Development of multidimensional sequence operation theory with applications to risk evaluation in power system generation scheduling

Sequence operation theory (SOT) is a powerful tool for solving complex probabilistic problems in power system. However, the basic single dimension SOT cannot satisfy the requirement of multi-state and multi-attribute analysis, which is often the case in actual power system practice. To address this problem, multidimensional sequence operation theory (MSOT) is developed. On the basis of previous research, this paper first categorizes the situations by the number of state variables and the number of attribute values, and defines the multidimensional sequence for single state variable and multiple attribute values, as well as the multidimensional sequence for multiple state variables and multiple attribute values. Corresponding to those definitions, four types of operations between two discrete multidimensional sequences are derived respectively. Therefore, the sequence is extended from single dimensional to multidimensional, establishing an integrated theory of multidimensional sequence operation. In particular, the basic single dimension SOT can be viewed as a special case of MSOT with only one state variable and one attribute value. Finally, the paper demonstrates the effectiveness of MSOT through an example of risk evaluation in power system generation scheduling.