also allows us to eventually implement this method to
dynamic pricing cases, in which the electricity rate is released by utility at
the beginning of the day based on load forecast.
It was shown by simulation that under the time-of-use electrical
pricing structure, EMPC brings substantial cost savings by automatically
triggering pre-cooling effect and shifting the peak demand away from
on-peak hours. Moveover, the simulation conducted in this work also
provided knowledge on the configuration of EMPC parameters for the
particular building modeled in EnergyPlus, which can make the practical
field tests more efficient, which will be presented subsequently.
61
Figure 4.1: Basic concept of MPC (Adapted from [6])
62
Figure 4.2: Pro-programmed (Open-loop) control strategies
63
Figure 4.3: Framework of the building energy simulation system
64
Figure 4.4: System diagram that enables Matlab and EnergyPlus exchange
data in real-time on BCVTB
Figure 4.5: Graphic interface of running Matlab and EnergyPlus co-
simulation on BCVTB
65
Figure 4.6: Time period division in MPC simulation
66
100
120
140
Demand cost @ t1 = 4
Demand cost @ t1 = 2
Demand cost @ t1 = 0
Energy cost @ t1 = 4
40
60
80
Electrical Cost ($)
Energy cost @ t1 4
Energy cost @ t1 = 2
Energy cost @ t1 = 0
0
20
40
Sun Mon Tue Wed Thu Fri Sat
Figure 4.7: Weekly electrical costs vs. varyingt
1
, (t
3
=t
4
= 12)
100
120
140
Demand cost @ t3 = 12
Demand cost @ t3 = 10
Demand cost @ t3 = 8
Energy cost @ t3 = 12
40
60
80
Electrical Cost ($)
Energy cost @ t3 = 10
Energy cost @ t3 = 8
0
20
40
Sun Mon Tue Wed Thu Fri Sat
Figure 4.8: Weekly electrical costs vs. varyingt
3
, (t
1
= 2,t
4
= 12)
67
Sun 6 12 18 Mon 6 12 18 Tue 6 12 18 Wed 6 12 18 Thu 6 12 18 Fri 6 12 18 Sat 6 12 18 Sun
20
30
T
z1
(
o
C)
T
sp
T
z
Sun 6 12 18 Mon 6 12 18 Tue 6 12 18 Wed 6 12 18 Thu 6 12 18 Fri 6 12 18 Sat 6 12 18 Sun
20
30
T
z2
(
o
C)
Sun 6 12 18 Mon 6 12 18 Tue 6 12 18 Wed 6 12 18 Thu 6 12 18 Fri 6 12 18 Sat 6 12 18 Sun
20
30
T
z3
(
o
C)
Sun 6 12 18 Mon 6 12 18 Tue 6 12 18 Wed 6 12 18 Thu 6 12 18 Fri 6 12 18 Sat 6 12 18 Sun
20
30
T
z4
(
o
C)
Sun 6 12 18 Mon 6 12 18 Tue 6 12 18 Wed 6 12 18 Thu 6 12 18 Fri 6 12 18 Sat 6 12 18 Sun
20
30
T
z5
(
o
C)
Sun 6 12 18 Mon 6 12 18 Tue 6 12 18 Wed 6 12 18 Thu 6 12 18 Fri 6 12 18 Sat 6 12 18 Sun
0
10
20
Time of day (hr)
Power (kW)
Figure 4.9: Zone temperature and power profiles in the weekly simulation
68
0 3 6 9 12 15 18 21 24
17
21
25
29
33
Comfort Region
Zone1
Temperature (
°
C)
0 3 6 9 12 15 18 21 24
17
21
25
29
33
Comfort Region
Zone2
Temperature (
°
C)
0 3 6 9 12 15 18 21 24
17
21
25
29
33
Comfort Region
Zone3
Temperature (
°
C)
0 3 6 9 12 15 18 21 24
17
21
25
29
33
Comfort Region
Zone4
Temperature (
°
C)
0 3 6 9 12 15 18 21 24
17
21
25
29
33
Comfort Region
Zone5
Temperature (
°
C)
Time of day (Hour)

Weather temperature
Setpoint
Zone temperature
Figure 4.10: Zone temperature profile (one day)
69
0 3 6 9 12 15 18 21 24
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Time of day (Hour)
Power (kW)
Power

Off−Peak Mid−Peak On−Peak Mid−Peak
Cooling Coil
Fan
Power demand peak
occurs at11:00
Figure 4.11: Power profile (one day)
70
Chapter 5
Field Tests
5.1 Introduction
Although some cost savings brought by EMPC in simulated build-
ings are shown in previous chapters, the effectiveness of a new control s-
trategy is not completely confirmed until validated by experimental stud-
ies. Because no matter how complicated the simulation models are, there
are still a large portion of dynamic behavior in buildings that can not be
modeled by simulation. A method therefore, even has been tested by simu-
lation, needs to be robust enough to be successful in field tests.
This section presents an experimental study of applying EMPC in a
real building. The objective of this experimental study is to test the EMPC s-
trategy that minimizes energy costs by intelligently adjusting zone setpoints
of building HVAC during occupied and unoccupied periods. Compared to
other field tests carried out in real buildings [63, 3, 34], the work based on
proposed EMPC controller has the advantages in that:
The prediction models are obtained via data-based system identifica-
tion. Therefore, EMPC only takes advantage of existing BAS and does
71
not need to install additional sensors. Although most likely the model
performance will be improved given more types of data.
The EMPC that contains an economic objective function is generating
a cost-effective solution. Once its effectiveness is demonstrated and
validated, it has a promising prospect to be transferred into practical
products.
Solely selecting zone temperature setpoints as decision variables of
controller offers a solution that is very easy to implement. For the field
tests, the only implementation issue is to replace the existing building
controller with EMPC by proper configuration of data interface.
The constraints of zone temperature specify a range in which the tem-
perature is allowed, rather than reference trajectories to be tracked by
controllers. This feature is more flexible in satisfying different temper-
ature regulations of different buildings.
5.2 Field Tests
In the field tests described in this chapter, the experimental environ-
ment is set-up in a way that is as consistent as possible with the previous
simulation work. The tests are conducted simultaneously with other nor-
mal building operations without awareness of the building occupants.
72
5.2.1 Building information
One floor in a large office building located in Milwaukee, Wisconsin,
USA is selected as the testing bed. There are 16 zones on this floor, and each
of these zones is associated with a VAV box and sensors to measure zone
temperature and air flow rates. As shown in the floor map Fig. 5.1, isolated
areas, such as restrooms and conference rooms are set as separated zones
and all the rest area is grouped as one large subzone. Temperature setpoints
are shared and all the measurements are averaged in each grouped zone.
Regarding building internal loads, approximate 30 occupants are
working in the testing area during working hours. Roof lights in the
common area are turned on all the time, and those in conference rooms
are manually turned off when they are not in use. Working stations and
associated monitors and servers are also running in 24 hours. The occupied
period for the testing area is 7am 5pm. The AHU (Air Handling Units) is
on from 4 : 30am to 7pm.
An important difference between simulation and field tests is that in
the testing building, there is no direct power measurement for the HVAC al-
though a single AHU is dedicated for the testing area. Therefore the power
is approximately calculated by (5.1).
P (k) =
X
j
m
j
(k)C
p
(T
nj
(k)T
sa
(k)) (5.1)
wherem
j
(k) is the air flow rate,C
p
is the specific heat of air andT
sa
(k) is the
73
supply air temperature, which is usually fixed.T
nj
is the temperature of air
at the nodej.
The building is operated under the time-of-use rate plan described
in Table 5.1. Since there is a big difference of demand charge between peak
and off-peak hours, saving in costs is expected if significant amount of
peak power consumption can be shifted to off-peak hours. A facility charge
$17:26=day is not considered in the optimization scheme, because it is a fix
amount that needs to be paid no matter what kinds of control strategy is
applied.
Table 5.1: Time-of-use electricity rates[107]
Energy Charge Demand Charge
($/kWh) ($/kW)
Peak 0:06985 11:889
Off-Peak 0:04974 1:007
5.2.2 Test environment
The goal of setting up this control system is to test controllers sitting
in remote locations. An server based on FTP (File Transfer Protocol) is estab-
lished for exchanging data in real-time between the controller and building
automation system. The closed-loop structure of remote control system is
shown in the Fig. 5.2.
In each time step (Every 10 minutes), A data socket containing the
74
time step index and zone temperature setpoints is generated. The socket
is then written to the server and then picked up by the BAS to apply the
current setpoints to zones. At the same time the BAS constantly updates
log data which contain zone temperature and air flow rates to the server,
and those measurements are read by controller to close the loop.
The log data sent by BAS include 50 variables, which are the set-
points, zone temperatures and cooling air flow rates for each of the 16 zones,
plus supply air temperature and outside air temperature.
Due to the BAS configuration by default, the order of these variables
in the log is randomly decided for each time step. It is noted that the BAS
in this building is responsible for multiple tasks in addition to these tests so
that the log data are updated with more than one paces. It is necessary to
process the data before sending them to the controller.
Although the primary purpose of creating this remote control sys-
tem is to test the performance of EMPC. As a matter of fact, the established
control system is capable of being test bed for any setpoints control strate-
gies. It is flexible to the physical locations of controller, as long as internet
connections are available and reliable.
5.2.3 Test procedure
The tests are performed in two stages.
In stage 1, the excitation experiments as described in the section 2.3
75
are carried out. A PRBS signal with the binary levels of [70 75]F is gen-
erated for cooling setpoints of 10 work days. The time step is 10 minutes
and excitation signal is independent for each zone. While the input signal
is implemented to the building zones, actual zone temperature along with
other useful measurements, such as supply air temperature, ambient tem-
perature and cooling air mass flow rates, are collected from real-time log
data of the building automation system. Nine of the ten days data are used
to train models and the last day data are used for validation. At the end of
this stage, the prediction models are obtained to be used in EMPC design.
In stage 2, the EMPC controller is designed following the routine de-
scribed in the section 4.3. In the experimental study presented in this paper,
the EMPC controller is in place for testing via the remote control system for
four work days (Aug.30th, Aug.31st, Sep.4th and Sep.5th 2012), and three
baseline days (Aug.29th, Sep.6th and Sep.7th 2012) are tested for compar-
ison in which the setpoints are set constantly at 72F for whole occupied
hours.
5.2.4 Test results
5.2.4.1 Model performance
The input-output data from the excitation experiments are shown
as Fig. 5.3. It is seen that for the early morning and late afternoon, the
cooling setpoints are higher than zone temperature, during which the air-
76
conditioning is not working for cooling down the room. This results in the
fact of cooling saturation, which is an undesired effect for system identi-
fication. Therefore these portions of data are removed from the training
data-sets.
Fig. 5.4 and Fig. 5.5 show the performance of prediction models.
The prediction performance is no surprisingly not as good as that in the
previous simulation work as shown in the section 2.4, and turns worse as
the prediction errors aggregating over time. This is due to the fact that in
real buildings disturbances are much stronger and harder to model.
5.2.4.2 Control strategy tests
Fig. 5.6 and Fig.5.7 show the temperature and power profiles for a
baseline and EMPC testing day respectively. In the MPC testing day, it can
be seen that the major power consumption has been shifted before 10am,
which is the starting time of peak period. The power level in the afternoon
is lower than morning and its shape is quite flat.
A big power spike in early morning is observed in both the MPC
testing day and baseline day. This is because the air flow rate has a big step
change when AHU is turned on. This spike is expected to disappear in a
building whose AHUs are active during whole 24 hours.
From the temperature profiles in Fig. 5.7, the automatic precooling
action prior to occupied hours is triggered. From 8am to 10am, the temper-
77
ature setpoints stay in the lower part of thermal comfort region in order to
keep the cooling stored in building thermal mass, which is the automatic
action so called post-cooling. During the peak hours, the cooling is auto-
matically released in a way that cooling costs are minimized and thermal
comfort level can be maintained.
No complain from building occupants is submitted during the test-
ing periods.
5.2.4.3 Result analysis
Due to model mismatch and disturbance, sometimes the setpoints
are reset to lower values in late afternoon indicating the stored cooling is
exhausted. Although the status of linear programming always shows a fea-
sible solution is obtained, in Fig. 5.7 it is seen that for some period of time
the zone temperature is floating outside the thermal comfort region.
It is interesting to see how much cost savings over baseline strategy
are brought by EMPC. Simply comparing the values of objective function is
bias since other factors such as weather temperature can also affect the daily
power cost. In fact, MPC testing days happen to be warmer than baseline
days. The weather condition for the testing days are shown in the Table 5.2.
The cost savings brought by EMPC over the current baseline method
in this building is not confirmed given the short period of testing time. Fair
comparison with parallel tests is hard to implement in real-world situations.
78
Table 5.2: Weather conditions for the testing days
Date Control Average temperature (F) Max temperature (F)
08/29 Baseline 73.7 83.4
08/30 MPC 79.6 92.3
08/31 MPC 77.0 90.8
09/04 MPC 74.3 85.1
09/05 MPC 71.6 78.9
09/06 Baseline 72.4 82.6
09/07 Baseline 66.6 84.4
The advantage of EMPC over baseline strategy is shown by calculating the
ratio of power consumed in peak hours over non-peak hours, as shown
in Fig. 5.8. From this fair comparison, all MPC testing days have higher
portion of power consumption in non-peak hours, showing a successful
implementation of an advanced control strategy.
5.3 Summary
In this chapter, an experimental study for application of EMPC in a
large office building is presented. It is shown that under a time-of-use rate
structure with significant difference of demand charge in peak and non-
peak periods, the EMPC controller is capable of shifting major power con-
sumption to non-peak hours, so as to reduce the energy costs. The method
of calculating the ratio of power in peak hours over non-peak hours is a
simple alternative way to show the demand shifting effect of EMPC.
79
The internet-based control system established in this work provides
a platform to remotely test new control strategies, and not only limited to
MPC.
80
Up
1
5
4
6
10
11
9
14
16
13
15
8
7
30
29 28
12
# VMA1630-0
VMA1620-0 #
NORTH TEAM ROOM SOUTH TEAM ROOM
#
WRZ SENSOR
Note: Units 28 & 29
to be used for field
time-to-replace study
This device is a VMA1620 with the 6.0 boot/
main/application loaded. This represents a
wireless field trunk w/legacy & next
generation devices
Figure 5.1: Floor map of the testing area
81
Figure 5.2: Remote HVAC setpoints control via internet
0 4 8 12 16 20 24
65
70
75
80
Time of day (Hr)
Temperature (F)

Setpoints
Zone Temperature
Ambient Temperature
Figure 5.3: Excitation data (one day one zone)
82
2900 3000 3100 3200 3300 3400 3500 3600
72
72.5
73
73.5
74
74.5
75
75.5
Zone2 (sim)
Time Step
T
z2
(F)

Measured
Model T
z2
Figure 5.4: Temperature model prediction
2900 3000 3100 3200 3300 3400 3500 3600
0.5
1
1.5
2
2.5
3
3.5
x 10
5
P
proxy
(sim)
P
proxy
(W)

Measured
Model P
Figure 5.5: Power model prediction
83
0 2 4 6 8 10 12 14 16 18 20 22 24
65
70
75
80
Zone1
Temperature (F)
0 2 4 6 8 10 12 14 16 18 20 22 24
65
70
75
80
Zone2
Temperature (F)
0 2 4 6 8 10 12 14 16 18 20 22 24
65
70
75
80
Zone3
Temperature (F)
0 2 4 6 8 10 12 14 16 18 20 22 24
65
70
75
80
Zone4
Temperature (F)
0 2 4 6 8 10 12 14 16 18 20 22 24
65
70
75
80
Zone5
Temperature (F)
Time of day (Hr)

Setpoints
Zone Temperature
Ambient Temperature
0 2 4 6 8 10 12 14 16 18 20 22 24
0
0.5
1
1.5
2
2.5
3
3.5
x 10
5
Time of day (Hr)
Power
Proxy
Power(mΔT)
Figure 5.6: Temperature and power profiles for a baseline testing day
(08.29.2012)
84
0 2 4 6 8 10 12 14 16 18 20 22 24
65
70
75
80
Zone1
Temperature (F)
0 2 4 6 8 10 12 14 16 18 20 22 24
65
70
75
80
Zone2
Temperature (F)
0 2 4 6 8 10 12 14 16 18 20 22 24
65
70
75
80
Zone3
Temperature (F)
0 2 4 6 8 10 12 14 16 18 20 22 24
65
70
75
80
Zone4
Temperature (F)
0 2 4 6 8 10 12 14 16 18 20 22 24
65
70
75
80
Zone5
Temperature (F)
Time of day (Hr)

Setpoints
Zone Temperature
Ambient Temperature
0 2 4 6 8 10 12 14 16 18 20 22 24
0
0.5
1
1.5
2
2.5
3
3.5
x 10
5
Time of day (Hr)
Power
Proxy
Power(mΔT)
Figure 5.7: Temperature and power profiles for an EMPC testing day
(08.30.2012)
85
Figure 5.8: Ratio of power consumed in peak hours over non-peak hours
86
Chapter 6
Economic MPC in Microgrids
6.1 Introduction
Most of the world’s electricity system was built over the last 40 to
60 years, so the aging electricity infrastructure is inefficient and increasing-
ly unreliable. The electric system continues to be operated in the same way
for decades while new technologies have significantly changed the other in-
dustrial sectors. During high-demand period, utilities companies typically
rely on fast and flexible coal and gas-fired power stations, which are expen-
sive and polluting. The penetration of renewable energy is still limited and
the electric system still relies heavily on the fossil energy sources. In order
to reach a low carbon economy and deal with aging infrastructure and cli-
mate change, a strategic transformation of the electricity system is urgently
required.
Thanks to the deregulation processes and implementation of incen-
tives in the energy sector, the usage of small distributed energy resources
(DERs) has recently received considerable attention. There are two types of
DER in general: conventional dispatchable distributed generation (DG) and
non-dispatchable DG based on renewable energy sources, such as wind, so-
87
lar and geothermal power. The economical and environmental benefits of
integrating renewable energy into power systems have been clearly demon-
strated [56]. On the other hand, to increase the penetration of intermittent
energy resources which feature unpredictable behavior has become one of
the biggest challenges in smart grid.
Microgrids are increasingly being viewed as a means to promote the
deployment of DER, meanwhile improving system reliability at the distri-
bution level [48, 49]. Formed by a cluster of loads, small scaled generation
units and/or distributed energy storages, MicroGrids can be operated in
grid-connected or isolated-island mode, with the expectation to provide un-
interrupted power supply to the loads. DERs located near local loads can
offer improved reliability and higher energy quality, if they are properly
operated [114, 102]. A typical MicroGrid structure is illustrated in Fig. 6.1.
The MicroGrid Central Controller (MGCC) is one of the most critical
components in a MicroGrid architecture [67]. It controls the connection to
the main grid, manages controllable loads and optimizes system operation
based on information of power quality requirement, energy cost, demand-
side requests and special grid needs etc. It determines the amount of power
that the MicroGrid should draw from the main grid and from each local
DER respectively. The optimal (or near-optimal) decisions of power dis-
patch are made in a way that certain objectives are achieved, while a num-
88
ber of operational constraints need to be satisfied [32, 80]. In particular, the
problem becomes more complicated if the generation capacity of renewable
energy sources is significant, which asks for advanced modeling, optimiza-
tion and control techniques [58].
Modeling and optimization are two crucial components of MPC
implementations. Given that short-term forecasting methods for renew-
able energy resource output have been extensively studied [42, 109], the
scope of this chapter is to demonstrate the effectiveness of MPC with a
simulation-based model in solving the economic dispatch problems for
MicroGrids with intermittent DGs. MPC is technically favorable because
it naturally incorporates prediction models and constraints that can ensure
the MicroGrid is operated in desired region.
6.2 System Structure
In this work, a simplified MicroGrid model with conventional dis-
patchable DGs, wind and solar generators, energy storages and a single
bus connected to the distribution substation is studied. The project system
structure is illustrated in Fig. 6.2.
Although not in the scope of this study, modeling the intermittent
behaviors of DERs and load forecasting play important roles in the suc-
cess of MPC implementation. Utilizing historical data files of wind and
solar outputs, we suppose the difference between the predicted and actual
89
DER outputs is a white noise sequence. The load profiles are assumed to
be following certain pattern. An optimization problem is formulated over
the moving horizon for minimizing the total electricity generation cost. The
optimal control actions are obtained by MPC controller out of this optimiza-
tion with several constraints, and sent to the MicroGrid model before pro-
ceeding to the next time step.
The Microgrid is modeled in the OpenDSS simulation platform and
its specific configuration is described in the section 6.4.1.
6.3 MPC Problem Formulation
Based on the general MPC approach, the problem for maximizing
the penetration of renewable energy resources, in other words, optimizing
the generation cost (because the power generated by local renewable DGs
is much cheaper than demanding from the main grid), is formulated in this
section.
6.3.1 Objective Function
The length of prediction horizonN
p
and control horizonN
c
are set to
be identical, i.e. N
p
= N
c
= N. The time step for each interval is denoted
as t. At the current time step k, the objective function to be optimized
90
accounts for the total generation cost in the prediction horizon, as Eq.(6.1).
min
U
F (U;k) =
k+N1
X
t=k
(C
g
(t) +
X
m
C
cg;m
(t)) (6.1)
where C
g
(t) is the generation cost from the main grid, and is proportion-
al to the power demand P
g
(t). C
cg;m
(t) is the cost of the mth convention-
al distributed generator in the MicroGrid, which is usually expressed as a
quadratic polynomial with respect to its power outputsP
cg;m
(t).
C
g
(t) =b
g
(t)P
g
(t)t (6.2)
C
cg;m
(t) =a
m
+b
m
P
cg;m
(t)t +c
m
(P
cg;m
(t)t)
2
(6.3)
Note that in Eq.(6.2),b
g
(t) is a time varying cost coefficient, indicating
the rate depends on time-of-use.
The decision variable in Eq. (6.1) U is a vector containing control
actions in the entire control horizon,
U(t) =

u(k)
T
u(k + 1)
T
u(k +N 1)
T

T
(6.4)
For any single time step, the control signalu(t) includes power out-
puts of all controllable generators as well as energy storages. For simplicity,
it is assumed only one conventional generator and one energy storage in
the MicroGrid.
u(t) = [P
g
(t) P
cg
(t) P
es
(t)]
T
(6.5)
91
whereP
g
(t),P
cg
(t) andP
es
(t) denote the power from main grid, convention-
al DG and energy storage, respectively.
6.3.2 Constraints
The optimization problem subjects to the following constraints for
t2 [k;k +N 1].
6.3.2.1 Real power balance
P
g
(t) +P
cg
(t) +P
es
(t) =
^
P
l
(t)
X
^
P
r
(t)
^
P
loss
(t) (6.6)
where
^
P
l
(t) and
^
P
loss
(t) are the forecasts of total loads and real power losses
respectively.
^
P
r
(t) is the predicted output from renewable energy resources,
such as wind and solar generators.
6.3.2.2 Physical capacity
The power generated by each controllable generator should be with-
in its maximum capacity.
P
cg
(t)P
cg;max
(6.7)
Since all loads must be energized, there is no constraint imposed on
P
g
. As an isolated MicroGrid is studied, the supply capacity of the main
electricity grid can be treated as infinite large.
The energy storage has its maximum rates in both charging and dis-
92
charging modes. The stored energy in energy storageW
es
(t) should be be-
low its rated kWh value. Only steady-state behavior of energy storages is
considered here.
P
es char;max
P
es
(t)P
es disc;max
(6.8)
0W
es
(t)W
es;max
; t =k + 1;k + 2; ;k +N (6.9)
W
es
(t + 1) =W
es
(t)P
es
(t) t; (6.10)
6.3.2.3 Power
ow equations
A feasible control action should satisfy the power flow equations.
The voltage magnitude and angle at each bus can be determined by he well-
known Newton-Raphson method. From the complex power balance equa-
tion at busi (non-slack bus),
S
i
=P
i
+jQ
i
=V
i
X
k
Y

ik
V

k
(6.11)
Resolving into the real and imaginary parts, the mismatch equations are
P
i
=P
i
+
X
k
jV
i
jjV
k
j(G
ik
cos(
ik
) +B
ik
sin(
ik
)) (6.12)
Q
i
=Q
i
+
X
k
jV
i
jjV
k
j(G
ik
sin(
ik
)B
ik
cos(
ik
)) (6.13)
93
whereG
ik
andB
ik
are the corresponding elements of the system nodal ad-
mittance matrixY

. The system Jacobian matrix is factorized as
J =
2
6
4
@P
@jVj
@P
@
@Q
@jVj
@Q
@
3
7
5
(6.14)
The initial guess of unknownjV
i0
j and
i0
is usually made as a ”flat
start” in which all voltage magnitudes are set to 1:0 p.u. and all voltage
angles are set to zero. The power flow solution can be obtained by the
following iterations,
jVj
m+1
=jVj
m
+ jVj

m+1
=
m
+
(6.15)
where the incremental guess is given by

jVj

=J
1

P
Q

(6.16)
The iteration continues until a termination criterion is reached, e.g.
the norm of P and Q are below specified thresholds.
It should be noted that in this work, the realization of the power flow
equations is through the use of the OpenDSS simulator, instead of being
explicitly formulated in the optimization scheme. Doing this in practice
may bring problem because in iterations it requires considerable time and
computational cost to run the simulator many times. Therefore, system
identification technique is usually employed to obtain input-output models
out of experimental data, i.e. the work in [60].
94
6.3.2.4 Voltage limit
In the converged power flow solutions, all bus voltages need to be
maintained within permitted range. Typically, the range of [V
min
;V
max
] =
[0:95; 1:05] in p.u. value can ensure normal system operations.
V
min
V
i
(t)V
max
(6.17)
Note that in a practical application there should also be constraints
on current, i.e.,I
i
(t)I
rated;i
(t). For simplicity and the lack of rated current
parameters, the current constraints are not included in the optimization.
6.4 Simulation Studies
The Matlab optimization toolbox is used to solve this nonlinear con-
strained optimization problem in the above section using interior point al-
gorithm. Matlab and OpenDSS are integrated to a co-simulation scheme,
where Matlab takes charge optimization and control, and OpenDSS simu-
lates the distribution network.
6.4.1 OpenDSS Simulator
The OpenDSS (Open Distribution System Simulator, used version
7.4) is developed by Electric Power Research Institute (EPRI) as a compre-
hensive open-source simulation tool for electric utility distribution systems
[22]. It aims at providing a flexible research platform and a foundation for
95
special distribution applications such as DG analysis. It can be used as ei-
ther a stand-alone executable program or an in-process COM server to be
driven from external software programs.
6.4.1.1 IEEE 13 node system
The IEEE 13 node radial test feeder system which is one of the bench-
mark systems in the OpenDSS software package, is selected as the testing
system for this work. It is a three-phase unbalanced system, whose param-
eter specification and power flow for the base case can be retrieved from
[28]. Since originally there is no DG installed in the network, additional
DSS scripts are added to the feeder model for modification as shown in Fig.
6.4. Wind farms and solar photovoltaics are installed in the network along
with a conventional DG and energy storages. The capacity of renewable
generations is about 20% of the average load level. There are two capacitors
installed on bus 675 (3 phases) and 611.C and a load locates on the bus 670
invisible in Fig. 6.4, which is connected between the bus 632 and 671.
6.4.1.2 Distributed generators
As shown in Fig. 6.4, one conventional dispatchable distributed gen-
erator, one wind generator and one solar generator are added to the system,
specifying their rated capacities and the buses to which they are connected.
The conventional DG output in kW P
cg
is to be passed by the controller
96
in Matlab in each time step. The wind and solar generator daily output-
s would follow the multiplication of rated kW values and duty schedules
generated from historical data files. Wind output is essentially a stochastic
disturbance and solar power contributes only during day time.
6.4.1.3 Energy storage
In OpenDSS, the energy storage element is essentially treated as a
special class of generator that can be designated to either produce power
(in discharging mode) or consume power (in charging mode) with its power
rating and stored energy capacity.
The working mode of energy storage is set as discharging/charging
depending on the positive/negative sign of the demanded power P
es
(t),
and the discharging/charging rate in kW (jP
es
(t)j) is passed from Matlab to
the OpenDSS model in each time step.
The energy storage module is used in a snapshot mode to compute
the power flow for a deterministic state. This means that its dynamic
transient behavior is not considered at present. The default value of 90%
for both charging and discharging efficiency is applied, making a nominal
round trip efficiency of 81%. The energy storage is placed at the center of
MicroGrid, with the hope to conveniently compensate for short term power
variations caused by intermittent generations.
97
6.4.1.4 Load schedule
A loadshape object is defined for varying loads in OpenDSS to carry
out real-time simulations. The load schedule is stored in a data set, as shown
in Fig. 6.3. The level indicates the ratio of current and maximum load.
White noise with standard deviation of 0:025 is added to the load level to
account for the load estimation error.
6.4.2 Simulation Results
A 24 hour simulation is conducted on the MicroGrid model de-
scribed above. The length of prediction horizon is set as 4, meaning an
one-hour ahead prediction is applied. The contribution to loads from
each energy source is shown in the stacked graph as Fig. 6.5. Power from
main grid follows the load variation because the main grid is treated as a
swing source. Conventional distributed generator and energy storage are
used as auxiliary resources to maintain the power balance and as assets
to optimize the total generation costs. It can be seen that the conventional
DG is mainly utilized during the peak hours (8 : 00 18 : 00) when higher
price is applied to the grid power. The behavior of energy storage is subject
to a slow-charging fast-discharging pattern, which allows it to compensate
to unpredictable change of renewable outputs and avoid sacrificing the
power stability.
An ordinary control strategy is implemented to compare with MPC,
98
in which no prediction effect is incorporated. The controller makes decision
to achieve minimum cost only based on the current measurements. The
total electricity generation cost is shown in Fig. 6.6. The advantage of MPC
appears from 8 a.m. the generation cost begins to increase, showing the
capability of MPC to foresee the price change and take appropriate actions
in advance.
Fig. 6.7 shows the bus voltages in the MPC test. The voltages are
repeatedly measured after the convergence of power flow in each time step
with under the control inputs given by MPC. All bus voltages are within the
feasible region showing that the voltage constraints are always satisfied.
6.5 Summary
In this chapter, a renewable energy integration problem in a Micro-
Grid taking advantage of MPC method is studied. With a prediction model
embedded, MPC is capable of reducing the generation cost over a future
horizon. A number of constraints can be naturally satisfied to ensure the
power quality and network stability.
In a co-simulation framework, Matlab optimization toolbox is used
to solve the nonlinear optimization problem and OpenDSS is the platform
to simulate virtual distribution system model with renewable energy re-
sources and energy storage installed.
This work can be continued and extended in the following directions:
99
1) Although modeling for the wind and solar generators is not the
focus of this work and we assume accurate models are available by certain
techniques, incorporating the forecast models that are not built from histor-
ical data to optimization in MPC is still challenging.
2) In addition to steady-state, taking in to account dynamic behavior
of devices such as energy storages is of significance.
3) Due to the complexity of power flow equations, the optimization
cannot be readily formulated as a programming problem that can be analyt-
ically solved. Therefore, the nonlinear optimization executed by the Matlab
built-in functions usually gives local optima and it requires a deep look into
the iterations to track the searching trajectory of optimal solutions.
This demonstrating work also shows that the EMPC presented in
previous chapters has promising values in other energy system areas. Fig.
6.8 shows the side-by-side comparison between the two projects. Since
these two projects try to find the optimal solutions from supply side and
demand side respectively, it is interesting to investigate the possibility of
integrate this two projects together, to find an optimal solution within a
integrated system, which is a Microgrid with demand response buildings.
100
Utility Grid
MicroGrid Central MicroGrid Central
Controller (MGCC)
MicroGrid
MC MC LC LC
DG / Microsources Controllable Loads
Figure 6.1: Schematic diagram of a typical MicroGrid
Load Shape
Predictions
Generation
Forecasts
(Wind, Solar)
MicroGrid
(OpenDSS)
Prediction
Noise
MPC
(Matlab)
Electricity cost
Power loss
(Objectives)
Power flow
(Constraints)
Figure 6.2: Project block diagram
101
0 3 6 9 12 15 18 21 24
0
0.2
0.4
0.6
0.8
1
1.2
Time (hr)
Load Level
Figure 6.3: Load level daily schedule
3 phase unbalanced system
Wind farms
Energy storage
Distributed generator
Solar photovoltaics
Distributed generator
Figure 6.4: Modified IEEE 13 node test feeder
102
Time (hr)
Power output (kW)

3 6 9 12 15 18 21 24
−0.5
0
0.5
1
1.5
2
2.5
3
3.5
4
Energy Storage
Solar Power
Wind Power
Conventional DG
Main Grid
Figure 6.5: Generation output profiles under MPC
0 3 6 9 12 15 18 21 24
1
2
3
4
5
6
7
Time (hr)
Cost (10
3
$)

Ordinary
MPC
Figure 6.6: Generation cost comparison between ordinary control strategy
and MPC
103
650 633 634 671 645 692 675 611 652 670 632 680 646
0.9
1
1.1
Phase A
Volts (pu)
650 633 634 671 645 692 675 611 652 670 632 680 646
0.9
1
1.1
Phase B
Volts (pu)
650 633 634 671 645 692 675 611 652 670 632 680 646
0.9
1
1.1
Phase C
Volts (pu)
Node number
Figure 6.7: Bus voltage distribution measured after convergence of each
power flow calculation
104
Figure 6.8: Comparison between the EMPC application in buildings and
Microgrids
105
Chapter 7
Conclusions
This dissertation presents two novel applications of economic model
predictive control (EMPC) technology in building HVAC and electric pow-
er systems. The presented work aims at developing an effective solution
to replace the open-looped control settings in most of the current build-
ings, where the temperature setpoints schedule is preprogrammed which
will cause high power consumption during peak hours as the cooling loads
increasing.
It is demonstrated that under time-of-use rate structure, significant
cost savings for building HVAC systems could be achieved by simply
changing the HVAC setpoints control strategies. Model predictive control
is a promising method because it can give the controller the ability to
anticipate the upcoming peak hours, and take correct actions in advance to
avoid high peak demand.
The demonstration work is firstly carried out through simulation s-
tudies. After reviewing the current state-of-the-art building energy simula-
tors, the simulation model of a single-floor multi-zone commercial building
located in Chicago, IL is crated in EnergyPlus. System identification is de-
106
ployed to obtain the empirical models that are to be used in MPC design.
Linear ARX is chosen as the model structure. The temperature prediction
model has HVAC setpoints as inputs and actual zone temperature as out-
puts, while the power model has direct cooling power consumption as out-
puts. The identified models have good prediction performance, which is
validated by comparing with EnergyPlus models.
The identified models are initially high-ordered, and their order in-
creases steeply as the increasing of building complexity. The high order,
although is usually not a big issue in simulation, could be troublesome in
practical implementations. Balanced model reduction technique is investi-
gated in this work to lower the model order, while capturing the important
input-output relations.
After the models are obtained, they are embedded into the EMPC
design. An economic objective function is developed to represent the sum-
mation of energy and demand charges, which forms a min-max problem.
Constraints are formulated including the permitted temperature region and
model relation. The decision variables contain a sequence of control actions
in a shrinking prediction horizon, and only the temperature setpoints for
current time step are applied to the zones. The optimization is converted to
a linear programming form and solved effectively.
A weekly simulation in summer season is carried out to demonstrate
the effectiveness of EMPC. Substantial savings in cost over the baseline case
107
and other open-looped alternative strategies are observed.
A field test in a real building is performed following the simulation
studies. A large office building in Milwaukee, WI is chosen as the test-
bed. A control system is established over internet to remotely overwrite
the HVAC setpoints in the building. Similar routine as the simulation s-
tudy is implemented in the field test. Experimental results show that the
EMPC controller is capable of taking demand response actions, such as pre-
cooling, automatically, and shifting major power consumption away from
peak hour.
The application of EMPC in a Microgrid is attached. The Microgrid
considered in this work is operated while connected to the main grid, has
local distributed generations (DG), including renewable energy resources
like wind turbines and solar photovoltaic. Energy storage is also installed in
the system for adding more flexibility for power dispatch. An optimization
is formulated to minimize the total generation cost within the Microgrid,
while satisfying all loads and constraints for voltage and current. Renew-
able energy outputs are treated as disturbance inputs, and expected to be
utilized in an optimal means.
In sum, the work presented in this dissertation shows a couple of
successful applications of economic model predictive control in energy sys-
tems. When an economic objective is considered, the MPC can give optimal
control actions to minimize cost so that the delivered control strategy pro-
108
vides more incentives to the customers to upgrade their systems. The field
tests in real building show that the presented work has made practical im-
pacts.
The work could be extended in the following aspects. 1) Consider
adaptive MPC in which the model structure or parameters can be updated.
A control performance monitoring module can be designed on top of MPC
and trigger the model adaptation when necessary. 2) If a weather forecast
is available, it can be used as a feed-forward variable. 3) It would be inter-
esting to add additional terms, such as thermal comfort indices, setpoints
tracking errors etc., to the objective function, and investigate what the con-
trol results will be.
109
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Abstract (if available)

Abstract In the United States, buildings account for nearly three quarters of electricity consumption and about 40% of greenhouse gas emissions. The heating, ventilation and air-conditioning (HVAC) systems are responsible for approximately one third of the energy usage in commercial buildings. The inefficiency in operation and control of HVAC systems in most of the current buildings places significant energy saving potentials. Even more importantly, under advanced electricity rate structures in the nowadays utility market with demand response, the energy cost for building HVAC systems can be very high due to the high peak power demand associated with the ordinary control strategies. ❧ In this dissertation, we present a cost-effective supervisory control strategy for the building HVAC systems. The goal of this work is to propose and demonstrate an advanced control solution to optimize building energy cost under the time-of-use rate structure, while maintaining the thermal comfort level and indoor air quality. Model Predictive Control (MPC) is the core methodologies investigated in this work, which is carried out in two stages. ❧ In the first stage, we develop a simulation framework, in which a commercial building model crated in EnergyPlus acts as the building to be controlled. Since the simulation model is not suitable to be directly used in MPC, system identification is performed to obtain the empirical models, which relate the thermostat setpoints to the zone temperature as well as power consumption. Balanced model reduction technique is then applied to lower the model order, while the major input-output dynamic relation is captured. ❧ The MPC problem is formulated utilizing the identified models with reduced-order. Due to the slow building thermal dynamics, an economic objective is combined with the underlying dynamic models, which forms the Economic MPC (EMPC). The optimization in terms of building energy cost has a min-max objective function to account for the combination of energy and demand charges, and a number of constraints to represent allowed temperature range and model relation. The optimization is converted to a linear programming and solved effectively in each time step, giving the optimal zone temperature setpoints. ❧ The effectiveness of EMPC is demonstrated by a weekly simulation. Substantial cost savings are brought by EMPC over the baseline and other open-looped strategies. The simulation system established in this work can also be used as a test-bed for other control algorithms. ❧ In the second stage of this work, the proposed EMPC method is implemented in a large office building located in Milwaukee, WI. The EMPC controller is located at USC and connected to the building automation system (BAS) via the Internet. Field tests results show that the EMPC strategy is capable of shifting significant portion of power consumption out of peak hours, therefore brings cost savings to the building. ❧ In addition, another application of EMPC to the power dispatch problem in Microgrid is described. It shows the potential of EMPC in the area of renewable energy integration. A Microgrid with renewable generation resources and controllable energy storages is considered. Simulation-based EMPC structure is formulated to minimize the overall power generation cost within the Microgrid.

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Asset Metadata

Creator Ma, Jingran (author)

Core Title Economic model predictive control for building energy systems

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Chemical Engineering

Publication Date 11/13/2012

Defense Date 10/24/2012

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag building energy systems,HVAC,model predictive control,OAI-PMH Harvest,system identification

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Joe, Qin (committee chair), Qiang, Huang (committee member), Shing, Katherine (committee member)

Creator Email jingranm@usc.edu,ma.jingran@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-109685

Unique identifier UC11290000

Identifier usctheses-c3-109685 (legacy record id)

Legacy Identifier etd-MaJingran-1288.pdf

Dmrecord 109685

Document Type Dissertation

Rights Ma, Jingran

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA