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Article Excerpt
INTRODUCTION
Significant improvements to cooling system efficiency can be achieved by integrating what we will refer to as the low-lift cooling technologies: 1) variable-speed compressor and transport motor controls, 2) radiant cooling with dedicated ventilation air dehumidification and distribution, and 3) cool storage. The energy requirements of all combinations of presence or absence of the foregoing three low-lift elements (Cases 1-8) are presented in a companion paper (Armstrong et al. 2009). This paper describes the component and subsystem models needed to estimate cooling system performance of the eight cooling system configurations over a wide range of balance-of-plant performance (standard- (1), mid-, and high-performance buildings) and a wide range of climate conditions.
The paper begins with an assessment of simulation requirements. Compressor, condenser, and evaporator component models are developed. Transport energy models are also developed for the condenser air side and the chilled-water loop. A special model is developed to represent a radiant ceiling panel array, the evaporator, and the chilled-water loop as a single subsystem. An idealized storage model that reduces computational effort and broadly addresses the potential energy saving role of thermal energy storage (TES) is described. Chiller and dedicated outdoor air system (DOAS) subsystem models and methods of simultaneously solving the component states and control actions needed to satisfy loads under any given condition with minimal input energy are presented. The method of representing a subsystem's performance map by one or more biquadratic or bicubic functions is described, and the role of the performance map within the peak-shifting optimal control algorithm is documented. Two-speed chiller performance is estimated by computing duty fraction after evaluating the bicubic at half- and full-capacity operating points. The paper concludes with a summary of the modeling process and some remarks about variable-speed chiller system performance. The main contribution of this work is the simultaneous optimization of chiller and distribution system operation over a wide range of lift and capacity fraction using a new semi-empirical positive-displacement compressor model and first-principles models of most of the other components.
SIMULATION REQUIREMENTS
To estimate annual energy consumption of a building that uses the baseline HVAC (1) configuration, the full low-lift system configuration, or some partial low-lift configuration, an appropriate simulation framework and accurate component or subsystem models are needed. Several issues must be addressed to obtain meaningful estimates of energy savings:
* supervisory control of chiller capacity and thermal energy storage must be near optimal
* compressor speed, distribution, and heat rejection flow rates must be controlled so as to maximize COP (2) over the entire domain of cooling load and outdoor condition
* HVAC configuration models (Cases 1-8) must provide for fair performance comparisons
* for each HVAC configuration, the corresponding chiller model must be consistent over wide ranges of capacity fraction and conditions
The computational burden of chiller dispatch with a 24-hour look-ahead controller is central to the formulation of subsystem and component models. Optimal control of thermal energy storage is a multidimensional, nonlinear search problem. It is solved by evaluating equipment performance and storage inventory many times in the search for a least-cost dispatch sequence over a specified control horizon. The choice of search technique may substantially affect computation time but even the best technique will suffer if the embedded performance models are not sufficiently accurate and efficient.
The control of variable-speed fans, pumps, and compressors presents another search problem. In contrast to the chiller-storage scheduling problem, an off-line optimization process may be used, and the resulting optimally controlled chiller or HVAC subsystem may be represented in the main simulation by a function that maps optimal performance over conditions and loads.
The models used to simulate the components of the eight HVAC configurations (cooling and associated transport equipment) must be comparable in an engineering sense. To satisfy this requirement, identical component models are used for fans, pumps, compressors, condensers, and evaporators that are common to the eight HVAC configurations. Also, the same component models, with appropriate adjustment of parameters, are used for chiller, refrigerant-side economizer, and dehumidification equipment.
The accuracy of component and subsystem models over all possible conditions and capacity fractions is another requirement. Many simulation programs treat solar radiation, envelope components and their integration, and schedules pertaining to occupancy, thermostat set points, internal gains and equipment operation in great detail while relying on manufacturer performance curves for HVAC equipment models. Performance data for chillers and compressors, fans, pumps, and heat exchangers are typically limited to the operating regions of most concern to designers: that is, the regions of moderate to heavy load and extreme conditions. For reliable performance assessment over a wide range of lift and capacity fraction, models based entirely on first principles, or models that reflect the basic physics with parameters inferred from credible published data, are developed. Refrigerant properties must also be accurately represented so that the comparison of two systems with distinctly different dominant regions of operation is not biased.
The chiller and dehumidifier components modeled in the analysis are vapor-compression machines for which refrigerant properties must be evaluated accurately over a wide range of conditions.
In summary, to satisfy the foregoing simulation requirements, performance map models or mathematical models of the key components--chiller, DOAS, and radiant panels--have been developed over the widest possible range of conditions and load using detailed models. The chiller and storage dispatch optimization has been programmed to use building load sequences generated by the DOE-2.2 (Jacobs 2002) simulation program as input. Details of the component models are presented in the next several sections, and model integration and application are summarized in the concluding section.
THERMAL ENERGY STORAGE AND PEAK SHIFTING
Low-lift cooling will be attractive primarily to designers of high-performance buildings in which cooling loads (except for the metabolic component) will be half or less of those experienced in buildings built to current standards (ASHRAE 2004). For the purpose of assessing low-lift energy savings, we assume that the existing building mass is capable of absorbing the design-day cooling load with small room temperature excursions. In cases where balance-of-plant performance does not satisfy this assumption, a designer can compensate by installing phase-change material (PCM) or additional interior mass, or by further reducing the design-day heat gains. Having achieved the necessary intrinsic TES by one or a combination of these efforts, we postulate that the storage process can be modeled adequately for scoping purposes by a very simple algorithm with the following properties:
* thermal storage carryover is limited to one day
* effect on daily load of small changes in average room temperature is negligible
* effect on chiller performance of small changes in room temperature is negligible
* storage losses are negligible
The foregoing properties result in an idealized TES that is practical and realistic in size but optimistic in efficiency. Some implementations that approach the postulated ideal TES are 1) a TES that uses a substantial mass and surface area of distributed PCM, 2) a discrete PCM storage with very low thermal and transport losses, 3) a well-stratified water storage system with very low thermal and transport losses, and 4) heavy constructions with decks exposed on both sides, double wallboard partitions, and high-performance envelope. Use of an idealized TES results in a simple statement of the optimal supervisory control problem as developed below.
The peak-shifting controller must find the time-shifted cooling load trajectory that minimizes input energy, given a building cooling load trajectory and the performance characteristics of a chiller and associated mechanical (transport) equipment. It is assumed that the 24-hour cooling load can be forecast with perfect accuracy (Henze and Krarti 1999). The situation is further simplified by using energy, not energy cost, as the objective function. This approach is generally most sensitive to equipment part-load performance. Given a reliable and complete chiller performance map, the sequence of 24 hourly chiller cooling rates Q(t) is sought, which minimizes daily chiller input energy given by the following objective function:
Minimize J = [24.summation over (t = 1)][Q(t)/COP(t)] (1)
subject to just satisfying the daily load requirement
[24.summation over (t = 1)][Q.sub.Load](t) = [24.summation over (t = 1)]Q(t)
and to the capacity constraints
0[less than or equal to]Q(t)[less than or equal to][Q.sub.Cap]([T.sub.x](t),[T.sub.z](t)) t = 1:24
where
COP = f([T.sub.x], [T.sub.z], Q) = chiller coefficient of performance (k[W.sub.th]/k[W.sub.e])
[T.sub.x] = outdoor dry- or wet-bulb temperature
[T.sub.z] = cooling load source temperature--e.g., zone temperature
Q = evaporator heat rate--positive for cooling (Btu/h, ton, or k[W.sub.th])
[Q.sub.Load] = building cooling load with no peak-shifting
[Q.sub.Cap] = f([T.sub.x], [T.sub.z]) = chiller cooling capacity at full speed operation
The Q(t) constraint describes dispatch vector upper and lower bounds in just the form needed to cast the problem as a bounded, but otherwise unconstrained, search--which is advantageous in terms of reliable convergence and computational efficiency. Note that the idealized TES model involves no interaction between hourly cooling rate and indoor temperature; the indoor temperature trajectory for the TES cases is assumed to be the same as that for the baseline (no TES) case.
The vector of uniform hourly average cooling rates based on the total daily load works well as an initial search point:
Q[(t).sub.Initial] = [1/24][24.summation over (t = 1)][Q.sub.Load](t) (2)
Given a building's hour-by-hour cooling load trajectory, the outdoor dry-bulb (3) temperature trajectory and a room temperature setpoint schedule, the optimization can be run throughout the whole year in 365 one-day blocks to find the hourly chiller cooling rates (the so-called peak-shifted load trajectory), which minimizes HVAC input energy for the year.
The large number of function calls during the search for a solution to each of the 365 24-hour control horizons makes the peak shifting control problem a computationally intensive one. It is critical that the chiller efficiency function evaluate in an accurate, yet computationally efficient manner. Performing a search for the optimum compressor, condenser fan, and chilled-water pump speeds at each chiller operating point in the 24-hour search process is out of the question.
Therefore, the chiller optimization is performed once at each point on a predefined grid of operating conditions, and a response surface is fitted, represented by a function that can be evaluated in just a few floating-point operations, to the resulting performance grid. The chiller component models are described next, followed by a description of the formulation for optimal chiller operation, and, finally, by a description of the performance functions fit to optimal solution points on a predefined chiller performance grid.
CHILLER COMPONENT MODELS
Each chiller component is represented by a model. The component models that are formulated in a manner familiar to most readers (i.e., condenser, simple evaporator, fan, and pump) are briefly documented. Component models that depart, such as the compressor (whose model must return mass flow and input power over a wide range of pressure ratio and shaft speed for the low-lift application) are presented in greater detail.
Subsystem models are then developed. The chiller and radiant cooling subsystem (RCS) are modeled together as a single system responding to indoor and outdoor conditions and imposed cooling load with input power being the response of interest. Solution methods that determine the minimum system power required to satisfy a given cooling load for any given indoor and outdoor temperature are documented for the main chiller in compressor mode and in free cooling mode. The chiller with all-air distribution (4) uses a similar model and identical components, except that distribution goes only as far as the chilled-water loop. The main internal variables for all three of these subsystems (chiller-variable air volume [VAV], chiller-RCS, and chiller-RCS in free-cooling mode) are pump, fan, and compressor motor speeds, condenser and evaporator refrigerant saturation temperatures, and the fraction of the condenser devoted to de-superheating. The coefficients and a goodness-of-fit metric of the bicubic performance map used to represent each chiller system (chiller-RCS, chiller-RCS in free-cooling mode, chiller-VAV) are presented.
For the DOAS dehumidifier, the evaporator saturation temperature is determined by a separate model. Given evaporating temperature and condenser air-side flow rates, the compressor input power is then determined by a subsystem model that solves for condenser saturation temperature and compressor speed. The DOAS dehumidifier model does not require a performance map.
Compressor
The compressor model returns refrigerant flow rate and input power given shaft speed, inlet temperature, and inlet and outlet pressures. For this project, a model was developed based on data generated by a publicly available (5) sizing tool, in which is embedded a proprietary compressor model. A dataset was generated by this tool for shaft speeds of 900, 1100, 1300, 1525, and 1750 rpm; condensing temperatures of 80[degrees]F, 90[degrees]F, 100[degrees]F, 110[degrees]F, and 130[degrees]F (26.67[degrees]C, 32.22[degrees]C, 37.78[degrees]C, 43.33[degrees]C, and 54.44[degrees]C); evaporating temperatures of 30[degrees]F, 35[degrees]F, 40[degrees]F, 45[degrees]F, and 50[degrees]F (-1.11[degrees]C, 1.67[degrees]C, 4.44[degrees]C, 7.22[degrees]C, and 10.0[degrees]C); and evaporator superheat...
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