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Description
Received October 31, 2006; accepted March 12, 2007
A near-optimal control method was developed for charging and discharging of cool storage systems when real-time pricing (RTP) electric rates are available The algorithm requires relatively low-cost measurements (cooling load and storage state of charge), requires very little plant-specific information, is computationally simple, and ensures that building cooling requirements are always met (e.g., storage isn't prematurely depleted). The control method was evaluated for ice storage systems using a simulation tool for different combinations of cooling plants, storage sizes, buildings, locations, and RTP rates. The simplified method worked well in all cases and gave annual costs within approximately 2% of the minimum possible costs associated with optimal control.
INTRODUCTION
The primary objectives of the work described in this paper were to develop and evaluate a simple control strategy for cool storage systems that works well with real-time pricing (RTP) utility rate structures. RTP options are offered by many utilities to commercial and industrial customers and incorporate time-varying rates that more closely approximate actual costs of providing service than conventional rate structures. The RTP rates vary hourly and are provided electronically by utilities up to one day in advance of their application. Customers having cold storage systems and energy management and control systems could incorporate controllers that respond to RTP rates by adjusting charging and discharging rates of storage at different times of day. However, no simple algorithms have been developed and demonstrated that provide near-optimal control of thermal storage systems with RTP rates.
A number of simple control strategies have been developed for cold storage systems operating with conventional utility rates having on-peak and off-peak energy and demand charges (Rawlings 1985; Tamblyn 1985; Spethmann 1989; Braun 1992; Drees and Braun 1996; Henze 2003a). All of these strategies assume that storage is fully charged prior to each occupied period and incorporate chiller-priority and/or storage-priority discharge strategies. With chiller-priority discharge, storage only operates to satisfy the difference between the load requirement and the maximum chiller cooling capacity. This type of strategy minimizes the use of storage and is appropriate in situations where the cost of operating the chillers is less than the cost of recharging storage during the charging period. On the other hand, storage-priority strategies maximize the use of storage during the on-peak occupied period. With a maximum-discharge storage-priority strategy, the chiller only operates to satisfy the difference between the load requirement and the maximum storage discharge capacity. With a demand-limiting or load-limiting storage-priority strategy, the discharge rate varies in order to maintain a peak power or load at or below a specific target.
Relatively little work has been performed related to the development and evaluation of controllers for cool storage systems in combination with RTP. Henze et al. (1997; Henze 2003b; Henze and Krarti 1999) developed a predictive optimal controller that determines optimal trajectories for charging and discharging storage based upon minimizing an integral cost function with RTP rates. Implementation of the method requires predictive models for the cooling plant and cool storage, forecasts for cooling loads and ambient temperatures, and knowledge or forecasts of RTP rates some hours in advance. Henze et al. (1997) showed that optimal control results in very significant savings for systems with RTP rates as compared with conventional strategies that are typically employed for systems with conventional time-of-use energy and demand charges. However, the requirement of developing/configuring models for each application is probably cost-prohibitive, and there is a need for a simple strategy that performs well in relation to optimal control.
This paper develops and validates a simple method for controlling the charging and discharging of thermal storage systems having RTP utility rates. The development starts with the method of Drees and Braun (1996), a modified version of which is described in chapter 41 of the 2003 ASHRAE Handbook--HVAC Applications. The original strategy was developed for systems with conventional time-of-use rates that employ discrete on-peak and off-peak energy and demand rates. The strategy switches between chiller-priority, maximum-discharge storage-priority, and load-limiting storage-priority strategies based upon economics and availability of storage and uses forecasting to ensure against premature depletion of storage. The primary contributions of the current paper are (1) the recognition that the method of Drees and Braun (1996) can be applied to systems having continuously varying RTP rates by using effective on-peak and off-peak periods, (2) development of a method for determining the effective on-peak and off-peak periods, and (3) an extensive simulation evaluation of the method for different combinations of cooling plant configurations and sizes, thermal storage sizes, buildings, locations, and RTP rates. A benchmark optimization tool was developed to determine the "true" optimal control for the simulated systems, and the performance of the simplified algorithm is measured relative to the benchmark.
SYSTEM MODELING
Figure 1 shows a schematic of the system configuration considered in this paper. This system is representative of configurations employed for ice storage systems having internal-melt, ice-on-pipe tanks with water-cooled chillers. Air-cooled chillers are also considered in this study because they are common for medium and light commercial applications. Internal-melt, ice-on-pipe storage tanks are the most common type of thermal storage system. A mixture of water and glycol is the working fluid that circulates between the building and the cooling plant. At any given time, the building load can be met by running the chiller or by depleting the storage or by a combination of the two. The chiller loading is dictated by the setpoint for the supply temperature from the chiller ([T.sub.chws]). The ice storage tank provides any additional cooling necessary to maintain the required supply temperature to the building cooling coils ([T.sub.coil]). During charging mode, the chiller supply and load supply temperature setpoints are set to low values below the freezing point of water to ensure that the chiller operates at full capacity, all of the flow goes through storage, and ice is produced. Charging generally occurs during the unoccupied period when the load requirements are either nonexistent or are small and most or all of the plant water/glycol supply flow is short-circuited to the return line.
[FIGURE 1 OMITTED]
Sun et al. (2006) provide a detailed description of the simulation tool used in this study, whereas this section provides a brief overview of the modeling approach and plant characteristics.
Ice Storage Tanks
The storage tanks are considered to be internal-melt, ice-on-pipe configurations and are modeled using the semi-empirical model developed by West and Braun (1998). The storage model neglects any heat gains through the storage shell and assumes that the state of storage can be represented with a single variable that defines the fraction of the maximum available storage capacity. For any time interval k,
[x.sub.k] = [x.sub.k-1] + [u.sub.k][increment of t]/[Cap.sub.s], (1)
where [Cap.sub.s] is the maximum change in internal energy of the storage tank that can occur during a discharge cycle, u is the rate of energy addition to storage over the stage (positive for charging and negative for discharging), and [increment of t] is the simulation time step. The state of charge defined in this manner must be between zero and one. In this study, zero state of charge corresponds to a tank of water at a uniform temperature of 32[degrees]F (0[degrees]C) and a complete charge is associated with a tank that is frozen solid at 32[degrees]F (0[degrees]C).
The rates of charging and discharging of storage are limited by the storage heat exchanger area, secondary fluid... |
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