Complex power economic dispatch with improved loss coefficients

Standard economic dispatch (ED) of power generating units traditionally considers only real power generation and real power losses. Real power losses are often treated using the approximate B-loss coefficients, which are pre-calculated for a power system using load flow solution for certain base-case loading conditions. These coefficients do not assure accuracy for large deviations from the base-case loading conditions, as they are derived with few assumptions that assure an adequate accuracy for small deviations from the base-case conditions. Reactive power loss is unlike the real part as it does not have straightforward closed-form expressions for ED involving reactive power concerns. Inspired by old Kron’s loss formula derivations, this paper presents new original closed-form expressions for active and reactive power loss formulas, which are derived mainly to improve the deficiencies of the traditional ED formulations that use less accurate real power loss expressions and ignore reactive power demands and losses. The obtained coefficients are tested on four different-size test systems, and the results are compared with those obtained from solutions of both the load flow and B-coefficients for wide deviations from the base-case operating conditions. Then, the paper presents the mathematical model of the combined active-reactive complex power ED (CPED) including complex power losses using the new derived improved complex power loss coefficients that guarantee more accurate real power losses while considering reactive power concerns. The proposed CPED scheme using the new coefficients is then tested on the four test systems and compared for five costing methods of reactive power. Results and comparisons presented in this paper will show that the active and reactive power loss formulas can achieve more realistic results and accuracy for different system sizes and operating conditions, in addition to showing that reactive power consideration can significantly change outcomes of the standard ED.