J. Cent. South Univ. Technol. (2011) 18: 573-579
DOI: 10.1007/s11771-011-0733-3
Optimum control strategy for all-variable speed chiller plant
JIANG Xiao-qiang(蒋小强)1, 2, LONG Wei-ding(龙惟定)3, LI Min(李敏)1
1. College of Engineering, Guangdong Ocean University, Zhanjiang 524025, China;
2. College of Mechanical Engineering, Tongji University, Shanghai 200092, China;
3. Sino-German School of Applied Sciences, Tongji University, Shanghai 200092, China
? Central South University Press and Springer-Verlag Berlin Heidelberg 2011
Abstract: The optimum control strategy and the saving potential of all variable chiller plant under the conditions of changing building cooling load and cooling water supply temperature were investigated. Based on a simulation model of water source chiller plant established in dynamic transient simulation program (TRNSYS), the four-variable quadratic orthogonal regression experiments were carried out by taking cooling load, cooling water supply temperature, cooling water flow rate and chilled water flow rate as variables, and the fitting formulas expressing the relationships between the total energy consumption of chiller plant with the four selected parameters was obtained. With the SAS statistical software and MATHEMATICA mathematical software, the optimal chilled water flow rate and cooling water flow rate which result in the minimum total energy consumption were determined under continuously varying cooling load and cooling water supply temperature. With regard to a chiller plant serving an office building in Shanghai, the total energy consumptions under different control strategies were computed in terms of the forecasting function of cooling load and water source temperature. The results show that applying the optimal control strategy to the chiller plant can bring a saving of 23.27% in power compared with the corresponding conventional variable speed plant, indicating that the optimal control strategy can improve the energy efficiency of chiller plant.
Key words: chiller plant; control strategy; variable speed; cooling water flow rate; chilled water flow rate
1 Introduction
During the past several decades, the cost of variable speed devices has come down significantly due to the advances in technology, which allowed widespread applications of variable speed pumps in air-conditioning systems of buildings. An increased issue associated with the use of variable speed equipments is the control and optimization of their operation, for example, which device should be adjusted and how is the adjusting magnitude when the outside climate changes. It is especially the case related to all-variable chilled water plant.
Among the existing studies, HARTMAN is a pioneer who promoted all-variable speed chiller plants where all the chillers, condenser pumps and tower fans are driven by variable speed drives (VSD) [1]. He introduced the criteria for designing such plants, and recommended to select equipments of the same type in order to achieve the best overall plant performance under part load conditions. Based on his simulation analyses, the annual energy use of all-variable speed chiller plants with optimized controls would be on average 28% lower than the corresponding conventional constant speed plants with equipment of the same nominal efficiency under the design conditions. He also developed the equal marginal performance principle (EMPP) for designing efficient air-conditioning systems [2]. The EMPP involves understanding the power relationships between the system components and formulating the power based speed control algorithms to operate the variable speed equipment. YU and CHAN [3] examined how all-variable speed chiller systems with load-based speed control yield economic benefits and superior environmental performance with reduced electricity and water consumption compared with the conventional constant speed systems. Applying the load-based speed control to the variable speed chiller plant can decrease the annual total electricity use by 19.7% and annual water use by 15.9% relative to the corresponding constant speed plant. TAYLOR [4] stated that using variable speed chillers and/or variable flow, primary- only pumping systems is a viable means to eliminate significant degradation in system performance in the part load operation while accommodating the low “delta-T” syndrome of chilled water circuits. GORDON et al [5] established an analytic semi-empirical chiller model to study variations of the coefficient of performance (COP) of the chiller at different condenser water flow rates and highlighted that the condenser water flow rate could be a control variable in improving the energy performance of chiller systems.
All the past studies have brought individual contributions to promote the application of variable speed techniques in chiller system [6-12]. However, these studies either investigated variable chilled water flow rate while fixing the cooling water, or investigated the cooling water variable flow while fixing chilled water. In fact, the variable flow is always based on the constant temperature difference between the inlet and outlet of the chilled water or the cooling water, so the energy efficiency of chilled water plant may not be most efficient when using these control strategies. EMPP may be able to make the system more efficient, but it relies on a complex control system, and is not easy to be achieved. There is a lack of simple but generic approach to control all-variable speed chiller plants.
2 Formulation of optimal control strategy
In order to obtain the optimal adjustment scheme of equipment power in chiller plant under varied conditions, the optimal operating parameters must be found first. To determine the optimal operating parameters under various conditions, it is necessary to find the relationship between the total energy consumption of chiller plant with cooling load, supply cooling water temperature, cooling water flow rate and chilled water flow rate, and then obtain the optimal parameters and optimal adjustment scheme of devices.
The main parameters that influence the total power consumption of chiller plant include cooling load, chilled water flow rate, cooling water flow rate, supply cooling water temperature and supply chilled water temperature. The cooling load and supply cooling water temperature are determined by meteorological conditions and indoor loads; while the chilled water flow rate, cooling water flow rate and supply chilled water temperature can be controlled manually. Among the human controllable factors, the higher the supply chilled water temperature, the more energy-efficient the chiller plant. As to other two parameters, further analysis is essential. Therefore, this problem is summed as how to find the optimal chilled water flow rate and cooling water flow rate in all- variable chiller plant while the cooling load and supply cooling water temperature are dynamically changed.
In the following sections, a screw chiller model and a pump model were first established, and hence a chilled water plant simulation platform based on the TRNSYS (Dynamic Transient Simulation Program) software was designed. Then, taking cooling the water flow rate, chilled water flow rate as controlled variables while the cooling load and the supply cooling water temperature as uncontrolled variables, quadratic orthogonal experiments were implemented in order to find the best operating parameters. And the total energy consumptions of chilled water plant were compared under three difference control strategies.
3 Mathematical model
3.1 Screw-type chiller model
Taking into account that the screw chillers have better variable frequency performance than the centrifugal chillers, a screw-type chiller with shell and tube water cooling condenser and flooded evaporator is considered in this study. And the refrigerant is R134a [15].
3.1.1 Governing equation of compressor
The indicated work of screw compressor is given by
(1)
The condensing pressure and the evaporating pressure of refrigerant are given by
,
(2)
The mass flow rate of the refrigerant through the compressor is
(3)
The enthalpies at evaporator outlet and condenser outlet are
(4)
(5)
where Wi is the indicated work of screw compressor, W; n is the polytropic exponent; pcd and pev are the condensing pressure and evaporating pressure of refrigeration, respectively; pi is the suction pressure, Pa; Vin is the specific volume at compressor inlet, m3/kg; Vi is the specific volume just after complete compression, m3/kg; acl and bcl are the first and second coefficients in the Clausius-Clapeyron equation, respectively; mr,com is the mass flow rate of the refrigerant, kg/s; Qev is the cooling capacity, W; h1 and h3 are the enthalpies at evaporator outlet and condenser outlet, respectively, J/kg; hfgb is the vaporization enthalpy at standard boiling point, J/kg; hf0 is the enthalpy of saturated liquid at the reference temperature, J/kg; Cplip is the mean specific heat of refrigerant at saturated liquid state, J/(kg?K); Tc, Tb, T0, Tcd and Tev are the critical temperature, standard boiling temperature, reference temperature, condensing temperature and evaporating temperature, respectively, K.
Then, the compressor power input, Wcom, can be expressed by
(6)
where L1 and L2 are the loss coefficients of chiller power, and Wrated is the rated power of chiller, W.
3.1.2 Governing equation of evaporator
(7)
(8)
(9)
where 
is the mass flow rate of evaporator water, kg/s; Tw,ev,in and Tw,ev,out are the chilled water temperatures at inlet and outlet of the evaporator, respectively, K; ?Tev is the logarithmic mean temperature difference of evaporator, K; kev is the heat transfer coefficient of the evaporator, W/K; fev is the area of evaporator, m3; Cw is the specific heat capacity of water, J/(kg?K); C1 and C2 are the coefficients of polynomial.
3.1.3 Governing equation of condenser
(10)
(11)
(12)
where Qcd is the heat released from the condenser, W; 
is the mass flow rate of condenser water, kg/s; Tw,cd,in and Tw,cd,out are the cooling water temperatures at inlet and outlet of the condenser, respectively, K; ?Tcd is the logarithmic mean temperature difference of condenser, K; kcd is the heat transfer coefficient of the condenser, W/K; fcd is the area of condenser, m3; C3 and C4 are the coefficients of polynomial.
3.2 Pump model
For variable speed pumps, the equipment efficiency, namely wire-to-water efficiency, is often used to characterize how much energy applied to a pump-motor- VFD set results in useful energy to deliver the water. A typical pump-motor-VFD set consists of three sub- efficiencies, including the pump efficiency (ηpu), motor efficiency (ηm) and VFD efficiency (ηVFD). These three sub-efficiencies should be involved in the model of variable speed pump [7].
In this study, the performance of variable speed pumps was modeled using a series of polynomial approximations [8-9]. They are comprised of polynomials representing head versus flow and speed, and efficiency versus flow and speed. The head and efficiency characteristics are based on the manufacturers’ data at the full speed operation and extended to the variable speed operation using the pump affinity laws. The motor efficiency (ηm) is modeled using Eq.(13), which is a function of the fraction of the nameplate brake horsepower. And VFD efficiency is modeled using Eq.(14), which is a function of the fraction of the nominal speed [7]. The power input to a pump-motor- VFD set is computed using Eq.(15). The coefficients in these polynomials can be regressed using the pump performance data or performance curves, the motor efficiency curve and VFD efficiency curve provided by the manufacturers:
(13)
ηVFD=D0+D1n+D2n2+D3n3 (14)
(15)
where H is the pump head, m; η is the efficiency; g is the specific gravity of the fluid being pumped, N/kg; n is the fraction of the nameplate brake horsepower or the nominal speed; c5, c6, D0, D2 and D3 are coefficients, and subscripts “m”, “v” and “in” represent motor, VFD and input, respectively. For constant speed pumps, the power is constant.
3.3 Simulation platform of chiller plant
The cooling load profile of a reference office building was considered. Given that the peak load of the building is 1 400 kW, the chiller plant is composed of a screw chiller with a nominal cooling capacity of 1 406.8 kW (the nominal power is 254.2 kW), a cooling water pump with a nominal power of 28.5 kW, head of 30 m and the max flow rate of 80 kg/s, and a chilled water pump with a nominal power of 33 kW, a head of 42 m, and the max flow rate of 67 kg/s.
4 Results and discussion
4.1 Experimental scheme design
Taking into account of the actual variation range of the operating parameters and their influence on the energy efficiency of chiller plant, the following values of the four selected parameters are considered, as shown in Table 1.
According to the cooling load, supply cooling water temperature, cooling water flow rate, chilled water flow rate listed in Table 1 and orthogonal experiments design theory, an orthogonal experimental scheme is designed, as shown in Table 2. The simulation results from from TRNSYS platform are also shown in Table 2.
Table 1 Factors and levels of four-variable quadratic orthogonal experiment design
Table 2 Scheme and results of four-variable quadratic orthogonal experiments
Employing the SAS software to do regression analysis to the results listed in Table 2, the empirical equation (after excluding non-significant factor) relating the total power to the cooling load, cooling water supply temperature, cooling water flow rate and chilled water flow rate is obtained:
(16)
The variance, R, of Eq.(16) is 0.998 2 and F-test result for the regression model is
(17)
The regression model is significant, indicating that the fitting expression (Eq.(16)) is reliable. Therefore, Eq.(16) can be employed to do quantitative analysis between the total energy consumption and the four operating parameters.
4.2 Determination of optimal chilled water flow rate and cooling water flow rate
As to a moment, the cooling load and cooling water supply temperature could be forecasted. In order to obtain the optimal chilled water flow rate and cooling water flow rate at the moment, a data processing was done to Eq.(16). According to mathematics knowledge, the function obtains the extreme value for the variable cooling water flow rate and chilled water flow rate when the corresponding first-order partial derivatives equal zero, namely,
(18)
Apparently,
So Eq.(16) has a minimum value. By solving Eq.(18), the optimal values of chilled water flow rate and cooling water flow rate can be obtained:
(19)
Therefore, once the cooling load and cooling water supply temperature are known, the values of the optimal chilled water flow rate and cooling water flow rate can be calculated by Eq.(19).
4.3 Saving potential of new control strategy
In order to investigate the saving potential of the chilled water flow rate and cooling water flow rate determined by the optimal variable flow control strategy and four-variable quadratic orthogonal experiment, with regard to a chiller plant serving an office building, a chiller plant model was developed to perform the power consumption assessment under different control strategies such as constant speed control, conventional variable speed control with different variable flow rates and constant temperatures, optimal control strategy with variable flow rate and variable temperature.
4.3.1 Cooling load model
According to the actual cooling load of a building in Shanghai, a calculation model was established to forecast the annual energy consumption of chiller plant based on the simulation:
(20)
In Eq.(20), the weekday (D) is 1 when the day is work day, otherwise it is 0. Time (t) is the work time, ranging from 1 to 8 760 h, T is the dry bulb temperature of outside air.
Fig.1 shows the measured cooling load and the cooling load calculated by Eq.(20). Good agreement is obtained except for some peak or valley points of load.
Fig.1 Comparison between simulated and experimental data of cooling load
4.3.2 Calculation model of supply cooling water temperature
According to the variation characteristic of air temperature in Shanghai and water temperature of the Huangpu River, the water temperature can be obtained through regression analysis as [16]
(21)
where the R-value of Eq.(21) is 0.983.
4.3.3 Annual energy consumption
Controlling the chiller plant with optimal variable flow control strategy, three simulation platforms based on the TRNSYS were established (as shown in Fig.2). The hourly building cooling load and cooling water inlet temperatures during the cooling period from May 1st to Oct. 31st can be calculated via Eqs.(18) and (19), and then the cooling water flow rate and chilled water flow rate can be calculated via Eq.(17), and finally the annual energy consumption with the optimal variable flow control strategy can be obtained.
Fig.2 Simulation platform of chiller plant under optimal control strategy
The total annual energy consumption with the optimal control strategy is 5.992×105 kW?h. Using the same method, the annual energy consumption of constant flow system is 7.512×105 kW?h. And the simulation result is 6.246×105 kW?h for conventional variable flow with constant temperature difference. Comparison of annual energy consumptions under different control strategies is listed in Table 3.
Table 3 Comparison of chiller plant energy consumption under different control strategies
Clearly, the optimized variable flow control strategy can significantly reduce the total annual energy consumption of chiller plant. It is also suggested that applying orthogonal experiments to determine the operation characteristics of chiller plant and optimal operation parameters is reliable.
5 Conclusions
1) With orthogonal experiments, the relationship between the total energy consumption of chiller plant and cooling load, cooling water supply temperature, cooling water flow rate and chilled water flow rate could be established. Through data processing, the optimal chilled water flow rate and cooling water flow rate which result in the minimum total energy consumption can be obtained. And then the equipment power adjustment schemes could be given according to the optimal flow rate.
2) By comparing the total annual energy consumptions of chiller plant under three different control strategies: the optimal variable flow, conventional variable flow, constant flow, the optimal control strategy can save 7.72% relative to conventional variable flow, while could save 23.27% relative to constant flow system. The result shows that the optimal control strategy can effectively reduce the total energy consumption of chiller plant.
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(Edited by YANG Bing)
Foundation item: Project(G-0805-10156) supported by US Energy Foundation
Received date: 2009-12-14; Accepted date: 2010-10-22
Corresponding author: JIANG Xiao-qiang, PhD Candidate, Tel: +86-13553451730; E-mail: jxqiang2007@163.com
