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This paper proposes a market mechanism for multi-interval electricity markets with generator and storage participants. Drawing ideas from supply function bidding, we introduce a novel bid structure for storage participation that allows storage units to communicate their cost to the market using energy-cycling functions that map prices to cycle depths. The resulting market-clearing process--implemented via convex programming--yields corresponding schedules and payments based on traditional energy prices for power supply and per-cycle prices for storage utilization. We illustrate the benefits of our solution by comparing the competitive equilibrium of the resulting mechanism to that of an alternative solution that uses prosumer-based bids. Our solution shows several advantages over the prosumer-based approach. It does not require a priori price estimation. It also incentivizes participants to reveal their truthful cost, thus leading to an efficient, competitive equilibrium. Numerical experiments using New York Independent System Operator (NYISO) data validate our findings.

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.

This paper investigates the efficiency loss in social cost caused by strategic bidding behavior of individual participants in a supply-demand balancing market, and proposes a mechanism to fully recover equilibrium social optimum via subsidization and taxation. We characterize the competition among supply-side firms to meet given inelastic demand, with linear supply function bidding and the proposed efficiency recovery mechanism. We show that the Nash equilibrium of such a game exists under mild conditions, and more importantly, it achieves the underlying efficient supply dispatch and the market clearing price that reflects the truthful system marginal production cost. Further, the mechanism can be tuned to guarantee self-sufficiency, i.e., taxes collected counterbalance subsidies needed. Extensive numerical case studies are run to validate the equilibrium analysis, and we employ individual net profit and a modified version of Lerner index as two metrics to evaluate the impact of the mechanism on market outcomes by varying its tuning parameter and firm heterogeneity.

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.

This paper investigates the online station assignment for (commercial) electric vehicles (EVs) that request battery swapping from a central operator, i.e., in the absence of future information a battery swapping service station has to be assigned instantly to each EV upon its request. Based on EVs' locations, the availability of fully-charged batteries at service stations in the system, as well as traffic conditions, the assignment aims to minimize cost to EVs and congestion at service stations. Inspired by a polynomial-time offline solution via a bipartite matching approach, we develop an efficient and implementable online station assignment algorithm that provably achieves the tight (optimal) competitive ratio under mild conditions. Monte Carlo experiments on a real transportation network by Baidu Maps show that our algorithm performs reasonably well on realistic inputs, even with a certain amount of estimation error in parameters.

This paper proposes a certificate, rooted in observability, for asymptotic convergence of saddle flow dynamics of convex-concave functions to a saddle point. This observable certificate directly bridges the gap between the invariant set and the equilibrium set in a LaSalle argument, and generalizes conventional conditions such as strict convexity-concavity and proximal regularization. We further build upon this certificate to propose a separable regularization method for saddle flow dynamics that makes minimal requirements on convexity-concavity and yet still guarantees asymptotic convergence to a saddle point. Our results generalize to saddle flow dynamics with projections on the vector field and have an immediate application as a distributed solution to linear programs.

This chapter focuses on the operation aspect of an electric vehicle (EV) station system in the battery swapping context and investigates analytical scheduling methods for cost saving, efficiency improvement, and its complementarity with microgrids as an energy carrier. Specifically, we formulate an optimal scheduling problem for battery swapping in a microgrid that assigns to each 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. Due to the nonconvexity of standard power flow equations and the binary nature of station assignments, the joint battery swapping and optimal power flow problem is computationally intractable in general. We first summarize and discuss several representative linearized/convexified network models for microgrids. On this basis, we then provide two possible analytical solutions to the problem that may both find their application in real scenarios, either solving for an optimum in a centralized manner with potential difficulties in scaling or solving for one desirable suboptimum in a scalable distributed manner. Both solutions are numerically validated using a real test case.

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.