Security Constrained Stochastic Multi-objective Optimal Power Dispatch

A stochastic multi-objective line security constrained problem is formulated to minimize non-commensurable objectives viz. operating cost, polluting gaseous emission and variance of active power generation and reactive power generation, with explicit recognition of statistical uncertainties in the thermal power generation cost coefficients, gaseous emission coefficients, power demands and hence power generations and bus voltages, which are considered random variables. Specific technique is put forth to convert the stochastic models into their respective deterministic equivalents. Fuzzy set theory has been exploited to evaluate the different objectives that are quantified by defining their membership functions. Security of transmission lines with respect to expected active power flow is considered in the form of fuzzy objective function. The solution set of such formulated problems is non-inferior due to contradictions among the objectives undertaken. The weighting method is used to simulate the trade-off relationship between the conflicting objectives in the non-inferior domain. Generally, the weights are either simulated or searched in the non-inferior domain. In the paper Evolutionary search technique is implemented to search the ‘preferred’ weightage pattern in the non-inferior domain, which corresponds to the ‘best’ compromised solution. Among the non-inferior solutions, the system operator selects the ‘preferred’ optimal operating point that provides maximum satisfaction level of the most under achieved objective in terms of membership function and is termed as fitness function. The validity of the proposed method has been demonstrated on an IEEE system comprising of 11-nodes, 17-lines and 5-generators.