Scalable Stochastic Siting and Sizing of Distributed Generators Using Separable Approximation

We propose a scalable two-stage stochastic planning framework for siting and sizing of renewables-based distributed generators using a separable projective approximation routine. The framework learns a separable approximation of the value function from the sample subgradient information. An efficient analytical procedure is developed to compute bounds that assess the quality of the obtained solutions. Efficiency of the framework is demonstrated on IEEE 123-bus and 9500-node distribution systems. Results show that the framework provides high-quality solutions with an optimality gap below 1% in most instances, while reducing computation time by one to two orders of magnitude compared to extensive formulations (EF) and progressive hedging (PH) algorithms. Furthermore, the learned value function enables rapid sensitivity analysis over varying planning parameters by solving each optimization problem within seconds, requiring only 0.006% to 2.2% of the computation time of EF and PH while maintaining comparable solution quality. This substantial reduction in computational complexity makes the framework suitable for large-scale systems without the need for high-performance computing resources.