AC–DC optimal reactive power flow model via predictor–corrector primal‐dual interior‐point method

Abstract

This study presents a quadratic optimal reactive power flow (ORPF) models for ac-dc hybrid power system. In the ac system, the load tap changing transformer is represented by an ideal transformer and its series impedance with an artificial node located between them. The ideal transformer is further replaced by the current injections at the two terminal nodes. The artificial node voltage and the current injections are used to express the relationship between the quantities at both sides. For the dc system, some variables are introduced to formulate the dc equations. Finally, utilising their couplings, the ac and dc equations expressed in different coordinates can be integrated into a unified quadratic ac-dc ORPF model, which is simply expressed in the block form. The predictor-corrector primal-dual interior-point method is used to solve the optimisation problem. The quadratic model results in the constant Hessians that all have elements of 1 or −1, and mostly being zero and multiplication is not required to form the full Hessian, thereby accelerating the entire optimal process significantly. Extensive numerical simulations have shown the validity and superior performance of the proposed model than the conventional one.

A Mixed-Integer Second-Order Cone Programming Algorithm for the Optimal Power Distribution of AC-DC Parallel Transmission Channels

“…In the above OPD model of the AC-DC parallel transmission channels for Equations (1)- (14), Equations (2) and (3) are used to calculate the active power loss of the AC and DC lines in the objective function, Equations (5) and (6) are used to calcute the transmission power of the AC and DC lines, Equations (9) and (10) are used for the operating characteristics of the converters, and the injected power balance equation is Equation 12of the AC buses in the constraints. All the equations include the nonlinear items of the triangular functions or quadratic functions.…”

“…At present, the conventional OPF model for AC-DC systems is generally used in the optimal operation of AC-DC systems [5][6][7][8][9][10][11][12][13][14]. The optimal reactive power flow (ORPF) problem for AC-DC systems was studied in [5][6][7][8][9]. In [5], a heuristic genetic algorithm was used to solve the ORPF problem of a multi-terminal high voltage direct current (HVDC) transmission system.…”

“…In [5], a heuristic genetic algorithm was used to solve the ORPF problem of a multi-terminal high voltage direct current (HVDC) transmission system. In [6], a quadratic ORPF model for an AC-DC hybrid power system was proposed, and it was solved with the predictor-corrector interior point method. Yu et al [7] proposed an AC-DC ORPF model with generator capacity constraints, which was solved by a heuristic algorithm.…”

The Optimization of the Location and Capacity of Reactive Power Generation Units, Using a Hybrid Genetic Algorithm Incorporated by the Bus Impedance Power-Flow Calculation Method

“…The search algorithms contain backtracking [9], cuckoo [10], differential [11], direct [12], and harmony search methods [13]. The optimization algorithms (as conventional methods) involve decomposition methods [1], dynamic programming [14], gradient-based optimization [15], interior-point methods [16], linear approximation [17], mixed integer programming [18,19], quadratic programming [20], teaching-based learning [21], and decision-making algorithms [22].…”

Research on three‐phase optimal power flow for distribution networks based on constant Hessian matrix

“…The primal-dual interior point method has been widely used to solve the OPF problem for traditional power systems because of its advantages such as efficiency and fast convergence [10][11][12][13][14][15][16][17][18][19][20]. Reference [13] proposed a discrete variable processing method based on the Gaussian penalty function, but it does not compare the computation efficiency of the function with that of other penalty functions, e.g., the quadratic penalty function as introduced in [20].…”