Supervisory and optimal control of building HVAC systems: a review

Supervisory and optimal control of building HVAC systems: a review

Shengwei Wang

INTRODUCTION

The building automation system (BAS) is a tool that can be used for more effective and efficient management of building services systems (Carlson and Di Giandomenico 1991). One of the main achievable goals of effective use of BASs is to improve the building energy or cost efficiency and provide better performance. Control functions are the basic functions of BASs. Other major functions of BASs include risk management functions, information, and facilities management functions. Control functions of BASs can be divided into two categories, i.e., local control functions and supervisory control (or energy management) functions, as shown in Figure 1. Local control functions are the basic control and automation that allow the building services systems to operate properly and provide adequate services. Local control functions can be further subdivided into two groups, including sequencing control and process control. Sequencing control defines the order and conditions associated with bringing equipment online or moving them offline (ASHRAE 2003). The typical sequencing control in HVAC systems includes chiller sequencing control, cooling tower sequencing control, pump sequencing control, and fan sequencing control, etc. Process control is to adjust the control variables to achieve well-defined process objectives in spite of disturbances, using measurements of state and/or disturbance variables (Ramirez 1994). The typical process control used in the HVAC field is proportional-integral-derivative (PID) control. ON/OFF control (or bang-bang control), step control, and modulating control are the effective control actuation schemes of local process control loops in HVAC practice, and they have produced a great impact and profound significance on building automation. The control settings of these local controllers might be optimal and energy efficient or cost effective when certain subsystems or certain subsystem performance criteria are concerned. However, they may not be energy efficient or cost-effective when the overall system and overall system performance are of concern. Supervisory control, often named optimal control, seeks to minimize or maximize a real function by systematically choosing the values of variables within allowed ranges. It is the total system monitoring and overall control of the local subsystems (Levenhagen and Spethmann 1993). In the control of HVAC systems, supervisory and optimal control aims at seeking the minimum energy input or operating cost to provide the satisfied indoor comfort and healthy environment, taking into account the ever-changing indoor and outdoor conditions as well as the characteristics of HVAC systems. It is worth noting that minimizing system operating cost is not always equivalent to minimizing system energy input. Compared to the local control, supervisory control allows an overall consideration of the system level characteristics and interactions among all components and their associated variables. The knowledge of the system level characteristics and interactions can be utilized to minimize a well-defined cost function or objective function, which would lead to the improved system response and reduced operating cost. According to the classification scheme in Figure 1, supervisory and optimal control in HVAC systems could be classified into four categorizes, including model-based supervisory control method, hybrid supervisory control method, performance map-based supervisory control method, and model-free supervisory control method.

[FIGURE 1 OMITTED]

For many years, control has been a very active area of the research and development in the HVAC field, aiming at operation of HVAC systems in terms of reducing overall system operating cost, ensuring thermal comfort of occupants, and satisfying indoor air quality. Many efforts in the control of building HVAC systems have typically paid on the local level controls (Goswami 1986; Moore and Fisher 2003; Rishel 2003; Fredrik and Dennis 2004; Zhang et al. 2005; etc.). The success and popularity enjoyed by the application of PID control is one of the fruitful outputs of such efforts. While there are numerous effective optimal control strategies developed, growing concern on energy or cost efficiency, due to the extremely high fuel oil price and the shortage of energy supply, has evoked the society and building professionals to pay more attention on overall system optimal control and operation and provided incentives to develop the most extensive and robust supervisory and optimal control methodologies for HVAC systems. Over the last two decades or so, efforts have been undertaken to develop supervisory and optimal control strategies for building HVAC systems thanks to the growing scale of BAS integration and the convenience of collecting large amounts of online operating data by application of BASs.

Depending on the situations and objectives to be achieved, supervisory control plays different roles at different time periods (Levenhagen and Spethmann 1993). The earliest supervisory control stressed the building equipment automation, and the primary focus was on automating all equipment as much as possible to save labor. Later, supervisory control emphasized the building energy monitoring and automatic control, and the major concern was on energy efficiency by both automatic and manual control with the aid of system monitoring. However, the results obtained from both types of supervisory control are not likely to be energy efficient and cost-effective since much attention is paid to the automatic equipment with less consideration of their operating costs. Nowadays, the supervisory control highlights the importance of overall system performance involving energy or cost efficiency and indoor environmental quality, etc. Therefore, supervisory control is to optimize the operation of HVAC systems using a system approach by considering the system level or subsystem level characteristics and interactions among the overall system. The control system in this kind of supervisory control generally provides two levels of control, i.e., local control and supervisory control. Local control is the low level control, which is designed to guarantee the robust operation and keep track of the setpoint considering the dynamic characteristics of local process environment. Supervisory control is the high level control, which is designed to utilize global optimization techniques to find energy or cost-efficient control settings (i.e., operation mode and setpoints) for all local controllers, taking into account the system level or subsystem level characteristics and interactions. These energy or cost-efficient control settings are optimized in order to minimize the overall system energy input or operating cost without violating the operating constraints of each component and without scarifying the indoor environmental quality provided.

Chapter 41 of the 2003 ASHRAE Handbook–HVAC Applications (ASHRAE 2003) provides a critical overview of supervisory control strategies and optimization for HVAC systems. This chapter consists of three major sections. The first section defines the system and control variables considered. The general background on the effects and opportunities related to adjust these control variables is also presented in this section. The second section presents a number of simple strategies that can be implemented in practice for near-optimal control of HVAC systems. The third section provides basic methods for optimization of systems both with and without significant thermal energy storage. However, this chapter did not provide a basic classification scheme of supervisory control methods utilized in HVAC systems. The general information of optimization techniques used to formulate the supervisory control strategies is also not included. Foremost, the references involved in this chapter were published before 2001, and most of them (83.6%) were published before 1997. With the rapid development of technologies, many new methods and techniques have recently been used to develop more advanced supervisory and optimal control strategies for HVAC systems. Therefore, a comprehensive review of the research and development as well as application of supervisory and optimal control strategies in the HVAC field is essentially necessary to present the state of the art.

The organization of this paper is presented as follows. In the next section, “The General Optimal Supervisory Control Problem in HVAC Systems,” the general optimal supervisory control problem for HVAC systems is presented and used as a context for understanding the contributions of the others described in this paper. In the section that follows, “Supervisory Control Methods,” the framework for categorizing supervisory and optimal control methods in HVAC systems is provided in terms of what type of model is used in the control system. In this section, the advantages and disadvantages of the application of these methods are clearly identified. In the following section, “Optimization Techniques Used in Supervisory Control,” various optimization techniques utilized in supervisory and optimal control are presented, and the benefits of the application of these techniques in HVAC systems are critically analyzed. In the section entitled, “Research and Application of Optimal Control Strategies for HVAC Systems,” the research and development as well as the application of supervisory and optimal control strategies in HVAC systems are reviewed comprehensively according to the classification schematic of supervisory control methods. A brief assessment for major techniques is also provided in this section. Finally, the discussion and conclusion are presented.

THE GENERAL OPTIMAL SUPERVISORY CONTROL PROBLEM IN HVAC SYSTEMS

The optimal supervisory control for HVAC systems is to determine the optimal solutions (operation mode and setpoints) that minimize overall system energy input or operating cost while still maintaining the satisfied indoor thermal comfort and healthy environment. For different types of HVAC systems (i.e., electric-driven system, gas-driven system, hybrid gas/electric-driven system, the systems with and without energy storage, etc.), the optimal supervisory control problems are significantly different. For a particular optimization problem, different utility rate structures will lead to different solutions as well. Since the general optimal supervisory control problem for hybrid systems with significant energy storage is the most complicated system, the other systems can be considered simplifications of such systems. Therefore, the optimal supervisory control problem and cost function for hybrid systems with significant energy storage are presented in detail in the following.

The optimal supervisory control for hybrid systems with significant energy storage is extremely complex, affected by many factors including electrical and gas energy costs, electrical demand charges, maintenance costs associated with different chillers (electric or gas), chiller characteristics, storage characteristics, weather condition, and load profile, etc. For a utility rate structure that includes time-of-use differentiated electricity prices and demand charges and the fixed cost of natural gas over each billing period (e.g., a month), the overall optimization problem of such systems is to minimize the utility cost over the billing period (e.g., a month), and the cost function can be mathematically described as in Equation 1.

J = [N.summation over (k = 1)] [E.sub.e, k][P.sub.e, k][DELTA]t + [N.summation over (k = 1)] [E.sub.g][G.sub.g, k] + [N.summation over (k = 1)]([[N.sub.ch].summation over (i = 1)][([[gamma].sub.i]).sub.k]([C.sub.m]).sub.i][Q.sub.ch, rated, i])[DELTA]t + [max.sub.1[less than or equal to]k[less than or equal to]N]([D.sub.e, k][P.sub.e, k]) (1)

with respect to the [N.sub.c] control variables and subject to a series of constraints (i.e., basic energy and mass conservation, mechanical limitations, etc.) for each time interval k.

The variable J is the overall cost in the billing period; [DELTA]t is the time interval, typically equal to the time window over which demand charges are levied, e.g., 0.5 h; N is the number of the time intervals in a billing period; [E.sub.e,k] is the cost per unit of electrical energy within the time interval k ($/kWh), which can be available from the local utility tariff; [P.sub.e,k] is the total electrical power of the HVAC system in the time interval k (kW); [E.sub.g] is the cost per unit of natural gas usage ($/therm); [G.sub.g,k] is the total gas usage in the time interval k (therm); [N.sub.ch] is the number of chillers; [([[gamma].sub.i]).sub.k] is a control function that specifies whether the ith chiller (electric or gas) is in operation in the time interval k (1 denotes ON and 0 denotes OFF); [([C.sub.m]).sub.i] is the maintenance cost of the ith chiller (electric or gas) per unit of runtime and capacity ($/ton/h); [Q.sub.ch,rated,i] is the rated cooling capacity of the ith chiller (ton); and [D.sub.e,k] is the cost per unit of electrical demand in the time interval k ($/kW).

The first and second terms on the right-hand side of Equation 1 are the total costs of electricity and natural gas in the billing period. The third term on the right-hand side of Equation 1 is the total maintenance cost associated with using different types of chillers. The last term on the right-hand side of Equation 1 is the demand charge for the billing period. An even more complex cost optimization would result if the utility rate includes ratchet clauses in which the demand charge is the maximum of the peak demand charge for the billing period and some fraction of the peak demand charge for the previously billing period during the cooling season, and the installation costs of different types of chillers (electric or gas) are considered also.

As presented previously, the cost functions for other systems (i.e., all electric-driven systems with and without significant energy storage, all gas-driven systems, etc.) can be simplified on the basis of the above cost function. For instance, for a utility rate structure including both time-of-use differentiated electricity prices and demand charges, the cost function for all electric-driven systems with significant energy storage can be described as in Equation 2, which only includes the first and last terms on the right-hand side of Equation 1, while the cost function for the absorption chiller systems without significant energy storage can be simplified as in Equation 3, which includes the first, second, and last terms on the right-hand side of Equation 1. It is necessary to point out that the total electrical power of the absorption chiller systems for each time interval k could include water pump electrical power, fan electrical power, absorption chiller auxiliary electrical power, etc.

J = [N.summation over (k = 1)]([E.sub.e,k][P.sub.e,k][DELTA]t) + [max.sub.1[less than or equal to]k[less than or equal to]N]([D.sub.e,k][P.sub.e,k]) (2)

with respect to the [N.sub.c] control variables and subject to certain constraints for each time interval k.

J = [N.summation over (K = 1)][E.sub.e,k][P.sub.e,k][DELTA]t + [N.summation over (k = 1)][E.sub.g][G.sub.g,k] + [max.sub.1[less than or equal to]k[less than or equal to]N]{[D.sub.e,k][P.sub.e,k]} (3)

with respect to the Nc control variables and subject to a series of constraints for each time interval k.

The following important factors address the nature of optimization problems that should be seriously considered in order to develop the advanced optimal supervisory control strategies for HVAC systems:

* Both energy and demand charges are important for the optimization problems in HVAC systems. In large commercial and office buildings, the demand charges often contribute a significant amount to the monthly electric bill. The optimal supervisory control should minimize the overall utility cost.

* The variables involved in the particular optimization problem should be identified clearly. In general, there are three kinds of variables associated with the optimization problems in HVAC systems, i.e., uncontrolled variables, continuous control variables, and discrete control variables. Uncontrolled variables can be measurable but may not be controlled. However, they affect the overall utility cost. The typical uncontrolled variables in HVAC systems are ambient air wet-bulb temperature, ambient air dry-bulb temperature, and building cooling load. The continuous and discrete control variables are setpoints and operation mode that minimize the overall utility cost, which are the optimal solutions for the optimization problem searched by certain optimization techniques. The typical discrete control variables in HVAC systems are the numbers of different types of components in operation, such as the number of chillers in operation, the number of cooling towers in operation, etc. The typical continuous control variables in HVAC systems could be the temperature setpoints, pressure setpoints, the rate at which energy is added or removed from storage (if significant energy storage is used), etc.

* The subsystems in HVAC systems are interacted with each other, and the fact is that the reduction of energy input or operating cost of one subsystem might result in the increase of energy input or operating cost of the other subsystem with respect to the changes of certain control variables. Therefore, the optimal solution for the related control variable is the trade-off between the energy input or operating cost of both subsystems. For instance, for all electric-driven systems without significant energy storage, the optimal chilled-water temperature setpoint is the trade-off between the electrical power of both chillers and secondary chilled-water pumps, while the optimal condenser-water temperature setpoint is the trade-off between the electrical power of both chillers and cooling tower fans. For a particular system, all types of trade-offs that occur with respect to the changes of different control variables should be identified clearly.

* The optimizations for the systems with and without energy storage are significantly different. The optimization related to the systems without storage is a quasi-steady, single-point optimization, while the optimization associated with the systems with storage is the dynamic optimization determining a trajectory of setpoints. For different types of optimization problems, optimization methods applied to seek the optimal solutions would be different. Dynamic programming or some direct search methods can be used for the dynamic optimization, while static optimization techniques can be used for the quasi-steady, single-point optimization. The optimization techniques utilized in HVAC systems will be presented in the “Optimization Techniques Used in Supervisory Control” section in detail.

Based on the defined cost function and constraints for a particular system, considering the nature of optimization problems related to HVAC systems, the supervisory and optimal control strategy can be formulated using certain methods (i.e., model-based, model-free, etc.) and optimization techniques presented in the sections, “Supervisory Control Methods” and “Optimization Techniques Used in Supervisory Control,” respectively.

SUPERVISORY CONTROL METHODS

The selection of the control methods for a supervisory control application plays a critical role in the development of the effective control strategy to optimal operation of HVAC systems. For a given set of specifications for a targeted application, there always exist several supervisory control methods. Usually, each method has its own advantages and limitations over the others in some aspects.

Many researchers and experts in the HVAC field have devoted considerable efforts on the development and application of proper control methods for particular applications, especially during the last two decades. Numerous research papers and technique articles, and dozens of textbooks that specifically address the HVAC control and operation, can be found in literature (Honeywell 1989; Levenhagen and Spethmann 1993; Wang and Jin 2000; Zaheer-uddin and Zheng 2000; Hordeski 2001; Haines and Hittle 2003; Nassif et al. 2005; Wang 2006; etc.). An overall classification of main supervisory control methods used in HVAC systems is illustrated in Figure 1. Supervisory control in HVAC systems could be classified into four categorizes, including model-based supervisory control method, hybrid supervisory control method, performance map-based supervisory control method, and model-free supervisory control method. Such classification may not be perfect enough since there are no clear boundaries among some control methods. However, it can provide a very useful and helpful basis for comparing the advantages and disadvantages among different control methods. It is also very helpful for identifying the strengths and weaknesses of each method, as well as for analyzing the feasibilities of their online applications. It is worthwhile to point out that whether a method is specified as a model-based method or a model-free method in this paper is dependent on whether the numerical models are used. Here, a numerical model presents the knowledge on the system/component performance by the numerical correlations between the selected performance variables and condition variables. According to this clarification, the control methods using physical models, gray-box models, and black-box models can be classified into the category of model-based methods, while the methods using expert systems and pure learning approaches can be grouped into the model-free category.

Model-Free Supervisory Control Methods

Model-free supervisory control methods do not require a “model” of the targeted system. Expert systems and reinforcement learning approach can be utilized to design the model-free supervisory control methods. An expert system includes two distinct control functions, i.e., advisory control and supervisory control (Hordeski 2001). When an expert system acts as a supervisory controller, it has the capability to determine the energy or cost-efficient control settings to optimal operation of HVAC systems according to the given working condition. These energy or cost-efficient control settings are identified based on the combination of the rules defined in the knowledge base and information obtained from the BASs. The knowledge base in an expert system is derived from the specific knowledge of one or more human expert. An expert system can imitate human reasoning to make decisions for a given working condition based on the knowledge base. It also has the ability to deduce the reasonable solutions with an incomplete data set. An expert system is easy to program and easy to manage as well. However, application of an expert system is affected by the richness of the knowledge database since the rules are static and outside its domain of expertise, threatening significant error.

Reinforcement learning control is another example of a model-free supervisory control method. This method describes a learning paradigm in which a control system attempts to improve its behavior on the results of previous actions, without the requirement of a model of the environment or the effects of actions. This method can find the optimal or near-optimal solutions for the control problem without any prior knowledge of the environment. However, it always takes an unacceptably long time to make the controller “learn.” The performance of the controller is sensitive to many factors, i.e., the selection of the state-action, learning parameters, etc. These features make it almost impossible to implement in practice (Henze and Schoenmann 2003; Liu and Henze 2006a).

There are also other possible approaches that do not utilize any model in the control system to optimize the operation of HVAC systems. For instance, one conceptually simple yet inadequate strategy for all electric-driven systems without significant storage is to monitor the overall system power consumption in response to the changes of control settings continuously, and always proceed in the direction of the reduced power consumption. Since this method focuses on the overall system performance and no numerical model of the targeted system is required, it is a model-free supervisory control method. This online search procedure is fairly easy to implement in practice. However, it is inherently unstable due to the dynamic characteristics of the HVAC system and low response to the rapid changing of indoor and outdoor conditions (Braun and Diderrich 1990a).

Model-Based Supervisory Control Methods

In model-based supervisory control, the tools required to perform the supervisory control are the system and/or component models and optimization techniques. The main function of the models is to predict the system energy or cost and environment performance, as well as the system response to the changes of control settings. All of the models are connected with the power consumption or operating cost directly. Online measurements collected from the BASs are used to tune the model parameters to make them represent the actual system. The primary role of the optimization technique is to seek the energy or cost-efficient control settings (i.e., operation mode and setpoints) to minimize the system energy input or operating cost while still maintaining the satisfied indoor environment. At a sampling instant, the optimization technique is applied to these models to evaluate the control settings that minimize the power consumption or operating cost as characterized by the models. The control strategies determined in this manner react quickly to the rapid changes of indoor and outdoor conditions. According to the knowledge of the system utilized to formulate the models, the model-based supervisory control can be further divided into physical model-based supervisory control, gray-box model-based supervisory control, and black-box model-based supervisory control.

In the physical model-based supervisory control, physical models are utilized in the control system to predict the energy/cost and environment performance of the system of concern. A physical model begins with the description of a system or process of interest and uses a priori knowledge of the system or process to specify a model that serves as the basis for predicting the overall performance. This kind of models includes detailed physical models and simplified physical models. Based on fundamental laws of energy, mass, heat transfer, momentum, and flow balance, etc., a set of mathematical equations can be derived and solved. Generally, these detailed and simplified physical models have high performance in prediction and high control reliabilities within their allowed working conditions since the basic assumptions and laws utilized in the model development are effective and valid within their allowed ranges. These models require less training data as well. However, most physical models, particularly detailed physical models, are rather complicated, and the iteration process is always required in most of these models, which may result in instability and divergence as well as high computational cost and memory demand. These characteristics may seriously prevent their online applications. Concerning the advantages of physical models and problems of complex physical models in online applications, serious efforts in developing simplified physical models and gray-box models have been made in recent years.

In the gray-box model-based supervisory control, gray-box models are used to formulate the supervisory control methods. There are two different models that can be used to develop the gray-box models. One is from the black-box models. A priori knowledge of the system or process can be incorporated as constraints on the model parameters or variables. The other is from a specific model structure based on physical relations. Mathematical relations, which describe the behaviors of the process or system, are simplified to formulate the model. The main advantages of gray-box models are that the complexities of the model structures and computational costs to achieve the optimal solutions are reduced greatly, while the parameters in the models still have certain physical significance, which can make them be used for limited extrapolation outside the range of the training data covered. It is worthwhile to note that the accuracies of these models still strongly depend on the richness of data used to train the models.

In the black-box model-based supervisory control, black-box models are used. These models do not incorporate any kind of prior knowledge of the system or process. They are developed based on the empirical behaviors of the system or process of concern, and are to mathematically relate input variables to output variables directly. The parameters in these models have no physical significance. Typical representatives of black-box models are polynomial curve fits and artificial neural networks (ANNs). Generally, black-box models are simple enough since they do not require the detailed physical knowledge of the system or process of concern and computational costs are generally manageable. However, most of these models cannot ensure stable performance prediction although they are simple. They are reliable only for operating points within the range of the training data covered, and extrapolation outside this range may lead to significant error. In order to guarantee the high prediction performance, extensive and adequate training data are always required.

Hybrid Supervisory Control Methods

In hybrid supervisory control, different types of models and/or the model-based control method and the model-free control method are combined together to formulate the supervisory control strategies. For instance, some hybrid supervisory control methods utilize a mix of physical/ gray-box/black-box models to design the control system, in which some component models are physical models, while others are gray-box or black-box models. Some hybrid supervisory control methods use both the model-based approach and the model-free approach (e.g., reinforcement learning approach) to construct the supervisory control methods, in which the features of the model-based approach and the model-free approach are combined together to achieve high control performance. The supervisory control methods formulated by this manner might provide good control performance if the controllers are reasonably designed.

Performance Map-Based Supervisory Control Methods

Compared to the three supervisory control methods presented above, performance map-based supervisory control is somewhat different. This method often uses the results generated from the detailed simulation of the targeted system over the range of expected operation conditions to draw a performance map, and then utilizes this performance map to optimal control of HVAC systems. For instance, for an electric-driven chiller plant without significant thermal energy storage, using the component models, various combinations of cooling loads, ambient air temperatures, the numbers of operating chillers, the numbers of operating pumps, as well as the numbers of operating cooling towers and their individual fan speeds, can be used as inputs to the simulation platform. At each operating condition, the power consumptions or performance data for all combinations are computed, and the control settings giving minimum energy value or best performance are identified. A performance map can then be drawn using those combinations with minimum energy values or best performance identified from over the full operating range of a system, and can be further used as a supervisory controller to optimal operation of the HVAC system. It is worthwhile to notice that the performance map is not necessarily obtained by simulations. For example, it could be obtained by testing the system over a significant range of settings and operating conditions, although simulation is an effective tool. Performance map-based supervisory control strategies might be feasible and practical for small systems. However, they might be impractical for large systems since generating such a performance map often requires considerable work, and large control errors might result when the system does not operate as the manner of the performance map generated. They lack generality as well.

For practical online applications, the control reliability, control stability, and computational cost, as well as memory demand, are the critical and important issues that must be addressed and seriously considered. To achieve the desirable and satisfactory control performance, the models utilized in the model-based supervisory control should have relatively simple structures while still having physical meanings to ensure stable performance prediction. The parameters in the model can be identified using short-term easily available operation data. The models should require less computational cost and memory demand as well.

OPTIMIZATION TECHNIQUES USED IN SUPERVISORY CONTROL

Optimization is an area of mathematics that is concerned with finding the “best” points, curves, surfaces, etc. (Hull 2003). Finding the optimal solution to an optimization problem is a key issue for a supervisory control application. The difficulty related to optimization is to determine whether a given minimum is the global minimum or the local minimum. Similar to the supervisory control methods, for a given set of specifications, there always exist several optimization techniques, often with sharply different structures and characteristics. Each of the options is superior to all others in one or a few aspects, which is explicitly targeted during the development of the particular optimization technique. Figure 2 provides a relatively detailed classification schematic of optimization techniques utilized in most engineering optimization problems. It is modified and supplemented on the basis of the classification scheme provided by Nelles (2001).

[FIGURE 1 OMITTED]

In general, all optimization techniques could be summarized into two categorizes: linear optimization techniques and nonlinear optimization techniques. The linear optimization technique is the most simple and straightforward technique since there is always a unique optimum in a linear optimization problem. Linear optimization techniques include, e.g., direct method, recursive method, and iterative method, etc. Compared to linear optimization techniques, nonlinear optimization techniques are complex and sophisticated since many local optimums exist in a nonlinear optimization problem and the difficulties to find the global optimum increase greatly. Nonlinear optimization techniques can be further subdivided into two categories, including nonlinear local optimization techniques and nonlinear global optimization techniques. The major difference between them is that the nonlinear local optimization techniques always lead to a local–not global–optimum. Nonlinear local optimization techniques include, e.g., direct search techniques, gradient-based optimization techniques, etc. Nonlinear global optimization techniques include, e.g., simulated annealing, branch and bound, evolutionary algorithm, tabu search, etc.

In the HVAC field, linear optimization techniques can be used to solve many simple local optimization problems, while nonlinear optimization techniques can be utilized to deal with highly nonlinear and constrained optimization problems. Since the optimization problems related to supervisory and optimal control of building HVAC systems, as presented in the “The General Optimal Supervisory Control Problem in HVAC Systems” section, are often characterized with discretization, nonlinearity, and high constrainess, only nonlinear optimization techniques are mainly addressed in this paper. During the past two decades, much research has been carried out on the development and application of various nonlinear optimization techniques in HVAC systems (Olson and Liebman 1990; Koeppel et al. 1995; Kota et al. 1996; Wang and Jin 2000; Bassily and Colver 2005; etc.). These efforts have resulted in fruitful achievements, which provide building professionals an opportunity to effectively use these reliable and efficient optimization techniques for practical application while avoiding unreliable optimization techniques. The major optimization techniques utilized in building HVAC systems are examined and summarized in Table 1. A more detailed description of these techniques is given as follows. They are summarized according to three categories of nonlinear local optimization techniques, nonlinear global optimization techniques, and other optimization techniques. The strength and weakness of each technique for online applications are also identified and presented in Table 1. It provides the basic information for users in selecting the appropriate optimization technique for the particular optimization problem with the necessary confidence and the awareness of potential difficulties and problems that may arise in practice. The application examples of these techniques in HVAC systems are listed in Table 1 as well.

Table 1. Summary of Main Optimization Techniques

Used in Building HVAC Field

Techniques Strength

Direct search Simple and easy to be

understood and

implemented. No

derivatives are

required.

Sequential Can efficiently

quadratic handle a large number

of inequality

constraints.

Nonlinear Lagrange method Easy to be

Local implemented since

Techniques Lagrange formula does

not depend on the

order in which the

nodes are arranged

Conjugate gradient Overall computational

method cost is small for

large number of

decision variables

Univariate search Simple and easy to be

implemented.

Branch and bound Can provide a good

(B&B) and/or a subgood

solution. It is easy

to incorporate any

constraint into this

method.

Nonlinear Simulated Relatively easy to be

Global annealing implemented and has

Techniques strong ability to

provide reasonably

good solutions.

Evolutionary With high

algorithms and generalities and

genetic algorithm flexibilities, and

there are also robust

to find the global

minimum.

Weakness Application Examples

Often fails to obtain Wright and Hanby 1987;

an optimal solution. Sreedharan and Haves 2001;

It is less Braun and Chaturvedi 2002;

computationally etc.

efficient

Has to start from Olson and Liebman 1990;

initial guesses and House and Smith 1995; Kota

its convergence speed et al. 1996; Sun and Reddy

is affected by its 2005; etc.

initial guesses

Nonlinear The convergence is Hach and Katoh 2003; Chang

Local not always 2004; etc.

Techniques guaranteed

Less efficient and Nizet et al. 1984; etc

robust compared to

other technique,i.e.,

quasi-Newton method.

The convergence speed Hanby and Angelov 2000;

is quite slow and it Bassily and Colver 2005;

can not find the etc.

optimum values at

some cases

High computational Sousa et al. 1997; Chang

cost is always et al. 2005; etc

required and it is

possible to miss the

globally optimum

solution.

Nonlinear High computational Koeppel et al. 1995; Flake

Global cost and memory 1998; Chang et al. 2006;

Techniques demand are always etc.

required.

Extensive Huang and Lam 1997; Wang

computational cost and Jin 2000; Nassif et

and memory demand are al. 2005; Lu et al. 2004,

always required due 2005b; Fong et al. 2006;

to high number of etc.

fitness evaluations.

Nonlinear Local Optimization Techniques

* Direct search: It is based on the evaluation of loss function values only. No derivatives are required. Consequently, it is not reasonable to apply this method if the derivatives of the loss function are easily available with low computational effort. Although the direct search methods do not require the deviations to exist, higher performance can be expected on smooth functions (Nelles 2001).

* Sequential quadratic programming (SQP): Its basic idea is to linearize the constraints and set up a quadratic objective function to form a quadratic program (QP). The basic structure of an SQP includes four steps (Reklaitis et al. 1983): (1) set up and solve a QP subproblem, yielding a search direction; (2) test for convergence–if it is satisfied, then stop; (3) take a step along the search direction to a new point and (4) update the approximated Hessian matrix H used in the QP and return to step 1.

* Lagrange method: It is an exact method that optimizes the objective function using Lagrange multipliers to meet the Kuhn-Tucker conditions. The Lagrange multiplier of any constraint measures the change rate in the objective function, consequent upon changes in the constraint function. This information is valuable in that it indicates how sensitive the objective function is to the changes in different constraints (Luenberger 1984; Fletcher 1987).

* Conjugate gradient method: This method is based on conjugate search directions and the spirit of the Steepest Descent method. It is used to find the nearest local minimum of a function of n variables, which presupposes that the gradient of the function can be computed. It uses conjugate directions instead of the local gradient for going downhill (Wolfram Mathworld 2006).

* Univariate search: It is primarily developed for solving unconstrained nonlinear optimization problems. A single variable is changed at a time to obtain its optimal value with respect to the current values of all other variables of the optimization problem (Rao 1984).

Nonlinear Global Optimization Techniques

* Branch and bound (B&B): This is a tree-based search technique that is very popular for the solution of combinatorial optimization problems. The basic idea of this method is to build a tree that contains all possible parameter combinations, and to search only the necessary part of this tree. This method employs tests at each node of the tree, which allows one to cut parts of the tree, and thus saves computational cost as compared with an exhaustive search (Nelles 2001).

* Simulated annealing: This is a stochastic method, and the basic principle of this method is presented as follows: A warm particle is simulated in a potential field. Generally, the particle moves down toward lower potential energy, but since it has a non-zero temperature, i.e., kinetic energy, it moves around with some randomness and therefore occasionally jumps to higher potential energy. Thus, the particle is capable of escaping local minimum and possibly finding a global one. The particle is annealed in this process, and its temperature decreases gradually, so the probability of moving uphill decreases with time. It is well known that the temperature must decrease slowly to end up at the global minimum energy (Nelles 2001).

* Evolutionary algorithms and genetic algorithm: Evolutionary algorithms take their inspiration from natural selection and survival of the fittest in the biological world. They include a search from a “population” of solutions. Each iteration process consists of a competitive selection that discards poor solutions. The solutions with high “fitness” are “recombined” with other solutions by swapping parts of a solution with another. Solutions are also “mutated” by making a small change to a single element of the solution. Recombination and mutation are used to generate new solutions that are biased toward regions of the space for which good solutions have already been seen (Gray et al. 1997). The existing approaches to evolutionary algorithms include evolution strategy (ES), evolutionary programming (EP), genetic algorithm (GA), and genetic programming (GP). They all share the same basic model, but are considerably different from the ways of their representation (binary or real-valued), the means of their selection (stochastic or deterministic), and the essentials of crossover and mutation. Genetic algorithm is most popularly used among these algorithms.

Other Optimization Techniques

Other optimization techniques mean that some optimization techniques have been used in the optimization problems in building HVAC systems. However, they are used for solving the individual and/or particular rather than typical optimization problems in HVAC systems. For instance, a recursive numerical algorithm was used by Liu and He (1994) to optimize the thermal comfort level in an air-conditioned room. The Newton-Raphson solution method was used by Mullen et al. (1998) to solve the equations in an optimization problem in a room air-conditioning simulation model. Most of these conventional techniques might be effective and successful for a particular and simple optimization problem, but may not be efficient and reliable for high nonlinear and complicated typical optimization problems in building HVAC systems.

Most of these optimization techniques demonstrated their excellent performance for particular applications. The major difference among these techniques is that different optimization techniques possess different computation efficiencies, while some techniques may be divergent in some cases. Some optimization techniques may also result in a local optimal solution, and a globally optimal solution is not always guaranteed. Among all of these techniques, genetic algorithm (GA) is attracting growing attention of building professionals and has been widely used in academic research for global optimization (Huang and Lam 1997; Wang and Jin 2000; Chow et al. 2002; Nassif et al. 2005; Lu et al. 2005b; etc.). GA is a result-based method, and no derivatives are required during the calculation. This feature makes it possible to solve the complicated and global optimization problems. However, the extensive computational cost and memory demand may be an obstacle for online application of this technique. Further research of the robustness and feasibility of this technique for practical application is essentially required.

In practice, optimization techniques should be selected based on the combination of the complicity and characteristics of the system of concern, as well as the number of optimization variables involved for a particular optimization problem. The selected optimization technique should have less computational cost and memory demand to meet the requirements of practical application. The convergence should be always guaranteed. It should also have a simplified structure and should be easy to be understood by the practicing engineers.

RESEARCH AND APPLICATION OF OPTIMAL CONTROL STRATEGIES FOR HVAC SYSTEMS

Since control function is one of the major functions of a BAS, the building society and professionals have made serious efforts toward the development and application of various control strategies for HVAC systems. Figure 3 is a schematic of the scattered areas of the research and development of the control studies in HVAC systems. It can be found that most research related to HVAC system control focused on the local level control (area 1), while relatively few studies focused on the supervisory control (area 2). The reason is probably due to the easier implementation of local controllers in practice. Since sensor faults and/or component degradations in HVAC systems may cause significant energy consumption or increase overall system operating cost, the research on fault detection and diagnosis (area 3) in HVAC systems has been becoming a large research area and a hot research topic since the last decade. For a robust control strategy, it should have the ability of fault-tolerant control, in which the system can be controlled properly even if some faulty measurements and/or system component degradations exist. There are numerous studies that specifically pertain to fault-tolerant control in control engineering. However, it is still in its infancy in building HVAC field (area 4), and the practical applications are rare.

[FIGURE 3 OMITTED]

Targeted at providing the satisfied indoor thermal comfort and healthy environment with the least energy input or operating cost under dynamic indoor and outdoor conditions, many supervisory and optimal control studies related to HVAC systems have been reported (Huang and Lam 1997; Wang and Jin 2000; Wang and Burnett 2001; Chow et al. 2002; Nassif et al. 2005; Lu et al. 2005b; Sun and Reddy 2005; etc.). Chapter 41 of the 2003 ASHRAE Handbook–HVAC Applications (ASHRAE 2003) has provided a number of near-optimal strategies for cooling tower fan control, chilled-water reset with fixed and variable-speed pumps, sequencing and loading of multiple chillers, strategies for air-handling units, strategies for building zone temperature setpoints, cooling thermal storage control, etc. The implementation issues of most of these strategies are also presented. The readers are advised to go through this chapter for details, while a number of strategies will also be addressed in this paper.

In this section, a comprehensive review of the research and development as well as application of supervisory and optimal control in building HVAC field in last two decades is presented, which intends to summarize most of such studies completed up to date. All studies were reviewed according to the classification schematic of supervisory control methods presented in the “Supervisory Control Methods” section.

Physical Model-Based Supervisory Control Strategies

A few studies related to the supervisory control in building HVAC systems use dynamic and/or static governing equations and detailed and/or simplified physical models to construct the supervisory control methods. All these governing equations and physical models are derived based on fundamental laws of energy, mass, heat transfer, momentum, flow balance, etc.

Kaya et al. (1982) introduced a thermal model based on the governing equations for the space along with an index of energy use to develop the optimal control method for an HVAC space. The main objective of this study was to demonstrate the improvement in control performance and the reduction in energy consumption through controlling temperature, humidity, and velocity simultaneously rather than independently. The results indicated that this control strategy, which accounted for control variable interactions among the system, can result in reduced energy use.

Cumali (1988) adopted the global optimization technique to design optimal control and operation strategies for building HVAC systems. The optimization problem was formulated based on the laws of the first principles. The results showed that projected and/or augmented Lagrange multiplier methods did not perform well because of the equality constraints used in the problem formulation, while generalized reduced gradient methods appeared to provide consistent results if one starts with a reasonable solution.

House et al. (1991) and House and Smith (1995) described a system approach for optimal control of building HVAC systems, in which governing equations were derived from the principles of conservation of mass and energy. The interactive nature of system components, the multizone building system, and their associated variables were of concern. A nonlinear programming technique, in which the continuous control variables were discretized in the time domain to transform the infinite dimensional optimal control problem to a finite dimensional form, was used to solve the optimal control problem. Using discrete values of the state and control variables, the cost function was integrated numerically using the trapezoidal rule.

A predictive control policy that utilized a finite-time horizon with end-time constraints was described by MacArthur and Foslien (1993) and MacArthur and Woessner (1993). The control system was composed of two distinct components. One was the supervisor, which was used for sample rate selection and system identification (model development and adaptation). The other was the controller, which can generate a sequence of control signals to ensure acceptable servo-regulatory behavior. The control law minimized actuator movement while satisfying both process and control output constraints imposed at the end of the time horizon. The results showed that this control method offered adaptability and can easily accommodate system dynamics and interactions.

Zaheer-uddin and his collaborators have paid considerable efforts on the optimal and sub-optimal control of HVAC systems in buildings (Zaheer-uddin and Patel 1993; Zheng and Zaheer-uddin 1996; Zaheer-uddin and Zheng 2000, 2001). These optimal and sub-optimal control strategies were developed based on the physical models. The simulation results demonstrated that these optimal and sub-optimal control strategies, in which the multiple control variables were optimized simultaneously, can improve the system response and operational efficiency. They also demonstrated that multistage optimal control technique is an effective and useful tool for computing supervisory control profiles for building systems subject to time-of-day operating schedules.

The system performance and supervisory control for a direct-fired LiBr absorption chiller system were investigated by Koeppel et al. (1995) using simulation means. The detailed and simplified component models were used to predict the system energy and environment performance. Simulated annealing as a global optimization algorithm was used to determine the optimal control settings under different control options. The results showed that the optimal operation schedule for absorption chillers can be determined from the optimal control investigation under the simulation environment.

The performance of the differential dynamic programming (DDP) technique applied to optimal control of building HVAC systems was studied by Kota et al. (1996). The state equations utilized to describe the HVAC system were derived from mass and energy conservation principles. The optimization result was compared with that obtained from a nonlinear programming (NLP) technique using the SQP method. It was showed that DDP is more efficient compared with NLP for the example problems, while NLP is more robust and can treat constraints on the state variables directly.

Henze et al. (1997, 2005) devoted great efforts on predictive optimal control of building thermal storage systems using a physical model-based approach. Henze et al. (1997) developed a predictive optimal controller for thermal energy storage systems, and the performance of this controller was validated by simulations. This optimal controller minimized operating costs of the cooling plant over the simulation horizon. An optimal storage charging and discharging strategy was planned at every time step over a fixed look-ahead time window utilizing newly available information. The simulation results showed that this optimal controller can achieve a significant performance benefit over the conventional controls in the presence of complex rate structures, while requiring only a simple predictor. Henze et al. (2005) demonstrated model-based predictive optimal control of active and passive building thermal storage inventory in a test facility in real time using time-of-use differentiated electricity prices without demand charges. In their study, the building was modeled in the transient systems simulation program, TRNSYS, while the Matlab and its optimization toolboxes were used to interface with the building simulation program. The experimental results showed that the savings associated with passive building thermal storage inventory were small because the test facility utilized was not an ideal candidate for the investigated control technology.

Wang and Jin (2000) presented a supervisory control strategy using a system approach for VAV air-conditioning systems in which simplified physical models were utilized to predict the overall system performance, and genetic algorithm (GA) was used to solve the optimization problem of multiple control variables. It is the first application of GA in solving an optimal control problem formulated using a system approach in HVAC field. The simulation results showed that this online supervisory control strategy can improve the overall system energy and environment performance since it took into consideration the system level characteristics and interactions among the system variables.

The International Energy Agency (IEA) research project Annex 17 provided an example to demonstrate the advance of system simulation in testing and evaluating energy management and control systems (EMCS) supervisory control strategies for overall building systems, as well as control strategies implemented in real EMCS by means of emulation (Lebrun and Wang 1993). Several simulation platforms for building HVAC systems using detailed and simplified physical component models have been established to evaluate the energy performance and economic feasibilities of different supervisory and optimal control strategies for building HVAC systems (Sud 1984; Wang 1998, 1999). Simulation exercises based on these simulation platforms showed that energy or cost savings can be achieved when the supervisory and optimal control strategies are utilized as compared to the local control strategies. These simulation platforms are extremely useful and very helpful for testing and evaluating alternative control strategies and, thus, for determining the best control strategies for building HVAC systems prior to site implementation.

Zhang and Hanby (2006) presented a model-based supervisory control of renewable energy systems in buildings in which building models and plant component models were physical models. The objective of the control problem was to minimize the net external energy consumption of the system subject to a series of constraints. An evolutionary algorithm was used to seek the optimal and near-optimal control settings. Simulation results indicated that significant improvements in system operation are possible as compared to the existing rule-based control scheme.

These control studies using physical model-based supervisory control strategies demonstrated that system energy or cost efficiency and environment performance, as well as system response, can be improved greatly when such techniques are used. However, many parameters in governing equations are uncertain, and many parameters in detailed physical models require detailed information of the system or process of concern. The parameter identification and performance prediction of these governing equations and detailed physical models in the supervisory control strategies often require a lot of iterations, which may result in high computational cost and memory demand, as well as control instability. All of these characteristics are the major obstacles that may seriously prevent their online control applications. However, the results obtained from these governing equations and/or detailed physical model-based supervisory control methods by simulations are essentially helpful and useful to develop the most extensive and practical supervisory control strategies. For practical application, simplified physical models and/or gray-box model-based supervisory and optimal control strategies could be more suitable, which might be a feasible solution that can direct many advanced strategies to be applied in practice.

Black-Box Model-Based Supervisory Control Strategies

There are also a few studies that utilize black-box models to construct the supervisory control strategies in the HVAC field. These studies can be roughly classified into two categorizes: artificial-neural-networks (ANNs)-based supervisory control strategy and empirical-relationship-based supervisory control strategy.

ANNs-Based Supervisory Control Strategies

ANNs are simplified models of the central nervous systems. They are networks of highly interconnected neural computing elements that have the ability to respond to input stimuli and to learn to adapt to the environment (Goh et al. 2002). ANNs operate as black-box models because no detailed information about the system is required. They learn the relationships between input and output variables by studying the historical data. The main advantages of ANNs are their abilities to map nonlinear functions, to learn and generalize by experience, as well as to handle multivariable problems. These desirable properties may make ANNs feasible for control applications. However, they have the inherent deficiency of black-box models in that they are only reliable at the operation conditions where the range of training data covered.

The first ANNs controller was developed by Widrow and Smith (1963). They used adaline to stabilize and control the pole balancing act. Interest in using ANNs for process control only started in the latter 1980s. Kawato et al. (1987) and Guez et al. (1988) showed the computation speed advantage and nonlinear modeling capabilities of ANNs in feedback loop process control.

The research and development on ANNs in building HVAC systems started at the early 1990s and have stressed the importance of energy management (Curtiss et al. 1994; Curtiss 1997), system control and optimization (Curtiss et al. 1993; So et al. 1995; Gibson 1997; Bradford 1998; Chow et al. 2002; Massie 2002), and energy use prediction (Kreider and Wang 1992; Massie et al. 1998; Dodier and Henze 2004).

To optimize the overall system performance, ANNs-based supervisory control was utilized in several studies. Curtiss et al. (1993) discussed the results of a proof-of-concept experiment in which ANNs were used for both local and global control of a commercial building HVAC system. Data collected in the laboratory were used to train ANN models. The experiment results obtained from the laboratory testing showed that significant energy savings are possible when supervisory control is used.

ANNs-based supervisory controllers were developed by Curtiss et al. (1994) and Massie (2002) to minimize the total energy consumption of building HVAC systems. In their studies, the supervisory controller, namely, the global controller, consisted of two networks–training network and predictor network–working in parallel, as shown in Figure 4. The training network was used to learn the relationship between the various controlled and/or uncontrolled variables and the total power consumption of HVAC systems. The training network weights were then passed to the predictor network where they were used in the activation function of the predictor network. The predictor network subsequently found optimal values for the controlled variables that can minimize the overall system operating cost. The Curtiss et al. (1994) method was employed by Bradford (1998) to online supervisory control of a cooling plant without storage. ANNs were generated using historical data from a testing building. The output of the networks was the total power consumption of the HVAC system. The network was configured with two hidden layers of three and two nodes, respectively. These three studies demonstrated that ANNs-based supervisory control is robust in finding optimal solutions at any given working condition since such controller does not rely on any assumptions of the system or process of concern. The operating cost of building HVAC systems can also be reduced greatly.

[FIGURE 4 OMITTED]

The application of ANNs to serve as a system identifier and as an intelligent controller for an air-handling system was investigated by So et al. (1995). The objectives of this study were to minimize the total energy consumption and control errors between setpoints and corresponding control variables. The ANN behaved as an identifier by continuously keeping track of all the real-time parameters. Five actuating signals, which were produced based on the nonlinear error optimization of the outputs of the ANN, served as a controller. The results illustrated that the ANN identifier/ controller has excellent performance as compared to the conventional PID controller.

ANNs-based supervisory control for building HVAC systems was also studied by Gibson (1997) and Chow et al. (2002), in which ANNs were used to simulate system dynamic characteristics and genetic algorithm (GA) was served as a global optimization tool. Both studies discussed how the two techniques can be integrated into a working system. Gibson (1997) installed the developed supervisory controller at the central cooling system of a building in a high school. The system operation results showed that both GA and ANNs are effective techniques for online control. However, the important lessons learned by the author showed that great care should be given since GA and ANNS cannot always provide the desirable solutions. The results from the case studies by Chow et al. (2002) showed that considerable energy can be saved since such supervisory controller allows an overall consideration of the interactions among the systems and their controlled variables.

For energy use prediction, Dodier and Henze (2004) used ANNs as general nonlinear regression models. A statistical test, namely, Wald’s test, was applied to ANNs to evaluate the relevance of various inputs. The results of Wald’s test applied to the energy prediction data demonstrated that day and time variables are more relevant to predicting energy use targets than the environmental variables.

Xu et al. (2005) presented an optimization-based methodology to control HVAC units in stochastic settings. Considering the difficulties related to tuning the parameters for different buildings, a neural network was used to predict the dynamics of HVAC systems instead of using system dynamic governing equations. Lagrangian relaxation, a decomposition and coordinated approach, was used to obtain near-optimal solutions with quantified quality. Numerical testing and prototype implementation results showed that this method is significantly better than existing methods.

These studies using ANNs-based supervisory control strategies demonstrate that ANNs can play a role in the supervisory control of building HVAC systems. Energy or cost savings are possible when such controllers are used. However, most of these studies were performed from the view point of academic research. The practicability and effectiveness of the real-time application of such supervisory controllers are still suspended. Since ANNs operate as black-box models, significant control errors might result in when the system operates outside the range of ANNS trained, and/or the measurement faults, and/or component degradations occur. Moreover, the training of ANNs always requires extensive computational cost and memory demand, which makes it almost impossible and unacceptable to apply adaptive control in practice to improve the prediction accuracies of ANN models. The online practical application of such methods needs to be cautious.

Empirical Relationship-Based Supervisory Control Strategies

Empirical relationships, involving polynomial regression models and empirical models, etc., could be the simplest way to formulate and construct the system and/or component models. There are process historical data-based models. Both inputs and outputs are known and measured from the field monitoring. In the building HVAC field, there are a few studies that use empirical relationship-based models to construct the supervisory control strategies.

Braun et al. have devoted considerable efforts on developing optimal and near-optimal control strategies using quadratic relationships for chiller and water systems (Braun et al. 1987; Braun 1988; Braun et al. 1989a). These are detailed in Chapter 41 of the 2003 ASHRAE Handbook– HVAC Applications (ASHRAE 2003). These studies included the application of two basic methodologies for determining optimal or near-optimal values of the independent control variables in the system that minimize the instantaneous operating costs of chiller plant. One was a component model-based nonlinear optimization algorithm, in which power consumptions of chillers, cooling towers, condenserand chilled-water pumps, as well as supply and return fans were expressed as quadratic relationships. This methodology was used as a simulation tool for investigating the system performance. The other was a system-based methodology for near-optimal control, in which an overall empirical cost function of total power consumption of a chiller plant was developed using a quadratic function. This method allowed a rapid determination of near-optimal control settings over a range of conditions. Pape et al. (1991) extended Braun’s method to the overall HVAC system. The power consumption of the entire HVAC system was represented by a quadratic relationship in terms of control variables, loads, and ambient conditions. The optimal control was determined by equating the first derivative of the power with respect to each control variable to zero. This optimal control methodology can be used in fault detection. Braun’s method was also further extended by Cascia (2000) through simplifying the component models and providing the equations for determining the setpoints of near-optimal control. All component power consumptions (e.g., chillers, pumps, fans) were expressed as a function of temperature difference between chilled-water supply and return temperatures. The coefficients in the model were determined from the direct measurements of total power consumption and temperature difference obtained from a DDC system. A pilot test of this methodology was implemented at a small cooling plant. A third-party energy accounting program was used to track the energy savings due to the near-optimal control. The results showed a monthly energy reduction ranging from 3% to 14%. However, this strategy was based on the assumption that the condenser-water flow rate is unchanged.

Braun et al. (1989b) identified several guidelines for near-optimal control of chilled-water systems without significant thermal energy storage. They also identified that the optimal supervisory control of a chilled-water system was primarily a function of the total chilled-water cooling load and ambient wet-bulb temperature. These results formed the basis to develop the near-optimal control strategy for cooling towers (Braun and Doderrich 1990a). The cooling tower control algorithm was expressed as an open-loop control equation in terms of total chilled-water cooling load. This method was further extended by Braun (2007a) to develop a general control algorithm for cooling towers in cooling plants with electric and/or gas-driven chillers.

Olson and Liebman (1990) developed a nonlinear model for the chilled-water plant and solved it by the SQP method together with a heuristic approach to explore discrete equipment alternatives to help decide the optimal way to operate the entire system. By establishing an empirical model that is only dependent on cooling load, it is possible to predict the power that would be necessary to cool the building with various combinations of equipment. The results showed that computational cost can be reduced significantly by this approach.

For system based optimization, Austin (1993) used biquadratic polynomial models of chillers and cooling towers to optimize the condenser-water temperature setpoint. Based on the detailed analysis of chiller and cooling tower performance characteristics, the author emphasized that system modeling can help select the best combination of chillers and condenser-water temperature setpoints to meet different loads under various outdoor working conditions with the least energy input.

Ahn and Mitchell (2001) developed an optimal supervisory control strategy for a cooling plant. A quadratic regression equation was used to predict the power consumption of a total cooling system in terms of forcing function and controlled variables. The optimal control settings, e.g., supply air temperature, chilled-water temperature, condenser-water temperature, etc., were selected to make the total system power consumption minimized. The simulation result showed that minimum total system power consumption was the trade-off among power consumptions of different components. This control methodology is simple and easy to be implemented. However, there are 28 coefficients with no physical significance required to be identified from the monitoring data, which may result in significant prediction deviations for practical application.

An optimal operation strategy for a large cooling system was presented by Yao et al. (2004), in which empirical relationships among controlled variables, uncontrolled variables, and system performance were established using site measurement data. A system coefficient of performance (SCOP) was introduced to analyze the effects of energy savings of the cooling system. The results obtained from case studies showed that energy saving was likely to reach as high as 10% by applying the optimal operation strategy to the cooling system.

Lu et al. (2004, 2005a, 2005b, 2005c) presented a series of system optimizations for building HVAC systems. Interactive nature within and between components and their controlled variables in the system was seriously considered. The objective function of global optimization was formulated based on mathematical models of major components. Power consumption of chillers was predicted using an empirical model, while power consumption of water pumps and fans was modeled as a function of the ratio of water flow rate to the design water flow rate and the ratio of airflow rate to the design airflow rate, respectively. A modified genetic algorithm was utilized to search the optimal control settings. Simulation studies based on a small pilot-scale centralized HVAC plant showed that system level optimization can improve overall system operating performance significantly.

Sun and Reddy (2005) presented a general and systematic methodology, termed as complete simulation-based sequential quadratic programming (CSB-SQP), to determine the optimal control strategy for building HVAC systems. Linear approximation of Taylor expansion was utilized to formulate the system models. A case study on a simple cooling plant illustrated the efficiency and robustness of this methodology.

These supervisory control studies using empirical relationships also demonstrate the energyor cost-saving potentials in HVAC systems when such methods are utilized. Empirical relationship-based supervisory control methods are easy to implement in practice since the methodologies involved in such methods are relatively simple, and computation time is generally manageable. However, most existing strategies seem to lack generality because they were only validated by simulations or pilot tests with certain operating points. The application of such methods in large office or commercial buildings is lacking. The robustness of such methods is also a big issue in practice, especially when the systems operate at the range where the training data are not covered or system degradations or measurement faults occur. Although adaptive control can improve the prediction accuracies of these models to some extent, it is very dangerous to apply adaptive control to large and complicated HVAC systems at current stage. More research is essentially needed to further validate the feasibilities of adaptive empirical relationship-based supervisory control methods in practice and special care should be given when such methods are used.

Hybrid Supervisory Control Strategies

There are also a few studies that use a mix of different types of models and/or the model-based method and the model-free method to design the supervisory control strategies for building HVAC systems.

Braun (1990b) proposed an optimal control strategy for building thermal storage to reduce operating costs and peak electrical demand. In this study, the building model was a simplified physical model, while chiller plant models were quadratic relationships. Simulation results indicated that both operating costs and peak electrical use can be reduced significantly through optimal control of the intrinsic thermal storage within building structures. This control methodology was employed by Simmonds (1993) to minimize the system operating cost while maintaining the acceptable indoor comfort. The result showed that cost savings could be achieved if control was based on maintaining the predicted mean vote (PMV) rather than the dry-bulb temperature.

Kintner-Meyer and Emery (1995) presented a comprehensive analysis of optimal control of HVAC systems considering building thermal mass and cold storage equipment. The optimization strategy was formulated as a minimization of operating costs over a 24-hour period. The analysis was based on the thermodynamic modeling of the HVAC system, including the thermal response of the building structure. The chiller was modeled as a function of part-load factor, wet-bulb temperature, and chilled-water temperature, while pump power and fan power were modeled based on pump and fan affinity laws. The results of this analysis indicated that significant cost savings can be achieved by precooling the building during hours of low electricity rate.

Optimal supervisory control using a system approach for chilled-water plants was studied by Flake (1998). In his study, the chiller model was a quadratic relationship, while steam turbine, heat exchanger, and cooling tower models were physical models. Simulated annealing as a global optimization technique was used to determine the optimal control settings under different control options. The estimated cost saving using the optimal supervisory control method for a chiller plant was 4.3% over the conventional control method.

Nassif et al. (2005) utilized a two-objective genetic algorithm to optimize a model-based supervisory control strategy for building HVAC systems. In their study, a detail physical coil cooling model and an empirical chiller model served to calculate energy consumption during the optimization process, and system level interactions were considered seriously. The control settings, i.e., supply air temperature, supply duct static pressure, chilled-water supply temperature, minimum outdoor ventilation, reheat, and zone air temperature, were optimized with respect to energy use and thermal comfort. This optimization process was applied to an existing VAV system. The operation results showed that optimization of the supervisory control strategy could save energy by 16% for two summers while still satisfying minimum zone airflow rates and zone thermal comfort. The robustness of application this method was not reported.

A simulation optimization approach was proposed by Fong et al. (2006) for effective energy management of building HVAC systems, in which evolutionary programming was used to handle the discrete, nonlinear, and highly constrained optimization problems, and an empirical chiller model and a simplified cooling coil physical model were used to predict the system energy and environment performance. The simulation exercises for the HVAC system in a subway station showed that 7% energy saving can be achieved by optimizing the setpoints of chilled-water temperature and supply air temperature on a monthly basis.

A hybrid optimal control scheme combining the features of a deterministic model-based approach with model-free learning control for active and passive building thermal storage inventory was proposed in companion papers by Liu and Henze (2006a, 2006b). An experimental study was conducted to evaluate the performance of this controller on a full-scale laboratory facility. The results demonstrated that this hybrid control approach can provide reliable control performance. Cost savings are possible as compared to the traditional control schemes. However, the savings were lower than that of using the model-based predictive optimal control scheme.

Braun (2007b) presented a simple control strategy for hybrid cooling plants that could be readily implemented with low costs. The chiller performance was characterized in terms of COPs and cooling capacities, while the cooling tower was modeled using an effectiveness simplified physical model. This strategy was developed and evaluated using a simulation tool that could determine optimal control settings for specific simulated cooling plants. A near-optimal control strategy for cool storage systems with dynamic electric rates was proposed by Braun (2007c). In this strategy, the ice storage tank was modeled using a semi-empirical model, and the ice-making chiller plant was modeled using an empirical model. This strategy was evaluated for ice storage systems using a simulation tool for different combinations of cooling plants, storage sizes, buildings, locations, and real-time pricing electric rates. The results showed that 2% cost savings are possible when associated with the use of optimal control.

The hybrid supervisory control strategies might be feasible for practical application if different types of models are selected properly and/or the features of both the model-based method and the model-free method are combined effectively. However, most existing hybrid supervisory control strategies were evaluated by simulations, and their practical applications seemed to be missing. More research on application of hybrid supervisory control strategies in practice is highly needed.

Performance Map-Based Supervisory Control Strategies

There are also a few studies associated with using performance maps, often called control maps, to construct the supervisory and optimal control strategies for building HVAC systems.

Performance map-based supervisory control for chiller plants to minimize energy use was studied by Hackner et al. (1985) and Lau (1985). Both studies utilized component models to test and search the minimum power consumption for each combination of controlled and uncontrolled variables. The optimal control strategies were expressed in the form of performance maps, and these performance maps were then used to optimize the operation of building HVAC systems. The comparison studies showed that these performance maps using system optimization techniques can save more energy as compared to local optimization methods. The application of established performance maps for online control was advocated by Johnson (1985). The methodology utilized in the study of Braun (1990b) also included the development of an optimal performance map for a cooling plant.

For practical application, the operation strategy proposed by Yao et al. (2004) included the application of performance maps inherently. Based on the field tests of the system over a significant range of settings and operating conditions, a series of empirical equations for control variables, i.e., condenser inlet water temperature, the condensing temperature, and the evaporating temperature, can be regressed and then used to optimal control of the operation of HVAC systems. These empirical equations can be regarded as being regressed from control maps, while control maps are generated from field monitoring.

For real-time control applications, Sun and Reddy (2005) suggested using the simple control laws for near-optimal control of HVAC systems. Based on the developed CSB-SQP, optimal control maps can be generated using detailed simulations. The regression model for each control variable can then be developed from the control map of corresponding control variable and was used to near-optimal control of the operation of HVAC systems.

It might be practically beneficial to apply performance map-based supervisory control strategies for small HVAC systems. However, it is tedious and burdensome work for large systems. For practical application, it might not be the best choice.

Supervisory Control Strategies-Based on Other Techniques

The control studies addressing optimal control and operation of HVAC systems that do not fall into the above categories are grouped as supervisory control strategies based on other techniques here. These include the strategies using the model-free approach, the strategies using optimization analysis, experiment investigation, etc.

Kaya and Sommer (1985) presented a four-level control structure for a chiller system. The first-level controls were local controllers for chilled-water temperature, vane position, and condenserwater temperature. All the first-level controls were supervised by the second-level control to provide reasonable setpoints. The third-level control was used to optimally allocate the total load for each operating chiller and pump. The fourth-level control was used for supervisory coordination of the chilled-water temperature and scheduling of the chiller system operation. There was no actual energy savings due to the application of the supervisory control strategy.

An expert controller for a building HVAC system was designed by Ling and Dexter (1994) using a predictive control approach. The design of the predictive control algorithm was based on prior knowledge of the system. A rule-based supervisory method was used to optimize the control performance. Experimental results showed that the use of rule-based supervisory control can lead to significant cost savings without unacceptable increases in discomfort level. The result also demonstrated that this expert controller was able to compensate day-to-day variations in control performance.

Based on system analysis, Hartman (1995) pointed out that the implementation of direct digital control (DDC) systems can provide new approaches to the concept of global optimization. However, the amount of data accumulated and employed in calculations can be very large for large systems. This may place huge burdens on the communication network and computing capacities of DDC systems.

A novel control strategy using a system approach for optimizing variable-speed pumps of indirect water-cooled chilling systems was developed by Wang and Burnett (2001). This strategy includes an adaptive and a derivative method to optimize the speed of pumps by resetting the pressure setpoint according to the estimated derivative of the total instantaneous powers of chiller and water pumps with respect to pressure. The adaptive strategy identified the changes of the system parameters essential for the control strategy and updated the control accordingly. Simulation results showed that proper reset of seawater pressure control setpoint can provide

up to 10% of saving in total chilling system electricity consumption, while 5% of saving can be expected in most of cases investigated.

Henze and Schoenmann (2003) presented a model-free reinforcement learning controller for optimal operation of thermal energy storage systems. The reinforcement learning controller learns to charge and discharge a thermal storage tank based on the feedback it received from past control actions. The controller learns to account for the time-dependent cost of electricity (both time-of-use and real-time pricing), the availability of thermal storage, part-load performance of a central chilled-water plant, and weather conditions. The performance of this controller was evaluated by simulations, and the result showed that it has strong capability to learn a difficult task of controlling thermal energy storage with good performance. However, cost savings were less when using a predictive optimal controller.

To assist in improving the electrical efficiency of HVAC systems, Hartman (2005) developed a general system analysis principle, namely Equal Marginal Performance Principle (EMPP), to help in optimizing the system design, and to ensure optimal operation of nearly any modern HVAC system. This EMPP simply stated that energy performance of any system operating with multiple modulating components is optimized when the changes in system output per unit of energy input is the same for all individual components in the system. This principle is simple and powerful. It could be useful for designers in terms of how system components can be configured and make them operate more effective and efficient.

These studies attempt to apply advanced techniques to optimal control and operation of HVAC systems. Such efforts are essentially useful, which might be a way that can find more efficient and practical techniques or methods suitable for online practical control of HVAC systems.

DISCUSSION AND CONCLUSIONS

Based on the discussions of different supervisory control methods, the discussions of various optimization techniques, and a comprehensive review of existing supervisory and optimal control studies, some useful conclusions can be summarized below, and a few recommendations for future work in this direction are presented as well.

1. For online control applications, supervisory control methods and optimization techniques should be developed and/or selected applicable to a wide operating range of building HVAC systems, while still satisfying the requirements and constraints of practical application, i.e., control robustness, control accuracy, control efficiency, computational cost, and memory demand, etc. If system and/or component models are used in the control system to predict the control performance and system response, it is essential that these models have simplified structures and high prediction accuracy, require less calibration efforts and computational cost, and maintain certain physical significances of parameters. The optimization technique utilized to seek the optimal solutions should better have high computation efficiency and high capability to find global minimums. It should be easy to converge as well.

2. The research and development on supervisory and optimal control in building HVAC systems demonstrate energyor cost-saving potentials in buildings when optimal strategies are used. However, most existing studies related to supervisory and optimal control either the methodologies are too mathematical or the methods lack generality. Most proposed supervisory control strategies are only validated by simulations or by pilot tests on small-scale HVAC systems with limited operation points. The practical validation of these supervisory and optimal control methods on real HVAC systems, especially on large and complicated HVAC systems, is still missing.

3. Detailed physical model-based supervisory control strategies might not be suitable for practical application since detailed physical models often require a lot of iterations, which may result in high computational cost and memory demand, as well as control instability. However, the results obtained from these detailed physical model-based supervisory control strategies by simulations are essentially helpful and useful to develop the most extensive and practical supervisory control strategies.

4. Online practical application of black-box model-based supervisory control strategies needs to be cautious. Significant control errors may result when the system operates outside the operating range covered by the data used to train black-box models, and/or measurement faults, and/or component degradations occur. In addition, the training of some black-box models (such as ANNs) requires extensive computational cost and memory demand, which may make it impossible and unacceptable to use adaptive supervisory control strategies based on those models.

5. Compared to detailed physical model-based supervisory control strategies and black-box model-based supervisory control strategies, simplified physical model and/or gray-box model-based supervisory control strategies might be better and more suitable for practical application. These simplified physical models and gray-box models generally have relatively simple structures and require less computation time. The parameters in these models still have certain physical significance, which allows these models to be used for limited extrapolation outside the range covered by training data with acceptable prediction accuracy.

6. Hybrid supervisory control methods might be feasible for practical application if different types of models are selected properly and/or the features of both the model-based approach and the model-free approach are combined effectively. However, most existing hybrid supervisory control strategies were evaluated by simulations, and their validations in practical application are still missing.

7. Near-optimal control strategies were advocated for practical application in Chapter 41 of the 2003 ASHRAE Handbook–HVAC Applications (ASHRAE 2003). Near-optimal control strategies are often simple and easily developed and implemented in practice. However, near-optimal control strategies do not provide the true optimal settings, which might provide settings significantly different from the optimal settings. The more extensive and effective strategies for practical application could be formulated by effective combination of near-optimal control strategies and simple and practical optimization techniques.

The ultimate objective of any technique development comes to a point, i.e., its application. The key issues for the development and application of supervisory and optimal control for building HVAC systems may include:

* Selection of the supervisory control method

* Selection or development of models (if needed)

* Selection of the optimization technique

* Defining the cost or objective function

* Programming of control logic and strategies

* Testing and commissioning of the control program

One thing worthwhile to point out is the testing and commissioning of the control programs. Due to the increased complexity of the programs, system level parameters need to be identified, which would have high requirements on the efforts and skills of the application engineers to handle the testing and commissioning work.

There is still a long way to go for building HVAC scientists and professionals to make those methods and techniques attain desirable and satisfactory performance and prove to be convenient in practice, and, therefore, to fully utilize their capacities in practical application to optimize the control and operation of building HVAC systems to enhance the overall energy/operating efficiency and environmental performance.

ACKNOWLEDGEMENT

The research work presented in this paper is financially supported by a grant (PolyU 5283/05E) of the Research Grants Council (RGC) of the Hong Kong SAR.

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Shengwei Wang, PhD Zhenjun Ma

Member ASHRAE

Shengwei Wang is a professor and the acting head and Zhenjun Ma is a PhD student in the Department of Building Services Engineering, Hong Kong Polytechnic University, Kowloon, Hong Kong.

Received February 7, 2007; accepted June 29, 2007

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