Estimating the Impact of Electric Vehicle Demand Response Programs in a Grid with Varying Levels of Renewable Energy Sources: Time-Of-Use Tariff Versus Smart Charging

energies

Article Estimating the Impact of Electric Vehicle Demand Response Programs in a Grid with Varying Levels of Renewable Energy Sources: Time-of-Use Tariﬀ versus Smart Charging

Wooyoung Jeon 1, Sangmin Cho 2 and Seungmoon Lee 2,*

1 Department of Economics, Chonnam National University, Gwangju 61186, Korea; [email protected] 2 Korea Energy Economics Institute, Ulsan 44543, Korea; [email protected] * Correspondence: [email protected]; Tel.: +82-52-714-2223

Received: 21 July 2020; Accepted: 19 August 2020; Published: 24 August 2020

Abstract: An increase in variable renewable energy sources and soaring electricity demand at peak hours undermines the efficiency and reliability of the power supply. Conventional supply-side solutions, such as additional gas turbine plants and energy storage systems, can help mitigate these problems; however, they are not cost-effective. This study highlights the potential value of electric vehicle demand response programs by analyzing three separate scenarios: electric vehicle charging based on a time-of-use tariff, smart charging controlled by an aggregator through virtual power plant networks, and smart control with vehicle-to-grid capability. The three programs are analyzed based on the stochastic form of a power system optimization model under two hypothetical power system environments in Jeju Island, Korea: one with a low share of variable renewable energy in 2019 and the other with a high share in 2030. The results show that the cost saving realized by the electric vehicle demand response program is higher in 2030 and a smart control with vehicle-to-grid capability provides the largest cost saving. When the costs of implementing an electric vehicle demand response are considered, the difference in cost saving between the scenarios is reduced; however, the benefits are still large enough to attract customers to participate.

Keywords: electric vehicle; demand response; variable renewable sources; time-of-use; smart charging; virtual power plant

1. Introduction

1.1. Background and Motivation In 2017, the South Korean government implemented an energy transition policy to convert traditional fossil-fuel-oriented energy into eco-friendly renewable energy as a solution to high domestic and international pressure for greenhouse gas emission reduction. The goal of the energy transition policy is to displace coal and nuclear power generation quickly with variable renewable sources (VRS) such as wind and solar energy, which are free from greenhouse gas and ﬁne dust emissions. The plan is to increase the share of renewable sources for power generation in South Korea from 6.2% in 2017 to 20% in 2030 and 30–35% by 2040 [1,2]. The replacement of traditional power sources with VRS can help to build a more eco-friendly and less fossil-fuel-dependent power supply environment; however, VRS can undermine the reliability of the power supply. Unlike coal and nuclear power, VRS sources, such as solar photovoltaic (PV) and wind, cannot produce the required energy in periods of high demand, and the forecasting error for day-ahead dispatch planning is substantially higher. Combined with other uncertainty factors

Energies 2020, 13, 4365; doi:10.3390/en13174365 www.mdpi.com/journal/energies Energies 2020, 13, 4365 2 of 22 such as variable demand and transmission line failure, this can cause reliability problems in the power supply network. VRS cause problems in the power system mainly through two characteristics, which are variability and uncertainty. Solar PV typically has high variability issue due to concentrated generation during day time so it requires many fast ramping units to meet the rapid net load changes [3]. Wind power commonly has high uncertainty issue due to difficulty in accurate forecasting so this needs the power system to secure more reserve resources to meet net load deviation from the forecasted value [4]. To successfully implement the transition to a VRS-oriented power system, it is essential to secure enough flexible resources to support a power system undermined by the high variability and uncertainty inherent in VRS. Among various potential flexible resources, energy storage systems (ESS), such as pumped storage or lithium-ion batteries, are considered the most effective. ESS are an effective flexible resource for mitigating the duck curve phenomenon, in which the net load decreases during intense sunlight hours from 11 am to 5 pm due to concentrated PV generation, causing high inefficiency and reliability issues in the power system. ESS can reduce the effect of the duck curve by storing solar power during high generation times and discharging it when required. ESS can also be used as an effective reserve resource to complement the uncertainty of VRS. However, the most commonly used ESS, lithium-ion batteries, are not yet economically feasible as a dedicated resource for power systems, and it is difficult to build additional pumped storage due to geographical conditions and environmental issues. Demand response (DR) resources, especially electric vehicle (EV) DR resources, are drawing attention as an alternative to ESS. The number of EVs in Jeju Island, Korea, is expected to grow from 23,000 in 2019 to 377,000 in 2030 [5]. The high growth in the number of EVs creates an opportunity to significantly mitigate the variability of a VRS-based power supply if electricity demand from EVs can be shifted to duck curve hours, based on dynamic pricing mechanisms such as a time-of-use (TOU) rate or real-time pricing (RTP). Moreover, the benefits from the EV DR can be enhanced when virtual power plant (VPP) technology is combined to enable an aggregator to remotely control the charging and discharging of energy when EVs are connected to the power system. Using VPP technology, small batteries in individual EVs can be integrated to function like a large ESS, optimally controlled by an aggregator under the direction of the system operator. An integrated ESS provided by EVs via a VPP network can be economically viable as the cost of the EV battery is now compensated by both operating an EV and by supporting the power system.

1.2. Related Works Various studies, including References [6–8], discuss the potential benefits of EVs based on smart charging. Reference [6] estimated the benefits of EVs and thermal storage under a flat rate structure and an optimum rate structure which reflects cost saving in generation, reserve, and capacity. Reference [7] analyzed the potential financial return of EVs in a power system demand resources with vehicle-to-grid (V2G) capability when its dual-use service is correctly estimated, namely frequency regulation and peak load reduction. The authors demonstrated that V2G has economic potential for frequency regulation alone; however, when adopted as a dual-use service, the economic benefit is substantially higher. Zhang et al. [8] proposed regime-switching risk management based on vehicle-to-building power sources using EV resources. The authors proposed a two-regime structure: a low-risk regime, whereby the system objective is to minimize charging costs, and a high-risk regime, whereby the intention is to reduce high energy costs due to peak pricing. The results showed that regime-switching management is effective in reducing the cost of energy. Several studies discuss the impact of EV demand under dynamic pricing mechanisms. Reference [9] evaluated the cost of the new infrastructure required to implement TOU and real-time pricing programs to determine the benefits from policies for shifting EV charging from on-peak to off-peak hours. Reference [10] analyzed EV electricity tariffs based on three aspects: customer acceptance, the potential Energies 2020, 13, 4365 3 of 22 for load flexibility, and aggregator profitability. The authors concluded that a tariff should be suitable for customers to provide load flexibility and provide adequate benefits to aggregators as well. In addition, literature such as References [11–13] discusses the high potential of EV as demand resource in the microgrid environment. Reference [11] proposes the two-level microgrid problems such that charging strategy to minimize the charging cost and its impact on the power generation planning of small island grid. Reference [12] discusses two-stage smart charging algorithm in the building equipped with EVs, solar panels and heat pump, and showed V2G is cost-effective under optimal management despite of high degradation cost of EV battery. Reference [13] uses a metaheuristic-based vector-decoupled algorithm to optimally operate microgrid with EVs and stochastic renewable energy sources and showed the EV can provide meaningful services regarding voltage and frequency stabilization in a microgrid.

1.3. Objectives of This Study In this study, we analyze how effectively EV DR programs can reduce the operating cost and improve the reliability of the power supply system in Jeju Island, where rapid increase in VRS as well as EVs is expected. This study contributes to the literature in three distinct ways as follows. First, this study analyzes and compares the impact of three EV demand control methods: demand control under a TOU rate, smart charging control by an aggregator using VPP technology with grid-to-vehicle (G2V) capability (hereafter referred to as VPP1), and VPP1 with V2G capability (hereafter referred to as VPP2), which allows not only optimal charging but also discharging to the grid. The TOU program can be considered a passive application of EV DR, while VPP1 is a moderately active application and VPP2 a highly active application. The value of an EV DR program is estimated according to these three application methods. Second, the cost saving in an EV DR program is separately estimated in a power system with low levels of VRS in 2019 and high levels of VRS in 2030. This separate analysis allows us to compare the benefits from EV DR under variability and uncertainty caused by VRS. Third, monthly cost saving per EV customer is estimated by varying the participation rate in the DR program. In addition, costs induced to implement the DR program, such as aggregator commission fees for the VPP and battery cycling costs, are considered to estimate the net monthly cost saving that EV customers should realize. This study applies a multi-period security constraint optimal power flow (MPSOPF) method, which is a stochastic form of power system optimization model that allows us to derive the optimal operational plan for the power system by reflecting stochastic inputs such as VRS. The stochastic forecast profiles of VRS are derived for each renewable site based on weather data using two-stage autoregressive moving average with exogenous variables (ARMAX) modeling and the Monte Carlo simulation method. The remainder of this paper is structured follows. Section2 describes the objective function and characteristics of the MPSOPF model, discusses the methodology of deriving VRS forecast profiles, and presents information regarding EV driving and charging patterns. Section3 outlines the structure of the different DR programs and derives an optimal TOU rate and DR program. Section4 analyzes the results of the study, and Section5 discusses the conclusions and implications.

2. Methodology

2.1. The Power System Simulation Model The MPSOPF model applied in this study is a type of security constraint optimal power ﬂow model commonly used to simulate a power system. This model simulates a 24 h optimal dispatch plan that minimizes the operating costs of the power system from the perspective of day-ahead planning when security constraints are applied. The basic model structure seeks to derive a dispatch plan for each generator that minimizes energy and reserve costs under the various power system constraints Energies 2020, 13, 4365 4 of 22

regardingEnergies 2020 system, 13, x FOR security, PEER REVIEW network, contingency, and renewable energy variability as well as physical4 of 22 constraints, while meeting power demand requirements over a 24 h period. can Thererealistically are two analyze distinct the characteristics impact of renewa by whichble theenergy MPSOPF generation model on used the in power this study system diff ersby fromconsidering other common the forecasting power error flow in models. the day-ahead First, this scheme. model Second, can handle the amount a stochastic of operating form of reserve input, sorequired it can realisticallyto ensure stability analyze of th thee power impact system of renewable is derived energy from generationthe model as on internal the power solutions system when by consideringuncertainties the are forecasting imposed from error various in the day-ahead scenarios, scheme. such as Second,uncertain the renewable amount of energy operating generation, reserve requireddemand, toor ensurecontingency. stability These of the feat powerures enable system the is derived MPSOPF from model the modelto realistically as internal reflect solutions the variable when uncertaintiesand uncertain are characteristics imposed from of variousrenewable scenarios, energy suchgeneration as uncertain and analyze renewable the costs energy of operating generation, a demand,power system or contingency. with high levels These of features VRS. enable the MPSOPF model to realistically reflect the variable and uncertainEquation characteristics(1) shows the ofsimplified renewable objective energy function generation of andthe analyzeMPSOPF the model. costs ofThis operating objective a powerfunction system consists with of high four levels components: of VRS. generation cost, contingency reserve cost, load-following reserve,Equation and load-shedding (1) shows the simplifiedcosts. The objectiveMPSOPF functionmodel derives of the MPSOPFan optimal model. dispatch This plan objective that functionminimizes consists these offour four cost components: components. generation [14,15] The cost, detailed contingency definition reserve of cost,variables load-following is provided reserve, in the andTable load-shedding A1 in the Appendix. costs. The MPSOPF model derives an optimal dispatch plan that minimizes these four cost components. [14,15] The detailed definition of variables is provided in the Table A1 in the ()+ ( −) AppendixA. ,, ∈ ∈ ∈ ∈ P P P P + + ( −) [ (() +,)( ) min πtsk CGi Gitsk Incits Gitsk Gitx Gitsk,Ritsk,LNSjtsk t T s S k K ∈{ i I − ∈ ∈ ∈ + P∈ Dec (G G ) ] VOLL LNS (G R ) +its−itc (itsk)+ ( )+j (tsk)+, tsk jtsk( ) (1) − j J } ∈P ∈P + + ∈ + + (1) + ρt [C R + C− R− + C L + C− L− ] Rit it Rit it Lit it Lit it t T i I ( −) +( −) P P P ∈ P ∈ + + + i ∈ [Rp (G G ) + Rp G G ) + f (p p ) ρt ∈ ∈it its2∈ its1 it− its2 its1 s sc, sd t t 1 ts 0 − − t T s2 S s1 S i I 2 ∈ ∈ ∈ − +∈ (,) The powerpower systemsystem network network in in Jeju Jeju Island Island shown shown in in Figure Figure1 is 1 chosen is chosen for thisfor this study. study. Jeju IslandJeju Island has ahas population a population of 604,000, of 604,000, is popular is popular with with tourists touris fromts from neighboring neighboring countries, countries, and and is renowned is renowned for for its naturalits natural scenery scenery and clean and environment.clean environment. To maintain To amaintain clean environment, a clean environment, the island’s administration the island’s hasadministration implemented has an implemented aggressive agenda an aggressive to replace agen fossilda fuelto replace power plantsfossil fuel with power renewable plants energy with sources,renewable specifically energy sources, solar PV specifical and wind,ly solar and displacePV and conventionalwind, and displace vehicles conventional with EVs. Therefore, vehicles with Jeju IslandEVs. Therefore, is a suitable Jeju case Island to analyzeis a suitable the impactcase to analyze of an EV the DR impact program of an on EV a powerDR program system on with a power high levelssystem of with renewable high levels sources of renewable [1]. sources [1].

Figure 1.1. Power system network in Jeju Island (17-bus system).system).

Energies 2020, 13, 4365 5 of 22

The cost data is from the Korea Power Exchange (KPX) database of Electric Power Statistics Information System (EPSIS) [16] and reference costs used in this study are 40.5 USD/Gcal for natural gas and 53.9 USD/Gcal for oil. These unit heat costs for each fuel type are applied to cost functions of each generator to derive the generation cost of given power output. These costs are typically stable in Korea as they are in the long-term contract, so the cost data acquired from the Korea Power Exchange is used extensively. The original cost data is in KRW, and all cost results are converted to USD by apply 1200 KRW/USD ratio based on the oﬃcial conversion ratio reported on 3 March 2020.

2.2. Model for Renewable Generation Forecasting The wind and solar PV generation forecast profiles are estimated based on wind speed and solar radiation data from 2016 to 2018 from the Korea Meteorological Administration. Equations (2) and (3) below show the structure of the solar radiation and wind speed estimation models, respectively, based on the two-stage ARMAX model. The first stage uses deterministic information such as temperature and seasonal cycles to estimate the seasonal and temperature effect in wind speed and solar radiation, and the second stage takes the residual term of the first stage to estimate additional parameters through autoregressive moving average (ARMA) time series analysis [17,18]. This two-stage ARMAX model can be interpreted as capturing the variability of wind speed and solar radiation in the first stage and the uncertainty of the forecasting error in the second stage. Stage 1: Deterministic part( Ordinary Least Square (OLS) ) log(Windt,i + 1) = fD Deter mini stic Cyclest,i, Temperaturet,i + νt,i (2) where Deterministic Cyclest,i is a one-year, half-year, 24 h, and 12 h sine and cosine curve, and νt,i is the residual of the Stage 1 ordinary least squares estimation function. Stage 2: ARMA part Xp Xq i j (1 α L )vt = (1 + θ L )εt (3) − i j i=1 j=1 where εt is the white noise residual of the Stage 2 ARMA estimation function. Table1 show the two-stage ARMAX estimation results of Wind Site 1, respectively. Pseudo R2, which indicates the explanatory power of the model that includes both Stage 1 and Stage 2, is 0.734 for the Wind Site 1 model. Once the wind speed and solar radiation models are estimated for each wind and solar farm, the Monte Carlo simulation method is applied to create 1000 forecast profiles. Based on the covariance matrix of white noise residuals in Stage 2 of each econometric model, the simulation produces a random white noise residual assuming a normal distribution with variances along the covariance matrix, which results in 1000 wind speed and solar radiation forecast profiles. These generated forecast profiles are based on a variance-covariance matrix at each point, and therefore reflect spatial correlation for the six sites. The set of 1000 wind speed and solar radiation forecast profiles is converted to wind power and solar power profiles using conversion formulae. Based on the 1000 solar and wind generation forecast profiles, five representative profiles are selected to simplify the profile information and reduce the computational burden for the MPSOPF model. Of the five profiles, the middle profile is the median, the second and fourth profiles indicate the +1 and 1 standard deviations from the median, and the − top and bottom profiles are the +2 and 2 standard deviations from the median. These five chosen − profiles cover 95% variability of total VRS profiles as shown in Figure2. Energies 2020, 13, x FOR PEER REVIEW 6 of 22

Table 1. Two-stage ARMAX (autoregressive moving average with exogenous variables) estimation results for Wind1 (Hanlim).

Stage 1: OLS Model Stage 2: ARMA Model Variable Coefficient t-Value Variable Coefficient t-Value Intercept 1.22258 208.66 constant −4.1 × 10−5 0 Cosine_year 0.14264 17.41 MA1 0.27082 38.02 Sine_year 0.02394 4.49 MA2 0.04158 6.1 Cosine_half year −0.03084 −7.01 MA3 0.01328 1.97 Sine_half year 0.00414 0.87 MA4 0.008712 1.3 Cosine_day −0.12054 −29.11 MA5 0.004728 0.71 Sine_day −0.08894 −21.45 AR1 0.93123 261.22 Energies 2020, 13, 4365 6 of 22 Cosine_half day 0.00564 1.42 AR24 0.03472 5.6 Sine_half day 0.06246 15.67 Table 1. Two-stageCDD ARMAX1 (autoregressive0.03825 moving16.66 average with exogenous variables) estimation results for Wind1 (Hanlim). HDD2 0.01441 13.06 Stage 1: OLSR2: Model0.151 Pseudo Stage R2: 2: ARMA0.734 Model 1 CDD Variable(cooling degree day) Coe = maxﬃcient (temperaturet-Value –24 °C, 0), Variable2 HDD (heating Coe degreeﬃcient day) = tmax-Value (18 °C temperature,Intercept 0). 1.22258 208.66 constant 4.1 10 5 0 − × − OnceCosine_year the wind speed and 0.14264solar radiation models 17.41 are estimated MA1 for each 0.27082 wind and solar 38.02 farm, the Monte CarloSine_year simulation method 0.02394 is applied to 4.49create 1000 forecast MA2 profiles. 0.04158 Based on the 6.1 covariance matrix of white noise residuals in Stage 2 of each econometric model, the simulation produces a Cosine_half year 0.03084 7.01 MA3 0.01328 1.97 random white noise residual− assuming a normal− distribution with variances along the covariance Sine_half year 0.00414 0.87 MA4 0.008712 1.3 matrix, which results in 1000 wind speed and solar radiation forecast profiles. These generated Cosine_day 0.12054 29.11 MA5 0.004728 0.71 forecast profiles are based on −a variance-covariance− matrix at each point, and therefore reflect spatial correlationSine_day for the six sites. 0.08894 21.45 AR1 0.93123 261.22 − − TheCosine_half set of 1000 day wind speed 0.00564 and solar radiation 1.42 forecast AR24 profiles is converted 0.03472 to wind 5.6 power and solar powerSine_half profiles day using conversion 0.06246 formulae. 15.67 Based on the 1000 solar and wind generation forecast profiles, five representative profiles are selected to simplify the profile information and reduce the CDD 1 0.03825 16.66 computational burden for the MPSOPF model. Of the five profiles, the middle profile is the median, 2 the second andHDD fourth profiles0.01441 indicate the +1 13.06and −1 standard deviations from the median, and the top and bottom profiles areR2: the 0.151 +2 and −2 standard deviations from Pseudo the median. R2: 0.734 These five chosen 1 2 profilesCDD cover (cooling 95% degree variability day) = max of (temperaturetotal VRS –24profiles◦C, 0), asHDD shown (heating in degreeFigure day) 2. = max (18 ◦C temperature, 0).

(a) (b)

Figure 2. TheThe five ﬁve representative representative forecast forecast pr proﬁlesofiles for for sites sites Solar1 Solar1 and and Wind1: Wind1: (a) (Solar1a) Solar1 (Jeju (Jeju City); City); (b) (Wind1b) Wind1 (Hanlim). (Hanlim).

Based on the estimated forecast profiles, we estimated the net load patterns for Jeju Island for 2019 and 2030. As shown in Figure3, the net load in 2019 shows insignificant variability and uncertainty, although some duck curve characteristics can be observed. However, the net load in 2030 shows a severe duck curve, which causes a negative net load for the median profile. This could lead to a situation in which excess renewable energy must be returned to the mainland. EnergiesEnergies 2020 2020, ,13 13, x, xFOR FOR PEER PEER REVIEW REVIEW 7 of7 22 of 22

BasedBased on on the the estimated estimated forecast forecast profiles, profiles, we we estimated estimated the the net net lo adload patterns patterns for for Jeju Jeju Island Island for for 20192019 andand 2030.2030. AsAs shownshown in in Figure Figure 3, 3, the the net net lo loadad in in 2019 2019 shows shows insignificant insignificant variability variability and and uncertainty,uncertainty, although although some some duck duck curve curve characterist characteristicsics can can be be observed. observed. However, However, the the net net load load in 2030in 2030 showsshows a a severe severe duck duck curve, curve, which which causes causes a anegative negative net net load load for for the the median median profile. profile. This This could could lead lead to a situation in which excess renewable energy must be returned to the mainland. toEnergies a situation2020, 13 ,in 4365 which excess renewable energy must be returned to the mainland. 7 of 22

(a) (b) (a) (b) Figure 3. Forecasted net load for peak days in Jeju Island in 2019 and 2030: (a) 2019; (b) 2030. FigureFigure 3. Forecasted netnet loadload for for peak peak days days in in Jeju Jeju Island Island in in 2019 2019 and and 2030: 2030: (a) 2019;(a) 2019; (b) 2030.(b) 2030. 2.3. Assumptions for Electric Vehicle (EV) Driving and Charging Patterns 2.3.2.3. Assumptions Assumptions for Electric VehicleVehicle (EV) (EV) Driving Driving and and Charging Charging Patterns Patterns ToTo estimate estimate the the potential potential economic economic value of an EV DR program, itit isis importantimportant to to impose impose realistic realistic To estimate the potential economic value of an EV DR program, it is important to impose realistic constraintsconstraints for for charging charging and and driving driving patterns patterns of of EVs in thethe simulation.simulation. FigureFigure4 a4a shows shows a a profile profile of of constraints for charging and driving patterns of EVs in the simulation. Figure 4a shows a profile of thethe average average charging charging ratios ratios among among all all EVs EVs in in Jeju Jeju Island. This profileprofile isis aa weightedweighted averageaverage of of fast- fast- the average charging ratios among all EVs in Jeju Island. This profile is a weighted average of fast- andand slow-charging slow-charging profiles, profiles, with with ratios ratios of of 9% to 91%, and anan averageaverage chargingcharging duration duration time time of of 6.2 6.2 h h and slow-charging profiles, with ratios of 9% to 91%, and an average charging duration time of 6.2 h forfor slow slow charging charging and and 0.5 0.5 h h for for fast fast charging charging [19,20]. [19,20]. The aggregated chargingcharging ratio ratio profile profile increases increases duringforduring slow the thecharging night night from fromand 7 0.5pm 7 pm h to for to5 am, 5fast am, when charging when customer customers [19,20].s can The can take aggregated take advantage advantage charging of low of low electricity ratio electricity profile rates, increases rates, and increasesduringand increases the moderately night moderately from from 7 pm from 11 to am 115 am, amto 3 towhen pm, 3 pm, whencustomer when dem demandsand can istake is generally generally advantage highest. highest. of low Figure electricity4 b4b illustrates illustrates rates, and theincreasesthe hourly hourly moderatelyprofile profile of of the the from percentage percentage 11 am toof of 3the the pm, total when numbernumb demer ofofand carscars is onongenerally thethe roadroad highest. in in Jeju Jeju Island. Island.Figure The The4b profileillustrates profile spikesthespikes hourly during during profile commuting commuting of the percentage hours hours from from of 7 7 amthe am to total 10 am numb ander 66 of pmpm cars toto 9on9 pmpm the andand road showsshows in Jeju a a moderately moderatelyIsland. The high highprofile percentagespikespercentage during during during commuting the the day. day. hours from 7 am to 10 am and 6 pm to 9 pm and shows a moderately high percentage during the day.

(a) (b)

FigureFigure 4. 4. ChargingCharging ratio ratio(a) profile profile and and driving driving profile profile of EVs forfor JejuJeju Island:Island: ((aa)) chargingcharging(b) ratio ratio profile; profile; (bFigure()b driving) driving 4. Charging profile. profile. ratio profile and driving profile of EVs for Jeju Island: (a) charging ratio profile; 3. Scenario(b) driving Setup profile.

3.1. Construction of Scenarios

Table2 summarizes the structure of the four scenarios used in this study to estimate the potential value of an EV DR program. The ﬁrst scenario (Case 1) is an estimate of the operating cost of the power system when the current EV demand pattern is maintained. The second scenario (Case 2) measures the impact of the EV DR program under a TOU tariﬀ. The third scenario (Case 3) estimates the impact Energies 2020, 13, 4365 8 of 22 of EV demand when it is directly controlled by an aggregator using VPP technology; in this case, an aggregator uses a cyber-physical network to manage the aggregated EV DR resources as a virtual power plant under a direction from a system operator. Case 3 allows only the purchase of energy from the grid (grid-to-vehicle, G2V) and is referred to as VPP1. The fourth scenario (Case 4) assumes a smart control like VPP1 but allows both the G2V and vehicle-to-grid (V2G) and is referred to as VPP2. All four cases are analyzed in 2019, under moderate VRS levels, and in 2030, under high VRS levels.

Table 2. Structure of the scenarios.

Level of DR Participation Case Name Description Demand Control Rate of EV Jeju Island in 2019 Jeju Island in 2030 (Low VRS and EV) (High VRS and EV) Case 1: No Control Current EV electricity consumption pattern No control 10% Case 2: TOU EV charging pattern under TOU tariﬀ Passive control 25% Case 3: VPP1 (G2V only) Smart EV charging control by VPP Active control 50% 75% Smart charging and discharging control Highly active Case 4: VPP2 (G2V + V2G) 100% by VPP control

This analysis has three key objectives. The first objective is to analyze how the value of the DR program differs with varying levels of control over EV demand. The level of control for EV demand increases with each case, ranging from no control in Case 1 to highly active control in Case 4. The second objective is to determine how the value of the EV DR program changes with varying levels of renewable energy. To analyze this, the impact of EV demand is estimated for 2019 and 2030, with ratios of renewable energy capacity to peak demand of 46% and 210%, respectively. The third objective is to estimate the impact of different EV participation rates on the cost of supplying electricity and to see the actual compensation and cost that can be incurred to each EV customer by providing a DR service to the grid. A key characteristic of Case 1 is that the current EV charging pattern will be maintained until 2030, while in Case 2, the price elasticity of EV demand will be applied when determining the daily demand pattern under a TOU tariff. Case 3 assumes that EVs are connected to the grid at all times when they are not operating, and the aggregated charging power rate is determined based on the composition ratio of 7:2:1 for portable, slow, and fast chargers, respectively. A high portable charger rate strengthens the assumption that customers have high accessibility to the grid. In addition, it is assumed that VPP scenarios can provide not only energy but also ancillary services to the grid as they are optimally controlled based on the direction of a system operator. In Case 4, the available capacity of EV batteries for V2G capability is set at 70% to maintain performance and optimize battery life. Table3 summarizes the conditions and assumptions related to the technical characteristics of EVs separately in 2019 and 2030. The daily average driving distance and the average fuel efficiency are 52 km/day and 5.43 km/kWh, respectively, and by combining the two values, the daily average EV energy usage is computed as 9.39 kWh. The average EV battery capacity is set at 45.2 kWh for 2019 and 69.3 kWh for 2030 by assuming an average annual capacity increase of 4% due to advances in technology. If the current EV deployment plan for Jeju Island is achieved, the aggregated battery capacity will be approximately 1065 MWh in 2019 and 26,132 MWh in 2030, and the total daily electricity consumption by EVs will be approximately 247 MWh in 2019 and 5935 MWh in 2030. Projected figures in 2030 of Table3 are mainly based on [1,2,5,20–23]. Energies 2020, 13, x FOR PEER REVIEW 9 of 22

Table 3 summarizes the conditions and assumptions related to the technical characteristics of EVs separately in 2019 and 2030. The daily average driving distance and the average fuel efficiency are 52 km/day and 5.43 km/kWh, respectively, and by combining the two values, the daily average EV energy usage is computed as 9.39 kWh. The average EV battery capacity is set at 45.2 kWh for 2019 and 69.3 kWh for 2030 by assuming an average annual capacity increase of 4% due to advances in technology. If the current EV deployment plan for Jeju Island is achieved, the aggregated battery capacity will be approximately 1065 MWh in 2019 and 26,132 MWh in 2030, and the total daily Energies 2020, 13, 4365 9 of 22 electricity consumption by EVs will be approximately 247 MWh in 2019 and 5935 MWh in 2030. Projected figures in 2030 of Table 3 are mainly based on [1–2,5,20–23]. Table 3. EV characteristics in 2019 and 2030. Table 3. EV characteristics in 2019 and 2030. Variables 2019 2030 Unit Average dailyVariables driving distance 2019 52 2030 Same Unit km AverageAverage daily fuel edrivingﬃciency distance 5.43 52 Same Same km /kWh Average fuel efficiency 5.43 Same km/kWh Average daily electricity consumption 9.39 Same kWh Average daily electricity consumption 9.39 Same kWh Average battery capacity 45.2 69.3 kWh Average battery capacity 45.2 69.3 kWh Average daily driving hours 2.19 Same hour Average daily driving hours 2.19 Same hour Composition of chargers by charging speed (portable:slow:fast) 7:2:1 Same Composition of chargers by charging speed (portable:slow:fast) 7:2:1 Same − − Total number of EVs 23,667 377,217 Total number of EVs 23,667 377,217 − − Aggregated EV battery capacity 1065 26,132 MWh Aggregated EV battery capacity 1065 26,132 MWh Total daily electricity consumption by EVs 247 5935 MWh Total daily electricity consumption by EVs 247 5935 MWh Depth of discharge of battery 70% Same Depth of discharge of battery 70% Same − − Roundtrip battery eﬃciency 90% Same Roundtrip battery efficiency 90% Same − −

3.2.3.2. Estimation of EV Electricity DemandDemand under a Time-of-Use (TOU) ProgramProgram FigureFigure5 5 illustrates illustrates the the three-level three-level design design of of the th TOUe TOU program program used used in this in this study study based based on the on netthe loadnet load in 2019 in and2019 2030.and Currently,2030. Currently, TOU programs TOU progra in Koreams in have Korea three-level have three-level structures structures with diﬀ erentwith schemesdifferent toschemes meet the to load meet pattern the load of eachpattern season. of each They season. are commonly They are commonly built with 10 built h of with low-rate 10 h supply,of low- 8rate h of supply, mid-rate 8 supply,h of mid-rate and 6 hsupply, of high-rate and 6 supply. h of high-rate The proposed supply. TOU The structures proposed in TOU 2019 structures and 2030 are in designed2019 and based2030 are on designed these current based conditions. on these current conditions.

(a) (b)

Figure 5.5. Time-of-use (TOU) structuresstructures basedbased onon thethe netnet loadload inin 20192019 andand 2030:2030: ((aa)) 2019;2019; ((bb)) 2030.2030.

FigureFigure6 6a,ba,b illustrateillustrate thethe estimatedestimated demanddemand patternpattern ofof thethe EVEVDR DRunder underthe the TOU TOU programs programs presentedpresented above. Research Research on on how how electricity electricity demand demand responds responds to to a aTOU TOU tariff tari ffis islimited, limited, and and it itis isdifficult difficult to topredict predict this this response response due due to to the the lack lack of of data data and and uncertainty in customers’ behaviors. Therefore,Therefore, basedbased onon ReferenceReference [[24],24], itit isis assumedassumed thatthat thethe DRDR demanddemand patternpattern underunder TOUTOU isis thethe aggregation of three separate demand profiles incurred by three rate segments, which follows a truncated normal distribution with different peak levels. Energies 2020, 13, x FOR PEER REVIEW 10 of 22 Energies 2020, 13, x FOR PEER REVIEW 10 of 22 aggregation of three separate demand profiles incurred by three rate segments, which follows a Energiestruncatedaggregation2020 ,normal13 ,of 4365 three distribution separate with demand different profiles peak in levels.curred by three rate segments, which follows10 of 22a truncated normal distribution with different peak levels.

(a) (b) (a) (b) Figure 6. Electricity demand profiles responding to a TOU program in 2019 and 2030: (a) 2019; (b) Figure2030.Figure 6.6. ElectricityElectricity demand demand profiles profiles responding responding to ato TOU a TOU program program in 2019 in 2019 and 2030:and 2030: (a) 2019; (a) 2019; (b) 2030. (b) 2030. The resulting demand pattern under the TOU pr programogram is derived by superimposing the demand profilesprofilesThe in resulting the the form form demand of of a astandard standard pattern normal under normal thedistributi distribution TOU pronogram with with threeis derived three ratios ratios by adjusted superimposing adjusted for high-, for high-,the mid-, demand mid-, and andlow-rateprofiles low-rate insegments. the segments. form The of a ratios Thestandard ratios for each normal for segment each distributi segment are determinedon are with determined three based ratios on based adjustedactual on demand actual for high-, demand ratios mid-, in ratios each and insegmentlow-rate each segment forsegments. Jeju forIsland: The Jeju ratios Island:54% in for the 54% each low-rate in segment the low-rate segment, are determined segment, 33% in 33%the based mid-rate in theon actual mid-rate segment, demand segment, and ratios 13% and in in each 13% the inhigh-ratesegment the high-rate forsegment Jeju segment Island: [19]. 54% [Therefore,19]. in Therefore, the low-rateby imposing by imposing segment, these these33% segment in segment the mid-ratedemand demand segment,ratios, ratios, the theand actual actual 13% in price the elasticityhigh-rate ofsegment demand [19]. for EVs Therefore, is reflectedreflected by ininimposing thethe TOUTOU these programprogram segment demanddemand demand pattern.pattern. ratios, the actual price elasticityFigure of7 7demand shows shows howhow for EVs thethe patternpatternis reflected ofof thethe in netthenet loadloadTOU will willprogram changechange demand ifif demanddemand pattern. fromfrom thethe TOUTOU programprogram isis introducedFigure in7 shows 2019 and how 2030.2030. the pattern Although Although of the the the net 2019 2019 load re results sultswill changedo not ifshow demand a significantsignificant from the impactTOU program from the is TOUintroduced program in due2019 to and a lack 2030. of Although electricity demandthe 2019 fromfrreomsults EVs, do thenot 2030show results a significant reduce theimpact gap from between the theTOU lowest program and due highest to a lack demand of electricity periods demandby active actively frlyom raising EVs, thedemand demand 2030 resultsduring during reduce the the duck duck the curve curvegap between hours. hours. Thisthe lowest shows and that highest the TOU demand program periods helps to by improve actively theth raisinge eefficiencyfficiency demand of the during power the system duck by curve mitigating hours. theThis severe shows duck that curvecurvethe TOU problem.problem. program helps to improve the efficiency of the power system by mitigating the severe duck curve problem.

(a) (b) (a) (b) Figure 7. Net load changes with EV demand affect affecteded by a TOU program in 2019 and 2030: ( a)) 2019; Figure 7. Net load changes with EV demand affected by a TOU program in 2019 and 2030: (a) 2019; (b) 2030.2030. (b) 2030. 4. Results Analysis 4. Results Analysis 4.1. The Impact of an EV Demand Response (DR) under LowLow VariableVariable RenewableRenewable SourcesSources (VRS)(VRS) LevelLevel (2019) 4.1. The Impact of an EV Demand Response (DR) under Low Variable Renewable Sources (VRS) Level (2019)Figure 8 shows the 24 h expected dispatch profiles by generation sources for peak day demand (2019) in 2019.Figure It can 8 beshows seen the that 24 energy h expected inflow dispatch from the mainlandprofiles by through generation High sources VoltageDirect for peak Current(HVDC) day demand lines,in 2019.Figure diesel It power,8can shows be and seenthe thermal 24 that h expected energy power dispatch provideinflow electricityfromprofiles the by formainland generation base-load through sources demand, Highfor and peak combined-cycleVoltage day demand Direct thermalin 2019. power It can and be gasseen turbine that powerenergy are inflow employed from to the meet mainland peak demand through inJeju. High Voltage Direct

Energies 2020, 13, x FOR PEER REVIEW 11 of 22

Current(HVDC) lines, diesel power, and thermal power provide electricity for base-load demand, Energiesand combined-cycle2020, 13, 4365 thermal power and gas turbine power are employed to meet peak demand11 of in 22 Jeju.

Figure 8. Expected dispatch profiles for summer peak day in 2019. Figure 8. Expected dispatch profiles for summer peak day in 2019. Case 1 shows that high renewable energy generation in Jeju Island is causing a moderate duck curveCase at peak 1 shows hours. that In high Case renewable 2, as the size energy of the generati EV demandon in resourceJeju Island is is small, causing the eaff moderateect of the duck TOU programcurve at peak is not hours. apparent. In Case If the2, as program the size of is th smartlye EV demand managed resource by a VPP, is sma asll, in the Case effect 3, EV of the demand TOU increasesprogram inis thenot earlyapparent. morning If the hours program between is smartl 1 am andy managed 4 am, utilizing by a VPP, inexpensive as in Case generation 3, EV demand from TP. EVincreases demand in the is marginal early morning in Case hours 3 because between the 1 amount am and of 4 energyam, utilizing consumed inexpensive daily for generation each EV isfrom not highTP. EV in demand 2019. is marginal in Case 3 because the amount of energy consumed daily for each EV is not highIn Case in 2019. 4, the colored area above the base demand line (orange line) indicates that EVs are purchasingIn Case energy, 4, the andcolored the area belowabove the demandbase demand linemeans line (orange that EVs line) are indicates injecting that energy EVs back are intopurchasing the grid. energy, Case 4and shows the morearea below active the charging demand during line means the early that morning EVs are hours, injecting when energy energy back is inexpensive,into the grid. and Case more 4 shows active more discharging active duringcharging the during peak hours the early between morning 11 am hours, and 7 pm, when when energy energy is isinexpensive, expensive. Theand amountmore active of load discharging shifting is during much larger the peak than hours in Case between 3 because 11 EVsam and fully 7 utilize pm, when their batteryenergy capacityis expensive. to eff ectivelyThe amount shift of load. load As shifting a result, is the much duck larger curve than problem in Case is largely 3 because mitigated. EVs fully utilizeTable their4 summarizes battery capacity the daily to effectively power generation shift load. and As reserve a result, capacity the duck required curve for problem the summer is largely peak daymitigated. in 2019. Renewable generation and conventional generation are noted as expected values because the amountTable 4 ofsummarizes generation the varies daily stochastically power generation depending and onreserve renewable capacity generation required and for contingencythe summer scenarios;peak day in meanwhile, 2019. Renewable the reserve generation amount and is notedconven astional an actual generation value asare this noted is the as expected reserve amount values necessarybecause the to guardamount against of generation all uncertain varies scenarios stochastically in the simulation. depending on renewable generation and contingency scenarios; meanwhile, the reserve amount is noted as an actual value as this is the reserve amount necessary toTable guard 4. Daily against generation all uncertain and reserve scenarios for a summerin the simulation. peak day in 2019.

MWh/day c1_2019 c2_2019 c3_2019 c4_2019 Wind generation 1451.6 1451.6 1464.8 1463.0 Solar PV generation 1130.1 1130.1 1130.6 1130.4 Conventional generation 17,923.2 17,920.2 17,908.7 17,982.2 Total reserve 4899.0 4887.2 3295.4 1172.9 Load-following reserve 2731.7 2719.9 1741.0 748.6 Contingency reserve 2167.2 2167.2 1554.4 424.3

Load shedding 0.1 0.1 0.1 0.0 Energies 2020, 13, 4365 12 of 22

The results for Case 2 are similar to those for Case 1. The total reserve requirement decreases slightly due to the TOU program’s marginal contribution to the duck curve problem; however, the Case 3 scenario shows that the amount of conventional generation and reserve requirements are significantly reduced. The reduction in conventional generation is due to accommodating more renewable generation as EV electricity demand helps to mitigate variability from renewable sources; the reduction in the reserve requirement is due to the use of EV DR as ancillary service resources. Case 4 shows a significant reduction in the amount of reserve required, but conventional energy generation increases. This shows that EV DR could be used more effectively for ancillary services in the presence of V2G technology; however, electricity demand increases due to the round trip inefficiency of EV batteries charging and discharging, which results in an increase in conventional generation. Table5 summarizes the daily operating costs including generation and reserve costs for peak day demand in 2019. Case 2 shows a marginal reduction in the generation cost compared to Case 1 and does not achieve a significant reduction in the reserve cost. Case 3 shows a meaningful reduction in both generation and reserve costs—approximately 6200 USD/day and 5500 USD/day, respectively. The proportion of the total daily reserve cost is less than 1% of the total operating cost, but the reserve cost reduction takes approximately 47% of the total operating cost reduction which is composed of a 39.5% reduction in reserve cost and a 0.3% reduction in generation cost.

Table 5. Daily operating costs of generation and reserve for a summer peak day in 2019.

1000 USD/day 1 c1_2019 c2_2019 c3_2019 c4_2019 Generation cost 1794.2 1791.8 1788.0 1779.3 Total reserve cost 13.9 13.9 8.4 2.9 Load-following reserve cost 8.1 8.0 4.7 1.9 Contingency reserve cost 5.8 5.8 3.8 1.0 Load shedding * Value of lost load 0.7 0.7 0.7 0.1 Total operating cost 1808.8 1806.3 1797.1 1782.3

Generation cost reduction from c1 0.1% 0.3% 0.8% − Total reserve cost reduction from c1 0.0% 39.5% 79.0% − Total operating cost reduction from c1 0.1% 0.6% 1.5% − 1 A currency exchange rate of KRW 1200/USD is applied to all costs in this study.

Case 4 shows a 1.5% decrease in the total operating cost compared to Case 1, comprised in part of a 0.8% decrease in generation cost and a 79% decrease in reserve cost. The total operating cost reduction from the VPP2 program in Case 4 is almost three times higher than in Case 3. This is achieved by signiﬁcant reductions in both generation and reserve costs. The reserve cost is reduced by approximately 79% compared to Case 1, which shows that EV demand controlled by the VPP2 program can provide eﬀective ancillary service capacity for renewable sources.

4.2. The Impact of an EV DR Program under High VRS Level (2030) Figure9 shows the expected 24 h dispatch profiles for the summer peak day peak day in 2030. Case 1 shows that the Jeju Island power system has the problem of negative net load from 12 pm to 4 pm due to concentrated generation from renewable sources, particularly solar PV. In Case 2, EV DR under the proposed TOU program resolves the negative net load problem by increasing demand during duck curve hours. In Case 3, the demand control under the VPP1 program effectively resolves the duck curve by increasing EV demand during peak hours and reducing it during off-peak hours, providing a reliable and cost-effective power supply. Case 4 further shifts the net load supplied by expensive combined-cycle units to more cost-effective thermal power units. Energies 2020, 13, x FOR PEER REVIEW 13 of 22

4.2. The Impact of an EV DR Program under High VRS Level (2030) Figure 9 shows the expected 24 h dispatch profiles for the summer peak day peak day in 2030. Case 1 shows that the Jeju Island power system has the problem of negative net load from 12 pm to 4 pm due to concentrated generation from renewable sources, particularly solar PV. In Case 2, EV DR under the proposed TOU program resolves the negative net load problem by increasing demand during duck curve hours. In Case 3, the demand control under the VPP1 program effectively resolves the duck curve by increasing EV demand during peak hours and reducing it during off-peak hours, providing a reliable and cost-effective power supply. Case 4 further shifts the net load supplied by Energies 2020, 13, 4365 13 of 22 expensive combined-cycle units to more cost-effective thermal power units.

Figure 9. Expected dispatch profiles for a summer peak day in 2030. Figure 9. Expected dispatch profiles for a summer peak day in 2030. Cases 3 and 4 do not display significantly different results. This is because this analysis assumes 100%Cases EV demand 3 and 4 participation.do not display The significantly planned numberdifferent of results. EVs by This 2030 is isbecause significant this analysis compared assumes to the planned100% EV powerdemand system participation. capacity; The therefore, planned most number power of EVs supply by 2030 issues is wouldsignificant be resolved compared if allto the EV customersplanned power were system to participate capacity; in therefore, the VPP1 program,most power even supply with issues very high would VRSs. be resolved Hence, theif all VPP2 EV programcustomers does were not to greatly participate contribute in the additional VPP1 progra benefits.m, even To analyzewith very the high impact VRSs. of the Hence, VPP2 the program, VPP2 theprogram effect does of various not greatly EV participation contribute additional rates are assessed benefits. in To Section analyze 4.4 the. impact of the VPP2 program, the effectTable of6 summarizesvarious EV participation the daily amount rates of are generation assessed in and Section reserve 4.4. needed in the peak summer day in 2030,Table characterized 6 summarizes by the a high daily renewable amount of capacity generation situation. and reserve In Case needed 1, significant in the peak load summer shedding day occursin 2030, with characterized severe negative by a high net loads.renewable To achieve capacity a feasiblesituation. optimal In Case solution, 1, significant the MPSOPF load shedding assigns 10,000occurs USDwith/ MWh,severe negative or 100 times net loads. the normal To achieve peak a SMP, feasible as the optimal value solution, of lost load, the MPSOPF and allows assigns load shedding10,000 USD/MWh, if it is economically or 100 times feasible the normal even with peak high SMP, costs. as the value of lost load, and allows load shedding if it is economically feasible even with high costs. Table 6. Daily generation and reserve for a summer peak day in 2030.

MWh/day c1_2030 c2_2030 c3_2030 c4_2030 Wind generation 12,159.3 12,233.8 12,522.9 12,522.9 Solar PV generation 8654.3 8655.1 8679.5 8679.5 Conventional generation 21,683.7 21,666.2 21,355.8 21,803.1 Total reserve 25,907.9 28,881.8 8721.1 487.4 Load-following reserve 17,136.3 19,101.1 5786.2 415.2 Contingency reserve 8771.6 9780.7 2935.0 72.3 Load shedding 59.8 0.1 0.0 0.0

In Case 2, most of the load shedding problem is resolved as demand control under the TOU program effectively increases charging consumption during the hours that the power system suffers from a negative net load. Case 3, with very high EV demand capacity under the VPP1 program, accommodates substantially more wind energy compared to Case 1 by effectively mitigating wind Energies 2020, 13, 4365 14 of 22 variability; as a result, the amount of reserve needed is reduced to almost one-third of that in Case 1, and the amount of conventional generation is also reduced. Case 4 is similar to Case 3 due to the high level of EV participation in the demand program. However, Case 4 further reduces 95% of reserve required in Case 3. This means that a VPP2 program with V2G capability replaces reserve capacities effectively by actively reducing the variability of renewable energy sources. Table7 summarizes the daily operating costs of generation and reserve in 2030. Case 2 reduces the total operating cost by 23.9%, mainly due to a reduction in generation cost and the cost related to load shedding caused by the serious duck curve. In Case 3, both generation and reserve costs are considerably reduced, which leads to a total operating cost reduction of 31.9% compared to Case 1. In Case 4, generation cost is slightly increased but reserve cost is significantly decreased compared to Case 3, which shows that the optimal use of EV demand under a VPP2 program focus more on mitigating the variability of renewable energy sources and less on load shifting.

Table 7. Daily operating costs of generation and reserve for a summer peak day in 2030.

1000 USD/day c1_2030 c2_2030 c3_2030 c4_2030 Generation cost 2785.9 2545.7 2329.2 2339.2 Total reserve cost 82.3 91.4 30.5 2.3 Load-following reserve cost 54.3 60.2 20.2 2.1 Contingency reserve cost 28.0 31.2 10.3 0.2 Load shedding * Value of lost load 597.8 0.9 0.4 0.0 Total operating cost 3466.0 2638.0 2360.1 2341.5

Generation cost reduction from c1 8.6% 16.4% 16.0% − Total reserve cost reduction from c1 11.1% 62.9% 97.2% − − Total operating cost reduction from c1 23.9% 31.9% 32.4% − Total operating cost reduction without load shedding from c1 8.1% 17.7% 18.4% −

Figure 10 illustrates the monthly cost reduction per EV by the different DR programs in 2019 and 2030. In 2019, the cost reduction by the TOU program is limited, while the benefits from the VPP2 program are almost double that of the VPP1 program. The reserve cost saving is almost as large as generation cost saving in both VPP1 and VPP2 programs, which shows that it is an important contribution that EV DR can provide. In 2030, the cost savings per EV in Case 2 and Case 3 are increased as EV DR can effectively contribute to solve the problem caused by high VRS sources. However, the cost saving per EV in Case 4 is not very different to the cost saving of Case 3 and it is actually reduced compared to that in 2019. This is because the number of EV in 2030 is too large to the size of the system, so most problems are solved by VPP1 and only little additional cost reduction is achieved by V2G. In order to estimate the true contribution that each EV DR resource can provide to the system with varying VRS penetration, we analyzed the cost saving with the same number of EVs in 2019 and 2030. To equalize the number of EVs in 2019 and 2030, we assumed 6.2% of total EVs participate in the DR program in 2030. As shown in Figure 11, monthly cost saving in 2019 are 2.9 USD/month, 13.8 USD/month, and 31.5 USD/month for Case 2, Case 3, and Case 4, respectively, whereas those in 2030 are 28.5 USD/month, 65.8 USD/month, and 202.1 USD/month, respectively. This shows that the value of the EV DR is much higher in a power system with a high penetration of VRS sources because the EV DR can effectively reduce the high operating costs caused by the variability and uncertainty of VRS. Energies 2020, 13, x FOR PEER REVIEW 15 of 22

Energies 2020, 13, 4365 15 of 22 Energies 2020, 13, x FOR PEER( REVIEWa) (b) 15 of 22

Figure 10. Monthly cost saving per EV under varying DR programs in 2019 and 2030: (a) 2019; (b) 2030.

In 2030, the cost savings per EV in Case 2 and Case 3 are increased as EV DR can effectively contribute to solve the problem caused by high VRS sources. However, the cost saving per EV in Case 4 is not very different to the cost saving of Case 3 and it is actually reduced compared to that in 2019. This is because the number of EV in 2030 is too large to the size of the system, so most problems are solved by VPP1 and only little additional cost reduction is achieved by V2G. In order to estimate the true contribution that each EV DR resource can provide to the system with varying VRS penetration, we analyzed the cost saving with the same number of EVs in 2019 and 2030. To equalize the number of EVs in 2019 and 2030, we assumed 6.2% of total EVs participate in the DR program in 2030. As shown in Figure 11, monthly cost saving in 2019 are 2.9 USD/month, 13.8 USD/month, and 31.5 USD/month for Case 2, Case 3, and Case 4, respectively, whereas those in 2030 are 28.5 USD/month, 65.8 USD/month, and 202.1 USD/month, respectively. This shows that the value of the EV DR is much higher in a power system with a high penetration of VRS sources because the Figure 11. Adjusted monthly cost saving pe perr EV customer in 2019 and 2030. EV DR can effectively reduce the high operating costs caused by the variability and uncertainty of VRS. The implications of the scenario analyses in 2019 and 2030 can be summarized in two main points. First, EV demand is is an effective effective resource to enhance the reliability of a power system that is undermined by a high penetration of renewable ener energygy sources. In 2030, when the capacity of VRS increases to 210% of the peak demand, EV DR redu reducesces the operating cost sign significantlyificantly by by effectively effectively mitigating a severe duck curve problem. Second, Second, DR under under a a VPP VPP program program significantly significantly outperforms a TOU program; however, the additional benefit from V2G technology in the VPP2 program is not significant when the size of the EV demand resource is large relative to the size of the power system, because most existing issues are resolved by the VPP1.

4.3. Optimal Charging and Discharging Profiles of EVs by Different Control Structures Figure 12 illustrates the optimal charging and discharging profiles of EVs by the four different demand control programs in 2019 and 2030. In 2019, the low net load hours are from 1 am to 6 am, therefore all DR programs attempt to shift load to these hours, but the magnitude differs. Both the TOU and VPP1 programs slightly increase EV demand during the low net load hours, while the VPP2 program, whichFigure fully utilizes 11. Adjusted the EV monthly battery, cost shows saving a significantper EV customer demand in 2019 increase and 2030. in the early morning and substantial V2G discharging in the hours when expensive combined-cycle plants are heavily used. The diThefferent implications charging of profiles the scenario between analyses the VPP1 in and2019 VPP2 and programs2030 can be show summarized that V2G capabilityin two main can points.more actively First, EV contribute demand tois enhancean effective the eresourcefficiency to of enhance power system the reliability operation. of a power system that is undermined by a high penetration of renewable energy sources. In 2030, when the capacity of VRS increases to 210% of the peak demand, EV DR reduces the operating cost significantly by effectively mitigating a severe duck curve problem. Second, DR under a VPP program significantly outperforms

Energies 2020, 13, x FOR PEER REVIEW 16 of 22

a TOU program; however, the additional benefit from V2G technology in the VPP2 program is not significant when the size of the EV demand resource is large relative to the size of the power system, because most existing issues are resolved by the VPP1.

4.3. Optimal Charging and Discharging Profiles of EVs by Different Control Structures Figure 12 illustrates the optimal charging and discharging profiles of EVs by the four different demand control programs in 2019 and 2030. In 2019, the low net load hours are from 1 am to 6 am, therefore all DR programs attempt to shift load to these hours, but the magnitude differs. Both the TOU and VPP1 programs slightly increase EV demand during the low net load hours, while the VPP2 program, which fully utilizes the EV battery, shows a significant demand increase in the early morning and substantial V2G discharging in the hours when expensive combined-cycle plants are heavily used. The different charging profiles between the VPP1 and VPP2 programs show that V2G Energies 2020, 13, 4365 16 of 22 capability can more actively contribute to enhance the efficiency of power system operation.

(a) (b)

FigureFigure 12. 12.Optimal Optimal charging charging/dischar/dischargingging profiles profiles of DRof DR programs programs in 2019in 2019 and and 2030: 2030: (a) 2019;(a) 2019; (b) ( 2030.b) 2030. However, in 2030, demand increases for all four programs during duck curve hours, whenHowever, generation in from2030, renewabledemand increases sources isfor concentrated. all four programs DR underduring the duck TOU curve program hours, slightly when increasesgeneration during from therenewable duck curve sources hours, is butconcentrat unlike theed. 2019DR under scenario, the theTOU charging program profiles slightly for increases the VPP1 andduring VPP2 the programs duck curve are hours, similar but to eachunlike other. the 2019 As discussed scenario, earlier,the charging this is dueprofiles to the for large the sizeVPP1 of and the EVVPP2 resource programs in 2030: are similar under a to full each participation other. As discussed scenario, V2G earlier, technology this is due does to not the add large additional size of the value EV toresource improve in the2030: effi underciency a of full the participation power system. scenario, V2G technology does not add additional value to improve the efficiency of the power system. 4.4. Net Cost Saving from the EV DR Programs by Varying the Participation Rate 4.4. NetAs Cost presented Saving infrom Table the8 EV, the DR ratio Programs of EV by hourly Varying charging the Participation power capacityRate to peak demand is 1.58 underAs presented a 100% in participation Table 8, the scenario ratio of EV in 2030.hourly This charging means power the possible capacity amount to peak of demand energy that is 1.58 an EVunder can a charge 100% participation in an hour is 1.58scenario times in the 2030. peak This demand means ofthe the possible system, amount which isof very energy high that and an does EV notcan providecharge in the an analysis hour is for1.58 a times more realisticthe peak situation. demand of Hence, the system, we conducted which is an very analysis high withand does varying not participationprovide the analysis rates of for 10%, a more 25%, 50%,realistic and situation. 75%. As Hence, seen in we Table conducted8, the charging an analysis power with capacity varying to peakparticipation demand rates ratio of is 0.1610%, at25%, 10% 50%, participation, and 75%. whichAs seen is in a realisticTable 8, level the charging that can bepower achieved capacity in the to nearpeak future.demand ratio is 0.16 at 10% participation, which is a realistic level that can be achieved in the near future. Table 8. Charging power capacity to peak demand ratio by various EV participation rates in 2030.

Table 8. ChargingParticipation power Ratecapacity of EV to Demandpeak demand ratio by10% various 25% EV participation 50% 75% rates 100% in 2030. Charging PowerParticipation Capacity Rate to of Peak EV DemandDemandRatio 0.1610% 0.3025% 50% 0.79 75% 1.18 100% 1.58 Charging Power Capacity to Peak Demand Ratio 0.16 0.30 0.79 1.18 1.58 Figure 13 shows the expected 24 h dispatch profiles for varying EV participation rates in 2030. Figure 13 shows the expected 24 h dispatch profiles for varying EV participation rates in 2030. Case 2 shows marginal changes with different participation rates, and as EV demand increases, the low Case 2 shows marginal changes with different participation rates, and as EV demand increases, the net load slowly increases in duck curve hours. Case 3 shows significant improvement in the net load low net load slowly increases in duck curve hours. Case 3 shows significant improvement in the net in duck curve hours as the participation rate increases. In Case 4, when the participation rate is at 25%, the net load profile differs significantly from that of Case 3, which shows the beneficial impact of V2G technology. However, the difference between Case 3 and Case 4 reduces as the participation rate rises. Table9 summarizes the monthly gross cost saving, induced cost, and net cost saving per EV for the TOU, VPP1, and VPP2 programs compared to Case 1 by varying participation rate in 2030. Four seasonal representative days are selected to derive the annualized cost saving based on an interpolation method. The results show that the lower the participation rate, the higher the per-EV benefit, because EV demand reduces the most expensive cost factors first if it is optimally used in the grid. Under a realistic 10% participation rate scenario, the cost saving from the TOU, VPP1, and VPP2 programs is 23.3 USD/month, 59.4 USD/month, and 185.3 USD/month, respectively. Energies 2020, 13, x FOR PEER REVIEW 17 of 22

load in duck curve hours as the participation rate increases. In Case 4, when the participation rate is at 25%, the net load profile differs significantly from that of Case 3, which shows the beneficial impact of V2G technology. However, the difference between Case 3 and Case 4 reduces as the participation Energies 2020, 13, 4365 17 of 22 rate rises.

Figure 13. Expected 24-h dispatch proﬁles for varying EV participation rates in 2030. Figure 13. Expected 24-hour dispatch profiles for varying EV participation rates in 2030. Table 9. Monthly net cost saving per EV by varying participation rates (USD/month). Table 9 summarizes the monthly gross cost saving, induced cost, and net cost saving per EV for Gross Cost Saving Induced Cost Net Cost Saving the TOU, ParticipationVPP1, and VPP2 programs compared to Case 1 by varying participation rate in 2030. Four Rate TOU VPP1 VPP2 TOU VPP1 VPP2 TOU VPP1 VPP2 seasonal representative days are selected to derive the annualized cost saving based on an 10% 23.3 59.4 185.3 8.87 112.64 23.34 50.51 72.69 interpolation method. The results show that the− lower the participation rate, the higher the per-EV 25% 18.3 47.7 131.9 8.87 92.31 18.27 38.79 39.63 benefit, because EV demand reduces the most expensive− cost factors first if it is optimally used in the 50% 16.9 45.6 76.4 8.87 50.68 16.90 36.77 25.71 grid. Under a realistic 10% participation rate scenario,− the cost saving from the TOU, VPP1, and VPP2 75% 15.6 37.4 51.2 8.87 31.32 15.64 28.53 19.90 programs is 23.3 USD/month, 59.4 USD/month, −and 185.3 USD/month, respectively. 100% 14.7 31.7 33.8 8.87 22.91 14.73 22.88 10.84 − Table 9. Monthly net cost saving per EV by varying participation rates (USD/month).

ParticipatiIt should be notedGross that Cost this Saving monthly saving is Induced not entirely Cost realized by the Net consumer; Cost Saving additional costson relatedRate to providingTOU VPP1 the EV DRVPP2 should beTOU considered. VPP1 There VPP2 are three categoriesTOU of VPP1 additional VPP2 costs. 10%First, a commission 23.3 must 59.4 be paid 185.3 to the aggregator− 8.87 for operating 112.64 my 23.34 EV DR optimally 50.51 through 72.69 the VPP.25% Based 18.3 on the current 47.7 DR 131.9 program in− Korea, 8.87 the average 92.31 commission 18.27 for 38.79 EV demand 39.63 is estimated50% at 8.87 16.9 USD /month 45.6 (computed 76.4 based− on a 8.87 capacity 50.68 payment 16.90 of 35.8 USD 36.77/kW, anenergy 25.71 payment75% of 7.1 cents 15.6 /kWh, 37.4 and a commission 51.2 rate− to total 8.87 compensation 31.32 of 15.64 30%) [25 28.53]. This amount 19.90 is applied100% to the VPP1 14.7 program, 31.7 which 33.8 manages G2V− only. 8.87 It is assumed 22.91 that 14.73 the VPP2 22.88 program requires 10.84 more sophisticated and active demand control, and thus, we double the commission. The commission cost isIt notshould relevant be noted to the that TOU this program monthly as saving the TOU is not does entirely not require realized an aggregator.by the consumer; additional costsSecond, related to if EVproviding batteries the are EV actively DR should utilized be co asnsidered. DR resources, There are the three wear-and-tear categories of cost additional caused bycosts. frequent battery cycling should be considered. The battery cycling cost is estimated to be 118.3First, USD/ montha commission at the 10% must participation be paid to ratethe aggregator and 28.5 USD for/month operating (computed my EV basedDR optimally on an EV through battery packagethe VPP. cost Based of 300 on USDthe current/kWh, a DR battery program life span in Ko ofrea, 10 years, the average a battery commission cycle life of for 3000 EV cycles, demand and is a 70%estimated depth at of 8.87 discharge) USD/month at the (com 100%puted participation based on ratea capacity [26]. Figure paym 14ent demonstrates of 35.8 USD/kW, the reasonan energy for varyingpayment battery of 7.1 cents/kWh, cycling costs and for a di commissionﬀerent the participation rate to total compensation rate scenarios. of The 30%) black [25]. solid This line amount shows is theapplied expected to the energy VPP1 level program, in the batterywhich andmanages the red G2 dashedV only. line It showsis assumed the maximum that the usableVPP2 program capacity, which is 48.5 kWh/vehicle after applying a 70% depth of discharge rate. The green and blue dashed lines show the possible boundary of battery energy levels caused by the uncertainty of renewable sources, reﬂecting that the battery actively charges or discharges to provide reserve capacity for Energies 2020, 13, x FOR PEER REVIEW 18 of 22

requires more sophisticated and active demand control, and thus, we double the commission. The commission cost is not relevant to the TOU program as the TOU does not require an aggregator. Second, if EV batteries are actively utilized as DR resources, the wear-and-tear cost caused by frequent battery cycling should be considered. The battery cycling cost is estimated to be 118.3 USD/month at the 10% participation rate and 28.5 USD/month (computed based on an EV battery package cost of 300 USD/kWh, a battery life span of 10 years, a battery cycle life of 3000 cycles, and a 70% depth of discharge) at the 100% participation rate [26]. Figure 14 demonstrates the reason for varying battery cycling costs for different the participation rate scenarios. The black solid line shows the expected energy level in the battery and the red dashed line shows the maximum usable capacity, which is 48.5 kWh/vehicle after applying a 70% depth of discharge rate. The green and blue dashed Energieslines show2020, 13the, 4365 possible boundary of battery energy levels caused by the uncertainty of renewable18 of 22 sources, reflecting that the battery actively charges or discharges to provide reserve capacity for renewable energy sources. It is estimated that a 10% participation case has a cycle of 0.930.93/day/day and a 100%100% participationparticipation case has a cycle of 0.220.22/day./day. In order to estimate purely additional battery cycling cost for providing DRDR service,service, batterybattery cyclingcycling routinelyroutinely occurringoccurring duedue toto commutingcommuting isis subtracted.subtracted.

(a) (b)

Figure 14. AverageAverage cycling cycling pattern pattern of of an an EV EV battery battery fo forr 10% 10% and and 100% 100% participation participation rates rates in 2030: in 2030: (a) (10%a) 10% participation; participation; (b) (100%b) 100% participation. participation.

Third, the cost of inconvenience for customers in providing the DR service must be considered. Customers under a TOU program must voluntarily shiftshift demand from time to time,time, andand customerscustomers under the the VPP1 VPP1 and and VPP2 VPP2 programs programs are are required required to co tonstantly constantly connect connect their their vehicles vehicles to the to grid the using grid usingportable portable chargers chargers when not when in operation. not in operation. However, However, as this cost as thisis subjective cost is subjective and difficult and to di quantify,fficult to quantify,we calculate we calculatethe net thecost net saving cost saving for customers for customers and anddiscuss discuss whether whether it is it isenough enough to to offset offset the inconvenienceinconvenience ofof providingproviding thethe DRDR serviceservice inin thethe discussion.discussion. Figure 15 highlights the gross cost saving and net cost saving in the four EV DR programs after considering the induced costs presented in Table9 9.. AtAt aa 10%10% participation participation rate,rate, thethe VPP2VPP2 programprogram has a substantial gross cost saving of 185.3 USD/mo USD/month;nth; however, withwith high battery cycling costs and a commissioncommission for an aggregator,aggregator, thethe netnet costcost savingsaving isis approximatelyapproximately 72.6972.69 USDUSD/month./month. The VPP1 program has a lowerlower grossgross costcost savingsaving ofof 59.459.4 USDUSD/month,/month, butbut thethe aggregatoraggregator commissioncommission is lower and there is no additional battery cycling cost incu incurred;rred; thus, the net cost saving is is 50.51 50.51 USD/month. USD/month. The grossgross cost cost saving saving for for the the TOU TOU program program is much is mu lowerch atlower 23.3 USDat 23.3/month, USD/month, but there but is no there additional is no cost;additional thus, thecost; net thus, cost the saving net cost remains saving at 23.3remains USD at/month. 23.3 USD/month. While the analysis shows that the VPP2 program provides a significantly larger gross cost saving than the VPP1 program, the net cost saving reveals different results. As the EV participation rate increases, the net cost saving realized in the VPP2 program rapidly decreases due to decreased per-EV cost saving and high battery cycling costs. As a result, the net cost saving in the VPP2 program falls below that of the VPP1 program after the 25% participation rate is reached, and falls below the TOU program at the 100% participation rate. The benefits to customers at the 10% participation rate in the VPP2 and VPP1 programs are much higher than those in the TOU program, and considering the monthly average EV energy cost of 29.1 USD/month (estimated based on an average EV energy consumption of 9.39 kWh/day, an average electricity rate of 0.096 USD/kWh, and a monthly fixed rate of 1.99 USD/month), the VPP2 and VPP1 programs allow customers to run EVs for a negative net payment; in other words, customers get paid to run EVs by participating in the program. This shows that even when considering the inconvenience costs of providing DR services, the incentives to participate can be sufficient if the cost saving that EV DR customers provide is correctly transferred to the service providers. The net benefit from the TOU Energies 2020, 13, 4365 19 of 22 program is not as large as those of the other programs, but customers can still reduce approximately 80% of their EV energy cost. In addition, considering that the TOU program is very easy to implement

Energiesadministratively 2020, 13, x FOR and PEER technically, REVIEW this is also an eﬀective alternative to incentivize EV DR to participate.19 of 22

(a) (b)

Figure 15. MonthlyMonthly gross gross cost cost saving saving and and net net cost cost saving saving per per EV by varying participation rates (USD/month):(USD/month): ( a)) gross gross cost saving; ( b) net cost saving.

5. ConclusionsWhile the analysis shows that the VPP2 program provides a significantly larger gross cost saving than Inthe this VPP1 study, program, the economic the net valuescost saving of various reveal EVs different DR programs results. are As assessed the EV inparticipation a power system rate increases,with different the net levels cost of saving VRS forrealized JejuIsland, in the VP Korea.P2 program The main rapidly results decreases that this due study to decreased found can per- be EVsummarized cost saving below. and high battery cycling costs. As a result, the net cost saving in the VPP2 program falls belowFirst, the that cost of the saving VPP1 of anprogram EV DR after program the 25% is highly participation dependent rate on is thereached, level ofand VRS falls in thebelow power the TOUsystem. program In 2019, at the the cost 100% savings participation that can rate. be achieved by an EV customer for the TOU, VPP1, and VPP2 programsThe benefits are 2.9 to USD customers/month, at 13.8 the USD 10%/ month,participatio andn 31.5 rate USD in the/month, VPP2 and respectively; VPP1 programs in 2030 are with much the highersame EV than DR those capacity, in the the TOU cost program, saving is and 28.5 consider USD/month,ing the 65.8 monthly USD/ month,average andEV energy 202.1 USD cost/ month,of 29.1 USD/monthrespectively. (estimated The higher based benefits on inan 2030, average when EV the energy VRS capacity consumption is higher of 9.39 shows kWh/day, that EV an DR average is more electricityvaluable as rate it e ffofectively 0.096 USD/kWh, reduce the and high a operatingmonthly fixed cost causedrate of 1.99 by the USD/month), high variability the VPP2 and uncertainty and VPP1 programsof VRS sources. allow customers to run EVs for a negative net payment; in other words, customers get paid to runSecond, EVs by atparticipating a reasonable in the 10% program. EV participation This shows rate, that the even gross when cost considering saving per the EV inconvenience customer is costs23.3 USDof providing/month,59.4 DR USDservices,/month, the incentives and 185.3 USDto participate/month for can the be TOU, sufficient VPP1, if andthe VPP2cost saving programs that EVin 2030,DR customers respectively. provide When is thecorrectly costs requiredtransferred to implementto the service the providers. programs The are net considered, benefit from such the as TOUaggregator program commission is not as and large battery as those cycling of costs,the other the net programs, cost saving but is reducedcustomers to 23.2can USDstill /reducemonth, approximately50.5 USD/month, 80% and of 72.7their USDEV energy/month, cost. respectively. In addition, However, considering these that net the monthly TOU program cost savings is very are easystill higherto implement than the administratively average EV fuel and cost technically, of 29.1 USD this/month, is also andan effective the benefits alternative from both to incentivize the VPP1 EVand DR VPP2 to participate. programs are high enough to incentivize customers to join the DR program despite the inconveniences. The estimated benefit from the TOU program is marginally lower than the monthly 5. Conclusions fuel cost; however, it is the most easily implementable DR program and can potentially improve the efficiencyIn this of study, the power the economic system, especially values of when various coupled EV DR with programs critical peak are assessed pricing, to in make a power EV demand system withmore different responsive levels to price. of VRS for Jeju Island, Korea. The main results that this study found can be summarizedThird, when below. the EV participation rate increases, the monthly cost saving per customer in the VPP2 programFirst, rapidly the cost decreases saving of and an EV eventually DR program becomes is highly lower dependent than that inon the the TOU level program. of VRS in This the power shows system.that the optimalIn 2019, DRthe programcost savings that canthat achieve can be maximumachieved by operating an EV customer cost reduction for the will TOU, vary VPP1, depending and VPP2on the programs scale of EV are demand. 2.9 USD/month, 13.8 USD/month, and 31.5 USD/month, respectively; in 2030 with the sameAn EVEV DR capacity, program the can cost be saving an effective is 28.5 demand-side USD/month, 65.8 solution USD/month, with high and growth 202.1 USD/month, potential to respectively.mitigate the problemsThe higher caused benefits by highin 2030, levels when of VRSthe VR in theS capacity power system.is higher Moreover, shows that if EV the DR cost is saving more valuablethat EV DRas it can effectively achieve reduce in the systemthe high operation operating iscost eff ectivelycaused by transferred the high variability to customers, and uncertainty EV owners ofwill VRS be susources.fficiently incentivized to participate in the DR program. This shows that implementing an Second, at a reasonable 10% EV participation rate, the gross cost saving per EV customer is 23.3 USD/month, 59.4 USD/month, and 185.3 USD/month for the TOU, VPP1, and VPP2 programs in 2030, respectively. When the costs required to implement the programs are considered, such as aggregator commission and battery cycling costs, the net cost saving is reduced to 23.2 USD/month, 50.5 USD/month, and 72.7 USD/month, respectively. However, these net monthly cost savings are still higher than the average EV fuel cost of 29.1 USD/month, and the benefits from both the VPP1 and

Energies 2020, 13, 4365 20 of 22 appropriate DR program with an adequate compensation structure for customers will attract more DR customers to participate and this will help build a cost-eﬃcient and reliable power system that can accommodate more green energy. For future work, this study analyzed the value of EV demand resources in the Jeju grid which is approximately 1% of the national grid. To provide more valid evidence regarding the value of EV demand resources, this study must be extended to the national level by incorporating the national power grid and EV deployment plan.

Author Contributions: Conceptualization, W.J., S.C. and S.L.; methodology, W.J.; validation, W.J., S.C. and S.L.; formal analysis, W.J., S.L.; writing—original draft preparation, W.J.; writing—review and editing, S.C. and S.L. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2018S1A5A8028620). Acknowledgments: This research is partially based on the research report (19-25-03) from Korea Energy Economics Institute, but significantly improved and modified. Conflicts of Interest: The authors declare no conflict of interest.

Appendix A

Table A1. Deﬁnition of variables in multi-period security constraint optimal power ﬂow (MPSOPF).

Variables Description

T Set of time periods considered, nt elements indexed by t B Set of buses in the system, nb elements t S Set of states in the system in period t, ns elements indexed by s ts K Set of contingencies in the system in period t and state s, nc elements indexed by k tsk I Set of generators in the system in period t, state s, and contingency k, ng elements indexed by i tsk J Set of loads in the system in period t, state s, and contingency k, nl elements indexed by j πtsk Probability of contingency k occurring, in state s, period t ρt Probability of reaching period t Quantity of apparent power generated (MVA), active and reactive injections G itsk (p + √ 1q ) i t sk − i t sk Gitc Optimal contracted apparent power (MVA) tsk V Set of voltages in period t, state s and contingency k, nb elements for each bus in the system tsk θ Set of angles in period t, state s and contingency k, nb elements pitsk Active power generated (MW), 0 refers to base case(s), ng elements c pit Optimal contracted active power (MW), ng elements + Upward/downward deviation from active power contract quantity for unit i in p , p− itsk itsk post-contingency state k of state s at time t, ng elements C ( ) Cost of generating ( ) MVA of apparent power G · · + ( )+ Incits Cost of increasing generation from contracted amount · + Dec ( ) Cost of decreasing generation from contracted amount its− · VOLLj Value of lost load, ($) LNS( )jtsk Load not served (MWh) + · + Rit < Rampi (max(Gi t sk) Gi t c) , up reserves quantity (MW) in period t +( ) − CR Cost of providing ( ) MW of upward reserves · + · Rit− < Rampi (Gi t c min(Gi t sk)) , down reserves quantity (MW) ( ) − CR− Cost of providing ( ) MW of downward reserves + · · + Lit < Rampi (max(Gi,t+1,s) min(Gi t s)) , load follow up (MW) t to t + 1 +( ) − CL Cost of providing ( ) MW of load follow up · · + L− < Rampi (max(G ) min(G )) , load follow down (MW) it i t s − i,t+1,s C ( ) Cost of providing ( ) MW of load follow down L− · · +( )+ Rpit Cost of increasing generation from previous time period · + Rp ( ) Cost of decreasing generation from previous time period it− · Upward/downward load-following ramping reserves needed from unit i at time t for δ+, δ it it− transition to time t + 1 max+ max δit , δit − Upward/downward load-following ramping reserve limits for unit i fs(psc, psd) Value of the leftover stored energy in terminal states Energies 2020, 13, 4365 21 of 22

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