Predicting the Impact of Increasing Plug-In Electric Vehicle Loading on Bulk Transmission Systems

Predicting the Impact of Increasing Plug-in Electric Vehicle Loading on Bulk Transmission Systems

Carl Staiger, Benedict Sim, Gonzalo Constante, and Jiankang Wang Department of Electrical and Computer Engineering The Ohio State University [email protected], [email protected], constanteﬂ[email protected], [email protected]

Abstract—This paper proposes a methodology to assess the stochastic behavior of the charging profiles of PEV. The main impact of the increasing penetration of plug-in electric vehicles contributions of this paper are twofold: (PEV) in cascading failures. Our methodology captures the stochastic nature of the charging profiles of PEV and presents an • Propose an algorithm to generate a stochastic PEV charge algorithm to generate a PEV charge profile. A pseudo–inverse profile. based cascading failure model and the linearized (DC) power • Present a methodology to assess the impact of PEV flow equations are used in the framework of a Monte Carlo charging stations in transmission systems. simulation. Finally, we validate the proposed methodology in the New England IEEE-39 bus test system under different levels of The remainder of the paper is organized as follows. The PEV penetration. The results of this paper provide insights to theoretical background is presented in Section II. The proposed plan the expansion of transmission systems as well as to develop methodology and its assumptions is detailed in Section III. countermeasures to mitigate cascading failures caused by the In Section IV, we validate the proposed methodology with rising penetration of PEV charging stations. numerical tests. Finally, we present the main conclusions of Index Terms—Cascading failures, charge profile, Monte-Carlo Simulation, plug-in electric vehicles the paper in Section V.

II.BACKGROUND I.INTRODUCTION A. DC Power Flow Model Data obtained by The U.S. Department of Energy’s Alter- The DC Power Flow model, which is generally used in native Fuels Data Center indicates a steady increase of plug-in large-scale contingency analysis, is commonly recognized as electric vehicle (PEV) sales in the U.S. from 18,000 vehicles a suitable approximation for the more accurate AC Power in 2011 to 144,000 in 2016 [1]. Moreover, a report by The Flow model [16], [17]. Let us represent the power grid by Edison Electric Institute (EEI) and the Institute for Electric an undirected graph G = (V, E) where V is the set of n buses, Innovation (IEI) forecasted 7 million plug-in electric vehicles and E ⊆ V × V is the set of transmission lines. We assume on roads in the U.S. by 2025 [2]. As the number of PEVs grow, that each transmission line between nodes i and j is purely it is important to analyze the impact that such a large increase reactive and is characterized by its reactance xij and capacity in loading could potentially have on the power system. g f ij. Let C ⊆ V be the set of supply nodes and pi denote the The impact of high penetration of PEVs has been stud- active power generation at node i. Also, let D ⊆ V be the set ied at two voltage levels: distribution and transmission. At of demand nodes and pd denote the demand at node i. the distribution level, the impacts of PEV charging stations i Given the power supply/demand vector P ∈ n, the power include: distribution system operation [3], [4], coordinated R flow is a solution of the following system of equations [17]: charging strategies [5], interaction between PEV charging stations and distributed generation [6], maximum penetration X fij = pi, ∀ i ∈ V (1) [7], and grid asset depreciation [8]. At the transmission level j∈N (i) studies have been focused on: electricity markets [9], [10], θ − θ − x f = 0, ∀ (i, j) ∈ E (2) frequency regulation [11], [12], coordination with variable i j ij ij generation [13], maximum penetration [14], and transmission |fij| ≤ f ij, ∀(i, j) ∈ E (3) g g g expansion planning [15]. However, the impact of PEVs in pi ≤ pi ≤ pi , ∀ i ∈ C (4) relevant topics (e.g., voltage instability or cascading failures) 0 ≤ pd ≤ pd, ∀ j ∈ D (5) on bulk transmission systems has not been addressed yet. j j Although cascading failures are one of the most catastrophic where N (i) is the set of nodes in the neighborhood of node phenomena that can occur in power systems, to the best of i, fij denotes the power flow between node i and node j, g d our knowledge, the impact of PEVs on cascading failures has pi = pi − pi denotes the net active power at node i, θi is g d not been studied in literature. To bridge this gap, this paper the phase angle of node i, pi (resp. pi ) denotes the minimum proposes a methodology to study the impact of increasing (resp. maximum) active power output of the generator at node d penetration of PEVs in cascading failures considering the i, and pi denotes the nominal power demand at node i. In the given system of equations, (1) represents the power and close to 500,000 charging events across 17 major cities in flow balance, (2) describes the linearized dependency of the the U.S. We perform a polynomial regression to the minimum, power flow on the line reactances and phase angles, (3)–(5) median, and maximum percentages of PEV charging units as impose upper and lower bounds for the power flow, power shown in Fig. 1. generation, and load demand, respectively. Eqs. (1)–(2) can To produce a stochastic charging profile that resembled the be expressed in a matrix form as: extracted data, the following algorithm was implemented to randomly determine the PEV power demand at any time in BΘ = P (6) the day. Algorithm 1 shows the flow diagram of the algorithm used to generate the stochastic PEV charge profile. where B ∈ Rn×n denotes the admittance matrix of G and n Θ ∈ R the phase angle vector. Notice that, when G is Algorithm 1 Stochastic PEV Charge Profile connected and P pg = P pd, (6) has a unique solution. i∈C i i∈D i Input: Maximum base demand pˆ, percentage of PEV charging units Consequently, the same condition holds for a disconnected X = [x(0), . . . , x(T )]>, and Z. graph if the total generation and demand are equal within each Output: PEV power demand P = [p(0), . . . , p(T )]> of the connected components [16]. 1: m(t) ← polyfit(min(x(t))). 2: med(t) ← polyfit(median(x(t))). B. Cascading Failure Model 3: M(t) ← polyfit(max(x(t))). We implement the pseudo–inverse based Cascading Failure 4: for k = 0 to T do 5: coin(k) ←rand(0, 1). Evolution (CFE-PB) presented in [16], which relies on the 6: if coin(k) ≥ 0.5 then linearized (DC) power flow. Such algorithm focus on the 7: σ(k) ← (M(k) − med(k))/Z. impact of a single line failure on the power flow of the remain- 8: else ing lines of the system, and consequently on the cascading 9: σ(k) ← (med(k) − m(k))/Z. failure of the grid. The Moore–Penrose pseudo–inverse of the 10: end if 11: rand(k) ← normrnd(med(k), σ(k)). admittance matrix B of the system is used to develop an 12: if coin(k) ≥ 0.5 and rand(k) ≤ med(k) then efficient algorithm to assess the cascading failure evolution. 13: rand(k) ← rand(k) + |rand(k) − med(k)|. A line outage alters the topology of the grid, and changes 14: else if coin(k) < 0.5 and rand(k) > med(k) then the power flows through the remaining operating transmission 15: rand(k) ← rand(k) − |rand(k) − med(k)|. lines. The resulting power flow can exceed the capacity of 16: end if 17: p(k) ← pˆ × rand(k) another set of lines that will trip when protection equipment 18: end for or operators react to the thermal overloads. This sequence of events is known as one round of cascading failure. This process will repeat until the system stabilizes i.e., equations (1)-(5) are satisfied. There are edges, known as cut-edges, that can split the system into islands i.e., the grid becomes a disconnected graph. In this case, every island must satisfy the same equations to stop tripping due to thermal failures. Let B+ denote the Moore–Penrose pseudo–inverse of the admittance matrix B. Let e = (i, j) ∈ E and fe = |fij| = |fji|, ∀e ∈ E. Assume that the power fe is bounded from above by f e. Let Ok denote the set of outages during the kth ∗ round of cascading failure. Let Ok denote the set of cumulative outages including the kth round of failures. At each round, the CFE-PB algorithm determines the set of outages and power flows through the operating transmission lines. In our case, the set of initial outages O0 is determined by the overloaded lines due to the penetration of PEV. Fig. 1: Comparison between stochastic (Z=2) and extracted C. Charge Profile percentage of PEV charging units being used. To predict the effect of increasing PEV penetration on the stability of a power system, a stochastic method was used to To simplify the generation of the PEV charge profile, it determine a daily charge profile. First, data representing PEV was assumed that the PEVs under study utilized Lithium-ion charge profiles was obtained. The data was collected from batteries and thus the power demanded by a PEV remains The EV Project, a project performed by The U.S. Department constant during its charging duration. In the standard charging of Energy and 18 cities to collect data on charging stations procedure of a Lithium-ion battery, the current through the and PEVs [18]. The data obtained was the percentage of PEV battery is kept constant while the battery voltage increases charging units being used across time within a day. The study until it reaches its maximum, at which point the battery voltage conducted to collect this data involved 8,058 charging units is kept constant until the battery is fully charged. Simulation and experimental validation of the charging model [19] show Start that the power demanded by the battery is almost constant during its charging period. For this study, it is assumed that t ← 0 the charge profile of the PEV battery is ideal. m ← 1

III.PROPOSED METHODOLOGY Perform DC power ﬂow A. Assumptions

To simplify our analysis, we made several key assumptions. Compute power 1) We assume that a satisfactory PEV charging profile flow margins fe, ∀e ∈ E model could be created using data from a segment of the electric vehicle market rather than taking into account every PEV currently available to consumers. yes Set O∗ ∃ f > f¯ 0 2) We employ the DC power flow equations. Under extreme e e Run CFE-PB conditions (e.g., cascading failures) the AC formulation may fail to converge since it depends on an initial no

guess. Also, most of the methods for AC power flow m ← m + 1 yes ∗ m < M equations are fast or converge in a couple of iterations O0 ← ∅ (e.g., Newton-Raphson). However, its implementation in a Monte Carlo simulation (MCS) is computationally no expensive and slow compared with the DC formulation. t ← t + 1 yes t < T 3) We consider a static model for the cascading failure m ← 1 evolution i.e., the system evolution over time is not no studied. Hence, any transmission line with power flow End exceeding its power rating would be instantly removed from operation by the protection system. Fig. 2: Methodology flowchart 4) To consider the worst-case scenario of the system load- ability, we select load demand data from the day with TABLE I: IEEE 39-bus test system bus definition highest peak demand to represent the base demand for Type of bus Bus No. Demand the transmission system. Residential 3, 4, 14-18, 21, 24, 27 Time-varying B. Approach Industrial 1, 2, 5-13, 19, 20, 22, 23, 25, 26, 28-39 Constant Fig. 2 depicts the flowchart of the proposed methodology. For every time t and m MCS run, we compute an initial power flow considering the load demand curve and PEV load Second, we used normalized Five-Minute System Demand profile. We determine the base demand at each bus and sum data from ISO New England Reports [20] to create a realistic that with a PEV charging profile to determine a total demand demand profile curve across a 24-hour period of time. We ∗ at each bus. The set of initial failures O0 is defined by the selected data from July 12, 2017 since summer demand is lines whose power flow fe exceeds the line rating f e. Then, typically associated with high peak values. Although the ISO the cascading failure algorithm CFE-PB is performed. This New England Report data was the total system demand, we process is repeated until completing the M simulations runs used it as an approximate representation of the residential bus for every time T . change in demand over time. With the results, qualitative analysis can be conducted to The load demand curve was applied to the residential buses, draw conclusions about the relationship between base demand multiplied by a weighting factor representing a percentage of and PEV demand, and how various factors led to the cascading the total demand of the defined residential buses. This total blackout. Analysis can be also conducted to draw conclusions residential demand was the sum of the single point in time about the severity of the cascading blackouts. base demand values from the original IEEE 39-bus System for each bus defined as residential. IV. NUMERICAL TESTS To determine the final demand at each bus in the system, A. System setup the stochastic charging profile was used at each point in time. We validated the proposed methodology in the IEEE 39- By calculating the total PEV demand discussed above and bus test system. Without loss of generality, we defined the multiplying this value by a weighting factor representing a following buses to consider heterogeneous loads in a power percentage of the total demand of the defined residential buses, system: (i) a set of buses to represent residential demand with we were able to determine PEV demand at each residential a time-varying load demand curve; and (ii) a set of buses bus in the system. Fig. 3 depicts the load demand curve of representing industrial loads with constant demand over time. a residential bus under different penetration levels of PEV Table I details the residential and industrial buses selected. charging stations. Additionally, without loss of generality, we to anticipate and prevent possible issues that may arise. By pursuing further studies, more informed power system planning can be implemented to maintain and develop a system that will remain stable and reliable while considering future societal shifts in transportation.

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(b) PEV Demand 50% of Peak Base Demand. (b) PEV Demand 50% of Peak Base Demand.

(d) PEV Demand 70% of Peak Base Demand. (d) PEV Demand 70% of Peak Base Demand.

Fig. 4: Number of Lines in Initial Failure Fig. 5: Number of Total Lines Out after cascading failure