1、2011 ASHRAE 925ABSTRACTUnder a real-time pricing rate structure, the focus of oper-ating a chilled-water storage system is to determine the opti-mal starting and ending time of charging and discharging thetank. This paper proposes a simple method to determine theoptimal operation. The chiller plant
2、performance is simulatedwith a forward model based on wire-to-water efficiency toreflect the performance change with different chiller part-loadratios. The tank state is described with chilled-water volume,and the tank inventory change is described with tank chilled-water flow rate to ensure consist
3、ence in the whole cycle. Theelectricity price is simulated with an existing prediction model.The loop chilled-water delta-T is modeled with a linear regres-sion model. This method is evaluated with an illustrativechilled-water storage system. Simulation results show that,compared to the operation co
4、sts without storage, the annualelectric billing costs with the optimal tank operation can bereduced by almost one-third, the majority of which is achievedin summer. A near-optimal operation strategy is proposed byimplementing the constant starting and ending time of charg-ing and discharging cycles.
5、 The statistic results show that theannual billing cost savings only decrease by 2.2%. INTRODUCTIONThermal energy storage (TES) is a concept of generatingand storing energy in the form of heat or cold for future use.This concept has been used for centuries, but only recentlyhave large electrical use
6、rs taken advantage of this techniquefor demand-side management and cost reduction. Most TESsystems can be classified as ice storage and water storage. Theprimary objective of this paper is to develop a simple methodto find optimal operation of a chilled-water storage systemwith a real-time-pricing (
7、RTP) utility rate structure.The electricity rate is the main driving force and theeconomic incentive for the application of a TES system. Witha RTP rate, a meter is installed to record a customers electric-ity consumption at hourly (or subhourly) intervals, and a pric-ing system based on the wholesa
8、le cost of electricity duringthat hour is provided to its customer about 24 hours in advance.Consumers could obtain the maximum financial benefit possi-ble under this system by shifting consumption from hours withhigh wholesale prices to hours with low wholesale prices(Jiang 2005). Less than 50 elec
9、tric utilities that offer or willoffer this rate structure have been identified in a field survey,and these utilities predominantly service coastal areas and theSouth (Henze 2003). Sun et al. (2006) generated a RTP ratemodel that produced a time-varying price for the costs of elec-tricity that depen
10、ded on time of day and maximum tempera-ture for the day. The effect of the uncertainty of weatherprediction and the RTP model on the optimization resultsdeserves serious attention.Most research on thermal storage systems is related to anice storage system operated with conventional time-of-useutilit
11、y rates (Braun 1992; Krarti et al. 1995; Drees and Braun1996; Henze et al. 1997b) or RTP rates (Henze et al. 1997a).Dynamic programming is used to find the optimal controltrajectory. The optimization results were used to develop rule-based strategies. Braun (2007) developed a near-optimalcontrol met
12、hod for an ice storage system with RTP electricrates. It is an extension of methods developed and evaluated byDrees and Braun (1996). The simplified method worked wellin all cases and gave annual costs within approximately 2% ofthe minimum possible costs associated with optimal control.Optimal Opera
13、tion of a Chilled-Water Storage System with a Real-Time Pricing Rate StructureZhiqin Zhang, PhD Hui Li, PhDStudent Member ASHRAE Associate Member ASHRAEWilliam D. Turner, PhD, PE Song Deng, PE Member ASHRAEZhiqin Zhang is a PhD student in the Department of Mechanical Engineering and a graduate resea
14、rch assistant in the Energy Systems Labo-ratory, Hui Li is a post-doctorate and Song Deng is an associate director in the Energy Systems Laboratory, and William D. Turner is a profes-sor in the Department of Mechanical Engineering, Texas A&M University, College Station, TX.LV-11-0262011. American So
15、ciety of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions, Volume 117, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not permitted without ASHRAES prior written pe
16、rmission.926 ASHRAE TransactionsHenze et al. (2008) described the investigation of a chilled-water storage system applied to a group of large buildings.Mixed integer programming is adopted to optimize the chillerdispatch for any load condition and an overarching dynamicprogramming-based approach opt
17、imizes the charge anddischarge strategy of the TES system. Henze pointed out thatthe economic benefits of implementing TES in this facilityincluded energy cost savings and qualitative merits, such asthe avoidance of numerous safety measures necessary for achilled-water plant without storage, and a c
18、ost-effective addi-tion of supplemental chilled-water plant cooling capacity.Moreover, the overall system reliability and availability can besignificantly improved with TES.Little work has been performed related to the develop-ment and evaluation of optimal operation of a chilled-waterstorage system
19、 with RTP rate structures. Although they sharethe same idea of shifting electrical load, there are still obviousdifferences between chilled-water and ice storage systems.Compared to ice storage, the primary advantage of water stor-age is that there is no plant efficiency penalty during the charg-ing
20、 cycle. There will be more capacity loss, however, due tomixing effects. A second difference is that the charging anddischarging rate of water storage is determined by the accept-able chilled-water flow rate and stored warm and cool watertemperatures all the time. In practice, the design of water st
21、or-age systems could be various, and the actual charging anddischarging rate is determined by the distribution headers. Theheat transfer rate in terms of “tons of refrigeration” for an icestorage system is limited by several factors, and complicatedcorrelations are required (Drees and Braun 1995). I
22、n addition,the actual inventory of the water tank is dependent upon thetemperature difference between the tank inlet and outlet whilethe usable ton-hour capacity of the ice tank is determinedsolely by the ice volume. The experiences on an ice storagesystem may be used as a good reference for a water
23、 storagesystem. However, these differences indicate that it is not rigor-ous to transfer the conclusions from an ice storage system toa water storage system without a thorough analysis.This paper develops a simple method for determining theoptimal charging and discharging periods for a typical chill
24、ed-water storage system with an RTP rate. The tank state and statechange are described with tank chilled-water volume andcharging or discharging flow rate. The chilled-water produc-tion power is modeled with a forward plant model based on awire-to-water (WTW) efficiency. The loop chilled-watersupply
25、 and return delta-T fluctuation is considered by imple-menting a loop delta-T model. The optimal operating strategyshifts the tank between charging, idle, and discharging modesto maximize the utility cost savings. The optimal starting andending time for charging and discharging can be approximatedwi
26、th constant starting and ending time during the summer andwinter periods. The performance of the simplified strategy ismeasured relative to the optimal strategy.CHILLED-WATER STORAGE SYSTEMSystem ConfigurationFigure 1 shows the schematic of a naturally stratifiedchilled-water storage system consider
27、ed in this study. Itconsists of plant side, tank, and loop side. A primary-second-ary pump system is designed with variable-speed secondarypumps (SPMPs) and constant-speed primary pumps (PPMPs).All air-handling and terminal units are controlled by two-waycontrol valves. The TES tank parallels the ch
28、illers and func-tions like a system bypass with an extremely large volume.The water level in the tank also serves as a constant pressurepoint when the tank is vented. A pressure sustaining valve(PSV) and a check valve are necessary to avoid a vacuum in thepipes if systems are above the water level.
29、If the elevation ofusers is much higher than the tank water level, heat exchangerswill be designed to transfer the cooling from the tank loop sideto the user loop side. This system configuration is the mostpopular because it is easy to control and provides the lesserpumping energy consumption. Howev
30、er, it does supplychilled water to the system that is 2F5F (1.1C2.8C)higher than that delivered from the chiller plant to the heatexchanger. In retrofit projects, such a configuration is oftenadopted since the least system changes have to be made toprovide a good working system. As a result, this st
31、udy willfocus on this configuration. It should be noted that the diagramFigure 1 Schematic of a stratified chilled-water storage system.2011 ASHRAE 927in Figure 1 does not include the heat exchanger, for systemsimplification.There are no modulating devices on the tank in thisconfiguration. The tank
32、chilled-water charging or dischargingflow rate is the difference between the plant side total chilled-water flow and the loop-side chilled-water flow. Since theloop-side flow rate cannot be controlled by the plant, the TEScharging or discharging flow rate is determined by plant totalchilled-water fl
33、ow rate, and it can be controlled by modulatingor sequencing the PPMPs and chillers. The TES operationprofile is, in fact, a profile of chilled-water total flow ratesupplied by the plant. The plant total flow rate is alsoconstrained by some limits, such as chiller evaporator maxi-mum (avoiding erosi
34、on) and minimum (avoiding freezing)flow rates, PPMP maximum flow rate, and tank design maxi-mum charge and discharge flow rate to avoid intense mixing.Water Storage TanksThe storage tank considered in this study is column-shaped and the cold and warm water is naturally stratified. Thediffuser type e
35、mployed is the radial parallel plate design,which consists of a circular plate mounted parallel to a spread-ing surface to create a channel through which inlet or outletflow may pass. An upper and a lower diffuser are designed.During operating, the warm water enters or leaves the tankthrough the upp
36、er diffuser, while the cold water leaves orenters through the lower one. A thin thermal transition layer,called a thermocline, forms between the warm and coldvolumes of water due to the specific gravity differencebetween warm and cold water, heat conduction across theinterface, and mixing effects. C
37、ooling energy is also lost dueto heat gain through the tank walls. However, the mixing nearthe inlet diffuser has more significant effects on the tempera-ture distribution in the tank (Wildin 1990). Under designweather conditions, the losses through the walls are typicallyno greater than 1% to 2% of
38、 the nominal storage capacity(Bahnfleth and Musser 1998).In this study, the tank chilled-water volume ratio and thetank chilled-water charging or discharging flow rate areutilized to describe the tank state and inventory change rate. Inthis context, the state-of-charge x is explained as the cold wat
39、ervolume ratio relative to the tank total effective volume. Thestate of a full tank is unity and of an empty one is zero. Theprimary controlled variable VTank,ChWis defined as the ratechange of the state-of-charge xk.(1)(2)(3)Subject to the constraints(4)(5)(6)Specifically, UTankis the tank effectiv
40、e volume in gallons,UTank,ChW is chilled-water volume in the tank in gallons,VTank,ChW is the tank chilled-water volume change rate in gpm(positive is charging, negative is discharging, zero is idle), isa figure-of-merit (FOM) ( is 0.95 during charging and closeto unity during discharging or idle),
41、VPlant,ChW,k is the plant-side total chilled-water flow rate in gpm, VLp,ChW,k is the loop-side total chilled-water flow rate in gpm, and t is the timestep, normally one hour or quarter-hour. The tank minimumlevel is zero and maximum level is unity.The plant side maximum flow rate VPlant,ChW,maxisgo
42、verned by the PPMP maximum flow rate and chiller chilled-water flow rate upper limit, whichever is smaller. It is inad-missible if the control action VPlant,ChW,kleads to xkless thanzero or greater than unity. In addition, due to the limitations inthe flow rate into and out of the tank to restrain m
43、ixing effects,an additional constraint is applied to the tank maximal charg-ing (VTank,ChW,max) and discharging rate (VTank,ChW,min) basedon the tank design parameters.As the loop-side total chilled-water flow is subject to theloop-side demand, the tank charging or discharging flow rateis, in fact,
44、controlled by the plant operation. The tank levelchange can be calculated from Equation 3. A full charge anddischarge cycling period is one day or 24 hours.Plant Power ModelingA forward chiller plant model based on WTW efficiencyin kW per ton was developed to calculate the plant chilled-water produc
45、tion power at a given total plant chilled-waterflow rate (Zhang 2010). This model was utilized in the currentstudy. The plant power billed by utility companies can bedivided into chilled-water production power and non-chilled-water production power. The chilled-water production powerconsumption incl
46、udes power for the chiller, condenser-waterpump, cooling tower fan, and primary chilled-water pump. AWTW efficiency in kW per ton is defined for each type of thesecomponents. Considering the fact that it is most complex andmost important in a plant, the chiller is modeled with a semi-physical model
47、called the Gordon-Ng model to accommodateextrapolation. The input parameters are chiller chilled-waterleaving temperature, condenser-water entering temperature,condenser-water flow rate, and cooling load and the output isthe motor power. The WTW efficiency can be induced fromthe basic formula of the
48、 Gordon-Ng model. The pump WTWxUTank ChW,UTank-=VTank ChW,dUTank ChW,dt-= VPlant ChW,VLp ChW,()xk 1+xk VPlant ChW k,VLp ChW k,()tUTank-+=xminxkxmax0 VPlant ChW,VPlant ChW max,VTank ChW min,VTank ChW,VTank ChW max,928 ASHRAE Transactionsefficiency is calculated by dividing the cooling load trans-port
49、ed by the pump with the pump motor power, which iscalculated from pump head, flow, and efficiency. A regressionmodel is developed to calculate the cooling tower fan power asa function of the cooling tower approach temperature. Itshould be noted that the outside wet-bulb temperature isanother variable that will affect the fan power, and additionalsavings could be realized if a little more complex model isapplied. The power for chilled-water secondary pumps andmiscellaneous power, such as ligh
