Stochastic multi-objective optimization for economic-emission dispatch with uncertain wind power and distributed loads

• A stochastic economic-emission dispatch in power system is proposed.
• Uncertain wind power and distributed load variations are considered.
• Paired-bacteria optimizer is used to optimize the proposed dispatch problem.
• The relationships between the fuel cost, wind power and emission are analyzed.

This paper proposes a stochastic multi-objective optimization method for solving the Security-Constrained Optimal Power Flow (SCOPF) problem with uncertain wind power and distributed load variations. The dispatch objectives are formulated to not only minimize the expectation of fuel costs and the deviation of the fuel cost distribution, but also to maximize wind power penetration while also considering variations in wind speed and distributed loads. The computational complexity of the stochastic optimization is a crucial issue that is considered when using a Paired-Bacteria Optimization (PBO) algorithm, which is simpler than most Evolutionary Algorithms (EAs). This paper reports the simulation results obtained using an IEEE 30-bus system, including a comparison between the results achieved using the proposed method and those obtained from deterministic dispatch. The trade-off relationships between fuel cost, wind power penetration, and emissions are analyzed based on the Pareto set of feasible solutions resulted from PBO. This analysis allows for the determination of the optimal dispatch actions that simultaneously minimize all of the objectives while considering uncertainties in wind power and distributed loads.