The DN with PV access receives or transmits power to the higher power grid through the transmission line; the main power generation source is PV, and the power consumption sources are load and network loss, as shown in Figure 2. Among these, PV and load have uncertainty [29,30]. Robust optimization ensures that, even in the worst scenario, the optimization solution is feasible [31]. Refs. [32,33] established an adaptive robust stochastic optimization model to address the renewable power uncertainty modeled as a scenario-based ambiguity set. We describe the uncertainty of PV and load by this method. Furthermore, considering the absolute nature of PVHC, any solution within the uncertainty set should yield a value greater than the resulting PVHC. Therefore, the key to solving this uncertainty problem lies in identifying the worst-case scenario for PVHC calculation. As in (1)–(3), we describe the source–load uncertainty through box uncertainty sets.

where ${\phi }_{v,s}$, ${\phi }_{v,s}^{\prime }$, $\mathsf{\Delta }$${\phi }_{v+,s}$, and $\mathsf{\Delta }$${\phi }_{v-,s}$ are the actual, prediction, upward deviation, and downward deviation of PV power generation efficiency in scenario s; the box uncertainty set of ${\phi }_{v,s}$ is [${\phi }_{v,s}^{\prime }-\mathsf{\Delta }{\phi }_{v-,s}$, ${\phi }_{v,s}^{\prime }+\mathsf{\Delta }{\phi }_{v+,s}$]; $P_{d,i,s}$, $P_{d,i,s}^{\prime }$, $\mathsf{\Delta }$$P_{d+,i,s}$, and $\mathsf{\Delta }$$P_{d-,i,s}$ are the actual, prediction, upward deviation, and downward deviation of load in scenario s and bus i; the box uncertainty set of $P_{d,i,s}$ is [$P_{d,i,s}^{\prime }-\mathsf{\Delta }{P}_{d-,i,s}$, $P_{d,i,s}^{\prime }+\mathsf{\Delta }{P}_{d+,i,s}$]; ${\alpha }_{v+,s}$, ${\alpha }_{v-,s}$, ${\alpha }_{d+,i,s}$, and ${\alpha }_{d-,i,s}$ are the source–load uncertainty deviation coefficients, which have values between 0 and 1; and $P_{v,i,s}$, $S_{v,i,s}$ are the PV power generation and configured capacity in scenario s and bus i.