Factoring the Cycle Aging Cost of Batteries Participating in Electricity Markets

When participating in electricity markets, owners of battery energy storage systems must bid in such a way that their revenues will at least cover their true cost of operation. Since cycle aging of battery cells represents a substantial part of this operating cost, the cost of battery degradation must be factored in these bids. However, existing models of battery degradation either do not fit market clearing software or do not reflect the actual battery aging mechanism. In this paper we model battery cycle aging using a piecewise linear cost function, an approach that provides a close approximation of the cycle aging mechanism of electrochemical batteries and can be incorporated easily into existing market dispatch programs. By defining the marginal aging cost of each battery cycle, we can assess the actual operating profitability of batteries. A case study demonstrates the effectiveness of the proposed model in maximizing the operating profit of a battery energy storage system taking part in the ISO New England energy and reserve markets

Construction of solutions to parabolic and hyperbolic initial–boundary value problems

Assume that, in a parabolic or hyperbolic equation, the right-hand side is analytic in time and the coefficients are analytic in time at each fixed point of the space. We show that the infinitely differentiable solution to this equation is also analytic in time at each fixed point of the space. This solution is given in the form of the Taylor expansion with respect to time $t$ with coefficients depending on $x$. The coefficients of the expansion are defined by recursion relations, which are obtained from the condition of compatibility of order $k=\infty$. The value of the solution on the boundary is defined by the right-hand side and initial data, so that it is not prescribed. We show that exact regular and weak solutions to the initial-boundary value problems for parabolic and hyperbolic equations can be determined as the sum of a function that satisfies the boundary conditions and the limit of the infinitely differentiable solutions for smooth approximations of the data of the corresponding problem with zero boundary conditions. These solutions are represented in the form of the Taylor expansion with respect to $t$. The suggested method can be considered as an alternative to numerical methods of solution of parabolic and hyperbolic equations

Convex Hull Pricing in Electricity Markets: Formulation, Analysis, and Implementation Challenges

Abstract Widespread interest in Convex Hull Pricing has unfortunately not been accompanied by an equally broad understanding of the method. This paper attempts to narrow the gap between enthusiasm and comprehension. Most importantly, Convex Hull Pricing is developed in an understandable mannerstarting with a discussion of basic electricity market processes and ending with a new mathematical formulation of Convex Hull Pricing. From this mathematical formulation, a variety of important properties are derived and discussed. To illustrate that the [sometimes counterintuitive] properties of Convex Hull Pricing are not merely theoretical, several simple examples are presented. It is hoped that this paper will spur additional research on the pricing scheme so that an informed judgment can be made regarding its costs and benefits