Cost penalties of near-optimal scheduling control of BCHP systems: part II-modeling, optimization, and analysis results.INTRODUCTION Combined heat and power (CHP) components and systems are described in several books and technical papers (Petchers 2003; ASHRAE 2004). Systems meant for commercial/institutional buildings (building combined heat and power [BCHP]) involve multiple prime movers, chillers, and boilers and require more careful and sophisticated equipment scheduling and control methods compared to those in industrial CHP due to the large variability in thermal and electric loads, as well as the equipment scheduling issue. Equipment scheduling involves determining which of the numerous equipment combinations to operate-i.e., it is concerned with starting or stopping prime movers, boilers, and chillers. The second and lower-level type of control is called supervisory control, which involves determining the optimal values of the control parameters (such as loading of prime movers, boilers, and chillers) under a specific combination of equipment schedule. Research into methods to optimize energy consumption or cost of operation of building systems is not new (Braun et al. 1989a, 1989b; Braun 2006; Cumali 1988; Henze 2003; House and Smith 1995; Jiang and Reddy 2007; Sun and Reddy 2005; Wang 1998; Wang and Ma 2008). However, many of the efforts address optimization of one or two specific building systems (e.g., thermal storage or start/stop of chillers and/or boiler systems). Furthermore, most previous cost optimization efforts were based on flat electric rate schedules (non-time variant) with a demand charge. A primary intent for optimization is to avoid demand charges. Further, there are only a few papers that deal with optimization of CHP plants, and these are more academic than practical. Most of the work to date in the heating, ventilating, air-conditioning, and refrigerating (HVAC&R) literature on plant operational optimization is concerned with multiple electric and hybrid chillers and cooling plants. These focus on the lower level objective since the studies were concerned with simpler systems where the number of possible equipment combinations is relatively few. Currently, little optimization of the interactions among systems is done in buildings. Attempts in practice to optimize operations usually involve applying rules of thumb regarding when to turn on boilers or chillers, how to reset set points, and other heuristic actions. There is little or no analytic basis for control of scheduling and interactions in real time. Shedding of loads in response to day-ahead or hour-ahead notifications of need from utilities works well in practice, but as electric rate structures become increasingly time variant, real-time control of scheduling and system interactions become essential for cost-effective operation. Heuristic control normally used by plant operators often results in off-optimal operation due to the numerous control options available to them, as well as to dynamic, time-varying rate structures and relative changes in gas and electricity prices. Though reliable estimates are lacking in the technical literature, the consensus is that 5%-15% of cost savings can be realized if these multiple-equipment BCHP plants were operated more rationally and optimally. There are a few computer software programs that have been developed by federal agencies (e.g., Fischer and Glazer 2002), consultants, and equipment companies for designing BCHP plants. Many use simple models of equipment and simplistic operating scenarios. Most of these programs are design tools that are add-ons to existing programs such as DOE-2 (LBL 1989) or adopt bin-type analysis methods to determine type and size of BCHP systems to be used during the design and selection process. Several papers and books describe heuristic practices for operating cooling plants (Kelly and Chan 1999; Braun et al. 1989a, 1989b; ASHRAE 2007), hybrid cooling plants (Koeppel et al. 1995; Siemens 2004; Braun 2006) and even cogeneration plants (Honeywell 2006; Petchers 2003). However, there has been no systematic guidance on how to operate BCHP plants, and a proper understanding of the cost penalties associated with operating them in a nonoptimal manner is lacking. OBJECTIVES AND SCOPE The objective of this paper is to report on research results involving proper scheduling of equipment in BCHP systems for commercial/institutional buildings. Most of the work to date in the HVAC&R literature (specifically chiller plants) focuses on the lower level objective, since the studies are concerned with simpler systems where the number of possible equipment combinations is relatively few. Also, one needs to differentiate between two terms: optimal and near-optimal, which are used differently by different professionals. One manner of differentiating these is to view the latter as a simplification of the former in terms of the modeling equations describing the performance of the various equipment, the methods of framing and solving the optimization function, and whether the problem is treated as a static or a dynamic problem (i.e., treating the problem on an hourly basis or over a planning horizon, which could be several hours in a day or a whole month). A second viewpoint is to consider near-optimal as synonymous with simplified and heuristic strategies that are close to the optimum bit much simpler to implement in actual practice. Here, we have defined near-optimal scheduling control differently. From a practical operational viewpoint, BCHP operators are averse to switching equipment ON and OFF over the planning horizon, and they would prefer to select a particular set of BCHP equipment to start up at the beginning of the planning horizon and keep this set operational till the end with the ability to control the individual already operating equipment at smaller time steps (e.g., each hour) in an optimal manner. While optimal control is where both the equipment scheduling and control can be done optimally each hour, near-optimal is defined in this research as an operational strategy where one cannot change the equipment scheduling during the planning horizon, but whichever equipment is operating can be controlled so as to result in minimum operating cost. Thus, there will be as many near-optimal solutions as there are feasible combinations during the selected day. A quantity called cost penalty ratio (CPR) was defined as the ratio of the near-optimal to the optimal solutions, and the magnitude and variation of this quantity with building type, location, and price signal are studied. The research project (Maor and Reddy 2008) on which this paper is based involved two phases. The first involved the generation of necessary data for certain characteristic building types with rationally designed and sized BCHP equipment (Maor and Reddy 2009). This entailed specifying a methodology to select representative building types and geographic climates to perform careful design and sizing of the BCHP systems and equipment and to generate hourly building loads using a detailed simulation program. A matrix of representative building types at different geographic locations was defined, after which representative BCHP equipment and electric utility dynamic rate schedules were selected to study the effect of near-optimal control under several days of the year representative of seasonal variations. The second phase, whose results are reported here, involved performing the parametric simulations and studying the magnitude and variability of the CPR values across the various building scenarios selected and then distilling the results. LITERATURE REVIEW Successful operation of BCHP systems requires controls that can integrate information on the building load, the HVAC system, and the electric generator to identify optimal set points for the generator and HVAC systems in the buildings. The optimization problem has several notable characteristics of a large set of system equations: problem variables that are a mixture of integer and continuous variables, nonlinear inequality and equality constraints, and objective functions that can be discontinuous (e.g., Edgar et al. 2001). It seems that neither traditional gradient-based methods nor direct search methods are effective for the optimization problem. Several papers point out the appealing features of mixed integer programming (MIP) (Hui and Natori 1996; Sakawa et al. 2002; Yokoyama et al. 2002; Dotzauer 1997) and some heuristic methods like genetic algorithms (GA) and simulated annealing (SA) (Maia et al. 1995; Sakamoto et al. 1999; Curti et al. 2000). For simplified systems, some simple optimization algorithms, such as linear programming, can be used to solve the optimization problems. Baughman et al. (1989) developed a computer program to minimize the present worth of the electric and thermal energy costs as a function of the type and amount of cogeneration and thermal storage. The plant model, as well as a base model without thermal storage or cogeneration, was proposed, and a linear constrained optimization problem was formulated. The proposed model proved to be valuable in accurately determining the energy savings that various combinations of cogeneration and thermal storage equipment configurations might offer. Ehmke (1990) developed a methodology to extend an existing linear programming model for the optimization of the cogeneration plants. The new approach introduced capital cost and maintenance cost. The aim was to optimize the size of the cogeneration equipment, depending on the characteristics of plant load and tariff conditions. Increasing sophistication of the optimization algorithm allows more complicated models and conditions to be treated. Spakovsky and Frangopoulos (1994) proposed methodologies that combined not only energy use and financial resources expended but also environmental considerations in the construction of mathematical models for the analysis, improvement, and optimization of energy systems. This methodology was applied to a gas turbine cycle with cogeneration to demonstrate the applicability of this methodology, and results were then analyzed and compared with the results of the thermoeconomic optimization of the same cycle obtained in earlier works. Maia et al. (1995) used a combinatorial optimization technique (SA) to derive the flow sheets for systems that satisfy fixed demands of steam, electricity, and mechanical power. SA has been shown to be a powerful technique in the synthesis of a utility system. Also, the authors mentioned that further improvements in the model could consider uncertainty in the input data, since SA does not offer a simple way to perform sensitivity analysis. Sakamoto et al. (1999) described an optimization method for electric-type district heating and cooling plants based on the GA. First, in order to examine the characteristics of the GA method by simulation, a simulated plant was assumed to supply chilled and hot water simultaneously. Second, a pilot plant was actually constructed at a sewage treatment plant in order to better determine the benefits of using low-temperature energy. In the pilot plant, the GA method was applied to optimize the operation schedule for online processing. The study showed that the optimality of the plant schedule obtained by the GA was almost equal to that obtained by mathematical programming. Curti (2000) presented an environomic model (i.e., a model that also includes environmental considerations) for a district heating network based on centralized and decentralized heat pumps by applying the general environomic methodology. A complete set of results for the optimal synthesis, design, and operation of the network is given and discussed. The resulting solution space was highly nonlinear and noncontiguous and was effectively determined using GA. Results were shown for various district heating user distributions, as well as fuel and electricity prices. When properly optimized, solutions with heat pumps were economically very close to traditional district heating solutions, particularly when the main pollution costs are internalized. For comparison purposes, the same approach and models can be used to identify the life cycle exergetic optimum. This approach provides for a fast, comprehensive, and optimal reassessment of design options when economic conditions or the emphasis on pollution vary. Hui et al. (1996) studied the application of mixed integer programming (MIP) techniques for the optimization of site utility systems. The intent was to determine the best investment scheme to the utility system that maximizes the merit of exporting electricity. In other words, the objective was to identify the best combination of equipment to be added to the existing system that would maximize and stabilize the electricity export throughout the year. Decisions on process modifications, such as changing the steam pressure on some local waste heat boilers, were also taken into account. The study also showed that employing a multiperiod mixed-integer utility plant model can deal with minimum operating cost over a longer period involving discrete decisions. Yokoyama et al. (2002) proposed an optimal design method to determine the scheduling of energy supply systems over a year. A typical year was divided into three representative days for the summer, winter, and midseason, and each day was further divided into several periods. A decomposition method of solving linear MIP problems with the block angular structure was applied to derive a suboptimal solution close to the optimal one to shorten the computation time. A numerical study was performed on an energy supply system with a complex structure, and the validity and effectiveness of the decomposition method were investigated in terms of solution optimality and computation time. As a result, it turned out that the decomposition method, regardless of the scale of the problem, was computationally more efficient-i.e., it can find a better suboptimal solution close to the optimal one than could the conventional solution that combined the branch and bound method and the simplex algorithms. In recent years, methods based on Lagrangian relaxation have been widely adopted, motivated by the separable structure of the problem. Dotzauer (1997) presented an algorithm for short-term production planning of cogeneration plants. Model formulation considered internal plant temperatures, mass flow, storage losses, minimal up and down times, and time-dependent start-up costs. The demand for heat, the supply temperature from the plant, the return temperature to the plant, and price of electricity were assumed to be known quantities. The net electric power produced was sold at the estimated current price of electricity. The model and the algorithms were implemented in MATLAB, illustrated with numerical examples, and analyzed with numerical tests. Besides the most frequently used methods, such as MIP, GA, SA, and Lagrangian relaxation, artificial intelligence methods are also promising for solving the complicated problems in BCHP systems. Norford et al. (1998) developed a knowledge base and tested demonstration software to assist building operators in assessing the benefits of controlling electrical equipment in response to electricity rates that vary hourly. The software also includes thermal storage systems and on-site generation control algorithms, which have been proven to be optimal under limiting cases by comparison with mixed integer programming. Finally, the report by Katipamula and Brambley (2008) describes ongoing work on the development of algorithms for BCHP systems that can be used to ensure optimal performance, increase reliability, and improve O&M functions. This report only presents background information and a list of algorithms that will be developed, while subsequent work will involve the actual detailed specification of the algorithms and the detailed system level functionality and structure. SYSTEM MODELS The integration of the lower-level continuous control plant optimization into the high-level cost optimization is computationally demanding when the system has many components. Some strategies can be used to weed out combinations by imposing some physical constraints from practical experience (Olson,1988). A good approach that works well for a multispeed cooling tower is to treat the relative flows as continuous control variables and to select the discrete relative flow that is closest to that determined with continuous optimization (ASHRAE 2007). In fact, with many current designs, individual pumps are physically coupled with chillers, and it is impossible to operate greater or fewer pumps than the number of chillers operating. Such a practical constraint reduces the number of combinations greatly. The models to be used for optimization can be of three types. First are detailed simulation models originally developed for providing insights into design issues; papers of this nature abound in journals dealing with gas turbines and power plants and are deemed inappropriate to this research. Second are semi-empirical component models that combine deterministic modeling involving thermodynamic and heat transfer considerations with some empirical curve-fit models to provide a degree of modeling detail of subcomponents of the major equipment, such as the effect of back-pressure on turbine performance, individual heat exchanger performance, power for gas compression, etc.; papers related to this model include Bansal and O'Brien (2000), Jalaazadeh-Azar (2003), and Parsons and Li (2005). Third are semi-empirical inverse models, which can be either grey-box or black-box, depending on whether the underlying physics is used during model development. Though physical-based grey-box inverse models, such as the Gordon-Ng chiller models (Gordon and Ng 2000) for chillers, have been shown to be excellent, we have chosen to adopt the traditional black-box approach using rated equipment performance along with polynomial models to capture part load performance (e.g., Braun 2006). Figure 1 is a generic schematic of how the important subsystems of a BCHP system (namely, prime movers, vapor compression chillers, absorption chillers, and boilers) are often coupled to serve the building loads (namely, the noncooling electric load, the cooling thermal load, and the heating thermal load). The figure also indicates the nomenclature adopted for the various equipment models described below. Note that we exclude the option of electricity sell-back to the utility, which is consistent with how most BCHP plants are operated. [FIGURE 1 OMITTED] Prime Movers. Part-load electrical efficiency of reciprocating engines and microturbines is modeled as (Hudson 2005) [y.sub.Gen] = [a.sub.0] + [a.sub.1] * [x.sub.Gen] + [a.sub.2] * [x.sub.Gen.sup.2], (1a) where [y.sub.Gen] = relative electrical efficiency = (actual efficiency/rated efficiency). [x.sub.Gen] is the relative power output = (actual power/rated power) = ([E.sub.Gen]/[E*.sub.Gen]) (1b) where the asterisk (*) denotes rated conditions. The numerical values of the part-load model coefficients are given in Table 1. Since electrical efficiency of a prime mover is taken to be the electrical power output divided by the gas heat input, the expression for the natural gas heat input is
Table 1. Numerical Values of the Part-Load Model Coefficients in
Equations 1a, 4a, and 5a
Reciprocating Gas Turbine Fixed-Speed
Gas Engine (Hudson 2005) Electric Chiller
(Hudson 2005) (Braun 2006)
[a.sub.0] 0.4866 0.3279 0.640844639
[a.sub.1] 1.0214 0.1542 -1.17127875
[a.sub.2] -0.508 -0.4821 0.700897852
[a.sub.3] -- -- -0.340020092
[a.sub.4] -- -- 0.11196079
[a.sub.5] -- -- 1.04685144
Absorption Chiller (Braun 2006) Boiler (DOE-2)
[a.sub.0] -0.00383696435 0.082597
[a.sub.1] -0.211965721 0.996764
[a.sub.2] 0.385620532 -0.079361
[a.sub.3] 0.471911409 --
[a.sub.4] 0.372655123 --
[a.sub.5] -0.00716257434 --
[G.sub.Gen] = [E.sub.Gen] * [[G*.sub.Gen]/[E*.sub.Gen]] * [1/[y.sub.Gen]], (2a) or [G.sub.Gen] = [G*.sub.Gen] * [x.sub.Gen] * [1/([a.sub.0] + [a.sub.1] * [x.sub.Gen] + [a.sub.2] * [x.sub.Gen.sup.2]) (2b) The amount of waste heat that can be recovered from the prime mover under part-load conditions is also needed during the simulation. Under part load, prime mover electrical efficiency degrades and, consequently, a larger fraction of the supplied gas energy will appear as waste thermal heat. If we assume that the prime mover is designed such that the ratio of recovered waste heat to total waste heat is constant during its entire operation, then one can model to a close approximation the recovered thermal energy under part-load operation, [H.sub.Gen], as [H.sub.Gen] = [[H*.sub.Gen]/[G*.sub.Gen]] * [[G.sub.Gen]/[y.sub.Gen]], (3) where [y.sub.Gen] is the relative efficiency defined earlier by Equation 1. Standard reference conditions for testing reciprocating prime movers are 1000 mbar (or 100 m above sea level), 77[degrees]F (or 25[degrees]C) dry-bulb temperature and 30% relative humidity (RH). For microturbines, the ISO conditions are different: 59[degrees]F (15[degrees]C), 60% RH, and sea level. Unlike reciprocating gas engines, microturbine performance is impacted by inlet air temperature, and corrections to rated conditions are provided by the manufacturers in the form of performance curve corrections (MAC 2005). We found that the variation in efficiency is usually small. Typically, a microturbine's full load efficiency is about 29% under standard reference conditions and varies only by [+ or -]1.5% for ambient temperature variation from 30[degrees]F-120[degrees]F. However, on any given day, the ambient temperature variation is much smaller and, assuming a mean constant efficiency, would be deemed acceptable for this optimization study. Vapor Compression and Absorption Chillers. The approach follows Braun (2006), where the chiller part-load performance factor (PLF) is modeled as follows: PLF = [a.sub.0] + [a.sub.1] * PTR + [a.sub.2] * [PTR.sup.2] + [a.sub.3]PLR + [a.sub.4][PLR.sup.2] + [a.sub.5] * PLR * PTR (4a) where the numerical values of the model coefficients are given in Table 1. Since the type of power input to the vapor compression and absorption chillers are different, the PLF for vapor compression and absorption chillers are defined as [PLF.sub.VC] [equivalent to] [y.sub.VC] = [[E.sub.VC]/[E*.sub.VC]] and [PLF.sub.AC] [equivalent to] [y.sub.AC] = [[H.sub.AC]/[H*.sub.AC]] (4b) where [E.sub.VC] is the electric power consumed by the vapor compression chiller, and [H.sub.AC] is the thermal heat input to the absorption chiller. Instead of using the symbol PLR, which is the part-load ratio = (actual thermal cooling load/rated thermal cooling load), we will use [X.sub.VC] and [X.sub.AC] to denote the part-load ratios of the vapor compression and absorption chillers, respectively. [x.sub.VC] (or [x.sub.AC]) = [[Q.sub.VC]/[Q*.sub.VC]](or[[Q.sub.AC]/[Q*.sub.AC]]) (4c) Finally, PTR is the part-load temperature ratio of the entering condenser water temperature = [[T.sub.cdi]/[T*.sub.cdi]]. (4d) Gas-Fired Boilers. Modern boilers have very good part-load capabilities. We distinguish between combustion efficiency and boiler efficiency. There is generally little degradation in combustion efficiency down to at least 25% load. The Cleaver-Brooks fact sheet (1996) indicated that it would be adequate to assume a constant efficiency value, around 0.82-0.85. The boiler efficiency is conveniently modeled following polynomial relations adopted by the DOE-2 (LBL 1989) simulation program (see Table 1 for the model coefficients): BP = [a.sub.0] + [a.sub.1] * [x.sub.BP] + [a.sub.2] * [x.sub.B.sup.2]. (5a) where [x.sub.BP] = part load ratio = boiler heat output by its rated value [equivalent to] [Q.sub.BP]/[Q*.sub.BP] (5b) and [y.sub.boiler] = the heat input ratio or the ratio of fuel energy input to heat output under operating condition to that under rated condition = ([G.sub.BP]/[Q.sub.BP])/([G*.sub.BP]/[Q*.sub.BP]) (5c) (synonymous with HIR-FPLR used by DOE-2). Rearranging, we get the following: BP = [G*.sub.BP] * ([Q.sub.BP]/[Q*.sub.BP])([a.sub.0] + [a.sub.1] * [x.sub.BP] + [a.sub.2] * [x.sub.BP.sup.2] (5d) Cooling Tower Fans. A widely used approach to modeling cooling towers is the effectiveness-NTU model concept proposed by Braun (1989c). Though the relevant equations are well known, they require knowledge of airflows, condenser water flows, and certain specifics regarding tower construction and fan control (whether continuous, step, or one-speed). Further, there is a suboptimization involved in determining how the cooling tower fan needs to be operated in order to minimize the combined performance of both the chiller and the cooling tower. Such optimization procedures are well-described in several publications (e.g., Braun 2006). However, we have intentionally chosen not to incorporate such cooling tower-specific considerations requiring suboptimization given the scope of this research and simply assume that the cooling tower operates at its rated performance throughout. In other words, PTR = 1 in Equation 4a. This assumption results in no more than 2%-3% error in estimating diurnal costs during the optimization. Operation and Maintenance (O&M) Costs. Models for O&M costs for prime movers (natural gas reciprocating engines and microturbines) and heating and cooling equipment (vapor compression and absorption) are fully described in Maor and Reddy (2008). Their effect on the optimization has been found to be small and, consequently, these models are not presented in this paper, though the optimization itself does include their effect. Optimization Under Different Electric Utility Rates Background. Different utility price signals require different objective functions to be minimized. For example, the simplest case is for real-time pricing, which has no demand charge and is simply an energy charge that varies hourly over a certain time period of the day. In this case, the objective would be to minimize the cost of operation (electricity and gas use) given the thermal load, performance characteristics, and maintenance costs of each equipment item. The objective function could consider not only the static optimization case but also the start-up and shut-down costs, which would require a dynamic optimization approach (Jiang and Reddy 2007). An even finer level of analysis would be to consider the reliability associated with different equipment, since the chillers could be of different vintage and level of degradation. For the declining block structure (with no demand clause), the cost-of-operation component of the objective function is more elaborate and discontinuous. So, the formulation of the objective function and, hence, its mathematical treatment is different (calculus-based gradient search methods may fail). The problem of ratcheted demand is most difficult to treat given that the memory of the optimization has to extend to the last 12 months of operation. Three cases, based on different electricity rate structures (with only seasonal pricing rate structure used for gas), are considered, and relevant mathematical formulations are given below. All cases pertain to the instance where there is no option for on-site generated electricity to be sold back to the utility grid. Rather than perform a mixed-integer programming optimization, it is simpler to perform individual optimizations for each equipment combination and, thereby, deduce the optimal system combination to operate. In this manner, one is able to evaluate cost differences between the various combinations. To simplify the analysis, we shall also neglect the start-up costs and the start-up delay effects described earlier. Further, environmental benefits/concerns of BCHP plants have been intentionally excluded. Figure 1 provides a simple manner of visualizing the various energy flows between the primary BCHP equipment. Case 1--Static or Single-Period Optimization without Demand (1 Hour). The static optimization case without utility sellback involves optimizing the operating cost of the BCHP system for each time step (i.e., each hour) while it meets the building loads: the noncooling electric load ([E.sub.Bldg]), the thermal cooling load ([Q.sub.c]), and the building thermal heating load ([Q.sub.h]). The cost components only include steady state hourly energy costs for electricity and gas. So, the quantity to be minimized, J, is the total cost of energy consumption summed over all components that are operating, plus the equipment O&M costs. The energy consumption for each of the k components is a function of the component's characteristics and is dependent upon the controlled variables as given by the set of equipment modeling equations described earlier. The objective function to be optimized for a particular time step (or hour) and for a specific BCHP system combination is as follows: [~.J] = min{J} = min{[J.sub.1] + [J.sub.2] + [J.sub.3]} (6) where * cost associated with gas use is [J.sub.1] = ([G.sub.Gen] + [G.sub.BP] * [C.sub.g], (7a) * cost associated with electric use is [J.sub.2] = [E.sub.Purchase] * [C.sub.e], (7b) * and the operation and maintenance cost is [J.sub.3] = [M.sub.OM], (7c) subject to the inequality constraints that the building loads must meet (called functional constraints) * building thermal cooling load, [Q.sub.AC] + [Q.sub.VC] [greater than or equal to] [Q.sub.c]; (8a) * building thermal heating load, [Q.sub.BP] + [H.sub.Gen] - [H.sub.AC] [greater than or equal to] [Q.sub.h]; (8b) * building noncooling electric load, ([E.sub.Purchase] + [E.sub.Gen] - [E.sub.VC] - [E.sub.p]) [greater than or equal to] [E.sub.Bldg], (8c) and subject to boundary or range constraints * prime mover part load ratio, 0.30 [less than or equal to] [x.sub.Gen] [less than or equal to] 1.0; (9a) * vapor compression chiller part load ratio, 0.15 [less than or equal to] [x.sub.VC] [less than or equal to] 1.0; (9b) * absorption chiller part load ratio, 0.20 [less than or equal to] [x.sub.AC] [less than or equal to] 1.0; (9c) * and boiler plant part load ratio, 0.20 [less than or equal to] [x.sub.BP] [less than or equal to] 1.0, (9d) where the various terms are defined in the nomenclature. Note that we have allowed for the possibility of dumping either thermal cooling or thermal heating energy. The decision variables are the four part-load ratios ([X.sub.AC], [X.sub.BP], [X.sub.Gen], [X.sub.VC]) whose respective values are to be determined, which minimizes the objective function, J. As stated earlier, instead of resorting to a mixed integer problem, one can simplify the computation by performing the optimization for each BCHP system combination separately and then selecting the one with the least operation cost. If K is the number of BCHP system combinations, then the best BCHP combination among the K combinations is the one that has the lowest cost and is determined from [[~.J].sub.k*] = min{[J.sub.k]} for k [member of] [1 ... K], (10) where min {[J.sub.k]} is given in Equation 6 for a specific system combination k, and k* is the index for the optimal BCHP combination. This is the optimal solution for the BCHP supervisory control problem within the simplifying modeling and simulation assumptions stated earlier. Note that not all possible BCHP system combinations may be feasible. Some will be such that the inequality constraints (given in Equation 8) cannot be met; these combinations must be discarded as potential solutions. Case 2--Dynamic or Multiperiod Optimization without Demand Charge (Time Horizon of Several Hours During a Day). Multiperiod optimization, in this instance, refers to the dynamic case where one wishes to determine the optimal scheduling and operation of the BCHP plant under prestipulated building load profiles and electric use price signals (without a demand charge) during a certain planning horizon or period of the day. Let t be the subscript denoting the hourly periods, such that t [member of] [1 ... T]. One can distinguish between two cases as follows: Ideal or Optimal Operation. The BCHP plant equipment can be rescheduled at the start of each hourly period and the plant equipment is operated optimally at each of the T periods. The vector of optimal hourly scheduling control is [[[vector].J].sub.k*] = [[[~.J].sub.k*, 1], [[~.J].sub.k*, 2],..., [[~.J].sub.k*, t],...,[[~.J].sub.k*, T], (11a) where [[~.J].sub.k*,T] is found simply by solving Equation 10 separately for each time period. The optimal cost of operating the BCHP over the time horizon is sum ([J.sub.k*]) = [T summation over (t = 1)] [J.sub.k*, t*]. (11b) Near-Optimal Operation. Due to practical reasons discussed earlier, the BCHP operators would like to start a preselected combination of BCHP equipment at the beginning of the planning time horizon and keep that set operating throughout the T periods. Note that there is, however, the capability of controlling the part-load operation of the equipment that is already running at the start of each hourly time step so as to achieve optimal operation during that hour. In other words, [X.sub.AC], [X.sub.BP] [X.sub.Gen], and [X.sub.VC] can be viewed as being controlled hourly. This case is represented mathematically for each feasible combination k: sum([[~.J].sub.k]) = [T.summatioin over (t = 1)] min{[J.sub.k,t]} (12a) The computational algorithm starts by first selecting a specific BCHP system combination k and determining the minimum operational costs for each of the T hours of operation, individually. The sum of these hourly costs yields the total cost of operating that specific combination k' over the planning horizon. This is repeated for all the combinations (discarding the ones which are unfeasible). The feasible combination k' that has the lowest total cost over the planning horizon is the best near-optimal solution: sum([[~.J].sub.k']) + min{sum([[~.J].sub.k]) for k [member of] [1 ... k]} (12b) Case 3--Dynamic or Multiperiod Optimization with Demand Charge (Time Horizon of Several Hours During a Day). This case differs from Case 2 by the inclusion of an additional demand charge. However, the demand charge is imposed only once per month, and this day is referred to as a peak setting day. A simplification made in several studies (e.g., Olson 1988; Braun 2006) is to decouple the demand cost from the energy and maintenance costs function by (1) assuming the peak cooling plant electrical demand to be coincident with the total building peak and (2) expressing the demand as a constraint in the optimization. In other words, the optimization is performed with energy cost and maintenance costs only, with the constraint that the peak cooling plant demand cannot exceed a prestipulated maximum. We have assumed (1) above but not (2), since our planning horizon is usually less than a day as opposed to an entire month, as assumed in the two previous studies. The electric demand expression can be included explicitly in the objective function for the peak setting day by adding a fourth term in the objective function given in Equation 6. Let J4 be the demand charge for operating system combination k over a planning horizon of T hourly time periods, which is mathematically expressed as: [J.sub.4] = max{[E.sub.Purchase,t] * [C.sub.d,t]} for t [member of] [1 ... T] (13) where [C.sub.d,t] is the demand charges during time period t, and [E.sub.Purchase] is the electricity drawn from the grid. Then, Equation 10 can then be expressed as follows: [[~.J].sub.k*] = min{[J.sub.k] + max{[E.sub.Purchase,t,k] * [C.sub.d,t]} for t [member of] [1 ... T]} for k [member of] [1 ... K] (14) This equation can be extended in the same manner as explained in Case 2 to treat the optimal and near-optimal solutions for the case of demand charges, and we get expressions analogous to Equations 11 and 12. Simplifying Assumptions in Modeling and Simulation The simplifying assumptions made during the modeling, simulation and optimization are as follows: 1. The optimization is based on operating cost only. Issues related to environmental benefits/penalties of BCHP plants have been excluded. 2. The building does not have net metering-i.e., electric utility buyback is not an option. 3. Simulation is quasistatic-i.e., transient effects associated with power surge and extra energy consumed due to time delay in equipment start up and shut down are neglected (consistent with Braun 2006). 4. The cooling plant peak electric load is coincident with the building peak. 5. Nonchiller electricity, cooling thermal, and heating thermal loads of the building are known with certainty- i.e., they are deterministic. 6. Electricity and gas prices are known with certainty. 7. The cases of electric price signal with ratcheted demand or block energy pricing have not been considered in this research. 8. Simulation time step or time interval is assumed to be one hour, with the simulation time horizon for each scenario selected on a case by case basis. 9. Component models have no uncertainty. 10. Microturbine electric efficiency is assumed constant at a mean value, since the effect of ambient temperature is small (less than 3% relative error). 11. Chilled-water supply set points are constant at 44[degrees]F (Braun 2006) 12. The chillers operate on a primary/secondary configuration on the chilled-water side (i.e., all chillers operate under the same evaporator inlet water temperature) but have separate individual cooling tower loops on the condenser side. 13. Each chiller has its own dedicated condenser water pump and evaporator water pump with constant flow and ON/ OFF control. 14. Each chiller has its own dedicated cooling tower with variable fan control. 15. The cooling tower fan power is not included in the optimization. The fan control is assumed to maintain the rated value of the condenser inlet water temperature throughout the year. 16. Pump and/or fan electricity for either the secondary chilled-water loop or the air-handler loop on the building side are not considered in the optimization. 17. The boilers and heat recovery units have common supply and return headers, though each unit has its own dedicated water pump with constant flow and ON/OFF control. 18. The supply hot water header feeds the absorption chiller and the sensible heating of the building via dedicated constant-speed pumps with constant flow and ON/OFF control. 19. Domestic hot-water pumping electricity is not included. 20. Values of the minimum part-load ratio below which different important equipment is shut off are assumed as follows (Braun 2006; Hudson 2005): * prime movers: 0.3; * vapor compression chillers: 0.15; * absorption chillers: 0.2; * gas boilers: 0.2 21. The optimization considers the possibility of hot water and chilled water being dumped if necessary, though, in actual operation, BCHP operators are very unlikely to do so. Data Generation The process by which the buildings and the BCHP scenarios to be studied have been identified is described in the companion paper (Maor and Reddy 2009). This involved six subtasks having to do with identification of building type and size, climatic regions, type and size range of the prime mover and its fuel type, auxiliary BCHP equipment, and electrical and thermal rate signals. Design details of each of the seven scenarios, as well as details of the analysis results, are given in Maor and Reddy (2008). The procedure essentially involved 1. selecting the architectural features of the buildings that consist of designs typical of the corresponding building type, with two of them patterned after existing buildings; 2. selecting typical primary and secondary HVAC systems (without prime mover and absorption chiller) pertinent to the building type; 3. performing DOE 2.1E simulations of that building to generate hourly building loads (cooling thermal, heating thermal, and noncooling electric) during the entire year; 4. selecting electric price signals for the entire year, either from historic data or from published utility rates specific to the utility where the building is located geographically; 5. using the ORNL CHP Optimizer (Hudson 2005), with these hourly building loads and the hourly price signals as input, to arrive at cost-effective optimal capacities for the prime mover and the absorption chiller; 6. selecting equipment available commercially that closely matches the optimal primary equipment capacities determined above (while providing for redundant or excess capacity as needed by the building type) (see Table 2 for specifics of the BCHP equipment for all seven scenarios);
Table 2. Specifics of the BCHP Equipment for the Scenarios Studied
Equipment Description Scenario Scenario Scenario
1 3 4
Large Large Large
Hospitals School Hotel
Newark, NYC, NY Chicago,
NJ IL
Number of 54 36 36
combinations
Electric price RTP RTP RTP
structure
(a) Prime Mover Loop 2 Recips 1 Recip 1 Recip
Rated electric 590 590 988
output, kW
Rated net gas, 5.42 5.42 9.02
MMBtu/h
Prime Movers Rated electrical 37.2 37.2 37.4
efficiency %
Hot water at 2.64 2.64 4.38
190FMMBtu/h
Dedicated Aux. Rated power, HP 7.5 10.0 15.0
Pump
(b) Boiler Plant 2 Nos. 2 Nos. 2 Nos.
Rated heat 5.021 5.6 10.043
output, MMBtu/h
Boilers Natural gas use, 6.124 7.000 12.247
MMBtu/h
Thermal 81.0% 80.0% 82.0%
efficiency, %
Deticated Boiler Rated power, HP 5.00 7.5 10.0
Pumps
Supply Rated power, HP 7.5 7.5 10.0
Pump-Absorption
(c) Cooling Plant 2 Nos. + 1 2 Nos. + 2 Nos. +
No. 1 No. 1 No.
Vapor Cooling capacity, 600 257 700
tons
Compression Electric power 346 188.1 346
input, kW
Chillers COP, -- 6.1 4.8 6.1
Chilled Water Rated Power Hp 25.0 15.0 40.0
Pumps
Cond. Water Pumps Rated Power Hp 75.0 30.0 75.0
Cooling Tower Fans Rated Power Hp 40.0 15.0 40.0
Absorption Cooling capacity, 155 110 210
tons
Chiller COP, -- 0.7 0.7 0.7
Chilled Water Pump Rated Power Hp 7.5 7.5 15.0
Cond. Water Pump Rated Power Hp 20.0 20.0 25.0
Cooling Tower Fans Rated Power Hp 7.5 7.5 15.0
Equipment Description Scenario Scenario Scenario Scenario
6 7 2 5
Large Large Large Large
Office Office Hospital Hotel
Boston MA Los Los Hartford,
Angeles Angeles CT
CA CA
Number of 72 18 24 6
combinations
Electric TOU TOU TOU TOU
price
structure
(a) Prime 1 rec+1 2 Recips 1 MT 1 MT
Mover Loop MT
Rated 788+242 375 360 60
electric
output, kW
Rated net 7.22+2.84 3.97 4.866 0.811
gas, MMBtu/h
Prime Rated 37.3+29.0 32.2 29 29
Movers electrical
efficiency %
Hot water at 3.51+0.90 1.838 2.25 0.375
190FMMBtu/h
Dedicated Rated power, 10.0+5.0 7.5 7.5 3.0
Aux. Pump HP
(b) Boiler 2 Nos. None 2 Nos. 2 Nos.
Plant
Rated heat 6.695 -- 1.096 0.595
output,
MMBtu/h
Boilers Natural gas 8.165 -- 1.336 0.726
use, MMBtu/h
Thermal 81.8% -- 82.0% 82.0%
efficiency,
%
Deticated Rated power, 7.5 -- 3.0 1.5
Boiler HP
Pumps
Supply Pump- Rated power, 7.5 7.5 5.0 --
Absorption HP
(c) Cooling 2 Nos. + 1 2 Nos. + 1 No. + 1 --
Plant No. 1 No. No.
Vapor Cooling 600 350 267 --
capacity,
tons
Compression Electric 188.1 246 198.1 --
power input,
kW
Chillers COP, - 6.1 5.0 4.74 --
Chilled Rated Power 25.0 15.0 10.0 --
Water Pumps Hp
Cond. Water Rated Power 75.0 40.0 25.0 --
Pumps Hp
Cooling Rated Power 40.0 25.0 25.0 --
Tower Fans Hp
Absorption Cooling 155 240 110 --
capacity,
tons
Chiller COP, - 0.7 0.7 0.7 --
Chilled Rated Power 7.5 15.0 5.0 --
Water Pump Hp
Cond. Water Rated Power 25.0 50.0 15.0 --
Pump Hp
Cooling Rated Power 25.0 30.0 10.0 --
Tower Fans Hp
Unless otherwise indicated, all prime movers (recips and
microturbines), boilers, and absorption chillers for each scenario
are identical.
7. generating the circuit diagrams for heat recovery circuits, chilled water, and condenser water loops to size the auxiliary equipment (such as pumps, fans, etc.); 8. selecting certain days of the year during different seasons that contain extremes in loads and price signals (we have selected 12 for Scenarios 1 and 4, while only four for Scenario 5, Small Hotel). The intent was to identify days that will provide sufficient information to determine the rationale of intelligent control of BCHP plants (see Tables 3 and 4 for acronyms and description of the selected day types under RTP and TOU rates, respectively);and
Table 3. Description of the Selected Day types Under RTP
Acronym Description
1 FLHL-RTPH Fall high heating load, high RTP rate
2 FLHL-RTPL Fall high heating load, low RTP rate
3 FLCL-RTPH Fall high cooling load, high RTP rate
4 FLCL-RTPL Fall high cooling LOAD, low RTP rate
5 WLH-RTPH Winter load high (heating load), high RTP rate
6 WLL-RTPL Winter load high (heating load), low RTP
7 WLL-RTPH Winter load low (heating load), high RTP rate
8 WLL-RTPL Winter load low (heating load), low RTP rate
9 SLH-RTPH Summer load high (cooling load), high RTP rate
10 SLH-RTPH Summer load low (cooling load), high RTP rate
11 SLL-RTPH Summer load low (cooling load), high RTP rate
12 SLL-RTPL Summer load low (cooling load), low RTP rate
Table 4. Description of the Selected Day Types Under TOU
Acronym Description
1 FLHC Fall load high cooling
2 FLHH Fall load high heating
3 WHL Winter high heating load
4 WLL Winter low heating load
5 SLH Summer load high cooling
6 SLL Summer load low cooling
9. performing the optimal and near-optimal simulations for these selected days using published rated performance of the equipment selected (step 6) along with part-load performance models and optimization procedures described previously. There are several possible combinations of operating the various BCHP equipment. A single piece of equipment can assume two states (ON or OFF), while two identical pieces of equipment can assume three states: both ON, one ON, and both OFF. For Scenario 1 with two identical prime movers, two identical boilers, two identical vapor compression chiller, and one absorption chiller, the total number of combinations is (3 X 3 X 3 X 2 = 54). The total number of combinations for each of the scenarios is also given in Table 2. We note that the number of combinations is usually large (in the range of 18-72), except for Scenario 5, which had few components. The fact that there are so many combinations is problematic for BCHP operators, since starting the nonoptimal combination can result in a cost penalty. One of the objectives of this research was to evaluate this penalty. Three scenarios selected are under RTP pricing, and the other four are under TOU pricing for electricity (natural gas price is assumed to be fixed for a scenario year-round). The gas prices range from about $9-$13/MMBtu. Note that five of the scenarios involve large buildings (hospital, school, hotel, and office), while two are relatively small (hospital of 135,000 [ft.sup.2] and hotel of 72,000 [ft.sup.2]). The objective functions to be minimized are given in Equations 10-14 for both the optimal and near-optimal cases and under RTP and TOU price signals over a planning horizon consisting of several hours during a day. Recall that we have defined an optimal operating strategy as one where the equipment can be switched OFF and ON without any penalty on an hourly basis (the transients have been neglected in this research), and the best combination is run at any given hour. The total cost of operating the BCHP plant in this quasistatic manner, while meeting the needed buildings loads over the diurnal period of interest, is taken to be the optimal cost. On the other hand, near-optimal solutions are those where a certain combination of BCHP equipment is started at the onset of the planning horizon and the same pieces of equipment are kept running throughout the planning horizon with, however, the ability to control the individual equipment already operating each hour in an optimal manner. Thus, we have as many near-optimal solutions as there are feasible combinations during the selected day. The CPR (cost penalty ratio) is the ratio of the near-optimal to the optimal solution. Table 5 provides overall summary statistics (mean, median, min, and max values) of the CPR values for all scenarios and selected days. It also indicates the number of feasible combinations as well as the time horizon (in hours) over which optimization was done for each selected day. For example, for Scenario 1 under FLHL-RTPH, there are 26 feasible combinations out of a possible 54.
Table 5. Statistics of the CPR Values for all Scenarios and Selected
Days
Fall
FLHL-RTPH FLHL-RTPL FLCL-RTPH FLCL-RTPL
Scenario 1: Large Hospital, Newark,N J-RTP Rates
Simulation Horizon: 8:00 a.m. -7:00 p.m.
(12 hours)
Feasible Com # 26 42 28 22
Mean 1.35 1.27 1.16 1.09
Median 1.34 1.26 1.16 1.09
Min 1.14 1.00 1.00 1.02
Max 1.70 1.53 1.36 1.19
Scenario 3: Large School, NYC, NY--RTP Rates
Simulation Horizon: 7:00 a.m. -8:00 p.m.
(15 hours)
Feasible Com # 25 20
Mean 1.49 1.35
Median 1.50 1.34
Min 1.00 1.10
Max 2.01 1.59
Scenario 4: Large Hotel, Chicago, IL--RTP Rates
Simulation Horizon: 6:00 a.m. -ll:00 p.m.
(18 hours)
Feasible Com # 19 19 15 23
Mean 1.67 1.59 1.59 1.61
Median 1.65 1.58 1.54 1.63
Min 1.36 1.31 1.41 1.27
Max 2.10 1.95 1.76 1.96
Scenario 6: L arge Office, Boston, MA--TOU Rates
Simulation Horizon: 8:00 a.m. -5:00 p.m. (Summer)
and 7:00 a.m. -2:00 p .m. (Winter)
SF-Nonpeak SF-Peak
Feasible Com # 32 32
Mean 1.18 1.46
Median 1.18 1.46
Min 1.05 1.01
Max 1.30 1.90
Scenario 7: Large Office, Los Angeles, CA--TOU Rates
Simulation Horizon: 6:00 a.m. -9:00 p .m.
(16 hours)
FLHC_Nonpeak FLHC_Peak FLHH_Nonpeak FLHH_Peak
Feasible Com # 7 7 10 10
Mean 1.12 1.68 1.19 1.79
Median 1.12 1.76 1.19 1.80
Min 1.06 1.06 1.05 1.22
Max 1.18 2.52 1.33 2.47
Scenario 2: Small Hospital Los Angeles, CA--TOU
Rates Simulation Horizon: 9:00 a.m. -10:00 p.m.
(16 hours)
Feasible Com #
Mean
Median
Min
Max
Scenario 5: Small Hotel, Hartford, CT--TOU Rates
Simulation Horizon: 8:00 a.m. -ll:00 p. m.
(16 hours)
Feasible Com #
Mean
Median
Min
Max
Winter
WLH-RTPH WLH-RTPL WLL-RTPH WLL-RTPL
Scenario 1: Large Hospital, Newark,N J--RTP Rates
Simulation Horizon: 8:00 a.m. -7:00 p.m. (12 hours)
Feasible Com # 28 28 28 25
Mean 1.32 1.27 1.35 1.18
Median 1.32 1.27 1.37 1.17
Min 1.13 1.11 1.17 1.01
Max 1.63 1.46 1.68 1.39
Scenario 3: Large School, NYC, NY--RTP Rates
Simulation Horizon: 7:00 a.m. -8:00 p.m. (15 hours)
Feasible Com # 17 27 24 24
Mean 1.46 1.95 1.56 1.30
Median 1.43 1.95 1.55 1.30
Min 1.01 1.00 1.02 1.02
Max 2.07 2.84 2.23 1.59
Scenario 4: Large Hotel, Chicago, IL--RTP Rates
Simulation Horizon: 6:00 a.m. -ll:00 p.m.
(18 hours)
Feasible Com # 14 9 18 18
Mean 1.61 1.45 1.85 1.68
Median 1.64 1.43 1.79 1.62
Min 1.25 1.32 1.37 1.39
Max 1.97 1.66 2.52 2.18
WHL-Nonpeak WHL-Peak WLL-Nonpeak WLL-Peak
Scenario 6: L arge Office, Boston, MA--TOU Rates
Simulation Horizon: 8:00 a.m. -5:00 p.m.
(Summer) and 7:00 a.m. -2:00 p .m. (Winter)
Feasible Com # 18 18 24 24
Mean 1.16 1.39 1.20 1.35
Median 1.13 1.24 1.20 1.22
Min 1.02 1.01 1.08 1.02
Max 1.37 1.82 1.37 1.87
Scenario 7: Large Office, Los Angeles, CA--TOU Rates
Simulation Horizon: 6:00 a.m. -9:00 p .m.
(16 hours)
Feasible Com # 10 10 7 7
Mean 1.21 1.79 1.16 1.60
Median 1.21 1.80 1.16 1.66
Min 1.06 1.22 1.10 1.03
Max 1.35 2.46 1.24 2.37
Scenario 2: Small Hospital Los Angeles, CA--TOU Rates
Simulation Horizon: 9:00 a.m. -10:00 p.m.
(16 hours)
Feasible Com # 10 10 8 9
Mean 1.21 1.70 1.24 1.40
Median 1.23 1.50 1.28 1.18
Min 1.02 1.04 1.02 1.06
Max 1.30 2.97 1.34 1.98
Scenario 5: Small Hotel, Hartford, CT--TOU Rates
Simulation Horizon: 8:00 a.m. -ll:00 p. m.
(16 hours)
Feasible Com # 2 2 4 4
Mean 1.04 1.21 1.09 1.16
Median 1.04 1.21 1.07 1.05
Min 1.00 1.02 1.01 1.00
Max 1.08 1.41 1.22 1.52
Summer
SLH-RTPH SLH-RTPL SLL-RTPH SLL-RTPL Total #
Scenario 1: Large Hospital, Newark, N J--RTP Rates
Simulation Horizon: 8:00 a.m. -7:00 p.m. (12 hours)
Feasible Com # 16 16 22 16 54
Mean 1.12 1.13 1.22 1.05
Median 1.11 1.13 1.22 1.05
Min 1.00 1.09 1.01 1.02
Max 1.25 1.18 1.43 1.10
Scenario 3: Large School, NYC, NY--RTP Rates
Simulation Horizon: 7:00 a.m. -8:00 p.m.
(15 hours)
Feasible Com # 5 27 15 15 36
Mean 1.17 1.83 1.44 1.19
Median 1.08 1.88 1.35 1.19
Min 1.00 1.00 1.02 1.00
Max 1.36 2.53 1.85 1.33
Scenario 4: Large Hotel, Chicago, IL--RTP Rates
Simulation Horizon: 6:00 a.m. -ll:00 p.m.
(18 hours)
Feasible Com # 9 19 19 23 36
Mean 1.33 1.41 1.45 1.58
Median 1.35 1.42 1.43 1.58
Min 1.24 1.19 1.25 1.22
Max 1.41 1.65 1.64 1.95
Scenario 6: L arge Office, Boston, MA--TOU Rates
Simulation Horizon: 8:00 a.m. -5:00 p.m.
(Summer) and 7:00 a.m. -2:00 p .m. (Winter)
SLH-Nonpeak SLH-Peak SLL-Nonpeak SLL-Peak
Feasible Com # 21 21 40 40 72
Mean 1.06 1.26 1.10 1.37
Median 1.06 1.11 1.10 1.24
Min 1.01 1.00 1.00 1.00
Max 1.11 1.57 1.20 1.86
Scenario 7: Large Office, Los Angeles, CA--TOU Rates
Simulation Horizon: 6:00 a.m. -9:00 p .m.
(16 hours)
Feasible Com # 7 7 10 10 18
Mean 1.11 1.78 1.14 1.87
Median 1.13 1.91 1.13 1.95
Min 1.04 1.00 1.04 1.01
Max 1.16 2.84 1.22 2.97
Scenario 2: Small Hospital Los Angeles, CA--TOU Rates
Simulation Horizon: 9:00 a.m. -10:00 p.m.
(16 hours)
Feasible Com # 4 4 9 9 24
Mean 1.07 1.23 1.12 1.43
Median 1.08 1.03 1.14 1.16
Min 1.03 1.01 1.00 1.03
Max 1.10 1.87 1.20 2.12
Scenario 5: Small Hotel, Hartford, CT--TOU Rates
Simulation Horizon: 8:00 a.m. -ll:00 p. m.
(16 hours)
Feasible Com # 4 4 5 5 6
Mean 1.09 1.08 1.11 1.15
Median 1.08 1.03 1.09 1.05
Min 1.04 1.01 1.00 1.01
Max 1.16 1.24 1.24 1.33
Simulation and Data Analysis Analysis of the RTP Buildings (Scenarios 1, 3, and 4). We find a large variability in the CPR values (see Figure 2 for the 12 selected days for Scenario 1). The box and whisker plots of Figure 3 provide a clear indication of how the CPR values vary across selected days for the three scenarios. The span of the boxes represent the interquartile range--i.e., the CPR values of the 25%-50% range of the near-optimal solutions. The length of the whiskers is indicative of the differences in CPR values between the best and the worst near-optimal solution. We note that the possible range of variation of the CPR values is large, up to 250% excess energy in some rare cases. The largest CPR values for the large hospital are about 1.5, while those for the large hotel and the large school are around 2.0. Figure 4 illustrates the magnitude and variability of the optimal and the near-optimal cost values for Scenario 3 (large school in New York), while the variability of the CPR values for the days selected in winter and summer is illustrated in Figure 5. [FIGURE 2 OMITTED] [FIGURE 4 OMITTED] [FIGURE 5 OMITTED] We find that there is no clear, single near-optimal combination that is best for all cases. Of the three scenarios, the median CPR values of the feasible near-optimal combinations are lowest for Scenario 1 (large hospital) and generally highest for Scenario 4 (large hotel). We note that Scenario 3 (large school) has the largest variability among the near-optimal solutions indicating that bad choice in equipment scheduling can have a major cost penalty. However, it is the same Scenario 3 that, from the results, leads us to note that, in all but one selected day, the best near-optimal combination is as good as the optimal one (CPR = 1). This is not the case for Scenario 4 (large hotel), where the best near-optimal case has costs in the range of 20%-40% higher than the optimal combination. This suggests that it may be advantageous to consider an operating strategy where it is preferable to change equipment scheduling sometime during the planning horizon rather than try to maintain the same equipment combination throughout. The results for Scenario 1 (large office) seem to fall in between the two other scenarios. We were able to detect certain important trends in which equipment combinations tend to operate: 1. In many cases, there are several near optimal solutions with CPR values close to each other. For example, for Scenario 3 under WLH-RTPH, combinations 24, 30, and 48 seem equally good. There are, however, exceptions: for Scenario 4, during the fall and winter days, one near-optimal combination is clearly better than the rest. 2. For Scenario 1 (large hospital), the no-recip combinations are clearly poor except for fall days. The {one recip, two boiler, one VC chiller, and one AC chiller} option seems to be a good selection, overall, for winter with the {two recip and one boiler} combination being equally good. For the fall season {one recip, one boiler, one VC, and one AC chiller} is desirable, while for summer days, the combination involving {two recip, no boiler, and all three chillers) is preferable. 3. For Scenario 3 (large school), there is only one prime mover. For the fall season, the best combination seems to be {one recip, no boiler, and all three chillers operating}. During the winter and summer days, the {one recip, one boiler, and AC and VC chillers} operating seems to be the desirable combination, though the no-recip seems the better choice for certain days. 4. For Scenario 4 (large hotel), {one recip, two boilers, and AC chiller} seems to be the best overall choice for winter days, while for fall and summer seasons {no recips, two boilers, and AC chiller} seems the preferable selection. 5. In all three buildings, operating the AC chiller seems to be a good strategy, while operating one prime mover and one boiler seems to be advisable in most cases. Surprisingly, except for winter, data for the large hotel (Scenario 4) indicate that it is advisable not to operate either the prime mover or the VC chiller but, rather, to run both boilers. Analysis of the Large TOU Buildings (Scenarios 6 and 7). Recall that Scenario 6 has one recip and one microturbine, while Scenario 7 has two recips but no boilers. Also, Scenario 6 has constant diurnal rates that vary seasonally, while those for Scenario 7 have diurnal changes during summer. The planning horizon for Scenario 6 is taken to be from 8:00 a.m. to 5:00 p.m. during summer and 7:00 a.m. to 8:00 p.m. for winter days, while for Scenario 7, the period of 6:00 a.m. to 9:00 p.m. has been selected year round. The selection is based not just on the ON and OFF-peak periods for demand, but also on the specific behavior of the diurnal load. This selection has been made intentionally in keeping with current practice followed by BCHP operators. The box and whisker plots for the CPR values for both non-peak and peak-setting days are shown in Figure 6, while mean, min, and max values are assembled in Table 5. The analysis for each selected day was performed for two cases: peak setting day of the month (during which the demand charges apply) and non-peak setting day, when the demand charges do not apply and only the energy-use rate applies. An obvious fact is that the CPR values are much larger for the peak setting days: the 75th percentile is about 1.7 for Scenario 6 (large office in Boston), while it is close to 2.0 for Scenario 7 (in Los Angeles). However, the best near-optimal values are close to 1.0 in all cases for both scenarios (except for two days for Scenario 7). This suggests (1) the need for proper control is crucial for peak-setting days and (2) not selecting the best non-optimal solution can mean large cost penalties (about 1.4 at the 25th percentile in Los Angeles and 1.15 in Boston). [FIGURE 6 OMITTED] Analysis of the Small TOU Buildings (Scenarios 2 and 5). The two buildings considered are small buildings. Scenario 2 is a small hospital located in Los Angeles, CA, with one microturbine and two boilers, one VC, and one AC chiller. Scenario 5 is a small hotel located in Hartford, CT, with individual room-packaged terminal air conditioners (PTAC), hot-water coil, one microturbine, two boilers, and no chillers at all. While Scenario 2 has variable diurnal and seasonal rates and a constant diurnal and year-round demand charge, Scenario 5 has a diurnal energy-use rate and diurnal and seasonally variable demand rates. The planning horizon for Scenario 2 is from 9:00 a.m. to 10:00 p.m., and for Scenario 5 from 8:00 a.m. to 11:00 p.m., year-round. These correspond to the on-peak and off-peak periods for demand. The box and whisker plots for the CPR values are shown in Figure 7, while mean, min, and max values are assembled in Table 5. The analysis for each selected day has been made for two cases: peak setting day of the month (during which the demand charges apply) and non-peak setting day, when the demand charges do not apply and only the energy-use rate applies. Again, similar to the behavior for Scenarios 6 and 7, the CPR values are much larger for the peak setting days than for non-peak setting days when only energy charges apply. However, the best near-optimal values are close to 1.0 in all cases for both scenarios. The same conclusions as before can be drawn: (1) the need for proper control is very crucial for peak-setting days and (2) not selecting the best non-optimal solution can mean large cost penalties. [FIGURE 7 OMITTED] Overall Conclusions. Our data analysis results, discussed in previous sections, are summarized below: 1. BCHP plants serving large buildings typically have 1-2 prime movers, two boilers, two VC chillers, and one AC chiller. This results in a large number of equipment combinations (36 with one prime mover and 54-72 with two prime movers). The BCHP operator is, thus, faced with the daunting prospect of determining which combination to operate during the planning horizon, which spans several hours of a day. 2.Not all combinations are feasible solutions (that is, those that would allow the building loads to be met). The number of feasible combinations for the seven scenarios and for the selected days is given in Table 5, where we find that, generally, this number is between 10 to 30 for the large buildings; still a large choice. 3. We have defined an optimal operating strategy as one where the equipment can be switched OFF and ON without any penalty on an hourly basis, while near-optimal solutions are those where a certain combination of BCHP equipment is started at the onset of the planning horizon and the same pieces of equipment are kept running throughout the planning horizon with the ability to control each hour in an optimal manner the individual equipment already operating. In order to quantify the excess cost, we defined a quantity called cost penalty ratio (CPR), which is the ratio of the near-optimal to the optimal solution. 4. We find large variation in the CPR values between feasible solutions and large numerical values as well. The median values of CPR change from scenario to scenario and from day to day, but they are generally large. For the three RTP cases, we find median CPR values of 1.10 (i.e., 10% excess cost) to 1.40 for Scenario 1 (large hospital), 1.2-2.0 for Scenario 3 (large school), and 1.4- 1.8 for Scenario 4 (large hotel). The 75 percentile values are even larger (for Scenarios 3 and 4, about 2.0). 5. Large school (Scenario 3) has the highest variability among the three RTP scenarios, with the poorest near-optimal solutions having the largest CPR values. However, the best near-optimal solutions have CPR values close to unity. This suggests that schools are prime building types where the incorporation of a BCHP supervisory tool will have the most benefit. 6. For the large hotel (Scenario 4), the best near-optimal solutions have CPR values of 1.2-1.4, which suggests that an operating strategy involving equipment combination changes partway into the planning horizon may be advantageous. This does not seem necessary for the two other RTP scenarios. 7. For TOU price signals, the analysis has been done for the for two cases: for the peak setting day of the month (during which day the demand charges apply) and for the non-peak setting day (when the demand charges do not apply and only the energy use rate applies). It is clearly noted that the CPR values are much larger for the peak setting days: the 75th percentile is about 1.7 for Scenario 6 (large office in Boston), while it is close to 2.0 for Scenario 7 (in Los Angeles). However, the best near-optimal values are close to 1.0 in all cases for both scenarios (except for two days for Scenario 7). This suggests the need for proper control is very crucial for peak-setting days and that not selecting the best non-optimal solution can have large cost penalties (about 1.4 at the 25th percentile in Los Angeles and 1.15 in Boston). 8. The analysis also demonstrated that care should be taken towards supervisory control of BCHP systems for small buildings (Scenarios 2 and 5). Though the number of possible equipment combinations is small, and we found that certain combinations are clearly better than others with the best near-optimal ones being very close to the ideal one, we find (at least for the days selected) that large CPR values can result, especially for peak-setting days. Though the need for incorporating a supervisory tool for small buildings may not be as acute as it is for large buildings, there's still a need to develop simple tools or even a look-up table for such buildings. 9. The effect of including the costs associated with operation and maintenance of the specific equipment being scheduled was found to have almost no effect on the near-optimal solutions. Though the total estimate of cost over the planning horizon is affected, it is by very little compared to the fuel cost of the prime movers and the boilers. Hence, O&M costs can be overlooked during the optimization for identifying optimal and near-optimal scheduling. SUMMARY AND EXTENSIONS This study makes an effort to present the problem of supervisory control (as opposed to continuous control) of BCHP plants in a clear framework with a distinction made between optimal and near-optimal scheduling control. Considerable thought was given to how to define a matrix of representative scenarios for study, given that the number of combinations can grow exponentially because of the numerous combinations possible in terms of building type, BCHP equipment, location, and price signals (this aspect is described in the companion paper [Maor and Reddy 2009]). This paper also described the equipment modeling equations and how the objective function to be minimized was formulated under the RTP and TOU price signals. Simplifying assumptions in both modeling and simulation were clearly defined. This research involved the cost penalties associated with near-optimal scheduling control of BCHP plants. A quantity called cost penalty ratio (CPR), which is the ratio of the near-optimal to the optimal solutions, was defined, and it is the variation and magnitude of this quantity with building type, location, and price signal that has been the primary focus of this research. Secondary objectives were to identify preliminary heuristic guidelines for cost-effective operation of such BCHP plants. The parametric simulations allowed us to quantify the magnitude and variability of the CPR values across the seven building scenarios selected. This research revealed that there are no clear or simple rules for near-optimal scheduling of BCHP systems that apply to different building types, seasons, and price signals. A cookbook approach is likely to lead to large cost penalties, and this highlights the need to have a software tool for optimal scheduling and control of BCHP plants. However, some general trends were identified that are summarized in tabular form for each of the seven scenarios and the various seasons. It must be cautioned that the above findings are very specific to the buildings, price signals, and selected days in this research and should not be viewed as appropriate for all BCHP plants. Future extensions of this research should include the following: 1. Sensitivity to simplifying assumptions. Several assumptions were made in the present investigation whose influence on the results should be investigated in more detail. For example, the cooling tower effects have not be considered in the optimization assuming that the fan is operated at its rated capacity and that the condenser supply water temperature is at its rated conditions. 2. Improvements in equipment models. The part-load performance of various equipment was modeled using generic empirical part-load polynomials. The validity of these models, as well as developing physical models, are logical issues that need further investigation. 3. Effect of uncertainties. The building loads (cooling thermal, heating thermal, and noncooling electric) are assumed to be deterministic loads. The effect of such a simplification, as well as neglecting uncertainty in the equipment model parameters, should be investigated. 4. Refinements to objective function. The objective function does not include the important issue of environmental effects or the reduction in electric network congestion to the utilities that is provided by local onsite generation. These are important aspects of distributed generation that need to be considered. 5. Time step of simulation. The optimization was done with hourly time steps as the time step of simulation. In practical terms, this is the shortest interval for BCHP operators to change set points of operating equipment. The effect of subhourly time steps should be evaluated, since this is the norm in actual BCHP plant operation. 6. Improvement in definition of optimal control. In this study, optimal control does not include the costs associated with dynamic effects, such as start-stop penalties of equipment. This aspect, as provided by Jiang and Reddy (2007), needs to be included. 7. Alternative near-optimal strategies. Near-optimal control was defined in this research as that where, once a specific combination of equipment is started, the same set is kept operating during the entire planning horizon. The analysis revealed that, during certain days and scenarios, even the best near-optimal solution had large CPRs. Hence, strategies involving equipment combination changes part-way into the planning horizon should also be investigated. These would consider costs associated with start-up and shut down transients and energy and demand spikes. 8. Expansion to include continuous control. Though continuous control was implicitly included in the analysis, the focus of this research was on scheduling control. A future study should include cost penalties associated with this lower-level optimization aspect and also try to propose recommendations for continuous control of operating equipment. 9. More comprehensive study. The analysis should be repeated under a different selection of days for the seven scenarios selected, and the whole analysis should be repeated with other scenarios. This would further reinforce the conclusions reached in this study. 10. Prototype implementation. The proposed near-optimal control strategy should be implemented in a few selected BCHP plants to get practical feedback in terms of implementation of the optimization, actual cost benefits, and its acceptability by BCHP operators. This would indicate whether further development, field deployment, and commercial product development are warranted. As such, the results would benefit (1) facility and building managers, (2) EMCS and control manufacturers, (3) control system integrators, and (4) energy consultants, and could result in a totally new manner of operating BCHP plants. NOMENCLATURE [C.sub.e] = unit energy cost of electricity use, $/kWh [C.sub.g] = unit energy cost of natural gas, $/MMBtu [C.sub.d] = electric demand rate, $/kW [E.sub.Bldg] = noncooling electric building load demand, kWh/h [E.sub.Gen] = actual electric power output of prime mover, kWh/h [E.sub.Purchase] = amount of purchased electricity, kWh/h [E.sub.P] = parasitic electric use of the BCHP plant (pumps, fans, etc.), kWh/h [E.sub.VC] = electricity consumed by the vapor compression chiller, kWh/h [G.sub.BP] = amount of natural gas heat consumed by the boiler plant, MMBtu/h [G.sub.Gen] = amount of natural gas heat consumed by the prime mover MMBtu/h [H.sub.AC]= heat supplied to the absorption chiller, MMBtu/h [H.sub.Gen] = total recovered waste heat from the prime mover, MMBtu/h J= objective cost function to be minimized (given by Equation 6) K = total number of combinations of equipment scheduling k= index for equipment scheduling combination k'= index for best near-optimal combination k* = index for optimal equipment combination [M.sub.OM] = operation and maintenance costs of the BCHP equipment which are operated, $/h [Q.sub.AC]= amount of cooling supplied by the absorption chiller, MMBtu/h [Q.sub.BP] = amount of heating supplied by the boiler plant, MMBtu/h [Q.sub.c]= building thermal cooling load, MMBtu/h [Q.sub.h]= building heating load, MMBtu/h [Q.sub.VC] = amount of cooling supplied by the vapor compression chiller, MMBtu/h T= total number of hourly periods over planning horizon t = index for time period [X.sub.AC]= part load ratio of the absorption chiller (given by Equation 4c) [X.sub.BP] = part load ratio of the boiler plant (given by Equation 5b) [X.sub.Gen]= part load ratio of the prime mover (given by Equation 1b) [X.sub.VC] = part load ratio of the vapor compression chiller (given by Equation 4c) [y.sub.AC] = part load efficiency of absorption chiller (given by Equation 4b) [y.sub.BP] = part load thermal efficiency of boiler plant (given by Equation 5a) [y.sub.Gen]= part load electric efficiency of prime mover (given by Equation 1a) [y.sub.VC] = part load efficiency of vapor compression chiller (given by Equation 4b) Subscripts AC= absorption chiller BP= boiler plant Gen= generator or prime mover VC= vapor compression chiller ACKNOWLEDGMENTS This research was sponsored by ASHRAE TC 7.4: Building Dynamics, and co-sponsored by TC 1.10: Cogeneration Systems. We would like to acknowledge the following members of the project monitoring committee project for their timely and constructive criticism and support during the course of this research: Rich [H.sub.AC]kner (PMS Chair), Steve Blanc, Srinivas Katipamula, Riyaz Papar, and Timothy Wagner. The critical input of Gershon Grossman and Abdi Zaltesh, our two consultants on this project, is gratefully acknowledged. Several other colleagues provided advice, support, and help at different times related to different aspects of this research: James Freihaut, Rick Heinmann, Ted Lee, Randy Hudson, Wei Jiang, and Vivek Mahanta. REFERENCES ASHRAE. 2004. 2004 ASHRAE Handbook-HVAC Systems and Equipment. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. ASHRAE. 2007. 2007 ASHRAE Handbook-HVAC Applications. Atlanta: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. Bansal, P.K., and J.M. O'Brien. 2000. A new quasi-static cogeneration model. ASHRAE Transactions 106(2). Baughman, M.L., N.A. Eisner, and P.S. Merrill. 1989. Optimizing combined cogeneration and thermal storage systems: An engineering economics approach. IEEE Transactions on Power Systems 4(3). Braun, J.E., S.A. Klein, W.A. Beckman, and J.W. Mitchell. 1989a. Methodologies for optimal control of chilled water systems without storage. ASHRAE Transactions 95(1). Braun, J.E., S.A. Klein, J.W. Mitchell, and W.A. Beckman. 1989b. Application of optimal control to chilled water systems without storage. ASHRAE Transactions 95(1). Braun, J.E., S.A. Klein, and J.W. Mitchell. 1989c. Effectiveness models for cooling towers and cooling coils. ASHRAE Transactions. 95(2):164. Braun, J.E. 2006. Optimized operation of chiller equipment in hybrid machinery rooms and associated operating and control strategies. Final report of ASHRAE Research Project RP-1200. Prepared by Braun Consulting. Cleaver-Brooks. 1996. Fact sheet CB-7767-R1, http://www.cleaver-brooks.com. Cumali, Z. 1988. Global optimization of HVAC system operation in real time. ASHRAE Transactions 94(1):1729- 44. Curti, V., D. Favrat, and M. R. von Spakovsky. 2000. An environomic approach for the modeling and optimization of a district heating network based on centralized and decentralized heat pumps, cogeneration and/or gas furnace-Part II: Application. International Journal of Thermal Sciences 39:731-41. Dotzauer, E. 1997. Algorithms for short-term production-planning of cogeneration plants. Graduate thesis, University of Linkoping, Sweden. Edgar, T.F., D.M. Himmelblau, and L.S. Lasdon. 2001. Optimization of Chemical Processes, 2nd ed. Boston: McGraw Hill. Ehmke, H.J. 1990. Size optimization for cogeneration plants. Energy 15(1):35-44. Fischer, S., and J. Glazer. 2002. CHP Self analysis. Proceedings of the IMECE2002, ASME International Mechanical Engineering Congress and Exposition, New Orleans, LA. Gordon, J.M., and K.C. Ng. 2000. Cool Thermodynamics. Cambridge, U.K.: Cambridge International Science Publishing. Henze, G.P. 2003. An overview of optimal control for central cooling plants with thermal energy storage. Journal of Solar Energy Engineering 125(3):302-9. Honeywell. 2006. Modular integrated energy systems-Task 5: Control and optimization performance. Report prepared for Oak Ridge National Laboratory by Honeywell Laboratories, Minneapolis, MN House, J., and T.F. Smith. 1995. A system approach to optimal control for HVAC and building systems. ASHRAE Transactions 101(2):647-60. Hudson, C.R. 2005. ORNL CHP capacity optimizer: User's manual. Report ORNL/TM-2005/267, Oak Ridge National Laboratory, Oak Ridge, TN. Hui, C., and Y. Natori. 1996. An industrial application using mixed-integer programming technique: A multi-period utility system model. Computers & Chemical Engineering 20(S):1577-82. Jalalzadeh-Azar, A.A. 2003. A parametric analysis of a grid-independent BCHP system-Focusing on impact of technological advancements. ASHRAE Transactions 109(2). Jiang, W., and T.A. Reddy. 2007. Combining engineering optimization of primary HVAC&R plants with decision analysis methods-Part I: Deterministic analysis. HVAC&R Research 13(1):93. Katipamula, S., and M.R. Brambley. 2008. Advanced CHP control algorithms: Scope specification. Pacific Northwest National Laboratory Report PNNL-15796 under U.S. DOE contract DE-AC05-76RL01830. Kelly, D.W., and T. Chan. 1999. Optimizing chilled water plants. HPAC Journal, pp.145-47. Koeppel, E.A., S.A. Klein, J.W. Mitchell, and B.A. Flake. 1995. Optimal supervisory control of an absorption chiller system. HVAC&R Research 1(4):325-40. LBL. 1989. DOE-2 Supplement, v.2.1D. LBL Report No. LBL-8706 Rev. 5 Supplement. DOE-2 User Coordination Office, Lawrence Berkeley Laboratory, Berkeley, CA. MAC. 2005. Combined Heat and Power (CHP) Resource Guide. Chicago: Midwest CHP Applications Center, University of Chicago and Avalon Consulting Co. Maia, L.O.A., L.A. Vidal de Carvalho, and R.Y. Qassim. 1995. Synthesis of utility systems by simulated annealing. Computers & Chemical Engineering 19(4):481-88. Maor, I., and T.A. Reddy. 2008. Near-optimal scheduling control of combined heat and power systems for buildings. ASHRAE RP-1340 final report. Maor, I. and T.A. Reddy. 2009. Cost penalties of near-optimal scheduling control of BCHP systems-Part I: Selection of case study scenarios and data generation. ASHRAE Transactions 115(1). Norford, L.K., S.C. Englander, and B.J. Wiseley. 1998. Demonstration knowledge base to aid building operators in responding to real-time pricing electricity rates. ASHRAE Transactions 104(1):91-103. Olson, R.T. 1988. Optimal allocation of building cooling loads to chilled water equipment. PhD dissertation, University of Illinois at Urbana-Champaign. Parsons, J.A., and B. Li. 2005. A CHP system optimization with microturbine recuperation control. ASHRAE Transactions 111(1). Petchers, N. 2003. Combined Heating, Cooling and Power Handbook: Technologies and Applications. Lilburn, GA: Fairmont Press Inc. and Marcel Dekker Inc. Sakamoto, Y., A. Nagaiwa, S. Kobayasi, and T. Shinozaki. 1999. An optimization method of district heating and cooling plant operation based on genetic algorithm. ASHRAE Transactions 105(2). Sakawa, M., K. Kato, and S. Ushiro. 2002. Operational planning of district heating and cooling plants through genetic algorithms for mixed integer 0-1 linear programming. European Journal of Operational Research 137:677-87. Siemens. 2004. Cooling plant optimization application guide, version 3. Document No. 125-1898, Siemens Building Technologies, Zug, Switzerland. Spakovsky von, M., and C. Frangopoulos. 1994. The envi-ronomic analysis and optimization of a gas turbine cycle with cogeneration. Proceedings of ASME, New York. Sun, J., and T.A. Reddy. 2005. Optimal control of building HVAC&R systems using complete simulation-based sequential quadratic programming (SQP). Building and Environment Journal 40:657-69. Wang, S. 1998. Dynamic simulation of a building central chilling system and evaluation of EMCS on-line control strategies. Building and Environment 33:1-20. Wang, S., and Z. Ma. 2008. Supervisory and optimal control of building HVAC systems: A review. HVAC&R Research 14(1):3-32. Yokoyama, R., Y. Hasegawa, and K. Ito. 2002. A MILP decomposition approach to large scale optimization in structural design of energy supply systems. Energy Conversion and Management 43:771-90. T. Agami Reddy, PhD, PE Fellow ASHRAE Itzhak Maor, PhD, PE Member ASHRAE This paper is based on findings resulting from ASHRAE Research Project RP-1340 T. Agami Reddy is SRP Professor of Energy and Environment with joint appointments at the School of Architecture and Landscape Architecture and the School of Sustainability, Arizona State University, Tempe, AZ. Itzhak Maor is a manager of energy efficiency services at Johnson Controls Inc., Philadelphia, PA. |
|
||||||||||||||||||||||
Printer friendly
Cite/link
Email
Feedback
Reader Opinion