1、Extremum Seeking Controls for Efficient Operation of Multi-functional Variable Refrigerant Flow System Liujia Dong Yaoyu Li Timothy I. Salsbury ASHRAE member ASHRAE member John M. House Zhigang Wu Li Wang ASHRAE member ABSTRACT This paper proposes extremum seeking control (ESC) schemes for Multi-fun
2、ctional Variable Refrigerant Flow (MFVRF) system under different operational modes, in order to maximize the efficiency provided the satisfaction of thermal comfort. Extremum seeking control is a model-free control method, which can search for unknown and time-varying optimum input(s) that can optim
3、ize a given performance index without the need for plant model. There are five operational modes considered in this study, including Cooling Only, Heating Only, Cooling Dominated, Heating Dominated, and Heat Recovery mode. For all cases, the zone temperature setpoint is achieved by controlling the r
4、espective IDU fan speed, and the feedback required is the total power consumption of the compressor motor, ODU condenser fan and IDU evaporator fans. For different operational modes, the ESC inputs are chosen to be different combinations of compressor suction pressure setpoint, ODU fan speed, bypass
5、 flow valve opening, superheat setpoints for IDUs and ODU. To evaluate the proposed control strategy, a Modelica based dynamic simulation model is developed for the multi-functional VRF system considered. Simulation results demonstrate the capability for the ESC to achieve the optimal operation in m
6、odel-free fashion, as well as the potential for energy saving. INTRODUCTION The variable refrigerant flow (VRF) air conditioning systems feature multi-split ductless configurations using one outdoor unit (ODU) and multiple indoor units (IDU) (Park. et.al, 2001). The VRF systems are capable of contro
7、lling the refrigerant flow to the multiple evaporators of IDUs, by use of variable capacity compressor and electronic expansion valve (EEV), thus enabling different capacities of individual IDUs. VRF systems offer many advantages, such as elimination of duct loss of air distribution, design and inst
8、allation flexibility, compactness, integrated controls, quiet operation and reduced maintenance cost (Aynur. 2010). The VRF system can be configured to provide simultaneous heating and cooling operation for different zones via the so-called mode change unit (MCU) which is effectively a valve array t
9、hat regulates the refrigerant flows through the IDUs (Goetzler. 2007, Xia. et. al, 2002, Masuda. 1991) to achieve five possible operation modes: i) cooling-only; ii) heating-only; iii) cooling-dominated; iv) heating-dominated; and v) heat recovery (Hai. et. al. 2006, Shi. et. al. 2003, Xia. et. al.
10、2004). The multi-split nature and flexibility in configuration make the VRF systems more challenging for controls. Masuda et al. (1991) present a control method for a multi-split VRF system with two IDUs. Xia et al. (2002) applied a testing methodology to a VRF system of five IDUs with cooling only
11、mode. Choi and Kim (2003) investigate the performance of a multi-split VRF system with two IDUs. Hu and Yang (2005) developed a cost effective, energy efficient, five-IDU VRF system with a variable refrigerant volume scroll compressor instead of inverter aided compressor. Hai et al. (2006) conduct a
12、 performance study for a five-IDU three-pipe VRF. Aynur et al. (2006) present a field study on both individual and master control methods for a multi-split VRF system in an actual building to evaluate performance characteristics. Joo et al. (2011) study the performance characteristics of a simultane
13、ous cooling 2016 ASHRAE Winter ConferencePapers 1OR-16-C064and heating multi-heat pump with four IDUs at partial load conditions. Park et al. (2001) study the performance dependency of a two-IDU VRF system on the compressor frequency, total cooling load, and the cooling load fraction between two zon
14、es. Shi et al. (2003) developed a fluid network model to simulate the performance of three-pipe VRF with two IDUs. Xia et al. (2003) study the operating characteristics of a three-IDU VRF, and especially the coupled interactions of cooling capacity among the IDUs. Zhou et al. (2008) show that the CO
15、P of VRV system increases under part load conditions due to the high part load efficiency. Wu et al. (2005) present experimental study for a self-tuning fuzzy control strategy, for which the compressor speed and the EEV opening are used to regulate the suction pressure of the compressor and the room
16、 temperature, respectively. Compared with the experimental results by Zhou et al. (2008), the VRFs saved more than 20% energy compared to a variable air volume system and more than 10 % compared to a fan-coil plus fresh air system. Lin and Yeh (2007) study a feedback controller design for a three-ev
17、aporator air conditioning system with experimental validation. Elliott et al. (2013) presents a decentralized model predictive control (DMPC) for a multi-evaporator HVAC system. The compressor controls the discharge pressure of the first evaporator, and a discharge valve on the secondary evaporator
18、controls its pressure. The pressure and cooling setpoints are optimized by a DMPC that minimizes tracking error and energy consumption. Jain et al. (2014) present a partially decentralized control architecture for large-scale VRF systems. The first-principle models are developed, and one-way communi
19、cation is assumed from the individual decentralized controllers to a global controller. A linear quadratic (LQ) controller framework is applied. As controls of VRF system is challenged by large variation of ambient and load conditions, complexity in the inherent physical process, and loop interactio
20、ns among multiple subsystems especially due to the large number of IDUs. Therefore, it would be tedious and expensive to obtain plant models required by the aforementioned model based optimization and control techniques. An alternative approach is to develop model-free optimization and control metho
21、ds. As a nearly model-free approach for real-time setpoint optimization, extremum seeking control (ESC) has drawn significant attention (Ariyur. et. al, 2003). ESC applications to air-side economizer (Li. et. al, 2010) and chiller-tower plant (Li. et. al, 2013) has achieved interesting success. Rece
22、nt efforts on air-source heat pump (Li. et. al 2010, Xiao. et. al. 2014, Dong. et. al. 2015) have observed application to ASHP including condenser and evaporator fan speeds and superheat setpoint as the inputs. Jain et al. (2014) presents a hybrid control scheme for VRF system, combining an outer-lo
23、op ESC with model predictive control (MPC). Koeln and Alleyne (2014) present an optimal subcooling in vapor compression systems via extremum seeking control. Based on the success observed in the single-split ductless systems, this study aims to investigate the applicability of ESC to multi-split mul
24、ti-functional VRF systems. The aforementioned five operational modes are all considered. The ESC controllers are designed to maximize the system efficiency provided the thermal comfort is satisfied. For different operational modes, the sensitivity of different control inputs is considered, and thus
25、different sets of inputs are used for different operational modes. To evaluate the proposed control strategies, a Modelica based dynamics simulation model is developed for the multi-functional VRF system using Dymola (Dassault Systems, 2015) and TIL Library (Rochter. 2008, TLK-Thermo, 2014). The res
26、t of the paper is organized as follows. Section 2 describes the Modelica based dynamics simulation model of VRF system. Section 3 presents the overview of multivariable ESC. The ESC controllers for different VRF modes are presented in Section 4. The multi-variable ESC for VRFs design are described i
27、n Section 5. Section 6 shows the simulation results. Section 5 concludes this paper and discusses on possible future work. MODELICA BASED DYNAMIC SIMULATION MODEL OF VRF SYSTEM Fig. 1 shows the schematic diagram of the multi-functional VRF system considered for the simulation study. The system consi
28、sts of one ODU, one MCU and four IDUs. The ODU includes a variable speed compressor, a bypass valve (BPV), a heat exchanger (HX), an EEV (EEVO), and mode-control solenoid valves (COL, COR and HO). The inlet of BPV is connected to the compressor, and the two outlets of BPV are connected to COL and th
29、e heating-mode valves in MCU respectively. The BPV can distribute the refrigerant flow to the two branches by regulating the valve opening. When the ODU HX is operated as condenser (under higher cooling demand), valves COL and COR are opened while HO and EEVo are closed. The BPV is fully opened to t
30、he COL side when all IDUs are operated in the cooling mode. With one IDU or more working in the heating mode, the refrigerant flow out of the compressor is split 2016 ASHRAE Winter ConferencePapers 2by BPV: one goes to COL and other one to the heating IDU(s). When the ODU HX works as evaporator (und
31、er higher heating demand), HO and EEVo are opened while COL and COR are closed. The BPV is fully opened to the heating-mode valves in the MCU. The MCU consists of pairs of mutually exclusive solenoid valves (HMk and CMk, k = 1, 2, 3, 4), and each pair is connected to IDU-k. MCU can regulate the refr
32、igerant flow direction for each IDU to realize cooling or heating mode. The IDU each includes one HX, one EEV (EEVIk) and one heating-mode solenoid valve (HIk). Thermal model of an IDU is controlled by valve actions in both MCU and IDU. For IDU-k to work in the cooling mode, CMk and EEVIk are opened
33、 while HMk and HIk are closed; for IDU-k to work in the heating mode, CMk and EEVIk are closed while HMk and HIk are opened. For the four-zone scenario in this study, the five operation modes are denoted as as follows: 4C - all four IDUs in cooling mode, 1H3C - one IDU in heating mode and the other
34、three IDUs in the cooling mode, 2H2C - two IDUs in heating mode and the other two in cooling mode, 3H1C - one IDU in cooling mode and the other three in heating mode; 4H: all four IDUs in heating mode. Figure 1. Schematic diagram of a multi-functional VRF system. Three inner loop controls are applie
35、d to the VRF system. For each zone, the zone temperature is regulated by the mass flow rate of its IDU fan with a PI controller. For HXs working as evaporator, either for IDU or ODU, the superheat temperature is regulated by EEV opening with PI controller. When cooling demand dominates (i.e. for 4C,
36、 1H3C, and some 2H2C scenarios), the compressor suction pressure (PCS) is regulated by the compressor speed with a PI controller. When the heating demands dominates (i.e. 4H, 3H1C and some 2H2C scenarios), the compressor discharge pressure (PCD) is regulated by the compressor speed with another PI c
37、ontroller. To evaluate the proposed control strategy, a Modelica based dynamic simulation model is developed for the VRF system in Fig. 1, using Dymola 2014, TIL Library 3.2 and TIL Media Library 3.2. OVERVIEW OF MULTIVARIABLE EXTREMUM SEEKING CONTROL ESC is a class of model free adaptive control al
38、gorithms, which aim to search for the optimizing input uopt(t) for the generally unknown time-varying cost function l(t, u), where u(t) m is the input parameter vector. As shown in Fig. 2, the measurement of cost function l(t, u), denoted by y(t), is corrupted by noise n(t). The transfer function FI
39、(s) indicates the linear time-invariant approximation of input dynamics. FO(s) denotes the linear time-invariant approximation of output dynamics. The dither and demodulation signals are 1 1 1( ) s in ( ) s in ( )T mmd t a t a tand 2 1 1( ) s i n ( ) s i n ( ) T mmd t t t, respectively, where i are
40、the dithering frequencies for each input parameter channel, ai are the the dither amplitudes, and i are the phase angles introduced intentionally between the respectively dither and demodulation signals. Due to the small-amplitude nature of dither input, the perturbed output, based on 2016 ASHRAE Wi
41、nter ConferencePapers 3Taylor series expansion, contains the gradient information in the first-harmonics term. After filtering the DC component of the dithered output by the anti-notch filter FAN(s), the resultant signal is multiplied (demodulated) by Td2 , which shifts the gradient term to the DC t
42、erm. Applying the low-pass filter FLP(s) will produce a vector-valued signal proportional to the gradient of the cost function at the input of the multivariable integrator. In this study, the multi-variable ESC design follows the guidelines provided in (Rotea. 2000, Krstic. 2000). Figure 2. Block di
43、agram of multi-variable ESC based on dither-demodulation scheme. MULTIVARIABLE ESC CONTROLS FOR MULTI-FUNCTIONAL VRF SYSTEM A multi-variable ESC scheme is proposed as a modelfree solution to optimize the energy efficiency of the multi-functional VRF system under different operational modes, as shown
44、 in Fig. 3. The total power is used as the feedback for ESC, which is the power consumption of the IDU fans, the ODU fan and the compressor. The candidate inputs for ESC include: the compressor suction pressure (PCS) setpoint, the compressor discharge pressure (PCD) setpoint, the evaporator superhea
45、t (SH) temperature setpoint of each IDU when working in the cooling-operation units, the ODU fan mass flow rate, and the bypass valve opening. Table 1. Potential Reduction in Total Power for Individual Inputs of VRF System. Mode 4C 1H3C 2H2C 3H1C 4H Cooling-operation SH 4.13 % 7.42 % 4.72 % 4.11 % 3
46、.16 % PCS/PDS 9.21 % 12.77 % 9.72 % 8.86 % 8.78 % ODU Fan Mass Flow Rate 2.19 % 2.01 % 6.51 % 4.36 % 3.2 % Bypass Valve Opening N/A* 18.31 % 2.24 % N/A N/A For different operation modes, the ESC inputs are selected based on their impact on the possible change of the total power. In the static map te
47、st, all cooling IDU SH value changes from 2oC to 7oC (275.15K to 280.15K). The compressor suction pressure, for 4C, 1H3C and 2H2C modes, varies from 9.5 bar to 12.5 bar (137.79psi to 181.30 psi). The compressor discharge pressure, for 3H1C and 4H modes, varies from 23.5 bar to 26 bar (340.75psi to 3
48、77psi). The range of ODU fan mass flow rate is 0.4 kg/s to 1.0 kg/s (3174.65pph to 7936.64pph). The BPV opening changes from 20% to 80%. Assuming that ESC can locate the optimum operation, Table 1 summarizes the maximum percentage reduction of the total power for each input channel within the given
49、operational ranges. Table 2 shows the ESC input selection for different operation modes. Table 2. ESC Input Selection for Five Operation Modes of VRF System. Mode 4C 1H3C 2H2C 3H1C 4H Cooling-operation SH channel PCS/PDS channel ODU fan mass flow rate channel sKsKn1)()(1sFsFnII2016 ASHRAE Winter ConferencePapers 4Bypass Valve opening channel Figure 3. Schematic of multi-input ESC for VRF system. SIMULATION OF MULTIVARIABLE ESC FOR VRF SYSTEM The ESC controllers are design each VRF
