A Calculating Method for Stochastic Characteristics of Value of Lost Load

Value of lost load (VoLL) is a fundamental parameter in the study of frequency security and operational control in power systems. Its stochastic characteristics are crucial for the analysis of new power systems. This paper investigates these stochastic characteristics of VoLL. From a temporal perspective, it examines the differentiated characteristics of VoLL across various electricity consumption sectors, as well as the time distribution stochastic characteristics of load components at different nodes in the power system. Using historical load data, the Kernel Density Estimation (KDE) method is employed to derive numerical features of the time distribution stochastic of VoLL at each node. From a spatial perspective, the study analyzes the stochastic characteristics of the spatial distribution of the lowest frequency points, which are influenced by the stochastic nature of large power loss disturbances. The stochastic characteristics of the spatial distribution of lost load quantities are derived, and by integrating the differences in load components across various nodes, numerical features of the spatial distribution stochastic of VoLL are obtained. The temporal and spatial distribution stochastic characteristics of VoLL are formulated in a stochastic convolution framework. The proposed theory is validated using the IEEE 39-bus test system, with results demonstrating that VoLL exhibits significant temporal and spatial distribution stochastic characteristics, with first and second moments during daily operations reaching up to $23.61 \dddot{I} / \mathrm{kWh}$ and $19.27 \Psi^{2} / \mathrm{kWh}^{2}$, respectively.