Developing a Smart Grid that Customers can Afford: The Impact of Deferrable Demand.

• Author: Jeon, Wooyoung

1. INTRODUCTION

   With higher penetrations of variable generation from renewable sources, the need to install effective forms of storage capacity on the electric delivery system is critical. However, installing dedicated storage capacity that is designed only to mitigate the variability of generation from a wind farm, for example, is likely to be prohibitively expensive (Tuohy and O'Malley (2011)). A number of studies, including the works of Short and Denholm (2006), Goransson et al. (2010), Wang et al. (2010), Hodge et al. (2010), and Valentine et al. (2011) have shown how the discharging and charging of electric vehicles can be used to smooth daily load cycles as well as provide regulation to support the reliability of supply. If owners of electric vehicles are compensated correctly for providing these services, the overall cost of operating the vehicles is reduced. Since the primary purpose of the batteries in electric vehicles is to provide a means of transportation, the substantial capital cost of a battery is shared between transportation and supporting the grid. This provides a relatively inexpensive form of storage capacity for the grid. (Sioshansi andDenholm(2010))In spite of this potential, earlier research has shown that the total system effects of high penetrations of electric vehicles are still relatively modest. For example, the reduction of peak system load due to Vehicle-To-Grid (V2G) capabilities is very limited because much of the electric energy stored in the batteries is used for transportation.

   The objective of this paper is to extend the concept of deferrable loads to include thermal storage, and in particular, the use of ice batteries to replace standard forms of air-conditioning. A number of studies of thermal storage, including Khudhair and Farid (2004) and Sharma et al. (2009), have analyzed the benefit of using thermal storage for heating at the building level, Hasnain (1998) studied the technical characteristics of ice thermal storage using simple examples of optimum operational strategies, and Lee et al. (2009) and Chen et al. (2005) presented algorithms for the optimal operating strategies for Ice storage for air conditioning. These studies, however, only demonstrate optimum strategies for controlling thermal storage at the micro-scale, and they do not analyze how aggregated thermal storage could provide many services and benefits at the power system level. Therefore, using thermal storage as a form of deferrable demand in a power system with a high penetration of renewable generation to provide ramping services and reduce peak capacity needed for system adequacy represents a new contribution to the literature.

   The information that U.S. Energy Information Administration reported shows that the energy used for cooling accounts for approximately 30% of energy consumptions in the summer season (EIA (2001)). An econometric analysis of the hourly demand for electricity in New York City shows that roughly 38% of the total daily demand for electric energy and 36% of the peak demand for a hot summer day are temperature sensitive. The potential benefit of this type of storage is that a substantial amount of the peak system load on hot summer afternoons can be moved to off-peak periods at night. Instead of using air-conditioners when space cooling is needed, ice can be made when it is convenient for the electric delivery system. Similar arguments can be made for space heating using oil, for example, to store heat. In this way, thermal storage can be used to mitigate variable generation, reduce the total amount of generating capacity needed to maintain System Adequacy, and as a result, lower the total operating and capital cost of generating electricity.

   This paper presents an empirical analysis using data for a hot day in New York City to determine the effects of the deferrable demand associated with electric vehicles and thermal storage on total system costs. The results show how a System Operator can optimize the charging of batteries in electric vehicles and the use of thermal storage to make ice. In other words, the daily patterns of conventional (non-controllable) demand and wind generation are taken as exogenous inputs, together with a specified daily pattern of demand for cooling services and a minimum level of electric energy needed for commuting in electric vehicles.

   The results show how customers can reduce total system costs by 1) shifting load from expensive peak periods to less expensive off-peak periods, 2) reducing the amount of installed conventional generating capacity needed to maintain System Adequacy, and 3) providing ramping services to mitigate the inherent variability of generation from renewable sources. It is, however, essential to develop a regulatory environment in which all participants in the different markets for electricity and ancillary services, including customers and aggregators, pay for the services they use and are compensated for the services they provide. This will establish the economic incentives needed to develop a smart grid that customers can afford. The basic argument is that the savings in the total costs of conventional generation will lower customers' bills and help to cover the cost of the investments needed to install deferrable demand and the equipment for making the grid smarter.

2. MODEL SPECIFICATION

   2.1. The Model of Temperature-Sensitive Demand

   Electricity demand can be categorized as either Non-Temperature-Sensitive Demand (N-TSD) or Temperature-Sensitive Demand (TSD). N-TSD is any basic electricity demand not affected by temperature such as that required for lighting and home appliances. In contrast, TSD is affected by temperature, and air conditioning demand is the key source of TSD during the summer months. If the amount of TSD in the summer is estimated, it can be used to represent the potential amount of demand that can be shifted to the off-peak period using thermal storage. N-TSD is defined in a dynamic demand model with an intercept, lagged electricity demand, and cycles for daily, weekly, weekend and seasonal trends, and TSD is defined by temperature and interactions between temperature and the other variables. The temperature for cooling demand is measured by Cooling Degree Days (CDD = max(temperature F - 65,0)) and squared CDD. The general form of the model can be written as follows:

   [mathematical expression not reproducible] (1)

   The econometric model of electricity demand in the summer is composed of three parts which determine N-TSD, TSD, and a dynamic response. The first term [1] determines N-TSD which is mostly affected by weekly and daily cycles, and the second term [2] determines TSD which is a function of CDD and interactions between CDD and cycles. The third term [3] determines the dynamic response of demand.

   To summarize, the electricity demand in the summer is a function of a time trend, lagged summer electricity loads (1, 24, and 25 lags), various cycles, CDD, [CDD.sup.2] and interactions between CDD and the cycles. Data for the summer months from 2007 to 2010 are used to estimate the hourly electricity demand in New York City and correct for serially correlated residuals (using the AUTOREG PROC in SAS). The fit of the model is high with an [R.sup.2] of 99.8%. Predictions of the hourly total demand for the selected day are computed from the estimated equation. Predictions of the NTSD are determined by setting the temperature to 65[degrees]F in all hours, and the TSD is the difference between the predicted total demand using actual temperature and the predicted NTSD. Figure 1 shows the profiles of the predicted TSD, N-TSD and total demand. The estimated model implies that TSD accounts for approximately 36% of the peak system load and 38% of the total daily demand on the hot summer day used for the analysis in the next section. These values are consistent with data from the U.S. Energy Information Administration that shows roughly one third of the summer demand is associated with air conditioning (EIA (2001)). In the analysis that follows, the hourly pattern of deferrable demand is assumed to be proportional to the predicted TSD. A full description of the estimated model can be found in Mo (2012). The specific form of the model is:

   summerloa[d.sub.it] = [[beta].sub.i0] + [[beta].sub.i1] [t.sub.t] + [[beta].sub.i2]summerloa[d.sub.1t] + [[beta].sub.i3]summerloa[d.sub.24t] + [[beta].sub.i4]summerloa[d.sub.25t] + [[beta].sub.i5]c[h.sub.t] + [[beta].sub.i6]sh[t.sub.t] + [[beta].sub.i7]c[w.sub.t] + [[beta].sub.i8]weekendcycl[e.sub.t] + [[beta].sub.i10]CD[D.sub.t] * cht + [[beta].sub.i11] CDDt * sht + [[beta].sub.i12]CDDt * cwt + [[beta].sub.i13]CD[D.sub.t] * swt + [[beta].sub.i14]CD[D.sub.t]*weekendcycl[e.sub.t]+ [[beta].sub.i15]CD[D.sub.t]+ [[beta].sub.i 16][CDD.sup.2.sub.t] + [v.sub.it] (2)

   [v.sub.it] = - [[phi].sub.1] [v.sub.it - 1] - [[phi].sub.2][v.sub.it - 2] - ... - [[phi].sub.24][v.sub.it]-24 + [u.sub.it] (3)

   where, summerloa[d.sub.1] = summerload(-1)

   summerloa[d.sub.24] = summerload(-24)

   summerloa[d.sub.25] = summerload(-25)

   ch = hourly cycle captured by 24 hour period cosine curve

   sh = hourly cycle captured by 24 hour period sine curve

   cw = weekly cycle captured by one week period cosine curve

   sw = weekly cycle captured by one week period sine curve

   weekendcycle = 1 during weekday and followed by cosine curve during weekend

   CDD = Cooling Degree Days

   [v.sub.it] = residual

   2.2. The Model of System Costs and Demand

   This study is based on an optimization model that assumes the system operator controls all storage to minimize the total system cost of energy and reserves in the electricity market. Some of the generated electricity comes from an exogenous and variable source of wind generation at no cost and the rest from a linear supply function representing conventional generating units. Once decisions are made by the system operator, customers pay for both energy and reserves using the optimum payment...