We develop four algorithms for simulation-based optimization under multiple inequality constraints. Both the cost and the constraint functions are considered to be long-run averages of certain state-dependent single-stage functions. We pose the problem in the simulation optimization framework by using the Lagrange multiplier method. Two of our algorithms estimate only the gradient of the Lagrangian, while the other two estimate both the gradient and the Hessian of it. In the process, we also develop various new estimators for the gradient and Hessian. All our algorithms use two simulations each. Two of these algorithms are based on the smoothed functional (SF) technique, while the other two are based on the simultaneous perturbation stochastic approximation (SPSA) method. We prove the convergence of our algorithms and show numerical experiments on a setting involving an open Jackson network. The Newton-based SF algorithm is seen to show the best overall performance.
Abstract-Power flow tracing has been suggested as an approach for evaluating 1) transmission system usage (TSU) cost and 2) loss (MW) cost for generator and load entities in the system. Recently, optimal power flow tracing methods have been proposed to "explicitly" model fairness constraints in the tracing framework. This paper, further, strengthens the tracing-compliant min-max fair cost allocation approach. The min-max model proposed in this paper is robust. It addresses concerns like scalability, numerical stability and termination in a finite number of steps while searching the optimal solution. We also propose a methodology to model DISCOMs and GENCOs as coalition within min-max framework. Case studies on an all India network of 1699 nodes and comparison with average participation and marginal participation methods bring out the better conflict resolution feature of the proposed approach. A method to model HVDC lines within the marginal participation scheme is also proposed. Quantitative and qualitative comparison of various TSU cost allocation methods on such a large system is another noteworthy contribution of the paper.
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