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This paper considers a city with a large fleet of plug-in electric taxis (PETs) and studies the charging coordination problem of the fleet. The goal is to reduce charging cost for each PET, defined as the loss of service income caused by charging, by wisely choosing when and where to charge. Considering the fact that the fleet can contain thousands of autonomous PETs, this problem is approached in a distributed way. In detail, a two-stage decision process is designed for each PET in an online fashion upon receiving real-time information. In the first stage, a thresholding method is proposed to assist a PET driver in choosing a proper time slot for charging, with comprehensive consideration of state of charge of PET, time varying income, and queuing status at charging stations (CSs). In the second stage, a game-theoretical approach is devised for PETs to select CSs, so that the traveling and queuing time of each PET can be reduced with fairness. Extensive numerical simulations illustrate the following threefold benefits of the proposed approach: it can effectively reduce the charging cost for PETs, enhance the utilization ratio for CSs, and also flatten the unevenness of charging request for power grid.

In this paper, we formulate a cycling cost aware economic dispatch problem that co-optimizes generation and storage dispatch while taking into account cycle based storage degradation cost. Our approach exploits the Rainflow cycle counting algorithm to quantify storage degradation for each charging and discharging half-cycle based on its depth. We show that the dispatch is optimal for individual participants in the sense that it maximizes the profit of generators and storage units, under price taking assumptions. We further provide a condition under which the optimal storage response is unique for given market clearing prices. Simulations using data from the New York Independent System Operator (NYISO) illustrate the optimization framework. In particular, they show that the generation-centric dispatch that does not account for storage degradation is insufficient to guarantee storage profitability.

Renewable portfolio standards are targeting high levels of variable solar photovoltaics (PV) in electric distribution systems, which makes reliability more challenging to maintain for distribution system operators (DSOs). Distributed energy resources (DERs), including smart, connected appliances and PV inverters, represent responsive grid resources that can provide flexibility to support the DSO in actively managing their networks to facilitate reliability under extreme levels of solar PV. This flexibility can also be used to optimize system operations with respect to economic signals from wholesale energy and ancillary service markets. Here, we present a novel hierarchical scheme that actively controls behind-the-meter DERs to reliably manage each unbalanced distribution feeder and exploits the available flexibility to ensure reliable operation and economically optimizes the entire distribution network. Each layer of the scheme employs advanced optimization methods at different timescales to ensure that the system operates within both grid and device limits. The hierarchy is validated in a large-scale realistic simulation based on data from the industry. Simulation results show that coordination of flexibility improves both system reliability and economics, and enables greater penetration of solar PV. Discussion is also provided on the practical viability of the required communications and controls to implement the presented scheme within a large DSO.

Electric vehicle (EV) charging stations are increasingly set up to meet the recharge demand of EVs, and the stations equipped with local renewable energy generation need to optimize their charging. A basic challenge for the optimization stems from inherent uncertainties such as intermittent renewable generation that is hard to predict accurately. In this paper, we consider a charging station for EVs that have deadline constraints for their requests and aim to minimize its supply cost. We use Lyapunov optimization to minimize the time-average cost under unknown renewable supply, EV mobility, and grid electricity prices. We model the unfulfilled energy requests as a novel system of queues, based on whose evolution we define the Lyapunov drift and minimize it asymptotically. We prove that our algorithm achieves at most ${O({1}/{V})}$ more than the optimal cost, where the parameter ${V}$ trades off cost against unfulfilled requests by their deadlines, and its time complexity is linear in the number of EVs. Simulation results driven by real-world traces of wind power, EV mobility, and electricity prices show that, compared with a state-of-the-art scheduling algorithm, our algorithm reduces the respective charging costs by 12.48% and 51.98% for two scenarios.

This paper investigates a data-driven countermeasure for price spoofing in the context of cyber security and market-based frequency regulation. Market-based control of transmission power networks relies on cyber-physical infrastructure, which raises questions of system vulnerability in relation to cyber-security. In this paper, we consider the challenge of engineering a robust data-driven controller in the presence of price spoofing, i.e. where hacking mechanisms adjust price signals in an ex-post market. We extend a recently developed algorithm called deep dynamic mode decomposition to learn Koopman operators of nonlinear systems with affine inputs. Based on the learned input-Koopman operator model, a design algorithm for nonlinear controller synthesis is devised to compute optimal dynamic pricing policies that restore the nominal frequency and recover economic efficiency in the presence of price spoofing. The efficacy of the proposed data-driven Koopman controller synthesis approach is validated through tests on a IEEE 39-bus benchmark.

From the view point of a charging station (CS), it is important to design a simple, effective and implementable algorithm that reduces the cost, improves the time efficiency and enhances operational stability. Offline algorithms built on global information, in practice, cannot be implemented to achieve the best performance, since current charging rates of existing electric vehicles (EVs) need to be determined in the absence of future information. In the context of a current electricity tariff mechanism, commonly imposed in industry, which additionally charges for peak demand, this paper proposes an online two-stage charging scheduling algorithm (OTCSA) based on observed real time information and historical data to minimize charging cost, reduce charging time, as well as lower the maximum peak power. In the first stage, charging cost is minimized with guarantee to fulfill energy demand of each EV before its departure. The additional cost that penalizes peak demand inherently contributes to flattening the load profile of the CS with the deferrability of EV charging. In the second stage, we squeeze to save more charging time for EVs given the minimal cost. Simulations further validate the three-fold benefits of the proposed approach.

The cost and stability, in terms of stable charging load, are the main concerns of a charging station (CS). To this end, an online cost optimization algorithm is proposed by assuming that all electric vehicle (EV) users are selfless, so that they will report a real demand to the CS. However, in reality, all EV users are rational and they want to complete the energy demand in the fastest time and the lowest cost. Therefore, inspired by this characteristic of EV users, an online pricing mechanism is designed based on the online algorithm. There are three-fold benefits of the proposed pricing mechanism: giving discount to the flexibility of EV users, ensuring fairness among EV users and the individual optimal strategies of EV users jointly achieve minimizing cost of the CS. Numerical results based on real data further verify the effectiveness of the proposed online algorithm and the pricing mechanism.

International audience; In cyber-physical systems, mobile actuators can enhance system's flexibility and scalability, but at the same time incurs complex couplings in the scheduling and controlling of the actuators. In this paper, we propose a novel event-driven method aiming at satisfying a required level of control accuracy and saving energy consumption of the actuators, while guaranteeing a bounded action delay. We formulate a joint-design problem of both actuator scheduling and output control. To solve this problem, we propose a two-step optimization method. In the first step, the problem of actuator scheduling and action time allocation is decomposed into two subproblems. They are solved iteratively by utilizing the solution of one in the other. The convergence of this iterative algorithm is proved. In the second step, an on-line method is proposed to estimate the error and adjust the outputs of the actuators accordingly. Through simulations and experiments, we demonstrate the effectiveness of the proposed method.

Centralized planning of the electricity network, natural gas network and energy hubs (EHs) implicitly assumes a vertically integrated structure, which ignores the common independent ownership of different systems. A more practical approach should differentiate the electric system, gas system and each EH as separate stakeholders, and establish a distributed planning framework. Such a distributed planning framework based on the alternating direction method of multipliers (ADMM) is proposed in this paper, which uses the amount of electricity and natural gas required by EHs from each node as the decoupling information, and decomposes the joint planning problem into multiple planning sub-problems, respectively for the electric system, natural gas system and each EH. To reflect the operation more accurately in the planning stage, unit commitment is embedded in the planning model as its operation module. Finally, the proposed method is verified on an illustrative system composed of a modified IEEE RTS 24-bus electric system, Belgian 20-node natural gas system and four EHs. The case study demonstrates the impacts of unit commitment, gas price and penalty parameters on the planning scheme and the number of iterations.

This paper proposes a novel cooperative charging strategy for a smart charging station in the dynamic electricity pricing environment, which helps electric vehicles (EVs) to economically accomplish the charging task by the given deadlines. This strategy allows EVs to share their battery-stored energy with each other under the coordination of an aggregator, so that more flexibility is given to the aggregator for better scheduling. Mathematically, the scheduling problem is formulated as a constrained mixed-integer linear program (MILP) to capture the discrete nature of the battery states, i.e., charging, idle and discharging. Then, an efficient algorithm is proposed to solve the MILP by means of dual decomposition and Benders decomposition. At last, the algorithm can be implemented in a distributed fashion, which makes it scalable and thus suitable for large-scale scheduling problems. Numerical results validate our theoretical analysis.

We formulate an optimal scheduling problem for battery swapping that assigns to each electric vehicle (EV) a best battery station to swap its depleted battery based on its current location and state of charge. The schedule aims to minimize a weighted sum of EVs’ travel distance and electricity generation cost over both station assignments and power flow variables, subject to EV range constraints, grid operational constraints, and ac power flow equations. To deal with the nonconvexity of power flow equations and the binary nature of station assignments, we propose a solution based on second-order cone programming (SOCP) relaxation of optimal power flow and generalized Benders decomposition. When the SOCP relaxation is exact, this approach computes a global optimum. We evaluate the performance of the proposed algorithm through simulations. The algorithm requires global information and is suitable for cases where the distribution grid, battery stations, and EVs are managed centrally by the same operator. In Part II of this paper, we develop distributed solutions for cases where they are operated by different organizations that do not share private information.

In this paper, we formulate an optimal scheduling problem for demand response (DR) that schedules residential electrical appliances load to shave peak load. The schedule aims to minimize the total incentive cost and power loss over the power flow variables, subject to load capacity of users, grid operational constraints and the AC power flow equations. To deal with the nonconvexity of power flow equations, we present a solution based on second-order cone programming (SOCP) relaxation of optimal power flow. Furthermore, if the SOCP relaxation is exact, our algorithm yields a globally optimal solution. Finally, we evaluate the performance of our method by numerical simulations, which indicate that it is efficient and flexible.

This work investigates the increasing interactions between power network dynamics and market dynamics. A dynamical spot pricing mechanism for rational market behavior of generators and loads is designed to model market dynamics, which provably drives a power network to an equilibrium operating point, achieving secondary frequency control and economic dispatch.

This paper investigates a multi-generator-multiconsumer scenario in a day-ahead electricity market with high penetration of renewable energy and price-sensitive consumers. The electricity generated by renewables will also be traded in the market. To take care of both the supply and demand sides as well as achieve a balance in between, we propose a twofolded clearing mechanism. Specifically, at the demand side, we adopt an evolutionary game to model the selection behavior of the population of consumers, while at the supply side, a distributed optimization approach is employed to maximize the profit of generators. Finally, simulation results show that the proposed mechanism converges fast to clear the market. In addition, sensitivity analyses are carried out to assess the impact from the risk tolerance of consumers.

This paper aims at minimizing economical cost of a microgrid by jointly scheduling various devices, e.g., appliances, batteries, thermal generators, and wind turbines. To properly model the system, the characteristics of all devices is fully investigated; in particular, the chance constraint is introduced to capture the randomness of power generation of wind turbines. Then, this problem is formulated as a large-scale mixed-integer program with coupling constraints. In order to solve this problem efficiently, it is decoupled via dual decomposition into a set of subproblems to be solved distributedly on each appliance, battery, and generator. While the scheduling of generator is well studied in literature, this paper specially proposes an efficient method for appliance scheduling, and then employs Benders’ decomposition for battery scheduling. The performance of the proposed approach is verified by numerical simulations.

This paper formulates a multi-period optimal station assignment problem for electric vehicle (EV) battery swapping that takes into account both temporal and spatial couplings. The goal is to reduce the total EV cost and station congestion due to temporary shortage in supply of available batteries. We show that the problem is reducible to the minimum weight perfect bipartite matching problem. This leads to an efficient solution based on the Hungarian algorithm. Numerical results suggest that the proposed solution provides a significant improvement over a greedy heuristic that assigns EVs to nearest stations.

Electric vehicles (EVs) are vigorously promoted by policy makers in recent years, and expected to penetrate deeply in the near future. It is of great significance to develop efficient charging scheduling algorithms to optimize system operation. In this paper, we investigate the spatial scheduling problem of EVs, which aims to make recommendations of geographic distributed charging stations (CSs) for EVs to minimize the time of travelling and queuing. In order to ensure the fairness of the recommendations, an efficient game-theoretical approach is proposed. Numerical results illustrate the effectiveness of the proposed method in saving time, reducing charging piles' idle rate and EVs' queuing rate.

This paper proposes a complex system optimization method to obtain an optimal battery charging strategy. First, a real-world lithium-ion battery charging model is built as a complex system problem, which includes electric subsystem and thermal subsystem. The optimization objectives of electric subsystem includes battery charging time and energy loss, and the optimization objectives of thermal subsystem includes battery internal temperature rise and surface temperature rise. Then a called biogeography-based complex system optimization (BBO/Complex) algorithm is introduced, which is a heuristic method for complex system optimization. Finally, BBO/Complex is applied to the complex system of battery charging strategy, and the results show that the proposed method is a competitive algorithm for solving batter charging problem studied in this paper.

In Part I of this paper, we formulate an optimal scheduling problem for battery swapping that assigns to each electric vehicle (EV) a best station to swap its depleted battery based on its current location and state of charge. The schedule aims to minimize a weighted sum of EVs’ travel distance and electricity generation cost over both station assignments and power flow variables, subject to EV range constraints, grid operational constraints, and ac power flow equations. We propose there a centralized solution based on second-order cone programming relaxation of optimal power flow and generalized Benders decomposition that is applicable when global information is available. In this paper, we propose two distributed solutions based on the alternating direction method of multipliers and dual decomposition, respectively, that are suitable for systems where the distribution grid, stations, and EVs are managed by separate entities. Our algorithms allow these entities to make individual decisions, but coordinate through privacy-preserving information exchanges to solve a convex relaxation of the global problem. We present simulation results to show that both algorithms converge quickly to a solution that is close to optimum after discretization.

This paper proposes a complex system optimization method to solve economic emission load dispatch. First, a real-world economic emission load dispatch is modeled as a complex system problem, and the optimization objectives include economic load dispatch, emission load dispatch and transmission network loss. Then a called BBO/complex method is introduced, which extends biogeography-based optimization to a multi-archipelago environment to suit the structure of complex systems. Finally, the proposed method is applied to the economic emission load dispatch, and the results show that it can obtain good performance for economic emission load dispatch studied in this paper, and it is a competitive algorithm for solving complex system optimization problem.

With the wide deployment of smart meters in the power grid, it is becoming much easier to gather the detailed power consumption data of residential users, which enables the possibility of smarter and greener power grid. However, the fine-grained load profile of the individual user also introduces the severe concern of privacy leakage as the private information such as personal living habits may be inferred by the malicious third parties for unauthorized use and benefits. Different from most existing privacy-preserving energy management works which are solely based on the control of rechargeable batteries, we further introduce the proactive scheduling of widely used thermostatically controlled devices, including air conditioner, water heater, and laundry drier for effective load hiding. To minimize the weighed sum of financial cost, the deviation from the pre-defined load profile, and the user dissatisfaction, we formulate a novel load scheduling problem which is subject to both the device/battery physical dynamics and the practical user requirements. In order to solve the overall problem effectively under the uncertain price, we decompose the primal problem into a series of subproblems through dual composition, and design a stochastic gradient based two-level iterative distributed algorithm. Extensive simulations under various parameters are employed to demonstrate the effectiveness of our design.

We propose a model of a battery switching station (BSS) for electric buses (EBs) that captures the predictability of bus operation. We schedule battery charging in the BSS so that every EB arrives to find a battery ready for switching. We develop an efficient algorithm to compute an optimal schedule. It uses dual decomposition to decouple the charging decisions at different charging boxes so that independent subproblems can be solved in parallel at individual charging boxes, making the algorithm inherently scalable as the size of the BSS grows. We propose a direct projection method that solves these subproblems rapidly. Numerical results illustrate that the proposed approach is far more efficient and scalable than generic algorithms and existing solvers.