Chance Constrained Optimal Power Flow Using the Inner-Outer Approximation Approach

In recent years, there has been a huge trend to penetrate renewable energy sources into energy networks. However, these sources introduce uncertain power generation depending on environmental conditions. Therefore, finding 'optimal' and 'feasible' operation strategies is still a big challenge for network operators and thus, an appropriate optimization approach is of utmost importance. In this paper, we formulate the optimal power flow (OPF) with uncertainties as a chance constrained optimization problem. Since uncertainties in the network are usually 'non-Gaussian' distributed random variables, the chance constraints cannot be directly converted to deterministic constraints. Therefore, in this paper we use the recently-developed approach of inner-outer approximation to approximately solve the chance constrained OPF. The effectiveness of the approach is shown using DC OPF incorporating uncertain non-Gaussian distributed wind power

Strong Stationarity Conditions for Optimal Control of Hybrid Systems

We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general due to the presence of complementarity constraints, we provide a set of structural assumptions ensuring that the tangent cone of the constraints possesses geometric regularity properties. These imply that the classical Karush-Kuhn-Tucker conditions of nonlinear programming theory are both necessary and sufficient for local optimality, which is not the case for general mathematical programs with complementarity constraints. We also present sufficient conditions for global optimality. We proceed to show that the dynamics of every continuous piecewise affine system can be written as the optimizer of a mathematical program which results in a linear complementarity model satisfying our structural assumptions. Hence, our stationarity results apply to a large class of hybrid systems with piecewise affine dynamics. We present simulation results showing the substantial benefits possible from using a nonlinear programming approach to the optimal control problem with complementarity constraints instead of a more traditional mixed-integer formulation.Comment: 30 pages, 4 figure