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Lithium-ion batteries are increasingly being deployed in liberalised electricity systems, where their use is driven by economic optimisation in a specific market context. However, battery degradation depends strongly on operational profile, and this is particularly variable in energy trading applications. Here, we present results from a year-long experiment where pairs of batteries were cycled with profiles calculated by solving an economic optimisation problem for wholesale energy trading, including a physically-motivated degradation model as a constraint. The results confirm the conclusions of previous simulations and show that this approach can increase revenue by 20% whilst simultaneously decreasing degradation by 30% compared to existing methods. Analysis of the data shows that conventional approaches cannot increase the number of cycles a battery can manage over its lifetime, but the physics-based approach increases the lifetime both in terms of years and number of cycles, as well as the revenue per year, increasing the possible lifetime revenue by 70%. Finally, the results demonstrate the economic impact of model inaccuracies, showing that the physics-based model can reduce the discrepancy in the overall business case from 170% to 13%. There is potential to unlock significant extra performance using control engineering incorporating physical models of battery ageing.
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The rapid growth of electric vehicles (EVs) will include electric grid stress from EV chargers and produce a large number of diminished EV batteries. EV batteries are expected to retain about 80 % of their original capacity at the end of vehicle life. Employing these in second-use battery energy storage systems (2-BESS) as energy buffers for EV chargers further reduces the environmental impact of battery manufacturing and recycling. One of the obstacles that limits performance and cost to 2-BESS is the heterogeneity of second-use batteries. In this paper, we show that a structure for power processing within a 2-BESS with hierarchical partial power processing can be optimally designed for stochastic variation in EV demand, dynamic grid constraints, and statistical variation in battery capacity. Statistically-structured hierarchical partial power processing shows better battery energy utilization, lower derating, and higher captured value in comparison to conventional partial power processing and full power processing for similar power conversion cost.
This paper develops a safety analysis method for stochastic systems that is sensitive to the possibility and severity of rare harmful outcomes. We define risk-sensitive safe sets as sub-level sets of the solution to a non-standard optimal control problem, where a random maximum cost is assessed using the Conditional Value-at-Risk (CVaR) functional. The solution to the control problem represents the maximum extent of constraint violation of the state trajectory, averaged over the $alphacdot 100$% worst cases, where $alpha in (0,1]$. This problem is well-motivated but difficult to solve in a tractable fashion because temporal decompositions for risk functionals generally depend on the history of the systems behavior. Our primary theoretical contribution is to derive under-approximations to risk-sensitive safe sets, which are computationally tractable. Our method provides a novel, theoretically guaranteed, parameter-dependent upper bound to the CVaR of a maximum cost without the need to augment the state space. For a fixed parameter value, the solution to only one Markov decision process problem is required to obtain the under-approximations for any family of risk-sensitivity levels. In addition, we propose a second definition for risk-sensitive safe sets and provide a tractable method for their estimation without using a parameter-dependent upper bound. The second definition is expressed in terms of a new coherent risk functional, which is inspired by CVaR. We demonstrate our primary theoretical contribution using numerical examples of a thermostatically controlled load system and a stormwater system.
Fast and accurate optimization and simulation is widely becoming a necessity for large scale transmission resiliency and planning studies such as N-1 SCOPF, batch contingency solvers, and stochastic power flow. Current commercial tools, however, prioritize speed of convergence over accuracy by relying on initial conditions that are taken from the steady state solution of similar network configurations that are not guaranteed to lie within a convex region of a valid solution. In this paper we introduce a globally convergent algorithm to facilitate fast and accurate AC steady state simulation and optimization based on prior knowledge from similar networks. The approach uses a homotopy method that gradually and efficiently translates a previously known network configuration to the current network configuration. The proposed formulation is highly scalable, and its efficacy is demonstrated for resiliency study and optimization of large networks up to 70k buses.
Power electronic converters for integrating renewable energy resources into power systems can be divided into grid-forming and grid-following inverters. They possess certain similarities, but several important differences, which means that the relationship between them is quite subtle and sometimes obscure. In this article, a new perspective based on duality is proposed to create new insights. It successfully unifies the grid interfacing and synchronization characteristics of the two inverter types in a symmetric, elegant, and technology-neutral form. Analysis shows that the grid-forming and grid-following inverters are duals of each other in several ways including a) synchronization controllers: frequency droop control and phase-locked loop (PLL); b) grid-interfacing characteristics: current-following voltage-forming and voltage-following current-forming; c) swing characteristics: current-angle swing and voltage-angle swing; d) inner-loop controllers: output impedance shaping and output admittance shaping; and e) grid strength compatibility: strong-grid instability and weak-grid instability. The swing equations are also derived in dual form for two inverter types, which reveal the dynamic interaction between the grid strength, the synchronization controllers, and the inner-loop controllers. Insights are generated into cases of poor stability. The theoretical analysis and time-domain simulation results are used to illustrate cases of instability for simple single-inverter-infinite-bus systems and a multi-inverter power network.
This paper proposes a safety analysis method that facilitates a tunable balance between the worst-case and risk-neutral perspectives. First, we define a risk-sensitive safe set to specify the degree of safety attained by a stochastic system. This set is defined as a sublevel set of the solution to an optimal control problem that is expressed using the Conditional Value-at-Risk (CVaR) measure. This problem does not satisfy Bellmans Principle, thus our next contribution is to show how risk-sensitive safe sets can be under-approximated by the solution to a CVaR-Markov Decision Process. We adopt an existing value iteration algorithm to find an approximate solution to the reduced problem for a class of linear systems. Then, we develop a realistic numerical example of a stormwater system to show that this approach can be applied to non-linear systems. Finally, we compare the CVaR criterion to the exponential disutility criterion. The latter allocates control effort evenly across the cost distribution to reduce variance, while the CVaR criterion focuses control effort on a given worst-case quantile--where it matters most for safety.
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