Population Of Plug-in Electric Vehicles Research Articles

An optimal control problem for the continuity equation arising in smart charging

This paper is focused on the mathematical modeling and solution of the optimal charging of a large population of identical plug-in electric vehicles (PEVs) with mixed state variables (continuous and discrete). A mean field assumption is formulated to describe the evolution interaction of the PEVs population. The optimal control of the resulting continuity equation of the mixed system under state constraints is investigated. We prove the existence of a minimizer. We then characterize the solution as the weak solution of a system of two coupled PDEs: a continuity equation and of a Hamilton-Jacobi equation. We provide regularity results of the optimal feedback control.

Coordination of Plug-In Electric Vehicle Charging in a Stochastic Framework: A Decentralized Tax/Incentive-Based Mechanism to Reach Global Optimality

We address the problem of charging plug-in electric vehicles (PEVs) in a decentralized way and under stochastic dynamics affecting the real-time electricity tariff. The model is formulated as a Nash equilibrium seeking problem, where players wish to minimize the costs for charging their own PEVs. For finite PEVs populations, the Nash equilibrium does not correspond to the social optimum, i.e., to a control strategy minimizing the total electricity costs at the aggregate level. We accordingly introduce some taxes/incentives on the price of electricity for charging PEVs and show that it is possible to tune them so that (a) the social optimum is reached as a Nash equilibrium, (b) in correspondence with this equilibrium, players do not pay any net total tax, nor receive any net total incentive.

Efficient Model for Accurate Assessment of Frequency Support by Large Populations of Plug-in Electric Vehicles

In recent years, plug-in electric vehicles (PEVs) have gained immense popularity and are on a trajectory of constant growth. As a result, power systems are confronted with new issues and challenges, threatening their safety and reliability. PEVs are currently treated as simple loads due to their low penetration. However, as their numbers are growing, PEVs could potentially be exploited as distributed energy storage devices providing ancillary services to the network. Batteries used in PEVs are developed to deliver instantaneously active power, making them an excellent solution for system frequency support. This paper proposes a detailed dynamic model that is able to simulate frequency support capability from a large number of PEVs, using an innovative aggregate battery model that takes into account the most significant constraints at PEV and aggregate battery levels. The cost optimization algorithm, which is the most time-consuming process of the problem, is executed only at the aggregate battery level, thereby reducing the computational requirements of the model without compromising the obtained accuracy. The proposed method is applied to the power system of Crete exploiting detailed statistical data of EV mobility. It is proven that PEVs can effectively support power system frequency fluctuations without any significant deviation from their optimal operation.

A highly efficient control framework for centralized residential charging coordination of large electric vehicle populations

The potential for widespread adoption of plug-in electric vehicles (PEVs) brings with it the potential for negative impacts on the electric grid from electric vehicle charging. Uncoordinated PEV charging may increase electricity demand during peak hours, which could create concerns for the grid as the number of PEVs increases. Therefore, it is important to coordinate charging to alleviate potential negative impacts. Centralized charging coordination is preferred by grid operator over distributed control strategies because it can systematically allocate energy across a large population of PEVs and achieve global coordination benefits. However, centralized methods presented in the literature to date require prohibitively expensive computational resources and lack realistic PEV charging models. As a result, they cannot achieve the efficiency and accuracy required to implement charging coordination in the real world. This paper introduces a highly efficient receding horizon control framework that enables dynamic charging coordination for large PEV populations. A two-stage hierarchical optimization routine is proposed that aggregates individual PEV charging flexibility to reduce the computational complexity of the optimization process. The control framework is based on high-fidelity, validated charging system models and charging behavior models derived from a real-world data set of residential charging activities collected from thousands of charging stations over multiple years. Case studies illustrate that the proposed charging control framework is capable of effectively coordinating the charging of millions of PEVs using a standard desktop computer.

Decentralised optimal vehicle‐to‐grid coordination with forecast errors

Considering vehicle-to-grid (V2G) coordination schemes, plug-in electric vehicles (PEVs) are expected to be an energy storage system (ESS) to smooth out the fluctuation of the intermittent renewable energy source (RES) and the power load profile. In this study, firstly the optimal coordination of PEVs minimising total costs is shown to possess the valley-fill and peak-shift property for any pair of adjacent instants. Due to the decoupling relationship among the admissible sets of coordination behaviours of all the PEVs in the modelling issue, a decentralised algorithm is proposed by applying the gradient projection method, such that the coordination behaviours of individual PEVs can be updated locally and simultaneously. It is proved that the convergence and optimality of the proposed method are guaranteed in case the step-size parameter of the update procedure is in a certain region, and its performance does not rely on the shape of the net demand trajectory. Furthermore, a receding horizon-based algorithm is presented to account for the forecast errors occurred in the predictions of PEV populations, RES productions and inelastic load profiles. The results developed in this study are demonstrated with numerical simulations and comparisons with other decentralised methods are also provided.

A Mean-Field Game Method for Decentralized Charging Coordination of a Large Population of Plug-in Electric Vehicles

This paper develops a decentralized competitive charging coordination algorithm for a large population of plug-in electric vehicles (PEVs) using the concept of a mean-field (MF) game. The aim of each PEV is to find its optimal charging strategy by minimizing an objective function consisting of charging cost, battery degradation cost, and benefit from charging, subject to the input and state constraints. The strategy of a PEV affects the objective functions of other PEVs through the electricity price, and therefore, we can model the interactions among PEVs as a game problem. No information exchange is considered among the PEVs. Each PEV only sends its own control action value to a population coordinator, and the coordinator just broadcasts a common signal to all the PEVs. This common signal is an estimate of the average control actions of PEVs and is called the MF term. Utilizing an adjustment mechanism for the MF term, a decentralized MF-optimal control algorithm is proposed, and it is shown that the algorithm converges to the $\varepsilon _N$ -Nash equilibrium point of the game, with $\varepsilon _N$ uniformly converging to zero as the population sizes of the PEVs go to infinity. Simulation results and comparison with other methods are performed to clarify the advantages of the proposed method.

Could a bioenergy program stimulate electric vehicle market penetration? Potential impacts of biogas to electricity annual rebate program

AbstractThe biogas‐to‐electricity pathway under the Renewable Fuel Standard (RFS) allows for Renewable Identification Number (RIN) credits to be generated when electricity produced from biogas is used in the transportation sector. Though approved as a general pathway, EPA has proposed multiple credit allocation methods to functionalize this pathway. This study describes and evaluates a potential credit allocation framework where vehicle manufacturers generate electricity RIN (E‐RIN) credits and use these credits to increase the sales of plug‐in electric vehicles (PEVs). Under this framework, manufacturers use part of the credit value to reimburse electricity generators, offsetting potential higher biogas electricity generation cost. The remaining credit value is passed on to consumers as an annual PEV rebate to stimulate PEV sales. An iterative simulation framework is developed to fulfill two tasks: (a) to estimate the annual rebate amounts and their upfront value to consumers based on various factors, such as vehicle mileage, E‐RIN equivalence value, and biogas capacity, and (b) to evaluate potential impacts of the E‐RIN program on electrification of the future light‐duty vehicles (LDVs) and energy use. The annual rebate amount varies by vehicle technology and could be up to $870/year for battery electric vehicles (BEVs) and range between $230 and 825/year for plug‐in hybrid electric vehicles (PHEVs) depending on the electric range. These per vehicle rebates decrease when demand for electricity exceeds biogas electricity availability. The effectiveness of the program as modeled here is subject to different factors, such as the E‐RIN equivalence value, biogas electricity generation cost, biogas electricity generation capacity, and consumers’ valuation of the E‐RIN rebate. Our modeling results indicate that an E‐RIN program has the potential to produce nearly $12 billion in E‐RIN credits annually and to significantly increase PEV annual sales by up to 2.3 million and the PEV population by about 19.7 million in 2030.

A Hierarchical Algorithm for Vehicle-to-Grid Integration under Line Capacity Constraints

This work deals with the coordinated charging/discharging of a population of plug-in electric vehicles (PEVs) under energy efficiency, SOC, battery capacity, and power-line capacity constraints, to minimize energy cost. To address this, we introduce a framework in which the power grid is modeled as an undirected rooted tree, the root of this tree represents the generation/transmission side of the system and the leaves represent PEVs. Due to the several constraints, we are led to a non-convex optimization problem formulation subject to a complementarity constraint. We then show how a relaxed version of the problem can capture a wide set of optimal solutions for the original problem. After this, we propose a hierarchical algorithm for the computation of the PEVs’ charging/discharging profiles based on the relaxed problem formulation. The root generates a control signal based on the price per unit of power according to the demand for each time. Intermediate nodes represent congestible elements on the distribution side (e.g., transformers), which have a bound on the demand they can satisfy. In the proposed algorithm, intermediate nodes modify the control signal according to the difference between the demand they take care of, and its capacity upper bound. PEVs update their charging/discharging strategies according to this pricing signal. A proof of algorithm convergence to the optimizer of the problem is provided. Simulations demonstrate the algorithm performance and convergence rate.

ADMM-Based Multiperiod Optimal Power Flow Considering Plug-In Electric Vehicles Charging

When plug-in electric vehicles (PEVs) participate in grid operation, the intertemporal feature of PEVs charging transforms the traditional optimal power flow (OPF) problem into multiperiod OPF (MOPF) problem. In the case that the population of PEVs is huge, the large number of variables and constraints renders the centralized solution technique unsuitable to solve the MOPF problem. Therefore, a distributed algorithm based on alternating direction method of multipliers is developed to decompose the MOPF into two update steps that are solved in an alternating and iterative style. To improve the solution efficiency, the second update step is transformed into a Euclidean projection problem by approximating the original objective with a surrogate function. Then, a projection algorithm is utilized to solve the approximate problem. Numerical results show that this reformulated model obtains suboptimal solutions with small relative error, but gains considerable speed-up. Furthermore, its scalability and effectiveness are tested in the 119-bus and 906-bus distribution networks.

PDE Modeling and Control of Electric Vehicle Fleets for Ancillary Services: A Discrete Charging Case

This paper examines modeling and control of a large population of grid-connected plug-in electric vehicles (PEVs). PEV populations can be leveraged to provide valuable grid services when managed via model-based control. However, such grid services cannot sacrifice a PEV’s primary purpose—mobility. We consider an aggregator, which can control a fleet of PEVs with three possible charging rates: charging at a constant rate, discharging at a constant rate or idle. We develop a system of coupled partial differential equations for aggregating large populations of PEVs and transform its discretized version into a state space representation. We propose a linear quadratic regulator to track a power signal that provides load following services. We investigate the sensitivity of controller parameters, different bidding strategies and their impact on the performance of the provided balancing service. We examine this control design on a simulated case study and analyze sensitivity to a variety of assumptions and parameter selections.

Continuous-time Model Predictive Control for Real-time Flexibility Scheduling of Plugin Electric Vehicles

Abstract This paper proposes a continuous-time model predictive control (MPC) for co-optimizing the charging flexibility of plugin electric vehicles (PEVs) and generation schedule of generating units in real-time power systems operation. A continuous-time queuing model is developed to aggregate and cluster a large population of PEVs, which represents their aggregate flexibility to the power system operator. The proposed model integrates the most recent information about the system load and PEV arrival, and utilizes the flexibility of PEVs and generating units to supply the ramping requirements of load, while ensuring the delay-based and deadline-based service quality constraints of PEVs. The proposed model is implemented on the IEEE Reliability Test System, using PEV and load data of California. The simulation results demonstrate effectiveness of the proposed model to utilize the flexibility of PEVs in real-time power systems operation, which considerably reduces ramping requirements from conventional generating units.

Distributed Charge Scheduling of Plug-In Electric Vehicles Using Inter-Aggregator Collaboration

Plug-in electric vehicles (PEVs) are emerging as an eco-friendly and cost-effective alternative to conventional vehicles driven by internal combustion engines. However, uncoordinated charging of a large number of PEVs may cause grid failure. Therefore, charge scheduling of PEVs is an important problem. However, the charge scheduling by a single aggregator does not scale well as the PEV population grows. We propose a distributed framework for efficient PEV charging with multiple aggregators in a city where a PEV raises its charging request to a specific aggregator, and each aggregator has partial information about others. The aggregators collaborate among themselves for scheduling PEVs for charging in different charging stations owned by it or others. In this paper, we formulate a bi-objective charge scheduling optimization problem that attempts to maximize the total profit of the aggregators while maximizing the total number of PEVs charged. We first prove that the problem is NP-complete. We then propose distributed offline and online algorithms to solve the problem, and present simulation results for some realistic traffic scenarios.

Decentralized Convergence to Nash Equilibria in Constrained Deterministic Mean Field Control

This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and affected by the aggregate behavior of the overall population. For such large-scale systems, the theory of aggregative and mean field games has been established and successfully applied in various scientific disciplines. While the existing literature addresses the case of unconstrained agents, we formulate deterministic mean field control problems in the presence of heterogeneous convex constraints for the individual agents, for instance arising from agents with linear dynamics subject to convex state and control constraints. We propose several model-free feedback iterations to compute in a decentralized fashion a mean field Nash equilibrium in the limit of infinite population size. We apply our methods to the constrained linear quadratic deterministic mean field control problem and to the constrained mean field charging control problem for large populations of plug-in electric vehicles.

Optimal Charging of Electric Vehicles for Load Shaping: A Dual-Splitting Framework With Explicit Convergence Bounds

This paper proposes a tailored distributed optimal charging algorithm for plug-in electric vehicles (PEVs). If controlled properly, large PEV populations can enable high penetration of renewables by balancing loads with intermittent generation. The algorithmic challenges include scalability, computation, uncertainty, and constraints on driver mobility and power-system congestion. This paper addresses computation and communication challenges via a scalable distributed optimal charging algorithm. Specifically, we exploit the mathematical structure of the aggregated charging problem to distribute the optimization program, using duality theory. Explicit bounds of convergence are derived to guide computational requirements. Two variations in the dual-splitting algorithm are also presented, which enable privacy-preserving properties. Constraints on both individual mobility requirements and power-system capacity are also incorporated. We demonstrate the proposed dual-splitting framework on a load-shaping case study for the so-called California “Duck Curve” with mobility data generated from the vehicle-to-grid simulator.

A Distributed Charging Coordination for Large-Scale Plug-In Electric Vehicles Considering Battery Degradation Cost

Much research has focused on the issue of how to effectively coordinate the charging behaviors of large-scale plug-in electric vehicles (PEVs), like the valley-fill strategy, to minimize their impacts on the power grid. However, high charging rates under the valley-fill strategy may result in a higher battery degradation cost. Consequently, in this brief, we formulate a class of PEV charging coordination problems that deal with the tradeoff between the total generation cost and the accumulated battery degradation cost of PEV populations. Due to the autonomy of individual PEVs and the computational complexity of the system with large-scale PEVs, it is impractical to implement the solution in a centralized way. Alternatively, in this brief, we propose a distributed method such that all of the individual PEVs simultaneously update their own best charging behaviors with respect to a common electricity price curve, which is updated as the generation marginal cost with respect to the aggregated charging behaviors of the PEV populations implemented at the last step. The iteration procedure terminates in case the price curve does not update any longer. We show that by applying the proposed distributed method and under certain mild conditions, the system can converge to a unique charging strategy, which is nearly socially optimal. Simulation examples are studied to illustrate the results developed in this brief.

An optimization framework for workplace charging strategies

The workplace charging (WPC) has been recently recognized as the most important secondary charging point next to residential charging for plug-in electric vehicles (PEVs). The current WPC practice is spontaneous and grants every PEV a designated charger, which may not be practical or economic when there are a large number of PEVs present at workplace. This study is the first research undertaken that develops an optimization framework for WPC strategies to satisfy all charging demand while explicitly addressing different eligible levels of charging technology and employees’ demographic distributions. The optimization model is to minimize the lifetime cost of equipment, installations, and operations, and is formulated as an integer program. We demonstrate the applicability of the model using numerical examples based on national average data. The results indicate that the proposed optimization model can reduce the total cost of running a WPC system by up to 70% compared to the current practice. The WPC strategies are sensitive to the time windows and installation costs, and dominated by the PEV population size. The WPC has also been identified as an alternative sustainable transportation program to the public transit subsidy programs for both economic and environmental advantages.

Game‐Based Valley‐Fill Charging Coordination for Large‐Population Plug‐in Electric Vehicles

AbstractCharging coordination of large‐population autonomous plug‐in electric vehicles (PEVs) in the power grid can be formulated as a class of constrained optimization problems. To overcome the computational complexity, a game‐based method is proposed for the charging problems of the PEV population, which is composed of homogeneous subpopulations, such that individuals update their best charging strategies simultaneously with respect to a common electricity price determined by the total demand. To mitigate the oscillation behavior caused by the greedy behavior for the cheap electricity by individuals, a deviation cost is introduced to penalize against the deviation of the individual strategy from the average value of the homogeneous subpopulation. By adopting a proper deviation cost and following a best strategy update mechanism, the game systems may converge to the socially optimal valley‐fill Nash equilibrium. Simulation examples are studied to illustrate the results.

A decentralized charging control strategy for plug-in electric vehicles to mitigate wind farm intermittency and enhance frequency regulation

This paper proposes a decentralized charging control strategy for a large population of plug-in electric vehicles (PEVs) to neutralize wind power fluctuations so as to improve the regulation of system frequency. Without relying on a central control entity, each PEV autonomously adjusts its charging or discharging power in response to a communal virtual price signal and based on its own urgency level of charging. Simulation results show that under the proposed charging control, the aggregate PEV power can effectively neutralize wind power fluctuations in real-time while differential allocation of neutralization duties among the PEVs can be realized to meet the PEV users' charging requirements. Also, harmful wind-induced cyclic operations in thermal units can be mitigated. As shown in economic analysis, the proposed strategy can create cost saving opportunities for both PEV users and utility.

Decentralized Charging Control of Large Populations of Plug-in Electric Vehicles

This paper develops a strategy to coordinate the charging of autonomous plug-in electric vehicles (PEVs) using concepts from non-cooperative games. The foundation of the paper is a model that assumes PEVs are cost-minimizing and weakly coupled via a common electricity price. At a Nash equilibrium, each PEV reacts optimally with respect to a commonly observed charging trajectory that is the average of all PEV strategies. This average is given by the solution of a fixed point problem in the limit of infinite population size. The ideal solution minimizes electricity generation costs by scheduling PEV demand to fill the overnight non-PEV demand “valley”. The paper's central theoretical result is a proof of the existence of a unique Nash equilibrium that almost satisfies that ideal. This result is accompanied by a decentralized computational algorithm and a proof that the algorithm converges to the Nash equilibrium in the infinite system limit. Several numerical examples are used to illustrate the performance of the solution strategy for finite populations. The examples demonstrate that convergence to the Nash equilibrium occurs very quickly over a broad range of parameters, and suggest this method could be useful in situations where frequent communication with PEVs is not possible. The method is useful in applications where fully centralized control is not possible, but where optimal or near-optimal charging patterns are essential to system operation.

Transport-Based Load Modeling and Sliding Mode Control of Plug-In Electric Vehicles for Robust Renewable Power Tracking

This paper develops a modeling and control paradigm for the aggregate charging dynamics of plug-in electric vehicles (PEVs). The central goal of the paper is to derive a control policy that can adapt the aggregate charging power of PEVs to highly intermittent renewable power. The key assumption here is that the grid is able to directly control the charging power of PEVs in real-time, through broadcasting a universal control signal. Using the transport-based load modeling principle, we develop a partial differential equation model for the collective charging of PEVs. We use real driving data to simulate the model and validate it against a PEV Monte Carlo simulation model. Adopting the sliding mode control theory, we then develop a robust output tracking controller for the system. The controller uses the real-time error between power supply and demand as the only measured signal, and attempts to suppress it despite the variation of the population of PEVs on the grid. We examine the performance of the controller using numerical simulations on a real wind power trajectory.