Chance-Constrained Optimization Based PV Hosting Capacity Calculation Using General Polynomial Chaos

Increased penetration of renewable resources and new loads have increased the uncertainty levels in low voltage distribution systems (LVDS). This requires considering LVDS planning, such as computing photovoltaics (PV) hosting capacity (HC), as a stochastic problem. Traditionally, PV HC is computed using the iterative Monte Carlo method, which requires solving the power flow equations thousands of times. This paper proposes a chance-constrained optimization-based hosting capacity calculation technique, which eliminates the necessity of repetitive solving of power flow equations. The intrusive general polynomial chaos expansion is used to translate the input uncertainties defined by their probability density function to the hosting capacity of the network without the necessity of sampling, linearizing the power flow equations, or applying any relaxations. Chance constraints are applied for nodal voltages and thermal overload as per the norms, where the system can be congested for a certain time without affecting the power quality. Numerical illustrations show the computational time to compute the stochastic PV hosting capacity of a real large scale LVDS, and for the majority of the feeders, it falls within 100 sec. Furthermore, the estimated PV HC using this stochastic optimal power flow was, on average, 20% higher than its deterministic counterpart.