Variational Bayes to Accelerate the Lagrange Multipliers towards the Dual Optimization of Reliability and Cost in Renewable Energy Systems

Renewable energy sources are constantly increasing in the modern power systems. Due to their intermittent and uncertain potential, increased spinning reserve requirements are needed to conserve the reliability. On the other hand, each action towards efficiency improvement and cost reduction contradicts the participation of variable resources in the energy mix, requiring more accurate tools for optimal unit commitment. By increasing the renewable contribution, not only does the overall system inertia decrease with the decreasing conventional generation, but more generators that are expensive are also introduced. This work provides a radically different approach towards a tractable optimization task based on the framework of Lagrange relaxation and variational Bayes. Following a dual formulation of reliability and cost, the Lagrange multipliers are accelerated via a machine learning mechanism, namely, variational Bayesian inference. The novelty in the proposed approach stems from the employed acquisition function and the effect of the Gaussian process. The obtained results show great improvements compared with the Lagrange relaxation alternative, which can reach over USD 1 M in production cost credits at the least number of function evaluations. The proposed hybrid method promises global solutions relying on a proper acquisition function that is able to move towards regions with minimum objective value and maximum uncertainty.