A Bi-Level Optimization Approach to Charging Load ... - MDPI

energies Article

A Bi-Level Optimization Approach to Charging Load Regulation of Electric Vehicle Fast Charging Stations Based on a Battery Energy Storage System Yan Bao 1 , Yu Luo 1 , Weige Zhang 1 , Mei Huang 1 , Le Yi Wang 2 1 2

*

ID

and Jiuchun Jiang 1, *

School of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China; [email protected] (Y.B.); [email protected] (Y.L.); [email protected] (W.Z.); [email protected] (M.H.) Department of Electrical and Computer Engineering, Wayne State University, Detroit, MI 48202, USA; [email protected] Correspondence: [email protected]; Tel.: +86-10-5168-3907

Received: 20 December 2017; Accepted: 15 January 2018; Published: 18 January 2018

Abstract: Fast charging stations enable the high-powered rapid recharging of electric vehicles. However, these stations also face challenges due to power fluctuations, high peak loads, and low load factors, affecting the reliable and economic operation of charging stations and distribution networks. This paper introduces a battery energy storage system (BESS) for charging load control, which is a more user-friendly approach and is more robust to perturbations. With the goals of peak-shaving, total electricity cost reduction, and minimization of variation in the state-of-charge (SOC) range, a BESS-based bi-level optimization strategy for the charging load regulation of fast charging stations is proposed in this paper. At the first level, a day-ahead optimization strategy generates the optimal planned load curve and the deviation band to be used as a reference for ensuring multiple control objectives through linear programming, and even for avoiding control failure caused by insufficient BESS energy. Based on this day-ahead optimal plan, at a second level, real-time rolling optimization converts the control process to a multistage decision-making problem. The predictive control-based real-time rolling optimization strategy in the proposed model was used to achieve the above control objectives and maintain battery life. Finally, through a horizontal comparison of two control approaches in each case study, and a longitudinal comparison of the control robustness against different degrees of load disturbances in three cases, the results indicated that the proposed control strategy was able to significantly improve the charging load characteristics, even with large disturbances. Meanwhile, the proposed approach ensures the least amount of variation in the range of battery SOC and reduces the total electricity cost, which will be of a considerable benefit to station operators. Keywords: fast charging station; battery energy storage system; real time; rolling optimization; linear programming; model predictive control

1. Introduction To address the energy and environmental crises, and as a significant component of sustainable development and the low-carbon economy, transport electrification, including electric vehicles (EVs), is experiencing a worldwide period of rapid development. As the energy supply of EVs, the charging infrastructure plays a crucial role in its promotion [1–3]. Due to the shorter recharging duration required compared to AC charging, as well as the lower investment cost compared to battery-swap charging, DC fast charging has become the mainstream method used for electric bus, taxi, and emergency charging [4,5]. In addition, given the potential for increased battery capacity, DC fast charging is expected to be beneficial for daily use [6,7]. Increased battery capacity enables long distance travel and Energies 2018, 11, 229; doi:10.3390/en11010229

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range anxiety is eliminated with high power rapid recharging. Depending on the battery and vehicle types, a recharge range of greater than 100 km in less than 10 min is easily achievable. However, these short charging time and high-power properties generate a new type of load with a high peak load and fast power fluctuations, resulting in a low load factor. From our measurements of many real fast charging stations, the charging load valley can be zero, while the peak load almost reaches the maximum distribution capacity of the station, which can be between hundreds of kilowatts and several megawatts. The load factors are usually below 0.3. This creates new challenges to the reliable and economic operation of charging stations and distribution networks. Since the peak power of a fast charging station is much higher than the average power, the construction of the station based on peak load increases both the investment and operation costs. Currently, a large industrial electricity tariff standard is applied to fast charging stations in Beijing and other cities in China, of which a 32 CNY/kVA (4.8421 USD/kVA) per month basic electricity price is charged according to the capacity of the distribution transformer, in addition to the time-of-use (TOU) electricity cost. This high peak charging load requires a large extra power supply from the grid, which poses problems for choosing locations for the stations, and the cost of power grid capacity expansion is nearly 10,000 CNY/kVA. At the same time, the rapid and severe fluctuations disturb the distribution networks, and the voltage quality significantly deteriorates. Meanwhile, the power loss in distribution also increases [8–10]. Currently, charging load control or coordinated charging is achieved through several methods, two of which are: (1) Direct control is the direct regulation of the charging time, the number of charging vehicles, or the charging power due to the controllability of the charging load. This method is implemented by the charging station, aggregator, or distribution system operators (DSO). Based on aggregators and DSO, a hierarchical coordinated charging framework for EVs minimizes the electricity cost and peak load [11]. The total charging cost minimization was achieved in the aggregator using a strategy that directly interrupts the charging process [12]. With the goals of peak-shaving and valley-filling, the number of charging electric vehicles in a certain period was calculated in order to attain direct control [13]. In addition to directly regulating the charging load to reduce the power loss of the grid, optimal integration place was pursued [14]. Temporal and spatial joint control strategies were proposed to reduce the level of charging congestion [15,16]. Based on stochastic charging time switching control of on-board electric vehicle (EV) chargers, Zhang et al. [17] proposed a decentralized strategy to coordinate charge operation of electric vehicles. Silvestre et al. [18] devised an optimal strategy to control the recharge start time for a given parking lot to minimize losses or the energy cost. In addition, various algorithms have been applied to the charging management of parking stations and battery swapping stations [19,20]. (2) Demand side management-based charging price guiding coordinates the charging behavior of EV users with a TOU charging price or other market mechanisms to attain indirect control over charging loads. Based on the TOU electricity price, Yang et al. [21] proposed one approach to obtaining the TOU charging price in order to reduce the charging peak-valley load difference. A game-theoretic approach for optimal TOU pricing was introduced to improve the efficiency of operation [22]. Another optimization model for determining the optimal charging prices for EVs, to maximize the EV-parking lot owner’s profit was presented by Awad et al. [23]. Yang et al. [24] considered electric vehicle route optimization by using the time-of-use price to minimize the total distribution costs. EV charging was coordinated to absorb excess wind energy via dual-tariff schemes [25]. The first type of control strategy directly regulates the charging process or power, and has a favorable charging load control effect. However, direct control may affect the vehicle user’s demand, and user-friendliness is relatively low. Using a price mechanism to guide the user’s charging behavior seems to be a more suitable method. Although the method is user-friendly, the price mechanism itself may still conflict with users’ demand or behavior. For example, when some users are not sensitive to the guiding price, the load control effect will deteriorate in a high-power fast charging scenario,

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even if insensitive users are rather rare. This can also be described as a lack of robustness against load disturbance caused by user sensitivity, driving habits, or traffic conditions. Recently, to reduce the impact of the EV charging on node voltages and feeder currents, Islam et al. [26] chose an appropriate combination of solutions, such as upgrading the grid, and deploying onsite PV or battery energy storage system (BESS), or both, and found the optimal PV and BESS sizes for the chosen combination. Graber et al. [27] presented a stochastic sizing method to determine the number of different types of EV charging stations in urban parking lots while considering BESS. These studies focused on the design and configuration of the charging station rather than real-time operation and load control. To address the problem of controlling the high power needed from fast charging operations, a BESS was used as the buffer to store energy and control the load demand [28]. However, this solution dispatches the batteries only when demand exceeds a reference maximum value. This approach is simple, but lacks optimization ability, such as electricity cost reduction and the optimal usage of batteries, and always causes the net demand to exceed the limit value. This paper introduces lithium-ion battery-based BESS to the charging load control of the fast charging station. To address the objectives of charging load peak-shaving and TOU tariff-based economic operation while reducing the charging load change rate, this novel method is more user-friendly and flexible, and is independent of the user’s personal price sensitivity and behavior and other disturbances, compared to the existing charging load control methodology. In this paper, we propose a BESS-based bi-level optimization strategy for regulating the charging load of the electric vehicle fast charging station. In the first level day-ahead strategy, the optimization model to achieve both reduced daily electricity cost for the station and charging load peak-shaving is established with multiple constraints. Afterward, based on the optimal charging load obtained with linear programming, the day-ahead optimal planned load deviation band is established. Using this optimal planned load deviation band, the BESS capacity margin for the remainder of the daily operation time can be considered to avoid control failure caused by insufficient BESS energy. In the following real-time strategy, since the BESS state has typical Markov properties in real-time operation, model predictive control (MPC) was used to optimize the rolling of the BESS power in a fast charging station. During this real-time optimization process, and based on the day-ahead optimal planned load deviation band set at the first level, the variation in the BESS state-of-charge (SOC) range was optimized to improve the expected battery life. This paper is organized into the following sections. The main problems and motivation for this paper are described in Section 2. Section 3 introduces the proposed BESS-based bi-level optimization strategy in detail. The basic control model and control logic of the strategy are outlined. Then, the day-ahead level optimization strategy is detailed, after which the day-ahead optimal planned load deviation band is established. Subsequently, the real-time model and basic control are detailed. Then the MPC-based real-time rolling optimization model is proposed and detailed in Section 4. In Section 5, a case study of day-ahead level optimization is presented first, as well as a horizontal comparison of two real-time control approaches, namely direct control and MPC-based control. Longitudinal comparison of the control robustness is examined through three cases with different load disturbances. Finally, conclusions are drawn in Section 6. 2. Problems and Motivating Scenarios This study was motivated by problems seen in fast charging stations, in which the charging loads suffer from severe power fluctuations, high peak loads, and low load factors. A typical electric bus fast charging station, in which BESS is included, is depicted in Figure 1.

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Figure 1. Typical topology of a fast charging station. Figure station. Figure 1. 1. Typical Typical topology topology of of aa fast fast charging charging station.

Power of Charging Loads (kW) Power of Charging Loads (kW) 充电负荷/kW 充电负荷/kW

In this fast charging station, eight DC chargers are individually connected to the grid through a In fast charging eight chargers are individually connected totocurve the a 10 kV/0.4 transformer. actual charging load ofthrough this fast In this this kV fastdistribution charging station, station, eightDC DCThe chargers aremeasured individually connected thegrid grid through 10 kV distribution transformer. The actual measured charging load curve of this fast station, which is transformer. located in the Huairou District incharging Beijing, China, is of shown in Figure 2. acharging 10kV/0.4 kV/0.4 kV distribution The actual measured load curve this fast charging charging station, which is located in the Huairou District in Beijing, China, is shown in Figure 2. The peak and isvalley power the loadDistrict curve in areBeijing, 1244.3 China, kW and 0 kW, respectively, whereas the station, which located in theofHuairou is shown in Figure 2. The peak and The andofvalley power the1244.3 load curve 1244.3 kW and 0whereas kW, respectively, the dailypeak average power iscurve onlyofare 276.5 kW.kW Therefore, the load factor is 0.222, iswhereas rather low valley power the load andare 0 kW, respectively, thewhich daily average power daily power is only 276.5 kW. the This load factor is compared 0.222, which is rather low compared other common theTherefore, utility will result in higher and is onlyaverage 276.5tokW. Therefore, theloads load in factor is 0.222,grid. which is rather low toinvestment other common compared to other common loads in the utility grid. This will result in higher investment and operation power capacityand drawn fromcosts, the due utility grid during loads in thecosts, utility due grid. to Thisthe willredundant result in higher investment operation to the redundant operation costs, due to theelectricity power the electricity utility grid during construction and the basic price paid capacity once per drawn month. Additionally, severe charging power capacity drawn from theredundant utility grid during construction andfrom the basic price paid construction and the basic electricity price paid once per month. Additionally, severe charging power fluctuations may affect the voltage quality and power loss in the distribution networks. If the once per month. Additionally, severe charging power fluctuations may affect the voltage quality and power fluctuations may affect the voltage quality and power loss in the distribution networks. If the stationloss is integrated into a weak powerIfgrid, the point of common coupling voltagegrid, in the power in the distribution networks. the station is integrated into a weak power thehigher point station isdistribution integrated into awill weak the distribution point of common coupling voltage in the higher voltage of common couplingareas voltage indeteriorate. thepower highergrid, voltage areas will deteriorate. voltage distribution areas will deteriorate. 1400

Peak power Peak power

1400 1200 1200 1000

Daily average power Daily average power

1000 800

Valley power

800 600 Valley power 600 400 400 200 200 0 0

6

8

10

12

6

8

10

12

14

Time 时间/h 14 (h) Time (h) 时间/h

16

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Figure 2. 2. Actual charging load load curve curve of of an an electric electric bus bus fast fast charging charging station. station. Figure Actual charging Figure 2. Actual charging load curve of an electric bus fast charging station.

Compared to the two existing types of charging load control, introducing BESS to fast charging Compared to the two existing types ofthese charging load control, introducing BESS to fast charging promising way to manage problems, since this method is user-friendly, and stations isisaapromising way to manage these problems, since this method is user-friendly, and robust stations is a promising way to manage these problems, since this method is user-friendly, and robust against the vehicle user’s individual characteristics and real-time load perturbations. BESS is against the vehicle user’s individual characteristics and real-time load perturbations. BESS is able to robust against the vehicle user’s individual characteristics and real-time load perturbations. BESS is able to effectively control of a fast charging station. However, battery costisfor BESS is a effectively control the load the of aload fast charging station. However, the batterythe cost for BESS a limitation able to method. effectively control theprice load of of batteries athe fastprice charging station.considerably However, thewith battery for BESS a limitation of this method. Though ofdecrease batteries will decrease considerably with the of this Though the will the cost increasing useis of limitation of this method. Though the price of batteries will decrease considerably with the increasing use ofminimizing electric vehicles, minimizing degradation of the batteries is essential to the electric vehicles, the degradation of the batteries is essential to the optimal operation of increasing use of electric minimizing the planned degradation of the batteries to the optimal operation of optimal BESS.vehicles, The day-ahead optimal deviation band aessential pivotalmethod, aspect BESS. The day-ahead planned load deviation band is aload pivotal aspect in the is proposed optimal operation of BESS. The day-ahead load strategy. deviation band is a pivotal aspect in the method, is also the strategy. firstoptimal step of planned the proposed and is proposed also the first step ofand the proposed in the proposed method, and is also the first step of the proposed strategy.

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3. Control Model and Bi-Level Optimization Strategy 3.3.1. Control Model and Bi-Level Optimization Strategy The BESS-Based Fast Charging Station Control Model

Based on the typical topology of a Control fast charging 3.1. The BESS-Based Fast Charging Station Model station depicted in Figure 1, the basic control model of this system can be expressed as follows: Based on the typical topology of a fast charging station depicted in Figure 1, the basic control model of this system can be expressed as P follows: (1) b ( t ) = Pg ( t ) − Pc ( t )

) t=) =PgE(t()t − EP(bt(+tΔ ) −PPcb(t()t ) Δt

(1) (2)

∆t) = PEg ((tt))−isPbthe (2) (t)∆tgrid-side power of the fast charging where Pb ( t ) is the output powerE(oft +BESS, where Pb (tP)c is power of BESS, Pg (tof thefast grid-side power of theE fast charging Pc (t) ) isthe the charging load power charging station, is the energystation, of the BESS, station, ( t )theisoutput isand the tcharging power ofand the fast station, E is the energy of the BESS, andtwo t and ∆t are and Δt load are the time the charging BESS calculation step time, respectively. These equations the time and the BESS calculation step time, respectively. These two equations are derived from the are derived from the principle of the power and energy balance of the fast charging station. principle of the power and energy balance the fast charging station. To address the control objectives ofof charging load peak-shaving, TOU tariff-based economic To address the control objectives of charging load peak-shaving, TOU tariff-based operation, minimization of BESS SOC variations [29–31], and avoidance of control failureeconomic caused by operation, minimization of BESS SOC variations [29–31], and avoidance of control failure caused insufficient BESS energy, a BESS-based bi-level optimization strategy for regulating the charging by insufficient a BESS-based bi-level optimization for regulating load of the EVBESS fast energy, charging station is proposed in this paper.strategy The strategy involves the twocharging levels of load of the EV fast charging station is proposed in this paper. The strategy involves two levelsand of optimization: the first is a day-ahead optimization level, which creates a peak-shaving optimization: the first is a day-ahead optimization level, which creates a peak-shaving and economic economic operation control plan; and the second is a real-time rolling optimization level, which operation control plan; and theand second is a real-time rollingand optimization level, whichofachieves theA achieves the day-ahead plan guarantees the lifetime the available energy the BESS. day-ahead plan and guarantees the lifetime and the available energy of the BESS. A diagram of the diagram of the bi-level optimization strategy is shown in Figure 3, which displays the logical bi-level optimization strategy is shown in Figure 3, which displays logical relationship between the relationship between the two levels and the distribution of thethe objectives in the two optimization two levels and the distribution of the objectives in the two optimization processes. processes.

Figure 3. Logic diagram of the bi-level optimization strategy. Figure 3. Logic diagram of the bi-level optimization strategy.

3.2. Day-Ahead Level Optimization Strategy 3.2. Day-Ahead Level Optimization Strategy As the first level of the bi-level optimization strategy, the day-ahead level is implemented in As the first level of the bi-level optimization strategy, the day-ahead level is implemented in the the energy management system (EMS) of the fast charging station, based on the day-ahead charging energy management system (EMS) of the fast charging station, based on the day-ahead charging load load forecasting data obtained from a load forecasting system and other constraint information. forecasting data obtained from a load forecasting system and other constraint information. Since the Since the electricity charge is the variable portion of the daily production costs in a charging station, electricity charge is the variable portion of the daily production costs in a charging station, minimizing minimizing the electricity charge is one way to increase profits. The TOU electricity rates stipulated the electricity charge is one way to increase profits. The TOU electricity rates stipulated in a fast in a fast charging station are the fixed electricity prices, and usually contain peak, flat, and valley

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charging station are the fixed electricity prices, and usually contain peak, flat, and valley prices that vary based on the time of day in order to promote reasonable timing of electricity consumption. Therefore, to reduce the operation costs, minimizing the daily electricity cost of the fast charging station was chosen as the objective function: ( minC = min

n

∑ c(i) Pg (i)τ

)

(

= min

i =1

n

∑ c (i )

h

i

)

Pb (i ) + Pc f (i ) τ

(3)

i =1

where C is the daily electricity cost, c(i ) is the TOU electricity rate during the time index i, n and τ are the number of time index and the time interval, respectively, which depend on the input charging load forecasting data interval, and Pc f is the total forecasted charging power by time. Since the objectives of reducing the peak loads and the charging load change rate are rigid, they can be handled as constraint conditions in the strategy, for the sake of simplicity. Therefore, the constraint conditions that should be satisfied in the optimization are as follows: The peak-shaving grid-side power constraint is: Pgmin ≤ Pg (i ) ≤ Pgmax

(4)

The charging load change rate constraint is: γmin ≤

Pg (i + 1) − Pg (i ) ≤ γmax Pt

(5)

The BESS energy constraint is: λmin E ≤ Eb (i ) ≤ λmax E

(6)

Pbmin ≤ Pb (i ) ≤ Pbmax

(7)

The BESS power constraint is: where Pgmin and Pgmax are the minimum and maximum grid-side power, respectively; γmin and γmax are the minimum and maximum charging load change rates, respectively; Pt is the power capacity of the transformer; λmin and λmax are the minimum and maximum permitted BESS energy percentage, respectively; Pbmin and Pbmax are the minimum and maximum BESS output power, respectively, which are always the rated power of the BESS converter. Since the objective function, constraints, and feasible range of the day-ahead level constitute a nonempty bounded convex set, this problem can be solved with a linear programming algorithm, through which the day-ahead optimal planned load curve can be obtained. This day-ahead optimal planned load curve includes optimal objective information, such as peak-shaving, electricity cost minimization, and charging load change rate reduction. 3.3. Day-Ahead Optimal Planned Load Deviation Band Since each battery has an energy limitation, the BESS capacity margin for the rest of the daily operation times should be considered in order to avoid control failure caused by the insufficiency of BESS energy. In addition, for the optimal usage of BESS to extend the lifecycle of batteries, the concept of the load deviation band is introduced in this paper on the basis of the day-ahead optimal planned load curve, making the peak-shaving objective a load band, rather than a load curve. This is a kind of constraint relaxation, actually. The mathematical model of the day-ahead optimal planned load deviation band is as follows:   Pu (i ) = min Pgmax , Pg (i ) + δmax Pg (i )

i ∈ {1, 2, · · · , n}

(8)

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  Pgmin , Pglower Pg (i ) of the (9) (i ) = (i ) − δmax i ∈day-ahead {1, 2, · · · , noptimal } where Pu and Pl Plare themax upper and boundaries planned load

where Pu and Pl are the upper and the day-ahead optimalby planned load deviation Pg (lower i ) is boundaries the optimalofplanned load derived the day-ahead level deviation band, respectively; band, respectively; Pg (i ) is the optimal planned load derived by the day-ahead level optimization; optimization; and δ is the band deviation coefficient, which is between 0 and 1. and δ is the band deviation coefficient, which is between 0 and 1. A schematic diagram of the day-ahead optimal planned load deviation band is shown in Figure 4. A schematic diagram of the day-ahead optimal planned load deviation band is shown in Figure 4. Without the load deviation band, the original real-time charging load peak at time k1 is shaved to the Without the load deviation band, the original real-time charging load peak at time k1 is shaved to the planned value of the day-ahead optimal load. However, at time k2, the peak-shaving failed due to planned value of the day-ahead optimal load. However, at time k2 , the peak-shaving failed due to exhausting the capacity of BESS. With the load deviation band applied, the strategy does not shave exhausting the capacity of BESS. With the load deviation band applied, the strategy does not shave the the load peak at the time k1 to the optimal value determined by the day-ahead level optimization, but load peak at the time k1 to the optimal value determined by the day-ahead level optimization, but to to a higher value than the optimal one, which saves BESS energy for time k2 and enables peak-shaving a higher value than the optimal one, which saves BESS energy for time k2 and enables peak-shaving at at time k2. time k2 .

(a)

(b)

Figure 4. Schematic diagram for the day-ahead optimal planned load deviation band: (a) Without a Figure 4. Schematic diagram for the day-ahead optimal planned load deviation band: (a) Without load deviation band; (b) With a load deviation band. a load deviation band; (b) With a load deviation band.

3.4. Real-Time Rolling Optimization 3.4. Real-Time Rolling Optimization At the real-time optimization level, the strategy that is embedded in the EMS of a fast charging At the real-time optimization level, the strategy that is embedded in the EMS of a fast charging station is implemented in real time. Therefore, online optimization of the BESS output power or the station is implemented in real time. Therefore, online optimization of the BESS output power or the grid-side power is required to follow the day-ahead optimal planned load deviation band during this grid-side power is required to follow the day-ahead optimal planned load deviation band during process. this process. The real-time optimization strategy must achieve the day-ahead optimization objectives, The real-time optimization strategy must achieve the day-ahead optimization objectives, represented by the load deviation band, and optimize the BESS usage to conserve energy for the represented by the load deviation band, and optimize the BESS usage to conserve energy for the following load peaks online. In addition, based on the load deviation band, the variation in the following load peaks online. In addition, based on the load deviation band, the variation in the range range of the SOC of BESS can be minimized during charging load regulation. This will improve the of the SOC of BESS can be minimized during charging load regulation. This will improve the battery battery life during operation, since lithium-ion batteries with a reduced SOC range of around 50% life during operation, since lithium-ion batteries with a reduced SOC range of around 50% exhibit exhibit a significantly slower capacity loss rate [32–34]. a significantly slower capacity loss rate [32–34]. During real-time operation, considering the uncertainty and perturbations of the charging During real-time operation, considering the uncertainty and perturbations of the charging loads, loads, as well as the period of ultra-short-term charging load forecasting, rolling optimization as well as the period of ultra-short-term charging load forecasting, rolling optimization (Figure 5) for (Figure 5) for the BESS power, by transferring the control process into a multistage decision-making the BESS power, by transferring the control process into a multistage decision-making problem, is problem, is proposed in this paper. proposed in this paper.

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Figure 5. The principle diagram BESS rolling optimization strategy. Figure 5. The principle diagram of of thethe BESS rolling optimization strategy.

Figure 5 depicts the the rolling optimization strategy principle. MoreMore specifically, the first ofline this of Figure 5 depicts rolling optimization strategy principle. specifically, theline first figure the time axis. Theaxis. second shows single-stage decision-making optimization period this is figure is the time The line second linethe shows the single-stage decision-making optimization at period time index k during optimization. Similarly,Similarly, the third and the fourth lines showlines the show rollingthe at time index rolling k during rolling optimization. the third and the fourth optimization process, which scrolls forward by step. time areindices used asare rolling optimization process, which scrollsstep forward stepInbyFigure step. 5, In four Figure 5, indices four time anused example. Theexample. optimization, is a single-stage process, is implemented within is as an Thewhich optimization, whichdecision-making is a single-stage decision-making process, theimplemented optimization within period at time index.period When at theeach solution, the output power ofwhich the BESS theeach optimization time which index. isWhen the solution, is the after optimization, obtained, first value inisthe optimal only trajectory is applied output power ofis the BESS only after the optimization, obtained, the first value tointhe theprocess. optimal Attrajectory the next time index, the entire procedure is repeated. optimization continues to scroll is applied to the process. At the next timeThis index, the entire process procedure is repeated. This forward to constantly generate BESS control commands. Based on the above illustrations, during each optimization process continues to scroll forward to constantly generate BESS control commands. decision-making period, the objective function ofdecision-making the optimization period, model isthe as objective follows: function of the Based on the above illustrations, during each optimization model is as follows: m

∑ m[s(k) − L]2 2 min J k==1  s ( k ) − L 

minJ =

(10) (10)

k =1

where m is the number of time indices in a rolling optimization period, k is the time index in m is rolling the number of time indices a rolling optimization period, thereal-time time index in the thewhere real-time optimization, and its in time interval is the control step kofisthe rolling real-time rolling optimization, and its time interval is the control step of the real-time rolling optimization, s is the state-of-charge of the BESS, and L is a reference value equal to 0.5. optimization, theabove state-of-charge BESS, the andvariation L is a reference valuerange equalto toensure 0.5. battery In addition stoisthe objective of of the reducing in the SOC In addition to the above objective of reducing the variation in the SOC range to ensure battery life, other objectives for charging load control are as follows: life, other objectives for charging load control are as follows: The grid-side power constraint for peak-shaving using the day-ahead optimal planned load Theband grid-side power constraint for peak-shaving using the day-ahead optimal planned load deviation is: deviation band is: P (k) ≤ P (k) ≤ P (k) (11) k ∈ {1, 2, · · · , m} g

l

u

Pl ( k ) ≤ Pg ( k ) ≤ Pu ( k ) The BESS energy constraint is: The BESS energy constraintEis: (k) ≤ λmax λmin ≤ b E E k

λ

The BESS power constraint is:min

≤

k ∈ {2, 3, · · · , m + 1}

b( ) ≤ λmax

E

The BESS power constraint is:P (k) ≤ P Pbmin ≤ b bmax

k ∈ {1,2, ⋅⋅⋅, m}

Pb min ≤ Pb ( k ) ≤ Pb max

k ∈ {2,3, ⋅⋅⋅, m+1} k ∈ {1, 2, · · · , m}

4. MPC-Based Real-Time Rolling Optimization Model

k ∈ {1,2, ⋅⋅⋅, m}

(11) (12)

(12) (13)

(13)

In this paper, to solve the above real-time rolling optimization problem, we used the model 4. MPC-Based Real-Time Rolling Optimization Model predictive control approach. With MPC, also known as receding horizon control, an optimization this solvetime the step above real-time rolling used The the model problemIncan bepaper, solved to at each to determine a plan ofoptimization action over a problem, fixed timewe horizon. first predictive control approach. MPC, also known receding horizon control, an isoptimization input from this plan is applied toWith the system. At the next as time step, the planning process repeated, problem can optimization be solved at each time step determine a planshifted of action fixed timeThe horizon. The solving a new problem withto the time horizon oneover stepaforward. control first input from this plan is applied to the system. At the next time step, the planning process is repeated, solving a new optimization problem with the time horizon shifted one step forward. The

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policy involves feedback, since real-time measurements are used to determine the control input. MPC is a nonlinear control policy that handles input constraints, output constraints, and various control objectives. Moreover, MPC is a high-speed solver that can be applied to real-time application [35,36]. Accordingly, we propose a MPC-based real-time rolling optimization strategy that ensures the grid-side power follows the day-ahead optimal planned load deviation band and improves the battery life. The state space model of the fast charging station can be written as follows: (

x (k) = u(k) − r (k) y(k + 1) = y(k) − T1 x (k)

(14)

where x (k ) is the BESS output power Pb , u(k) is the grid-side power of the fast charging station Pg , r (k) is the charging load power of the fast charging station Pc , y(k) is the state-of-charge of the BESS, and T is the time constant determined by the control step. For example, if the control step is 5 min, and 1 h is used as the reference, then T = 60 5 = 12 . For simplification, T = 12 will be used in the following deduction and optimization. Equation (14) can be transformed to the following style: (

X =U−R Y = Yp + M T ( R − U ) = Yp +

(15)

M 12 ( R − U )

where:           y (1) y (2) r (1) u (1) x (1)      ..   ..     ..  . . . . X =  . , U =  , Yp =  . , M =  , R =  . , Y =  . .   y (1) y ( m + 1) u(m) r (m) x (m) 

1 0 1 1 .. .. . . 1 1

 ··· 0 ··· 0   ..  .. , . .  ··· 1

and the number of time indices in a rolling optimization period m is the prediction horizon in MPC. Therefore, ignoring the constant terms, the objective function in Equation (10) can be represented as: minJ = Y T Y − 2Lc T Y (16)   L  ..  where Lc =  . . L By substituting the prediction expression in Equation (15) into the objective function in Equation (16), and ignoring the constant terms, the objective function can be expressed as: minJ

 T U + − T2 MT Yp − T22 MT MR + T2 MT Lc U  T   T 1 = 12 U T M72M U + − 16 MT Yp − 72 MT MR + 16 MT Lc U

= 12 U T



2MT M T2



(17)

Since the objective function can be solved by quadratic programming (QP) in MPC, transforming the following standard formula of QP is necessary: min J = x

s.t.

1 T x Hx + hT x 2

(18)

lb ≤ x ≤ ub

(19)

where x is the vector of the optimization variables; H and h are the matrices of the quadratic

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term and the first term in the equation, respectively; lb and ub are the vectors of the constraint condition boundaries. T 1 Therefore, in Equation (17), H = M72M , h = − 16 MT Yp − 72 MT MR + 61 MT Lc . According to Equations (11) to (13), the constraints can be expressed as: C1 ≤ U ≤ C2

(20)

C3 ≤ X ≤ C4

(21)

C5 ≤ Yp +

M ( R − U ) ≤ C6 12

(22)

where: 

           Pl (1) Pu (1) Pbmin Pbmax λmin E λmax E             .. .. .. .. .. .. C1 =  , C2 =  , C3 =  , C4 =  , C5 =  , C6 =  . . . . . . . Pl (m) Pu (m) Pbmin Pbmax λmin E λmax E

Then, Equation (20) to Equation (22) can be transformed into:    C1 ≤ U ≤ C2 C3 + R ≤ U ≤ C4 + R   M−1 12Y + MR − 12C
≤ U ≤ M−1 12Y + MR − 12C
p p 6 5

(23)

Based on Equation (23), the vectors of the constraint condition boundaries in Equation (19) in the MPC-based real-time rolling optimization can be derived: h h n oiT  lb = max D1 T = max C1 h

n

ub = min D2

T

oiT



= min

h

C2

C3 + R

M−1 12Yp + MR − 12C6

C4 + R

M −1

12Yp + MR − 12C5


iT T

(24)


iT T

(25)

In Equations (23) and (24), the symbols ‘max’ and ‘min’ stand for calculating the maximum or minimum value in every column of the matrix D1 T or D2 T . In the standard QP form, the MPC-based rolling optimization can be easily implemented with the Matlab optimization toolbox, which can be applied to an actual charging station using the hybrid programming of C# and Matlab. 5. Case Studies and Validation Based on the above theory and methodology, case studies and their results are presented in this section. A real fast charging station with eight 230 kW fast chargers and a 500 kWh/800 kW BESS, which is described in Section 2, was chosen for the case study, the topology of which is shown in Figure 1. This charging station is located in the Huairou District in Beijing, China and serves 50 electric buses. All the data used in this paper were obtained from the actual monitoring system in the station. This section is organized as follows. First, day-ahead optimization is performed in Section 5.1. Next, real-time rolling optimization is implemented for three cases in Section 5.2. In each case, a horizontal comparison of the results with or without BESS is performed, in which the BESS is controlled by two different real-time approaches. For robustness testing against load disturbance caused by driving habits or traffic conditions, longitudinal comparison is performed for Case I, II, and III, with the charging loads of three different day-ahead forecasting accuracies.

Next, real-time rolling optimization is implemented for three cases in Section 5.2. In each case, a horizontal comparison of the results with or without BESS is performed, in which the BESS is controlled by two different real-time approaches. For robustness testing against load disturbance caused by driving habits or traffic conditions, longitudinal comparison is performed for Case I, II, Energies 11,the 229 charging loads of three different day-ahead forecasting accuracies. 11 of 21 and III,2018, with 5.1. Day-Ahead Level Optimization Case Study 5.1. Day-Ahead Level Optimization Case Study The day-ahead forecasted charging loads from a charging load forecasting system are shown The day-ahead forecasted charging loads from a charging load forecasting system are shown in in Figure 6. The root mean squared error (RMSE) between the observed and predicted data was Figure 6. The root mean squared error (RMSE) between the observed and predicted data was used used to describe the accuracy of the day-ahead charging load forecasting. In Figure 6, the accuracy to describe the accuracy of the day-ahead charging load forecasting. In Figure 6, the accuracy of the of the day-ahead charging load forecasting is 100% for an ideal situation, meaning the forecasting is day-ahead charging load forecasting is 100% for an ideal situation, meaning the forecasting is precise. precise. The peak charging hours are mainly concentrated at 10:00 to 11:00 a.m. and 6:00 to 8:00 p.m., The peak charging hours are mainly concentrated at 10:00 to 11:00 a.m. and 6:00 to 8:00 p.m., and the and the maximum peak load is 1048 kW. maximum peak load is 1048 kW. 1200 1000

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Figure 6. 6. Day-ahead Day-ahead forecasted forecasted charging chargingloads loadsof ofthe thefast fastcharging chargingstation. station. Figure

The parameters parameters in in this this case case study study are are listed listed in in Table Table1.1. The The large large industrial industrial electricity electricity tariff tariff The standard applied to fast charging stations in Beijing is shown in Table 2. standard applied to fast charging stations in Beijing is shown in Table 2. Table1.1.Parameters Parametersof ofthe theday-ahead day-aheadlevel leveloptimization. optimization. Table

Parameter Maximum grid-side power Maximum grid-side power Minimum grid-side power Minimum grid-side power Maximum charging change Maximum charging loadload change rate rate

Value 600 600 0 0 10%10%

Parameter

Value

Minimum charging load change rate Maximum permitted percentage of BESS energy Minimum permitted percentage of BESS energy BESS original SOC Maximum output power of BESS Minimum output power of BESS

−10% 80% 20% 50% 800 −800

Unit Unit kW kW kW kW -kW kW

Table 2. Large industrial time-of-use (TOU) electricity tariff in Beijing. Time

Price Grade

Price (CNY/kWh)

0:00–7:00 7:00–10:00 10:00–15:00 15:00–18:00 18:00–21:00 21:00–23:00 23:00–24:00

Valley Flat Peak Flat Peak Flat Valley

0.3946 0.6950 1.0044 0.6950 1.0044 0.6950 0.3946

Based on the parameters in Tables 1 and 2, the day-ahead optimal planned load curve was obtained using linear programming, as shown in Figure 7. The peak charging load on the day-ahead

18:00–21:00 21:00–23:00 23:00–24:00

Peak Flat Valley

1.0044 0.6950 0.3946

on229the EnergiesBased 2018, 11,

parameters in Tables 1 and 2, the day-ahead optimal planned load curve 12 ofwas 21 obtained using linear programming, as shown in Figure 7. The peak charging load on the day-ahead optimal planned load curve was significantly reduced to 598.4 kW from 1048.64 kW, and optimal loadfrom curve17.19% was significantly reduced to 598.4 from kW, and thebenefit load the loadplanned factor rose to 30.13%. As outlined in thekW first two1048.64 sections, this will factor rose from 17.19% to 30.13%. As outlined in the first two sections, this will benefit both the station both the station operator and the power system. Using this day-ahead optimal planned load curve, operator and the power system. Using day-ahead optimal planned curve, peak-valley the peak-valley difference would alsothis improve, from 1048.64 kW toload 598.4 kW.the The maximum difference would also improve, from 1048.64 kW to 598.4 kW. The maximum charging load change charging load change rate would decrease to 9.2%, which is below the constraint of 10%. rate would decrease to 9.2%, which is below the constraint of 10%. Furthermore, the daily electricity Furthermore, the daily electricity cost of the fast charging station would decrease from 3805.84 CNY cost of the fast charging would decreaseand from 3805.84 CNYthe to operator 3530.08 CNY, which is abecause 7.25% to 3530.08 CNY, which station is a 7.25% reduction, would benefit of the station reduction, and would benefit the operator of the station because of the yearly electricity cost savings of of the yearly electricity cost savings of 100,652.4 CNY. 100,652.4 CNY. 1200 Day-ahead forecasted load Day-ahead optimal planned load

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Figure7.7.Day-ahead Day-aheadoptimal optimalplanned plannedload loadcurve curveofofthe thefast fastcharging chargingstation. station. Figure

The output 8. Energies 2018, 11, 229 power 13 of 23 The output powerand andthe theSOC SOCof ofthe theBESS BESSin inday-ahead day-aheadoptimization optimization are are shown shown in in Figure Figure 8. 600

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The Theoutput outputpower powerand andthe theSOC SOCofofthe theBESS BESSare arewithin withintheir theirconstraint constraintranges. ranges.

Time(h)

Figure 8. 8. Output Output power power and and state-of-charge state-of-charge (SOC) of the BESS during day-ahead optimization. Figure

Therefore, the optimal planned load load curvecurve satisfies all the control including Therefore, theday-ahead day-ahead optimal planned satisfies all theobjectives, control objectives, peak-shaving and electricity cost minimization, and can be applied in real-time as a reference planasfor including peak-shaving and electricity cost minimization, and can be applied in real-time a the following reference planday. for the following day. 5.2. Real-Time Real-Time Level Level Rolling Rolling Optimization Optimization Case Case Study Study 5.2. Three cases cases are are provided Three provided here here to to illustrate illustrate the the control control effects effects of of the the real-time real-time rolling rolling optimization optimization level, and validate the bi-level optimization strategy. In addition, by comparing these three cases with with level, and validate the bi-level optimization strategy. In addition, by comparing these three cases different day-ahead charging load forecasting accuracies, the robustness of the proposed strategy is different day-ahead charging load forecasting accuracies, the robustness of the proposed strategy is

validated. Note that all three cases are based on the day-ahead optimal planned load curve provided in Section 5.1. In this section, the parameters are the same as those listed in Table 1, except for the number of time indices in a rolling optimization period. Instead, m = 12 and the real-time control step is 5 min. 5.2.1. Real-Time Optimization Case I

including peak-shaving and electricity cost minimization, and can be applied in real-time as a reference plan for the following day. 5.2. Real-Time Level Rolling Optimization Case Study Three cases are provided here to illustrate the control effects of the real-time rolling optimization 13 of 21 level, and validate the bi-level optimization strategy. In addition, by comparing these three cases with different day-ahead charging load forecasting accuracies, the robustness of the proposed strategy is validated. day-ahead optimal optimalplanned plannedload loadcurve curveprovided providedin validated.Note Notethat thatall allthree three cases cases are are based on the day-ahead inSection Section 5.1. In this section, the parameters are the same as those listed in Table 1, except the 5.1. In this section, the parameters are the same as those listed in Table 1, except for the for number number time in indices in aoptimization rolling optimization period.mInstead, = 12 and thecontrol real-time step of time of indices a rolling period. Instead, = 12 andmthe real-time stepcontrol is 5 min. is 5 min. 5.2.1. Real-Time Optimization Case I 5.2.1. Real-Time Optimization Case I In Case I, the day-ahead charging load forecasting accuracy is 100% as ideal, as shown in In forecasting accuracy are is 100% as ideal,and as shown in Figure 9. FigureCase 9. InI, the thisday-ahead case, twocharging types ofload BESS-based strategies performed compared: direct Incontrol this case, two types of BESS-based strategies are performed and compared: direct control and and MPC-based control. MPC-based control. Energies 2018, 11, 229

1200 Real load Day-ahead optimal planned load Day-ahead forecasted load

1000

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800 600 400

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Figure9.9.Day-ahead Day-aheadforecasted forecastedload, load,day-ahead day-aheadoptimal optimalplanned plannedload, load,and andreal realload loadcurves curvesfor forCase CaseI.I. Figure

Figure9,9, the the variance variance between loads is 0. InInFigure between the the day-ahead day-aheadforecasted forecastedloads loadsand andthe thereal real loads is As 0. detailed in Section 5.1, the peak charging load on the day-ahead optimal planned load curve was As detailed in Section 5.1, the peak charging load on the day-ahead optimal planned load curve reduced to 598.4 kWkW from 1048.64 kW,kW, whereas thethe load factor increased from 17.19% to to 30.13%. was reduced to 598.4 from 1048.64 whereas load factor increased from 17.19% 30.13%. (1) The direct control strategy directly determines the BESS output from the difference between the day-ahead optimal planned value and the current charging load, considering the power and energy constraints of the BESS. Unlike rolling optimization, direct control does not have a rolling period, focusing only on control in the current moment and does not consider the future operation demands. The direct control result is shown in Figure 10. From Figure 10, the control objectives have essentially been satisfied, as evidenced by the low day-ahead forecasting errors. However, from 7:05 to 7:25 a.m., 10:05 to 10:10 a.m., and 6:05 to 6:15 p.m., the SOC of the BESS reached the upper limit of 80%. This results in zero power output of the BESS, and may even cause the failure of the plan tracking for peak-shaving at those moments. (2) The MPC-based real-time optimization strategy is a rolling optimization multistage decision-making problem approach. The control result is shown in Figure 11. The results illustrate that the MPC-based strategy also satisfied the objectives. Moreover, over the entire day, the SOC of the BESS never reached the upper limit of 80%, meaning that the MPC-based approach performed better than the direct control approach because of the rolling optimization mechanism. The results and the horizontal comparison of the three different real-time charging load control approaches are shown in Table 3. As shown in Table 3, the charging load control performance of the two real-time strategies were almost the same in Case I, but the variation in the SOC ranges were considerably reduced by MPC compared to direct control. The basic electricity cost per day was also reduced due to the reduced peak load caused by introducing the BESS. The TOU electricity costs per day were reduced by each of the three different real-time approaches.

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(1) The direct control strategy directly determines the BESS output from the difference between the day-ahead optimal planned value and the current charging load, considering the power and energy constraints of the BESS. Unlike rolling optimization, direct control does not have a rolling Energies 2018, 11,period, 229 focusing only on control in the current moment and does not consider the future operation demands. The direct control result is shown in Figure 10.

14 of 21

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(b) Figure 10. Real-time control results by direct control strategy in Case I: (a) The charging load control Real-time results by direct control results; (b)control The output power and SOC of the BESS. strategy in Case I: (a) The charging load

Figure 10. results; (b) The2018, output Energies 11, 229power and SOC of the BESS.

control

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From Figure 10, the control objectives have essentially been satisfied, as evidenced by the low day-ahead forecasting errors. However, from 7:05 to 7:25 a.m., 10:05 to 10:10 a.m., and 6:05 to 6:15 1200 p.m., the SOC of the BESS reached the upper limit of 80%. This results in zero power output of the Load deviation band BESS, 1000 and may even cause the failure of the plan tracking for peak-shaving at those moments. Real load Day-ahead optimal plannedoptimization load (2) The MPC-based real-time strategy is a rolling optimization multistage Real Load with BESS decision-making problem approach. The control result is shown in Figure 11. The results illustrate 800 that the MPC-based strategy also satisfied the objectives. Moreover, over the entire day, the SOC of 600 never reached the upper limit of 80%, meaning that the MPC-based approach performed the BESS better than the direct control approach because of the rolling optimization mechanism. 400

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(b) Figure 11. Real-time control results of the model predictive control (MPC)-based strategy in Case I: Real-time control of the(b)model predictive strategy (a) The charging loadresults control results; The output power andcontrol SOC of the(MPC)-based BESS.

Figure 11. (a) The charging load control results; (b) The output power and SOC of the BESS.

in Case I:

The results and the horizontal comparison of the three different real-time charging load control approaches are shown in Table 3. Table 3. Comparison of the results of two different real-time approaches for Case I.

Item Peak load (kW) Load factor Peak-valley difference (kW) Maximum SOC

Without BESS-Based Control 1048.64 17.19% 1048.64 -

Direct Control 598.4 30.13% 598.4 80%

MPC 600 30.53% 600 63.74%

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Table 3. Comparison of the results of two different real-time approaches for Case I. Item

Without BESS-Based Control

Direct Control

1048.64 17.19% 1048.64 3805.84 1597.93

598.4 30.13% 598.4 80% 20% 60% 3530.08 911.85

Peak load (kW) Load factor Peak-valley difference (kW) Maximum SOC Minimum SOC Variation range of SOC TOU electricity cost (CNY/Day) Energies 2018, 11, 229 cost (CNY/Day) Basic electricity

MPC 600 30.53% 600 63.74% 39.17% 24.56% 3584.73 914.29 16 of 23

5.2.2. Real-Time Optimization Case II 5.2.2. Real-Time Optimization Case II In Case II, the day-ahead charging load forecasting accuracy was 87.27%, as shown in Figure In Case II, the day-ahead charging load forecasting accuracy was 87.27%, as shown in Figure 12. 12. The variance between the day-ahead forecasted loads and the real loads was calculated as The variance between the day-ahead forecasted loads and the real loads was calculated as 15,145.4 15,145.4 which also means a larger load disturbance during daily operation. which also means a larger load disturbance during daily operation. 1400 Real load Day-ahead optimal planned load Day-ahead forecasted load

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Figure12. 12. Day-ahead Day-ahead forecasted Figure forecasted load, load, day-ahead day-aheadoptimal optimalplanned plannedload, load,and andreal realload loadcurves curvesininCase CaseII.II.

Power(kW)

(1)The Thecontrol controlresults resultsof ofthe thedirect directcontrol controlstrategy strategyfor forCase CaseIIIIare areshown shownininFigure Figure13. 13. (1) From Figure 13, from 7:35 to 7:45 p.m., the SOC of the BESS almost reached the lower boundary, and its1400 energy was insufficient to shave the load peak to a value below the maximum constraint. This control failureReal was caused by the increased day-ahead forecasting errors, and the direct control load 1200 Day-ahead planned loadfuture demand and excessively consumed BESS energy in strategy itself, which does optimal not consider Real Load with BESS order to shave the peak to about 500 kW during the 6:20–6:50 p.m. time frame. Control failure 1000 (2) The control results of the MPC-based real-time rolling optimization strategy are shown 800 in Figure 14. Compared to the direct control results, the load peak from 7:35 to 7:45 p.m. was successfully shaved to the maximum acceptable power of 600 kW, due to the optimal usage of the 600 BESS, which avoided the excessive consumption of BESS energy during the previous peak time frame 400 of 6:20–6:50 p.m.

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Energies 2018, 11, 229

16 of 21 (1) The control results of the direct control strategy for Case II are shown in Figure 13. 1400 Real load Day-ahead optimal planned load Real Load with BESS

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Figure 14. Real-time control results bypower the MPC-based strategy for Case II: (a) The charging charging load control results; obtained (b) The output and SOC of the BESS. load control results; (b) The output power and SOC of the BESS. The results and the horizontal comparison of the two different real-time charging load control approaches are shown in Table 4. As shown in Table 4, compared to the original situation with direct control and without BESS-based control, the MPC-based rolling optimization strategy significantly improved the charging load characteristics in Case II, even with disturbances. The peak load with direct control was 783.45

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The results and the horizontal comparison of the two different real-time charging load control approaches are shown in Table 4. As shown in Table 4, compared to the original situation with direct control and without BESS-based control, the MPC-based rolling optimization strategy significantly improved the charging load characteristics in Case II, even with disturbances. The peak load with direct control was 783.45 kW, 2018, 11, 229 18 of 23 which is Energies more than the constraint of 600 kW, causing a failure in the charging load control. Additionally, the variation in the SOC than ranges was considerably MPC compared to direct kW, which is more the constraint of 600 kW, reduced causing a by failure in the charging load control.control, decreasing from 60%thetovariation 42.06%.inThe totalranges electricity cost, including the and the Additionally, the SOC was considerably reduced byTOU MPC electricity compared tocost direct control, decreasing 60% to cost,real-time including the TOU electricity basic electricity cost, wasfrom reduced by42.06%. aboutThe 17%total by electricity BESS-based control, whereas cost the direct and MPC-based the basic electricity cost, was reduced by about 17% by were BESS-based real-time control, whereas the control and optimization total electricity costs almost identical. direct control and MPC-based optimization total electricity costs were almost identical.

Table 4. Comparison of the results of the two different real-time approaches for Case II. Table 4. Comparison of the results of the two different real-time approaches for Case II.

Item Without BESS-Based ControlDirect Direct Control MPC MPC Item Without BESS-Based Control Control Peak load (kW) 1244.37 783.45 Peak load (kW) 1244.37 783.45 600600 Load 14.35% 22.88% 30.24% Loadfactor factor 14.35% 22.88% 30.24% Peak-valley difference (kW) 1244.37 783.45 600600 Peak-valley difference (kW) 1244.37 783.45 Maximum SOC 80% 73.36% Maximum SOC 80% 73.36% Minimum SOC 20% 31.3% Minimum SOC 31.3% Variation range of SOC - 60% 20% 42.06% Variation range SOC 60% 42.06% TOU electricity costof(CNY/Day) 3790.283546.27 3747.06 Basic cost (CNY/Day) 1896.18 1193.83 914.29 TOUelectricity electricity cost (CNY/Day) 3790.28 3546.27 3747.06 Basic electricity cost (CNY/Day) 1896.18 1193.83 914.29

5.2.3. Real-Time Optimization Case III

5.2.3. Real-Time Optimization Case III

In Case In III,Case theIII, day-ahead charging load forecasting accuracy was rather low, only 82.57%, as the day-ahead charging load forecasting accuracy was rather low, only 82.57%, as shown inshown Figure 15. The variance between forecasted loads the loads real loads in Figure 15. The variance betweenthe theday-ahead day-ahead forecasted loads andand the real was was calculated as 28,399.05, which is much higher inthe theprevious previous cases indicates calculated as 28,399.05, which is much higherthan thanthose those in cases and and indicates a very a very large load disturbance in daily operation. large load disturbance in daily operation. 1200 1000

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Figure 15. Day-ahead forecastedload, load, day-ahead optimal planned load, andload, real load curves Casecurves III. Figure 15. Day-ahead forecasted day-ahead optimal planned and realfor load for Case III.

(1) The control results of the direct control strategy for Case III are shown in Figure 16. As can be seen from Figure 16, from 7:00 to 7:15 p.m., an extreme situation occurred in which As can be seen from Figure 16, from 7:00 to 7:15 p.m., an extreme situation occurred in which the maximum peak of the charging load was not reduced, due to a large day-ahead forecasting the maximum peak ofsimultaneously, the charging load was not reduced, due to aoflarge day-ahead forecasting error error occurring and the lack of optimization ability the direct control strategy. occurring simultaneously, and the lack of optimization the directstrategy controlfor strategy. (2) The control results of the MPC-based real-timeability rolling of optimization Case III are shown in Figure 17. Compared to the results of direct control, load peak from 7:00 to for 7:15Case p.m. III are (2) The control results of the MPC-based real-time rolling the optimization strategy was successfully shaved to the maximum acceptable power of 600 kW due to the optimal usage of p.m. shown in Figure 17. Compared to the results of direct control, the load peak from 7:00 to 7:15 the BESS. This illustrates that the MPC-based real-time rolling strategy achieved the control was successfully shaved to the maximum acceptable power of 600 kW due to the optimal usage of the objectives, even with a large load disturbance, due to the proposed optimization mechanism, which BESS. This illustrates the MPC-based real-time rolling strategy achieved the control objectives, considers futurethat operation demands.

even with a large load disturbance, due to the proposed optimization mechanism, which considers future operation demands. (1) The control results of the direct control strategy for Case III are shown in Figure 16.

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Figure 16. Real-time of the direct strategy for Case Theload charging load control (b) Theresults output results power and SOC ofcontrol the BESS.strategy Figureresults; 16.control Real-time control of the direct control for Case III: (a) III: The (a) charging control results;control (b) The output and SOC of of the results; (b) Thepower output power and SOC theBESS. BESS. 1200 Load deviation band Real load Load deviation band Day-ahead optimal planned load RealLoad loadwith BESS Real Day-ahead optimal planned load Real Load with BESS

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Figure 17. control results; (b) The output power and SOC of the BESS.

The results and the horizontal comparison of the two different real-time charging load control approaches are shown in Table 5. Table 5. Comparison of the results of the two different real-time approaches for Case III.

Item Peak load (kW) Load factor Peak-valley difference (kW)

Without BESS Based Control 1134.84 16.45% 1134.84

Direct Control 1134.84 16.72% 1134.84

MPC 600 31.59% 600

load

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The results and the horizontal comparison of the two different real-time charging load control approaches are shown in Table 5. Table 5. Comparison of the results of the two different real-time approaches for Case III. Item Peak load (kW) Load factor Peak-valley difference (kW) Maximum SOC Minimum SOC Variation range of SOC TOU electricity cost (CNY/Day) Basic electricity cost (CNY/Day)

Without BESS Based Control

Direct Control

MPC

1134.84 16.45% 1134.84 3946.15 1729.28

1134.84 16.72% 1134.84 80% 20% 60% 3777.82 1729.28

600 31.59% 600 67.9% 27.25% 40.65% 3902.7 914.29

As shown in Table 5, the direct control completely failed at peak-shaving, but the MPC-based rolling optimization strategy significantly improved the charging load characteristics in Case III, even with large disturbances. This verifies the robustness of the MPC-based control strategy against load forecasting error and load disturbance. Finally, based on the longitudinal comparison of the results of the three cases, we reached the following conclusions. Firstly, the MPC-based real-time rolling optimization strategy can significantly improve the charging load characteristics and satisfy the objectives and constraints, even with large forecasting errors, which also illustrates the robustness of the proposed approach. Secondly, the variation in the SOC range will increase with the decrease in the day-ahead charging load forecasting accuracy, but the MPC-based strategy can still ensure the smallest variation in the SOC range. Thirdly, the MPC-based real-time rolling optimization strategy can reduce the total electricity cost to benefit the station operator. The bi-level optimization control strategy proposed in this paper is meant to be applied to the daily operation of a fast charging station. For practical applications, based on the day-ahead forecasted charging load, day-ahead level optimization generates the optimal planned load curve that satisfies the multiple control objectives. Then, using this day-ahead optimal planned load curve as the reference, real-time level rolling optimization can be used to attain the control objectives. This second level of optimization is an online real-time BESS control strategy that can be embedded into the energy management system of a charging station. 6. Conclusions This paper introduces BESS to the charging load control of fast charging stations, to address the challenges posed by the unique fast charging characteristics. Consequently, we proposed a BESS-based bi-level optimization strategy for charging load regulation of the electric vehicle fast charging station to achieve multiple control objectives. The results of the case studies show that: (1) through linear programming, the day-ahead level optimization can generate a day-ahead optimal planned load curve or a deviation band as a reference to achieve the objectives of charging load peak-shaving, electricity cost minimization, and charging load change rate reduction. (2) By using the proposed MPC-based control, real-time level rolling optimization can achieve the day-ahead plan, and ensure the lifespan and available energy of the BESS. (3) The real-time level control approach, namely MPC-based control, exhibits better performance in peak-shaving, total electricity cost reduction, and minimizing the variation in the SOC range compared to the results without BESS introduced or with only direct control, due to the day-ahead optimal planned load deviation band and real-time rolling optimization. (4) The robustness of our bi-level optimization strategy against load disturbance was validated by the comparison of the results from the three case studies with different day-ahead charging load forecasting accuracies, which might have been affected by the driver’s personal habits or the traffic conditions. In addition, many potential extensions of the work reported in this paper are possible, such as case studies based on fast charging stations for different types of vehicles.

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Acknowledgments: This work was supported by the National Key R&D Program of China [grant number 2016YFB0900500]; and the Fundamental Research Funds for the Central Universities [grant number 2016RC029]. Author Contributions: Yan Bao proposed the bi-level optimization model and strategy; Yu Luo performed the simulations; Yan Bao, Yu Luo, Weige Zhang, and Mei Huang analyzed the results; Le Yi Wang modified the paper; Jiuchun Jiang organized the structure of the paper. Conflicts of Interest: The authors declare no conflict of interest.

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