Predictor-corrector Primal-dual Interior Point Method Research Articles

Loss Minimization With Optimal Power Dispatch in Multi-Frequency HVac Power Systems

Low-frequency high-voltage ac transmission scheme has recently been proposed as an alternative approach for bulk power transmission. This paper proposes a multi-period optimal power flow (OPF) for a multi-frequency HVac transmission system that interconnects both conventional 50/60-Hz and low-frequency grids using back-to-back converters with a centralized control scheme. The OPF objective is to minimize system losses by determining the optimal dispatch for generators, shunt capacitors, and converters. The OPF constraints include the operational constraints of all HVac grid and converter stations. The resulting mixed-integer nonlinear programing problem is solved using a proposed framework based on the predictor-corrector primal-dual interior-point method. The proposed OPF formulation and solution approach are verified using a multi-frequency HVac transmission system that is modified from the IEEE 57-bus system. The results with the optimal dispatch from the proposed method during a simulated day show a significant loss reduction and an improved voltage regulation compared to those when an arbitrary dispatch is chosen.

Optimal Placement and Dispatch of LV-SVCs to Improve Distribution Circuit Performance

In this paper, a two-stage optimization framework is proposed for optimal placement and centralized real-time control of low-voltage static var compensators (LV-SVCs) in unbalanced distribution circuits to achieve feeder level benefits namely voltage regulation and energy loss minimization. The number, locations, and the optimal real-time reactive power injections from the LV-SVCs are determined from a proposed three-phase unbalanced ac optimal power flow (ACOPF). The ACOPF is formulated as a multi-objective optimization with operating constraints written in rectangular coordinates. The resulting nonlinear nonconvex problem is solved using the predictor-corrector primal-dual interior point method. The proposed approach is scalable for application to large distribution circuits, treats the constraints of physical space limitations effectively, and can take advantage of communication capabilities of LV-SVCs for centralized real-time control. The benefits of the proposed real-time control of LV-SVCs as compared to their operation with local autonomous voltage-based distributed control is demonstrated. The results show that, the proposed approach addresses the LV-SVC placement and control problem effectively to minimize energy losses while maintaining the voltage regulation.

Exact Optimal Power Dispatch in Unbalanced Distribution Systems With High PV Penetration

Smart inverters provide additional control capability to help optimize the operation of distribution systems. This paper proposes a framework for exact optimal active and reactive power dispatch of distributed photovoltaic (PV) generation, switched capacitors, and voltage regulators in large multi-phase unbalanced distribution systems. The objectives of the optimal dispatch are minimization of the energy loss, PV active power curtailment, and operations of capacitors and voltage regulators, in addition to elimination of voltage violations and reverse power flow. The optimization problem is formulated in rectangular coordinates as a nonlinear, nonconvex problem. Effective computational strategies are proposed to allow the application of predictor-corrector primal-dual interior point method to solve optimization problems in real-time with a large number of constraints and variables, including discrete variables corresponding to switched capacitors and voltage regulators. The accuracy of the numerical solution and the ability to implement the proposed framework are validated using the unbalanced multi-phase IEEE 34-bus and EPRI 2,998-bus distribution systems with 15-minute load and PV data. The results show a significant loss reduction and elimination of both voltage violations and reverse power flow.

PCPDIPM based optimal reactive power flow model with discrete variables

Abstract This paper presents a new approach to deal with the optimal reactive power flow (ORPF) problem with the discrete control variables. First, a quadratic ORPF model based on augmented rectangular coordinates is established by treatment with the TLC branch; and then quadratic penalty functions are incorporated into the proposed model to handle the discrete control variables; at last, the predictor corrector primal dual interior point method (PCPDIPM) is used to implement the optimization. In the PCPDIPM based ORPF solution, the quadratic discretization formulation results in the constant Hessians that all have elements of 1, or −1, or the penalty factor, and mostly being zero, thereby accelerating the entire optimal process significantly. Experimental results are provided comparing the performance of the proposed discretization approach with that of the conventional one.

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

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.

PCPDIPM-based optimal reactive power flow model using augmented rectangular coordinates

A novel optimal reactive power flow (ORPF) model using augmented rectangular coordinates is established. The load tap changing (LTC) transformer is represented by an ideal transformer and its series impedance with a fictitious node located between them. The ideal transformer is replaced by the current injections at the two end nodes, and the constraint equations relating the current injections and voltages between two sides are formed. Meanwhile, the nodal voltages, injection currents, reactive power injections, and transformers turn ratio are considered as optimization variables. By the procedure, the ORPF model turns into quadratic and can be expressed in the blocked-matrix form. The predictor-corrector primal-dual interior point method is used to implement the optimization. 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. Column Approximate Minimum Degree algorithm is used to order the coefficient matrix, resulting in great reduction of the number of the fill-in elements. The proposed and the conventional methods are programmed in MATLAB for comparison. Extensive numerical simulations on test systems ranging from IEEE 14 to 300 buses have shown the validity and higher efficiency of the proposed model than the conventional one. Copyright © 2013 John Wiley & Sons, Ltd.

Predictor‐Corrector Primal‐Dual Interior Point Method for Solving EconomicDispatch Problems: A Postoptimization Analysis

This paper proposes a predictor‐corrector primal‐dual interior point method which introduces line search procedures (IPLS) in both the predictor and corrector steps. The Fibonacci search technique is used in the predictor step, while an Armijo line search is used in the corrector step. The method is developed for application to the economic dispatch (ED) problem studied in the field of power systems analysis. The theory of the method is examined for quadratic programming problems and involves the analysis of iterative schemes, computational implementation, and issues concerning the adaptation of the proposed algorithm to solve ED problems. Numerical results are presented, which demonstrate improvements and the efficiency of the IPLS method when compared to several other methods described in the literature. Finally, postoptimization analyses are performed for the solution of ED problems.

Real power loss minimization using interior point method

An efficient predictor–corrector primal–dual interior point method (IPM) is applied to reactive power optimization. A linear model is introduced in which control variables and voltage increments are linked by a modified Jacobian matrix, and transmission losses are represented as a function of voltage increments. Since this method does not calculate any matrix inversion or second-order derivatives of Hessian matrix at each iteration for solving the linear program, its solution will save computation time and memory space. Numerical results show that this technique is very effective and fast for large reactive power optimization.

On the Convergence of the Mizuno--Todd--Ye Algorithm to the Analytic Center of the Solution Set

In this work we demonstrate that the Mizuno--Todd--Ye predictor-corrector primal-dual interior-point method for linear programming generates iteration sequences that converge to the analytic center of the solution set.