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Energy efficient operating strategies for building combined heat and power systems.

Introduction

A critical area for energy efficiency is to improve building operating strategies. Indeed, most of the potential for near-term improvement in the energy performance of buildings is associated with tight integration of building systems coupled with distributed power generation and dynamic control. Managing the energy flows within a building to meet the needs of the occupants is essential for obtaining optimal performance.

A central coal-burning utility power plant makes steam to drive a steam turbine/generator and has efficiency in the range from 25% to 35%. About two-thirds of the energy input from the fuel is lost as waste heat. In contrast, if the power generation is done onsite, both the electrical power output and heat produced can be utilized to meet heating, cooling, and electrical loads in the building. This process will be referred to as combined heat and power (CHP). The use of the "waste" heat offsets the need for supplemental energy for heating and cooling, resulting in an overall reduction in energy consumption and emissions associated with the building. This well-known benefit is responsible for much of the interest in distributed generation in addition to the potential use as a "back up" power system for critical applications.

To maximize the economic and energy efficiency potential of CHP, operation strategies must continue to be advanced by the scientific community. There are technical issues that must be overcome regarding CHP grid integration. Pecas Lopes et al (2007) highlighted many of these issues. Likewise, much research has gone into the optimization of CHP system design. Different techniques from traditional optimization approaches using mixed-integer programming (MIP) (Ehmke 1990) to heuristic approaches using evolutionary algorithms (Wright et al. 2008; Fong et al. 2008) have been utilized to evaluate optimal systems.

Chicco and Mancarella (2006) provided insights that aid the decision-making process for designing such systems. Their study simulated multiple system configurations for the annual energy utilization factor, fuel energy savings ratio, and payback time. Electric load-following (ELF) and thermal load-following (TLF), along with as-designed operation strategies, were considered. Models used for this study take into account performance degradation of equipment at part-loads. The simulations indicate that TLF is an effective operation strategy.

Hudson (2005) described a stand-alone tool that follows a methodology that optimizes a CHP system sizing for economic return. One area of focus in the methodology is to simulate utility rate and tariff structures in evaluating economic return of a CHP system. The discussion highlights that current utility buyback tariff structures can be restrictive and need to be incorporated to properly evaluate optimal system performance. To find the optimal system, the tool utilizes a controlling optimization algorithm that maximizes net present value. The tool, like many other studies, uses an hourly time-step for the evaluation.

While thermo-economic analysis has largely been used to evaluate steady- and quasi-steady-state industrial applications, Piacentino and Cardona (2007) provided an examination of thermo-economics for the optimization and design of CHP systems. Their study made use of exergoeconomic models, and they asserted that depreciation costs are correctly accounted for with such an analysis.

The nature of the thermal energy produced by the prime mover (i.e., amount, temperature) depends on the prime mover type. Most commonly, reciprocating engines or gas turbines are used, and heat can be captured from the exhaust stream and engine cooling and lubricating systems as appropriate (International Energy Agency 2002). Building heating requirements, such as space or water heating, can be accomplished in a straightforward manner using a hydronic system with suitable heat exchangers and pumps. Using thermal energy to meet building cooling requirements generally requires the use of an absorption chiller, which uses the waste heat as thermal input to the absorption system generator. As previously mentioned, there has been a great deal of interest and activity related to distributed power generation at the building level. Wu and Wang (2006) provided a review of CHP research.

Efficiency at part-load for CHP systems is an important factor to incorporate into simulated performance evaluation. Grossman and Rasson (2003) discussed the effects of part-load operation of both a prime mover and its associated absorption chiller. Highlighting the sensitivity of the absorption chiller capacity to the temperature of the driving heat source, Zaltash et al (2006) experimentally showed the effects of varied ambient conditions on a micro-turbine generator and absorption chiller.

Research has been conducted to simulate systems by accounting for varied component performance. Jiang (2005) thoroughly covered research into component-based system performance modeling for HVAC&R plants. One recurring technique is to use MIP to define the systems and insert into an objective function. Ito et al. (1994), Spakovsky et al. (1995), and Lozano et al. (2009) all utilized the technique to address the system-wide optimization question.

Maor and Reddy (2009) described steps taken to establish a sample of representative buildings and associated CHP systems and subsystem profiles. Their aim was to establish feasible model specifications that would facilitate more realistic simulations for optimization analysis. Parameters evaluated in establishing the different models included prime move fuel type, building type, building size, climactic variation, realistic equipment selection, realistic equipment sizing, and appropriate electric and fuel rate structures. To facilitate appropriate system sizing, the stand-alone tool described by Hudson (2005) is used.

In the second part of their study, Reddy and Maor (2009) provided results of their modeling and optimization. The models for the different equipment were traditional black-box models based on rated equipment performance and polynomial curve fits emulating equipment performance at part-loads. The study defined a cost penalty ratio (CPR) as the ratio of near-optimal to optimal results. The CPR was used in evaluating the optimization of the different CHP scenarios for three different utility rate structures.

The idea of load-following is shown to be an important consideration for decisions regarding CHP system design and operation. Jalalzadeh-Azar (2004) compiled an analysis of TLF and ELF for a CHP system and, generally, found TLF most effective. To further the discussion of load-following in CHP systems, Mago and Chamra (2009) provided an analysis of annual performance optimization. Hourly building loads are simulated in EnergyPlus. The study incorporated thermal and ELF matched with an optimization of primary energy consumption, operation cost, or carbon dioxide emissions reduction. A hybrid electric-TLF (HETS) technique was also evaluated. HETS requires the prime mover to operate at a capacity to meet the largest electric and/or thermal load possible without dumping heat or electricity. The hybrid load-following produced annual results comparable to optimized TLF. The models for this study appeared to utilize constant equipment efficiencies over the range of part-load operations. Cho et al (2009) described a dispatch function capable of carrying out an optimized load-following technique and showed its performance on a small system.

Implementing the TLF strategy requires the prediction of the prime mover output required to produce the thermal energy needed to meet the heating and cooling loads. This is not a simple task, since absorption chiller performance will vary with load and other conditions. In fact, the efficiencies of each of the system components may vary with load ratios, making it critical to evaluate all of them over a full range of loadings for each combination of building loads in order to determine the optimum operating points (i.e., as loads are redistributed among system components, part-load-dependent component efficiencies and overall system energy performance will vary).

Overview of approach

While much work has been conducted to determine optimum operational strategies, there is room for improvement regarding tools that may help CHP operators determine appropriate scheduling decisions. Jiang and Reddy (2007) noted "complex HVAC&R plants are still scheduled by humans in a heuristic manner without the aid of computer supporting tools" (p. 120). A supervisory control technique that, if enhanced, could benefit operators is performance map-based control. Wang and Ma (2007) discussed performance map-based supervisory control research in their review of supervisory HVAC control. The method proposed in this article seeks to provide a performance map-based tool to assist operators in determining optimum component set-points and operating conditions to achieve maximum system efficiency.

The value of the presented method lies in its simplification of the system optimization problem such that a simple search may be conducted for a given set of anticipated loads. The method is based on models of the part-load efficiencies of the various components constituting the overall building electrical and space conditioning systems and determines the optimum utilization of the ensemble to meet any combination of building electrical, cooling, and heating loads on the basis of primary energy consumption. The method could also be slightly modified to enable the minimization of primary energy costs, emissions, or a weighted combination of energy, costs, and emissions. use of the method is demonstrated for several generic but realistic equipment characteristics, and the associated energy savings is presented. Implications of the use of the method on control systems configuration and operation are discussed.

A simple building CHP system is used to demonstrate the method. It consists of a single prime mover, heat recovery system to capture the waste heat from the prime mover and enable its provision to the building heating and cooling system, absorption chiller, electric chiller, and auxiliary heating boiler, as shown schematically in Figure 1. This is a fairly high-level view of the system that does not include all of the fluid distribution, heat transfer, and control equipment that would be required to obtain proper operation. Most of the lower-level control functions would be implemented by traditional feedback loop control in response to set-points applied by the operator or supervisory control system.

Description of method

The first step is to obtain a characterization of the input/output relationships for the prime mover, either from manufacturer's data, testing, or modeling. As the prime mover fuel input is varied, its electrical and thermal output will vary in some characteristic fashion, as represented conceptually in Figure 2. The shapes of the curves (or the underlying model) do not affect the procedure, so long as they are accurate for the specific device. Similar performance data or models are required for the other components, including the absorption and electric chillers, the boiler, and the heat recovery unit. These models are frequently formulated as polynomials with coefficients tailored for specific components. Grid efficiency is a special case, since it is an aggregate value that changes over time and needs to be obtained from the utility. This value includes the efficiencies of both the generation and distribution of the grid-generated electrical power.

[FIGURE 1 OMITTED]

The primary energy sources in the system shown in Figure 1 are the fuel input to the CHP prime mover, fuel input to the boiler, and fuel input to the utility power plant. The utility grid is included in the control volume to the extent that changes in site-generated electrical power could have an incremental effect on grid-generated power and, thus, fuel consumption. While the electric grid does not operate with a single primary energy source, the combination of all of the sources at any point in time can be represented by an average efficiency that will vary as different generating resources go on and off line. Energy drawn from the grid by the building can be associated with a certain amount of primary energy consumption, and energy sent to the grid can reduce grid primary energy by an equivalent amount. The basic energy flows are as follows:

* the prime mover consumes fuel, generates electrical power, and waste heat, a substantial fraction of which is recovered by the heat recovery unit

* the site generated electrical power is used to meet the building electrical load, and any excess is available for the electric chiller or to send to the grid; if there is a deficit, electrical power is drawn from the grid

* the recovered waste heat is available for meeting building heating loads or for the absorption chiller to meet cooling loads

* if heating loads are not met, the auxiliary boiler will provide the needed heating

* the electric chiller can use grid power to meet some or all of the cooling loads

[FIGURE 2 OMITTED]

The governing equations for the different component models are taken from the EnergyPlus Engineering Reference (U.S. Department of Energy 2010), with some modifications that were required to support the optimization analysis. See the Appendix for detailed model description. The procedure for systems simulation is presented in context to the referenced models.

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System simulation procedure

A schematic chart of the system simulation procedure is presented in Figure 3. The simulation begins by computing prime mover performance over the range of allowable part-load ratio (PLR) values. The heat output from the prime mover, which includes exhaust heat, jacket heat, and lube oil heat, is then delivered to the heat recovery unit (Section A). The recovered heat is then available for the absorption chiller and/or the heating load. The available heat is then evaluated over the range of possible allocations between full cooling and full heating. The number of points evaluated depends on the resolution used in the analysis. For any combination of PLR and heat fraction, three important comparisons will then be performed:

1) Compare the heating load with excess heat (Section B). If excess heat is less than the heating load, it would be necessary to run the hot water boiler to compensate the difference and meet the heating load.

2) Compare the cooling load with [[??].sub.evap,abs,ch] (Section C). If the operating capacity for the absorption chiller is less than cooling load, it would be necessary to run the electric chiller to compensate the difference and meet the cooling load.

3) Compare the electric load with [[??].sub.pM] (Section D). If the electric energy output from the prime mover is less than the electric load, it would be necessary to obtain electricity from the grid. It should be noted that the electricity required to run the electric chiller is accounted for as well in order to compute the total required electricity. Excess electricity, after meeting possible building and electric chiller loads, is sent to the grid.

The goal of this procedure is to minimize primary energy consumption, defined as the sum of prime mover energy input, boiler energy input, and incremental grid energy input. For any instant under quasi-equilibrium conditions, the energy rate formulation of this statement is

[P.sub.Ti] = [P.sub.pMi] + [P.sub.Bi] + [P.sub.Gi],

where

[P.sub.Ti] = total energy input rate,

[P.sub.PMi] = prime mover energy input rate,

[P.sub.Bi] = boiler energy input rate, and

[P.sub.Gi] = grid energy input rate.

Also, at any point in time, the building will have some combination of electrical loads (exclusive of cooling) [[??].sub.E], cooling loads [[??].sub.C], and heating loads [[??].sub.H]. The magnitudes of these will, of course, vary with weather, time of day, date, and season, among other factors. Consider first the case with only electric and heating loads (zero cooling loads). Figure 4 presents the relationship between prime mover electrical power output and heating capacity, which represents an operating curve. The only electrical/heating load combinations that can be exactly met by the prime mover are those that fall on the curve. That is likely to be a relatively rare occurrence, so most of the time, the load combination will lie somewhere off of the curve, say at points 1 or 2. For the load combination given by point 1, the prime mover could either meet the heating load but be deficient in meeting the electrical load (point b, TlF) or meet the electrical load and produce excess thermal energy (point d, ELF). The penalty for operating at point b is the primary input to the grid needed to satisfy the unmet electrical load labeled [DELTA][E.sub.1], while the penalty for operating at point d is the extra fuel input to the prime mover to go from point b to d (this assumes that the excess thermal energy associated with [DELTA][H.sub.1] is not useful). In contrast, for the load combination given by point 2, the prime mover could either meet the electric load but be deficient in meeting the heating load (point a, ELF) or meet the heating load while producing excess electrical power (point c, TLF). The penalty for point a is the boiler fuel input required to meet the heating load labeled [DELTA][H.sub.2], while the penalty for point c is the extra fuel input to the prime mover, which may be offset by the transfer of the excess electrical power labeled [DELTA][E.sub.2] to the grid. The determination of the primary energy input rates corresponding to each unmet or additional load term are based on the respective component models. It must be emphasized that this is not to suggest that any of the points identified in the figure are the preferred operating conditions, but rather merely to describe how the load combinations and component characteristics interact in affecting primary energy consumption. The determination of optimum operating conditions will be described in a later section.

[FIGURE 4 OMITTED]

Figure 5 presents a similar example for the case of only electrical and cooling loads (zero heating loads). For the load combination labeled 3, the prime mover could use TLF (point f), depending on the grid to provide electrical power [DELTA][E.sub.3], or use ELF (point h), thereby requiring more fuel input to the prime mover and producing more cooling capacity than is needed. For the load combination given by point 4, operating the prime mover at point e (ELF) would require supplemental cooling, labeled [DELTA][C.sub.4], while operating at point g (TLF) would produce excess electrical power [DELTA][E.sub.4] to send to the grid. The need for supplemental cooling raises several questions, since it could be provided by the electric chiller with power from the grid or electrical power from increasing the output of the prime mover. However, increasing the prime mover electrical output will also increase the output of thermal energy that could be used by the absorption chiller to provide additional cooling. The amount of additional electric power or thermal output required to meet the cooling load will depend on the fraction of the cooling load allocated to each chiller and their part-load efficiencies, and finding the optimum load fractions is not a simple task.

[FIGURE 5 OMITTED]

This leads to the third example and the crux of the methodology. The case of electrical, heating, and cooling loads is shown in Figure 6. The X and Y dimensions are heating load and cooling load, respectively. This figure is based on a specific set of prime mover and absorption chiller characteristics and shows the combinations of heating and cooling capacities that can be achieved for any fixed prime mover electrical power output (or prime mover PLR). The labeled curves represent constant electrical power outputs, which correspond to fixed thermal outputs that can be allocated for heating or cooling purposes in any manner. Any load combination that falls within the band of the constant electrical power curves (say point 5) can be met by the prime mover/absorption chiller duo, although there is no guarantee that that would be the most favorable option. It may be more advantageous to operate the prime mover at a higher output to send electrical power to the grid, or to operate the prime mover at a lower output, use grid power to make up the difference in electrical power needs, and use the electric chiller and/or boiler to meet some of the thermal loads. It is not obvious what the best course of action would be, and the answer would depend on the efficiency of grid-generated power and component part-load efficiencies.

[FIGURE 6 OMITTED]

The load combination represented by point 6 is even more challenging, since it lies beyond the capacity of the prime mover/absorption chiller duo and requires supplemental heating and/or cooling (the electrical load is not shown directly in this figure, but is assumed to be known and will be accounted for). In order to meet the heating and cooling loads associated with point 6, the prime mover electrical and thermal output can be allocated in any manner, combined with electrical power from the grid, the absorption and electric chillers, and the boiler. The optimum operating conditions are the PLRs for the four major system components that are under the control of the building (prime mover, absorption chiller, electric chiller, and boiler) that result in the minimum primary energy input, including the grid, and satisfy all of the building loads. The set of optimum PLRs will vary with load combinations, component efficiencies, and grid efficiency. Finding this optimum set can be challenging due to the large search space and multiple degrees of freedom presented by the four independent components. However, a method was developed that substantially compresses the search space, reduces the computational burden, and generates a performance map that can be used to visually or analytically determine the best operating condition.

The method for determining the optimum PLRs can be best described by referring back to Figures 5 and 6. Figure 5 incorporates the heating and cooling capabilities of the prime mover/absorption chiller combination for any prime mover PLR. Figure 6 maps the prime energy input that corresponds to the specific building heating and cooling load combination. Take, for example, the load combination at point 6 (the heating and cooling loads indicated, plus some known electrical load). Any location bounded by the 100% PLR curve for the prime mover is a potential operating point for the prime mover and is associated with a specific electrical power output, heating capacity, and cooling capacity for the prime mover/absorption chiller duo. For example, if the prime mover were operated at point i, its electrical power output would be 80% of its rated capacity, and the prime mover/absorption chiller would have a heating capacity of [[??].sub.Hi] and a cooling capacity of [[??].sub.Ci]. Additional heating in the amount of [DELTA][H.sub.i6] and cooling in the amount of [DELTA][C.sub.i6] would be required. Since the operating condition of the prime mover has been fixed at point i, the additional thermal loads, as well as any additional electrical power, can only be obtained from the electric chiller, boiler, and grid, respectively. Determining the primary energy required to satisfy the unmet loads is accomplished using the models described above (and in the Appendix), for a range of prime mover PLRs and thermal output fraction values. This is a two-dimensional operating space, which greatly reduces the size of the search space and associated computational burden compared to searching all possible combinations of prime mover, absorption chiller, electric chiller, and boiler load ratios.

Execution of the above method results in the generation of a performance map in the form of a two-dimensional array of values or a surface of height [P.sub.t], which can easily be checked to find the minimum point and the associated optimum PLRs, and the allocation of thermal energy from the prime mover to the heating and cooling functions. Figure 7 presents an example of such a surface for a particular load combination. While the modeling data used to generate the figure enables the determination of the optimal operating point, the figure itself aids in visualizing the impacts of different modes of operation and the effects of variables. It should be noted that this surface has been generated without regard to any constraints, such as minimum permitted PLRs. However, it is a simple task to enforce any such constraints when selecting the optimum operating condition by eliminating those areas from consideration. Also, the analysis could be extended to determine energy costs and/or emissions values and their associated optimum operating points.

[FIGURE 7 OMITTED]

Summary of method

1. Obtain or develop performance models for the system components.

2. estimate current electrical, heating, and cooling loads for the building based on metering and energy balances for the heating and cooling coils.

3. Obtain current values of independent variables needed to exercise the component models from the building energy management system or the electric utility.

4. Determine the prime mover load dependent characteristics for the current conditions.

5. Determine the total primary energy consumption surface for the current load combination.

6. Select the minimum operating point, subject to any constraints, such as allowable ranges.

7. Identify the prime mover PLR and allocation of thermal output to heating and cooling for the optimum operating conditions.

8. Direct the prime mover to the identified PLR and the control valves to position themselves to deliver the proper heat fractions to the heating and cooling systems.

9. Since the electric chiller and auxiliary boiler are operated in parallel, they will meet any thermal loads not satisfied by the absorption chiller and direct heating functions.

Modeling, simulations, and sample results

The building CHP system model and the optimization procedure were implemented using MATLAB. Specific sets of coefficients were selected from EnergyPlus reference input files to represent sample component characteristics. The equipment used for the simulations are not being represented as the best, and the relative merits of CHP are not being evaluated; they have simply been selected to allow the control methodology to be demonstrated. Since the purpose of this article is to describe and demonstrate a methodology for determining the optimum operating conditions as a function of building loads and equipment, no specific building or location was modeled. Instead, different combinations of electrical, cooling, and heating loads were chosen to demonstrate how the method would respond to changing conditions and provide guidance to the building operator or supervisory control system to attain optimum performance. The impact of the operating conditions on component and system energy efficiency and usage are also evaluated.

Eight different conditions were evaluated, including four load combinations, two chiller types, two grid efficiencies, and night versus day. Of course, a real building would be subjected to varying weather- and occupant-related factors throughout a year, which would result in a wide range of load combinations. The method should be able to respond appropriately to any combination of building loads, as evidenced by the specific subset used for the simulations. It should also be noted that the simulations are conducted assuming quasi-steady-state conditions for the building (i.e., loads are not changing rapidly). These types of conditions are not unusual in buildings, as thermal loads generally vary slowly throughout the day and night. If the building is undergoing rapid load changes, this is easily detected by the load monitoring system, and changes in operating conditions can be moderated if needed. The simulations do not model transient effects such as might be experienced by an absorption cooling system. Table 1 lists the assumptions and conditions used for the simulations.

Simulation results

A series of figures and a table were created to display the results of the simulations. Several different metrics were computed to investigate the use of the method and compare the results for the various load combinations. Total primary energy input rate was computed for the optimal CHP condition and a baseline condition without CHP, as was system efficiency at the optimal condition. The optimal PLR for the prime mover and the thermal output fractions applied to heating and cooling, along with any dumped heat, were also determined. Other metrics included the absorption chiller contribution to cooling load, recovered heat contribution to heating load, and the cooling load split between the absorption and electric chiller. The summary table follows the description of the figures.

Sensitivity analysis

When computing the performance map, there is a trade-off between simulation accuracy and computational burden that varies with grid size (or resolution). In order to examine this sensitivity, Cases 2b and 3b were selected to study the effect of changing the grid size for prime mover PLR and the thermal output fraction applied to heating and cooling on the total primary energy input rate. The number of grid points was increased, thereby providing greater resolution, and the change in computed total energy input plotted in Figure 8. This figure indicates minimal benefit from increasing the PLR resolution beyond 0.2; PLR resolution was selected to be 0.05 to assure accuracy in the calculations. Similarly, Figure 9 indicates that there is minimal benefit in increasing the thermal output fraction resolution beyond 0.04; thermal fraction resolution was selected to be 0.0345 to assure accuracy in the calculations. It should be noted that the model is not computationally expensive, and it is possible to increase the resolutions significantly if needed.

Load profile results

The first set of figures examines one condition in detail, while subsequent figures only show information that differs for each of the other conditions. Figure 10 presents the input and output characteristics of the prime mover as a function of its PLR. These values only need to be computed once for this prime mover, since its performance does not depend on ambient temperature or another uncontrolled variable. If the prime mover performance was sensitive to temperature, this would need to be computed based on the current values. The data in Figure 10, specifically the electrical power and thermal output, can then be used to determine the ability of the CHP system to meet the building electrical, heating, and cooling requirements. Figure 11 shows the heat input to the absorption chiller as well as its coefficient of performance (COP) as a function of its PLR. By comparison, Figure 12 shows the COP for the centrifugal (primary) electric chiller and reciprocal (alternative) chiller as a function of PLR. These underlying performance characteristics are used to determine the optimum operating points for the ensemble, which may not correspond to the individual optimum component operating points. The effect of utilizing a primary or alternative chiller will be investigated shortly.

[FIGURE 8 OMITTED]

[FIGURE 9 OMITTED]

[FIGURE 10 OMITTED]

[FIGURE 11 OMITTED]

Figure 13 shows the loads and operating curve for Cases 1a-4b. Figure 14 shows the possible heating and cooling load combinations that can be met by the CHP system over the range of PLRs, along with the actual load points for Cases 1a-4a. Figures 15-22 depict the surface plot associated with Cases 1a-4b. A quick examination shows considerable variation in the shapes of these plots, which represent performance maps for the particular load combinations, as well as the optimum (minimum) operating condition. A discussion of some important observations regarding Cases 1a-4b follows subsequently.

[FIGURE 12 OMITTED]

[FIGURE 13 OMITTED]

[FIGURE 14 OMITTED]

[FIGURE 15 OMITTED]

[FIGURE 16 OMITTED]

The effect of chiller characteristics is demonstrated by comparison of Figures 15 and 16 for Cases 1a and 1b. The chiller in Figure 16 has a different COP/PLR relationship, which changes the shape of the total primary energy rate surface and magnitude of the minimum primary energy rate shown in Figure 15 but not the location of the optimum operating point. This could have a greater impact for other load combinations or chiller characteristics.

Cases 2a and 2b have the same electric load, a cooling load of 25 kW (85 Btu/h), but still no heating load, and have different grid power efficiencies (0.33 and 0.38, respectively). Higher grid efficiency values can occur when the mix of generating sources shifts more toward renewables, particularly hydroelectric power or wind. As shown in Figure 13, the load point falls within the range of the CHP system. Figure 17 shows the primary energy rate surface for Case 2a, which has a noticeable bend. The optimum prime mover PLR is 0.65, and all of the heat output is directed to the absorption chiller, which is able to meet the full cooling load. Raising grid efficiency to 0.38 (Case 2b, Figure 18) causes a dramatic change in the shape and minimum value of the primary energy rate surface. Optimum prime mover PLR is 0.4, and the electric chiller meets 38% of the cooling load.

[FIGURE 17 OMITTED]

[FIGURE 18 OMITTED]

[FIGURE 19 OMITTED]

[FIGURE 20 OMITTED]

Cases 3a and 3b represent mixed heating/cooling loads, such as might be expected in a swing season, for night and day. Heating and cooling loads are both 25 kW (85 Btu/h), while electric load is 10 kW at night (Case 3a) and 50 kW during the day (Case 3b). The shape of the primary energy rate for Case 3b (Figure 20) is identical to Case 3a (Figure 19), with the entire surface being shifted vertically a substantial amount to account for the additional electric power required, which must be obtained from the grid.

[FIGURE 21 OMITTED]

Cases 4a and 4b examine a similar comparison for winter night and day conditions, respectively, with the difference being lower nighttime electric and cooling loads (10-kW electric load, 10-kW [31-kBtu/h] cooling load, and 100-kW [341-kBtu/h] heating load) than daytime loads (50-kW electric load, 25-kW [85-kBtu/h] cooling load, and 100-kW [341-kBtu/h] heating load). The optimal operating conditions are similar for both cases, with a prime mover PLR of 1.0 and all of the thermal output directed to meeting the heating load. All of the cooling is handled by the electric chiller, which is powered by the electric power from the CHP system. Excess electric power is sent to the grid for the night condition, resulting in a much lower primary energy rate than during the day.

[FIGURE 22 OMITTED]

The foregoing examples are intended to demonstrate how the method works and responds to different component characteristics and load combinations. One possible application of the method would be to pre-compute performance maps for a range of load combinations, and either chose the closest value or interpolate among the nearest neighbors. Table 2 contains a summary of the measurement results and metrics. Two metrics listed in the table that have not been discussed are the optimal to base primary energy rate ratio (OBPERR), and the system energy utilization factor (SEUF), which are defined as follows:

OBPERR--ratio of total primary energy rate for the optimal CHP-based system to a non-CHP-based system meeting the same building load combination. This factor primarily demonstrates the benefit of using a CHP system but also includes the incremental effects of the optimal operating strategy.

SEUF--ratio of the useful output to the energy input for the entire system, including the CHP system, boiler, and grid. The individual terms are the ratio of CHP electric power output and useful thermal power output, the heating load met by the boiler, and the electric power from the grid to the primary energy input to the CHP prime mover, plus primary energy rate input to the boiler and primary energy rate input to the grid power generation. This factor demonstrates the overall energy efficiency of the combined system. This metric mixes electric and thermal power without regard to their relative usefulness.

Use of the CHP system generally requires about 20% less power compared to a conventional system, with the OBPERR ranging from a low of 0.457 to a high of0.969. The greatest savings versus a conventional system corresponds to Case 3a, where 45 kW of electric power is sent to the grid, while the least savings occurs for Case 2b, which has the higher grid electrical power generation efficiency. The SEUF ranges from 0.54 to 0.87 but generally runs about .7, which is substantially better than conventional power generation. For the eight conditions simulated, the optimal operating strategies cover a range of component PLRs and thermal energy allocations, and considerably more variation would be expected for real building operation over an entire year. The electric chiller meets some or the entire cooling load when the capacity of the absorption chiller is exceeded, when the grid efficiency is higher, or when the prime mover thermal output is needed for heating loads. The prime mover operates at full load except for the two mild summer conditions.

These results are not intended to be an exhaustive analysis of all possible operating conditions, but rather to demonstrate the implementation of the method and how it responds to equipment characteristics and load combinations. Future work is needed to incorporate the effects of other variables on overall system performance and optimization and to model the control system operation more explicitly.

Discussion

One of the challenges of operating this type of system configuration lies with the many alternative ways of meeting building loads. For example,

* What should be the prime mover setting (PLR)?

* How should waste heat be allocated between heating and cooling?

* How should the cooling loads be allocated between the absorption and electric chillers?

* Should excess electrical power be generated and sent to the grid?

Answering these questions for any combination of loads requires a detailed understanding of the performance characteristics of each component, as well as the interactions among them. It also requires choosing performance evaluation criteria, such as minimizing primary energy consumption, energy cost, emissions, or some combination. While it is understood that many decisions are based on economic factors, this analysis focuses on minimizing energy usage, but the procedure may be extended to incorporate energy cost, emissions, or a desired combination through the use of suitable weighting factors (Treado and Holmberg 2010 ). It also should be noted that life-cycle economic analysis would include the effects of equipment first costs and expected lifetimes, which are important considerations for real-world projects but beyond the scope of this article. For the purposes of this analysis, it is assumed that if excess electrical power is generated onsite, it can be exported to the electrical grid, thereby offsetting an equal amount of grid-generated power. A combination of policy and technical factors are required to enable that process to occur, but it is certainly possible, and definitely desirable, from the point of view of minimizing primary energy consumption associated with buildings.

Summary and conclusions

A method was developed and demonstrated for evaluating and visualizing the optimal operating strategies for building CHP systems. The method uses models of the component load-dependent operating characteristics matched to specific electrical and thermal load combinations for the building in a framework that substantially reduces the size of the search space and associated computational burden. The overall system primary energy input is determined for possible operating conditions and represented as a performance map, allowing the optimal component PLRs and allocation of thermal energy to be determined. The method was demonstrated for eight scenarios; optimal operating conditions were determined along with the ratio of energy use for the CHP system to a conventional system and the overall system energy utilization factor.

The simulation results showed the method to be an effective means of generating system performance maps to enable operators or supervisory control systems to determine the optimum operation set-points for different electrical, heating, and cooling load combinations. The method simplifies the decision making required to achieve optimal control by eliminating the need to evaluate multiple conditional factors related to the operation of individual system components. The method also has modest computational requirements, although it does require accurate component models and current building load information to determine the performance map. One possible application of the method would be to pre-compute a set of performance maps over a range of expected building load profiles and then use the maps either manually or in an automated fashion to select optimal set-points as required.

Appendix

Internal combustion engine generator (prime mover)

Model inputs: nominal generating capacity, PLR

Model outputs: electric energy output, fuel energy input, total exhaust heat, exhaust gas temperature, recoverable jacket heat, recoverable lube oil heat

The electric energy output can be calculated from Equation 1:

PLR = electric energy output / nominal generating capacity. (1)

The electric energy output and PLR can then be used to compute the fuel energy input:

electric energy output / fuel energy input = [a.sub.1] + [a.sub.2]PLR + [a.sub.2][PLR.sup.2] (2)

Total exhaust heat and exhaust gas temperature can be calculated as follows:

total exhaust heat / fuel energy input = [d.sub.1] + [d.sub.2]PLR + [d.sub.2][PLR.sup.2] (3)

exhaust gas temperature {K} / fuel energy input = [e.sub.1] + [e.sub.2]PLR + [e.sub.2]PLR. (4)

Heat recovered from lube oil and water jacket are given by

recoverable jacket heat / fuel energy input = [b.sub.1] + [b.sub.2]PLR + [b.sub.2][PLR.sup.2], (5)

recoverable lube oil heat / fuel energy input = [c.sub.1] + [c.sub.2]PLR + [c.sub.2][PLR.sup.2]. (6)

Absorption chiller

Model inputs: rated chiller capacity, chiller evaporator operating capacity, evaporator outlet water temperature, condenser inlet water temperature, generator inlet water temperature

Model outputs: generator heat input

The model first calculates three capacity correction factors to compute the maximum chiller capacity from the rated chiller capacity:

[CAPFT.sub.evaporator] = a + b ([T.sub.evaporator]) + c[([T.sub.evaporator]).sup.2] + d[([T.sub.evaporator]).sup.2], (7)

[CAPFT.sub.condenser] = e + f([T.sub.condenser]) + g[([T.sub.condencer]).sup.2] + h[([T.sub.condenser]).sup.2], (8)

(hot water only),

[CAPFT.sub.generator] = i + j([T.sub.generator]) + k[([T.sub.generator]).sup.2] + l[([T.sub.generator]).sup.2] (9)

[[??].sub.evap,max] = [??]evap,rated([CAPFT.sub.evaporator]) x ([CAPFT.sub.condenser]) x ([CAPFT.sub.generator]), (10)

where

[CAPFT.sub.evaporator] = capacity correction (function of evaporator temperature) factor,

[CAPFT.sub.condenser] = capacity correction (function of condenser temperature) factor,

[CAPFT.sub.generator] = capacity correction (function of generator temperature) factor,

[T.sub.evaporator] = evaporator outlet water temperature,

[T.sub.condenser] = condenser inlet water temperature,

[T.sub.generator] = generator inlet water temperature,

[Q.sub.evap,max] = maximum chiller capacity, and

[Q.sub.evap,rated] = rated chiller capacity.

It should be noted that Equation 9 is only valid for the case of generators utilizing hot water only.

The absorption chiller model takes chiller evaporator operating capacity as an input. The PLR of the absorption chiller's evaporator can then be calculated from Equation 11 (the reverse absorption chiller will be discussed subsequently):

PLR = [[??].sub.evap] / [[??].sub.evap,max], (11)

where

PLR = PLR of chiller evaporator, and

[[??].sub.evap] = chiller evaporator operating capacity

The ratio of generator heat input to maximum chiller capacity is then calculated from Equation 12:

GeneratorHIR = a + b(PLR) + c[(PLR).sup.2] + d[(PLR).sup.2]. (12)

Two additional curves are available to modify the heat input requirements:

GenfCondT = e + f([T.sub.condenser]) + g[([T.sub.condenser]).sup.2] + h[([T.sub.condenser]).sup.2], (13)

GenfEvapT = i + j ([T.sub.evaporator]) + k[([T.sub.evaporator]).sup.2] + l[([T.sub.evaporator]).sup.2], (14)

where

GenfCondT = heat input modifier based on condenser inlet water temperature, and

GenfEvapT = heat input modifier based on evaporator outlet water temperature

Chiller cycling occurs if the chiller operating PLR is smaller than the minimum PLR. In this study, the chiller will run the entire time step (i.e. CyclingFrac = 1):

CyclingFrac = MIN (1, [PLR / [PLR.sub.min[??]]]), (15)

where

CyclingFrac = chiller part-load cycling fraction, and

[PLR.sub.min] = chiller minimum PLR.

The generator heat input can then be calculated from Equation 16:

[[??].sub.generator] = GeneratorHIR([[??].sub.evap,max]) x (GenfCondT)(GenfEvapT) x (CyclingFrac) (16)

Reverse absorption chiller

Model inputs: rated chiller capacity, generator heat input, evaporator outlet water temperature, condenser inlet water temperature, generator inlet water temperature

Model outputs: chiller evaporator operating capacity

The reverse absorption chiller is considered as one of the contributions of the current work. The significance of this model originates from the fact that it is necessary to have chiller evaporator operating capacity as an output of the model to evaluate

the contribution of the absorption chiller in meeting the cooling load. The model utilizes the same basic equations as the absorption chiller model; however, the coding is modified to compute the chiller evaporator operating capacity based on provided inputs including the generator heat input.

The model first calculates three capacity correction factors to compute the maximum chiller capacity from the rated chiller capacity using Equation 10. Equations 13-16 would then be used to compute GeneratorHIR. Equation 1 is then used to calculate the PLR. It should be noted that Equation 1 is a cubic equation, and not all three roots that satisfy this equation are admissible. Non-real or out of range roots are dismissed (0 [less than or equal to] PLR [less than or equal to] 1). Finally, Equation 11 is used to compute the chiller evaporator operating capacity.

Electric chiller

Model inputs: chiller capacity at reference conditions, load to be met by the chiller, leaving chilled water temperature, entering condenser fluid temperature

Model outputs: chiller compressor power

This model simulates the thermal performance of the chiller and the power consumption of the compressor. Performance information at reference conditions along with three performance curves for cooling capacity and efficiency are used to determine chiller operation at off-reference conditions. It should be noted that the electric chiller model is based on condenser entering temperature. The three performance curves are:

1. cooling capacity function of temperature curve,

2. energy input to cooling output ratio function of temperature curve, and

3. energy input to cooling output ratio function of PLR curve.

The above-mentioned performance curves are formulated in Equations 17, 18, and 1:

ChillerCapFTemp = a + b([T.sub.cw,l]) + c[([T.sub.cw,l]).sup.2] + d([T.sub.cond,s]) + e[([T.sub.cond,s]).sup.2] + f([T.sub.cw,l])([T.sub.cond,s]), (17)

ChillerEIRFTemp = a + b([T.sub.cw,l]) + c[([T.sub.cw,l]).sup.2] + d([T.sub.cond,s]) + e[([T.sub.cond,s]).sup.2] + f([T.sub.cw,l])([T.sub.cond,s]), (18)

where

ChillerCapFTemp = cooling capacity factor, equal to 1 at reference conditions;

ChillerEIRFTemp = energy input to cooling output factor, equal to 1 at reference conditions;

[T.sub.cwl] = leaving chilled water temperature, [degrees]C; and

[T.sub.cond,e] = entering condenser fluid temperature, [degrees]C.

The chiller's available cooling is then calculated from Equation 19:

[[??].sub.avail] = [[??].sub.ref](ChillerCapFTemp), (19)

where

[[??].sub.ref] = chiller capacity at reference conditions (reference temperature and flow rates defined by the user), and

[[??].sub.avail] = available chiller capacity adjusted for current fluid temperatures.

Chiller PLR is then calculated from Equation 20:

PLR = cooling load / [[??].sub.avail]. (20)

Energy input to cooling output factor is calculated subsequently from Equation 21:

ChillerEIRFPLR = a + b(PLR) = c[(PLR).sup.2], (21)

where

ChillerEIRFPLR = energy input to cooling output factor, equal to 1 at reference conditions.

The electrical power consumption for the chiller compressor(s) is then calculated using Equation 22:

[P.sub.chiller] = ([[??].sub.avail])(1 / [COP.sub.ref]) x (ChillerEIRFTemp) x (ChillerEIRFPLR) X (ChillerCyclingRatio), (22)

where

[P.sub.chiller] = chiller compressor power, [COP.sub.ref] = reference COP, and PLR/[PLR.sub.min][??], 1).

Simple hot water boiler

Model inputs: boiler load, nominal thermal efficiency

Model outputs: fuel used

This simple model calculates the fuel used by the boiler using Equation 23:

Fuel Used = Boiler Loard / (Nominal Thermal Efficiency)(Boiler Efficiency Curve Output). (23)

It should be noted that the boiler's nominal thermal efficiency is assumed to remain constant throughout the simulation (i.e., BoilerEfficiencyCurveOutput = 1).

DOI: 10.1080/10789669.2011.573757

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Received November 19, 2010; accepted March 4, 2011

Stephen Treado, PhD, PE, is Associate Professor. Payam Delgoshaei, is Postdoctoral Scholar. Andrew Windham, Student Member ASHRAE, is Postdoctoral Candidate.

Stephen Treado, * Payam Delgoshaei, and Andrew Windham

Department of Architectural Engineering, Pennsylvania State University, 104 Engineering Unit A, University Park, PA 16802, USA

* Corresponding author e-mail: streado@psu.edu
Table 1. Description of equipment and simulation conditions.

Building equipment Capacity

CHP prime mover 55 kW electric, 83.4 kW
 (285 kBtu/h) thermal
Absorption chiller 40 kW (136 kBtu/h) cooling
Electric chiller 30 kW (102 kBtu/h) cooling
Hot water boiler 100 kW (341 kBtu/h) heating

Operational assumptions
Grid efficiency 33%
Chilled water temperature 6[degrees]C (42.8[degrees]F)
Condenser water temperature 24[degrees]C (75.2[degrees]F)
Hot water boiler efficiency 82%
Recovered heat temperature 150[degrees]C (302[degrees]F)

Building load profile 1a Hot summer
Cooling load 60 kW (205 kBtu/h)
Heating load 0 kW
Electrical load 50 kW

Building load profile 1b Hot summer
Cooling load 60 kW (205 kBtu/h)
Heating load 0 kW
Electrical load 50 kW

Building load profile 2a Mild summer
Cooling load 25 kW (85 kBtu/h)
Heating load 0 kW
Electrical load 50 kW

Building load profile 2b Mild summer
Cooling load 25 kW (85 kBtu/h)
Heating load 0 kW
Electrical load 50 kW

Building load profile 3a Mixed
Cooling load 25 kW (85 kBtu/h)
Heating load 25 kW (85 kBtu/h)
Electrical load 10 kW

Building load profile 3b Mixed
Cooling load 25 kW (85 kBtu/h)
Heating load 25 kW (85 kBtu/h)
Electrical load 50 kW

Building load profile 4a Winter night
Cooling load 10 kW (34 kBtu/h)
Heating load 100 kW (341 kBtu/h)
Electrical load 10 kW

Building load profile 4b Winter day
Cooling load 25 kW (85 kBtu/h)
Heating load 100 kW (341 kBtu/h)
Electrical load 50 kW

Building equipment

CHP prime mover

Absorption chiller
Electric chiller
Hot water boiler

Operational assumptions
Grid efficiency
Chilled water temperature
Condenser water temperature
Hot water boiler efficiency
Recovered heat temperature

Building load profile 1a Comparison
Cooling load Centrifugal chiller
Heating load
Electrical load

Building load profile 1b Comparison
Cooling load Reciprocal chiller
Heating load
Electrical load

Building load profile 2a Comparison
Cooling load Grid efficiency 33%
Heating load
Electrical load

Building load profile 2b Comparison
Cooling load Grid efficiency 38%
Heating load
Electrical load

Building load profile 3a Comparison
Cooling load Electric load of 10 kW
Heating load
Electrical load

Building load profile 3b Comparison
Cooling load Electric load of 50 kW
Heating load
Electrical load

Building load profile 4a Comparison
Cooling load Electric load of 10 kW
Heating load Cooling load 10 kW
Electrical load

Building load profile 4b Comparison
Cooling load Electric load of 50 kW
Heating load Cooling load 25 kW
Electrical load

Table 2. Summary of simulation results.

 BLP 1a BLP 1b

Base electric chiller primary 61.2 (209) 62.3 (213)
 energy rate, kW (kBtu/h)
Base electricity primary energy 151.5 (517) 151.5 (517)
 rate, kW (kBtu/h)
Base boiler primary energy rate, 0 (0) 0 (0)
 kW (kBtu/h)

Base total primary energy rate, kW 212.7 (726) 213.8 (729)
 (kBtu/h)
Optimal net primary energy rate, 171 (583) 175 (597)
 kW (kBtu/h)
Optimal to base primary energy 0.803 0.819
 rate ratio
Optimal PLRCHP 1 1
Electric power sent to grid, kW 0 0
Optimal prime mover thermal 67 (229) 67 (229)
 output, kW (kBtu/h)
Optimal prime mover heating 0 (0) 0 (0)
 contribution, kW kBtu/h
Optimal prime mover cooling 67 (229) 67 (229)
 contribution, kW (kBtu/h)
Prime mover heat to heating 0 0
 load/prime mover thermal output
Heat to absorption chiller/prime 1 1
 mover thermal output
Dumped prime mover heat fraction 0 0
Absorption chiller contribution to 40 (136) 40 (136)
 cooling load, kW (kBtu/h)
Recovered heat contribution to 0 (0) 0 (0)
 heating load, kW (kBtu/h)
Prime mover heating 0 0
 contribution/heating load
Optimal hotwater boiler load, kW 0 0
Optimal electric chiller load, kW 20 20
Prime mover absorption chiller 0.67 0.67
 contribution/cooling load
Electric chiller 0.33 0.33
 contribution/cooling load
System energy utilization factor 0.72 0.71

 BLP 2a BLP 2b

Base electric chiller primary 26.8 (91) 23.2 (79)
 energy rate, kW (kBtu/h)
Base electricity primary energy 151.5 (517) 131.5 (449)
 rate, kW (kBtu/h)
Base boiler primary energy rate, 0 (0) 0 (0)
 kW (kBtu/h)
Base total primary energy rate, kW 178.3 (608) 154.8 (528)
 (kBtu/h)
Optimal net primary energy rate, 158 (539) 150 (512)
 kW (kBtu/h)
Optimal to base primary energy 0.886 0.969
 rate ratio
Optimal PLRCHP 0.65 0.4
Electric power sent to grid, kW 0 0
Optimal prime mover thermal 43 (147) 27 (92)
 output, kW (kBtu/h)
Optimal prime mover heating 0 (0) 0 (0)
 contribution, kW kBtu/h
Optimal prime mover cooling 42 (143) 27 (92)
 contribution, kW (kBtu/h)
Prime mover heat to heating 0 0
 load/prime mover thermal output
Heat to absorption chiller/prime 0.97 1
 mover thermal output
Dumped prime mover heat fraction 0.03 0
Absorption chiller contribution to 25 (85) 16 (55)
 cooling load, kW (kBtu/h)
Recovered heat contribution to 0 (0) 0 (0)
 heating load, kW (kBtu/h)
Prime mover heating 0 0
 contribution/heating load
Optimal hotwater boiler load, kW 0 0
Optimal electric chiller load, kW 0 9.4
Prime mover absorption chiller 1 0.62
 contribution/cooling load
Electric chiller 0 0.38
 contribution/cooling load
System energy utilization factor 0.60 0.54

 BLP 3a BLP 3b

Base electric chiller primary 26.8 (91) 26.8 (91)
 energy rate, kW (kBtu/h)
Base electricity primary energy 30.3 (103) 151.5 (517)
 rate, kW (kBtu/h)
Base boiler primary energy rate, 25 (85) 25 (85)
 kW (kBtu/h)
Base total primary energy rate, kW 82.1 (280) 203.3 (694)
 (kBtu/h)
Optimal net primary energy rate, 37.5 (128) 159 (543)
 kW (kBtu/h)
Optimal to base primary energy 0.457 0.782
 rate ratio
Optimal PLRCHP 1 1
Electric power sent to grid, kW 45 0
Optimal prime mover thermal 67 (229) 67 (229)
 output, kW (kBtu/h)
Optimal prime mover heating 25 (85) 25 (85)
 contribution, kW kBtu/h
Optimal prime mover cooling 42 (143) 42 (143)
 contribution, kW (kBtu/h)
Prime mover heat to heating 0.37 0.37
 load/prime mover thermal output
Heat to absorption chiller/prime 0.63 0.63
 mover thermal output
Dumped prime mover heat fraction 0 0
Absorption chiller contribution to 25 (85) 25 (85)
 cooling load, kW (kBtu/h)
Recovered heat contribution to 25 (85) 25 (85)
 heating load, kW (kBtu/h)
Prime mover heating 0.37 0.37
 contribution/heating load
Optimal hotwater boiler load, kW 0.12 0.12
Optimal electric chiller load, kW 0 0
Prime mover absorption chiller 1 1
 contribution/cooling load
Electric chiller 0 0
 contribution/cooling load
System energy utilization factor 0.85 0.71

 BLP 4a BLP 4b

Base electric chiller primary 17.9 (61) 26.8 (91)
 energy rate, kW (kBtu/h)
Base electricity primary energy 30.3 (103) 151.5 (517)
 rate, kW (kBtu/h)
Base boiler primary energy rate, 100 (341) 100 (341)
 kW (kBtu/h)
Base total primary energy rate, kW 148.2 (506) 278.3 (950)
 (kBtu/h)
Optimal net primary energy rate, 82.7 (282) 217 (740)
 kW (kBtu/h)
Optimal to base primary energy 0.558 0.780
 rate ratio
Optimal PLRCHP 1 1
Electric power sent to grid, kW 27.1 0
Optimal prime mover thermal 67 (229) 67 (229)
 output, kW (kBtu/h)
Optimal prime mover heating 67 (229) 67 (229)
 contribution, kW kBtu/h
Optimal prime mover cooling 0 (0) 0 (0)
 contribution, kW (kBtu/h)
Prime mover heat to heating 1 1
 load/prime mover thermal output
Heat to absorption chiller/prime 0 0
 mover thermal output
Dumped prime mover heat fraction 0 0
Absorption chiller contribution to 0 (0) 0 (0)
 cooling load, kW (kBtu/h)
Recovered heat contribution to 67 (229) 67 (229)
 heating load, kW (kBtu/h)
Prime mover heating 1 1
 contribution/heating load
Optimal hotwater boiler load, kW 33 33
Optimal electric chiller load, kW 10 25
Prime mover absorption chiller 0 0
 contribution/cooling load
Electric chiller 1 1
 contribution/cooling load
System energy utilization factor 0.87 0.73
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Author:Treado, Stephen; Delgoshaei, Payam; Windham, Andrew
Publication:HVAC & R Research
Date:May 1, 2011
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