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International audienceWe present a novel iterative algorithm to solve the distribution system optimal power flow problem over a radial network. Our methodology makes use of a widely studied second order cone relaxation applied to the branch flow model of a radial network. Several types of conditions have been established under which this relaxation is exact and we focus here on the situations where this is not the case. To overcome this difficulty, we propose to add increasingly tight linear cuts to the second-order cone problem until a physically meaningful solution is obtained. We apply this technique to a sample system taken from the literature and compare the results with a traditional nonlinear solver

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The increasing share of photovoltaic (PV) power in the global energy mix presents a great challenge to power grid operators. In particular, PV power's intermittency caused by varying weather conditions can lead to mismatches between energy production and expectation. Battery Energy Storage Systems (BESS) are often put forward as a good technological solution to these problems, as they are able to mitigate PV power forecast errors. However, the investment cost of such systems is still high, which questions the benefits in relation to the cost of using these systems in operational contexts. In this paper, we compare several strategies to manage a PV power plant coupled with a BESS in a market environment. They are obtained by stochastic optimization using a Model Predictive Control (MPC) approach. This paper proposes an approach that takes into account the aging of the BESS, both at the day-ahead level and in the real-time control of the BESS, by modeling the cost associated with BESS usage. As a result, the BESS arbitrates between compensating forecast errors and preserving its own life expectancy, based on both PV production and price scenarios derived from probabilistic forecasts. A sensitivity analysis is also carried out to provide guidelines on the optimal sizing of the BESS capacity, depending on market characteristics and BESS prospective costs.