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We present a method to find the maximum magnitude of any supply-shortfall service that an aggregator of energy storage devices is able to sell to a grid operator. This is first demonstrated in deterministic settings, then applied to scenarios in which device availabilities are stochastic. In this case we implement chance constraints on the inability to deliver as promised. We show a significant computational improvement in using our method in place of straightforward scenario simulation. As an extension, we present an approximation to this method which allows the determined fleet capability to be applied to any chosen service, rather than having to re-solve the chance-constrained optimisation each time.
For optimal power flow problems with chance constraints, a particularly effective method is based on a fixed point iteration applied to a sequence of deterministic power flow problems. However, a priori, the convergence of such an approach is not nec
This paper considers the optimal dispatch of energy-constrained heterogeneous storage units to maximise security of supply. A policy, requiring no knowledge of the future, is presented and shown to minimise unserved energy during supply-shortfall eve
The uncertainty of multiple power loads and re-newable energy generations in power systems increases the complexity of power flow analysis for decision-makers. The chance-constraint method can be applied to model the optimi-zation problems of power f
Recently, chance-constrained stochastic electricity market designs have been proposed to address the shortcomings of scenario-based stochastic market designs. In particular, the use of chance-constrained market-clearing avoids trading off in-expectat
We propose a sigmoidal approximation for the value-at-risk (that we call SigVaR) and we use this approximation to tackle nonlinear programs (NLPs) with chance constraints. We prove that the approximation is conservative and that the level of conserva