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 as a stochastic problem. Low voltage photovoltaics (PV) hosting capacity (HC) calculation is such a planning problem. Traditionally, this is solved by 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. General polynomial chaos expansion is used to translate the input uncertainties defined by probability density function to the hosting capacity of the network. Chance constraints are applied for the nodal voltages and thermal overloading. A case study for an actual LV feeder shows that the computational time of using the Monte Carlo based method is reduced from days to the order of seconds without any sampling, relaxation, or linearization. Furthermore, the stochastic HC calculated by the proposed Stochastic Optimal Power Flow (SOPF) method gives the upper bound of the distribution network HC which can also be identified using conventional methods.