1、4728 Neural Network Optimal Controller for Commercial Ice Thermal Storage Systems Darrell D. Massie, Ph.D., P.E. Member ASHRAE Jan F. Kreider, Ph.D., P.E. Member ASHRAE Peter S. Curtiss, Ph.D. Member ASHRAE ABSTRACT This paper describes the construction and measured performance of a neural network-b
2、ased optimal controller for an ice thermal storage system. The controller consists of four neural networks, three of which map equipment behavior and one that acts as a global controller. The controller self-learns equipment responses to the environment and then determines the control settings that
3、should be used. Issues to be addressed are the cost function and selection of a planning window over which the optimization is conducted. The neural network o controller then determines the sequence of control actions that minimize total cost over the planning window. Verijkation, reported on in a c
4、ompanion papei; is accomplished through computer simulation and on an operational plant. INTRODUCTION Using ice storage to cool commercial buildings is a load management strategy that can reduce electrical power or energy costs. Savings can be achieved by moving the cost of cooling buildings from ex
5、pensive “on-peak” periods to cheaper “off-peak” periods and through the installation of significantly smaller cooling plants. Ice storage has been a popular method of cooling churches and theaters for decades. Historically, ice storage enabled the installation of much smaller equipment by making ice
6、 over several days for use during short periods of occupancy. Most of todays installed thermal storage systems are employed to shift the cost of elec- tricity from on-peak to off-peak periods, thus reducing demand and energy charges. Unfortunately, many facility owners are often disappointed with sy
7、stem performance since these systems are not providing the expected load shifting. Poor control has been identified as the primary reason for their insufficient performance (Potter et al. 1995). Control strategies implemented in the field today do not consider the changes in buildings and equipment
8、from year to year, season to season, or even day to day. As a result, much of the potential cost savings of using thermal storage systems is lost. Optimal control has not been implemented because of perceived difficulties accommodating the complex interac- tions between equipment. Equipment behavior
9、 is highly non- linear and varies from one location to another, requiring experts to fine-tune and control these systems. Even for experts with broad experience in installing cool storage equip- ment, models are complex and require significant effort to calibrate. Furthermore, as equipment ages or u
10、ndergoes retro- fit, models that describe equipment behavior must be changed, requiring further expert assistance. The equipment modeling problem could be overcome if it were possible to develop a system that “learns” how equip- ment functions under different conditions and then controls the equipme
11、nt for best performance. This is possible through the use of neural network (NN) algorithms. Determining equipment setpoints for thermal storage control systems also presents a challenging problem because of the large number of possible solutions. In response to this problem, some of todays fielded
12、controllers (termed “rule- based” controllers) rely on heuristics that specify when ice should be made and melted. Use of rule-based controllers affords some cost savings but still falls far short of meeting the full load-shifting potential that ice storage can provide. This is largely because they
13、are developed using assumptions as to how equipment will operate in a field environment. - Darrell Massie is director, Mechanical Engineering Research Center, and associate professor, United States Military Academy. Jan Kreider is founding director, Center for Energy Management (JCEM), and professor
14、, University of Colorado, Boulder. Peter Curtiss is owner, Curtiss Engineering, Boulder, Colo. 02004 ASHRAE. 361 Because of the complexity of component models and the difficulties in modeling how components best work together and how building usage changes, optimal controllers exist only in computer
15、 simulation today. Just as complex compo- nent models can be replaced with NN models, traditional control techniques can be replaced with neural network-based controller approaches. Since the learning algorithms of neural networks are always similar, this type of controller has the potential of bein
16、g relatively simple to program and does not require a robust CPU or large memory requirements (this study used a 80486 computer with a math coprocessor and limited memory). COST FUNCTION Minimization of Operating Costs Akbari and Sezgen (1992) observed that there is a continuing need for research in
17、 optimal control for energy storage systems. According to his work, few TES systems take advantage of daily variations in climate and operating condi- tions so that charging and discharging are optimized. To find optimal solutions, different approaches have been used. Braun (1992) used an index of p
18、erformance over a one-day period to minimize energy or demand cost. In another 24-hour horizon study, Simmonds (1 994) investigated energy consumption and excluded the effect of price structure, which could vary by location. Kintner-Meyer and Emery (1 995a) investigated the sizing of thermal storage
19、 components and their impact on the overall system cost, and, in another study, Kintner-Meyer and Emery (1 995b) investigated the use of an ice storage facility in conjunction with the building thermal capacitance. Henze et al. (1 997a) developed a simulation environment that used a realistic plant
20、model covering a 168-hour (one-week) period. Henzes cost function included energy and demand cost plus a ratchet; also investigated was the theoretical limit on the oper- ating cost savings achieved by cool storage. All of the studies listed here assumed perfect knowledge of building load and weathe
21、r. There have been tremendous improvements in TES control over the past decade. Each of the above works is testa- ment to that. There are, however, limitations to the methods that have been used up to this point. Equipment modeling is complex and although classical models describe the general operat
22、ing trends of equipment, they lack the sophistication required to cover the broad range of steady-state and transient conditions found in installed plants. Classical models must also be individually created for each location. Objective Function. The main objective of this work is to develop a contro
23、ller that operates a chiller and storage system for least cost. Henze et al. (1997b), Kintner-Meyer and Emery (1 995b), and Braun (1992) each concluded that the use of ice storage is primarily driven by the reduction in operating cost. TWO basic cost functions are utilized in this study: a tradi- ti
24、onal utility rate structure that includes energy $/kWhl and . demand $/kW cost and a real-time-pricing (RTP) rate struc- ture that uses only an energy cost that varies by time of day. The traditional utility rate structure is further divided into a strong or a weak function, where the ratio of on-pe
25、ak to off- peak rates is large or small, respectively. The cost functions used in this study are the total cost that an electrical consumer pays for operating all components of the cooling plant. Optimal Planning Horizon. Henze et al. (1997b) inves- tigated the impact of varying the time horizon win
26、dow to determine the impact on optimal control given uncertainty in load forecast and equipment performance. This was accom- plished by using various load predictor models, such as an unbiased random walk, a bin prediction model, a harmonic predictor model, and an autoregressive neural network model
27、. The simulation also investigated the impact of equipment model accuracy. Results showed that a planning horizon of 15 hours yields nearly the same solution regardless of the load prediction method used. Furthermore, optimal control over the 15-hour horizon was only marginally sub-optimal compared
28、to a planning horizon of one week. A planning horizon of 2 1 hours yielded cost differences of less than two percent regard- less of the predictor method used. Investigation of inaccura- cies of the cooling plant model demonstrated that, although a poor model degrades results, it is less important t
29、han knowl- edge of the utility price structure when considering optimal control. It should also be noted that results depend upon size of both chiller and storage. Traditional Cost Function. Although a planning hori- zon of only 15 to 18 hours is sufficient to realize almost all of the cost savings
30、of optimal control, this study used a planning horizon of 24 hours due to the cyclic nature of TES operation. The traditional cost function has two parts: the cost of electri- cal energy kwh consumed over the billing period and the cost for peak electrical demand kW. A ratchet was not used in this s
31、tudy so that results could be compared with other work. Using two distinct rate periods, the cost J (expressed in units of $/month) of operating the cooling plant for one day can be simulated from i 24 2 = P(k)re(k)At+ pmax,vrd,v () 1 k= I v= I For simulations covering multiple days, the highest pow
32、er demand P, is the higher of the demand P that has occurred up to now in the billing period or to that projected P brojected, by the non-cooling load and chiller model as that computed by the controller. Real-Time Pricing Cost Function. Real-time pricing (RTP) is designed to charge the consumer mor
33、e for electricity during periods when electricity is more costly to produce. AS a result, there may or may not be a demand charge $/kW as found in traditional rate structures. Indications are that most true real-time pricing rate structures will consist of only an 362 ASHRAE Transactions: Research e
34、nergy charge $/kWhl that will vary for each hour of the day. The cost function for true RTP can then be written as P 24 J = P(k)r,(k)At . (3) i k=i System Model and Constraints This section describes the equipment models used in this study. The models differ from traditional models used in computer
35、simulations in that they were based on empirical data collected from actual installed equipment and do not include simplifjing assumptions such as those used by Drees and Braun (1996), for example. Traditional Models. Power consumption P includes the total for the cooling plant and the non-cooling l
36、oad. Power consumption can be computed using P = Pnon-cooling + Pplani + pump + PAHU (4) The key feature of thermal storage is to minimize the cooling plant power consumption cost by bridging the tempo- ral difference between supply and demand. The power consumption, however, is not a control variab
37、le but is instead a result of operation of the cooling system and non-cooling loads. In a system without storage, the building load must be met immediately by the chiller. With TES the ice storage can be used to meet the building load and the cost of replenishing the storage is movcd to a period whe
38、n electricity is less expen- sive. Therefore, in a system with thermal storage, there is a choice as to which source of cooling will be used at any partic- ular time. Cooling can be taken from the storage, the chiller, or some combination of the two. This decision is based on a comparison of operati
39、ng costs, The state of charge x of the storage tank can be repre- sented with a single variable that defines the fraction of maxi- mum ice formation. At any point in time, a decision is needed to either charge, discharge, or leave the ice inventory unchanged. For ice storage systems the state transi
40、tion equa- tion is (5) subject to the constraints %in xk+l xnzax (6) where xk+ is the state of charge of storage at the end of time k, SCAP is the ice tank storage capacity (e.g., kWh, Btu, or ton-hours), and uk is the charging (+) or discharging (-) rate of storage for time step k. The value of xmi
41、n can be set to zero if only the latent heat of fusion is to be considered or to a nega- tive value if sensible hcat is to be used. The maximum state of charge, xma, is set to 1 .O. In traditional optimal control studies, such as Henze et al. (1997a, 1997b), Drees and Braun (1996), and Braun (1992)
42、ASHRAE Transactions: Research Air-Handler Secondary Loop Three-way Valve Figure 1 Laboratory cooling plant conjiguration. each used uk, the rate of charge at hour k, as the control variable subject to the constraint min k max (7) where a value of less than zero implies discharging. Using the rate of
43、 charge as a control variable has the advantage of reduc- ing the number of combinations of setpoints required for find- ing an optimal solution. In this study the control variable is not the ice tank charge or discharge rate, because it cannot be controlled directly. Instead the chiller and ice tan
44、k are controlled by a combination of the chiller setpoint tempera- ture and primary loop three-way valve position as shown in Figure 1. This is physically useful when the controller is to be installed on an actual TES system. Adjusting the setpoint temperature at the chiller evapora- tor outlet cont
45、rols the chiller. The chillers internal controls are based on sophisticated algorithms that stage the chiller up or down so that the evaporator outlet temperature is maintained near the setpoint. A complete description of the laboratory where the tests were conducted is found in Kreider et al. (1 99
46、9). The primary loop three-way mixing valve, shown in Figure 1, located at the thermal storage tank outlet, determines how much brine coming from the chiller is circulated through the tank. When the valve is set to 100% (termed 100% open), all fluid leaving the chiller circulates through the ice tan
47、k. To charge the tank, the chiller setpoint temperature must be below 0C (32F) and the valve must be open. The lower the setpoint temperature and more open the valve, the faster the charge. When discharging the tank, if the majority of cooling load is to be met by the chiller, a combination of lower
48、ing the chiller setpoint temperature (now above freezing) and closing the valve will shift the load onto the chiller. Likewise if more of the cooling load is to be met by the ice tank, a combination of rais- ing the chiller setpoint temperature and opening the primary loop three-way valve must be ac
49、complished. In Figure 1, the secondary loop three-way mixing valve maintains the secondary loop supply temperature setpoint at 7C (44F). This valve works well under PI control, and flow through the secondary loop is not of importance in this study. It is not modeled in this work. 363 “I hour = current hour ifdischarge rate uk charge + then discharge rale u) =-charge u and state ofcharge sk+, = O t- I Giren: T, V, I nnd pnst vahe positions For any hour there are three critical pieces of required information: + compute evaporntor inlet temperature, T,
