Chance-constrained optimization-based solar microgrid design and dispatch for radial distribution networks

We consider a solar microgrid design and dispatch problem using an adaptive stochastic optimization framework. First, we propose a two-stage mixed-integer model for optimal placement and planning of distributed generation (DG) units and energy storage system units. We incorporate time series modeling into stochastic optimization approach to characterize the solar irradiance uncertainty. In the first stage, design decisions (e.g., location and sizing of DGs) are made and in the second stage, dispatch decisions (e.g., how much to generate, how much to store) are made such that electricity demand is met in a reliable and cost effective way. Chance constraints are employed to control the real load shedding within a predefined probability level. Then, we propose a combined sample average approximation (SAA) and linearization technique to solve this problem more efficiently. The advantage of this approach is that no additional binary variables are introduced while reformulating the chance constraints. Computational time, quality of solution, and load shedding percentage are compared with the traditional SAA. Moreover, we carry out a comprehensive out-of-sample simulation on a real-world case study in the state of Arizona assessing the effectiveness of our approach. Numerical experiments demonstrate that the chance constraints are effective tools for control of load shedding in distributed generation and the proposed approach outperforms traditional methods both in terms of true load shedding percentage and computational time.