Xue Li

Exploration of multifrontal method with GPU in power flow computation

Solving sparse linear equations is the key part of power system analysis. The Newton-Raphson and its variations require repeated solution of sparse linear equations; therefore improvement in efficiency of solving sparse linear equations will accelerate the overall power system analysis. This work integrates multifrontal method and graphic processing unit (GPU) linear algebra library to solve sparse linear equations in power system analysis. Multifrontal method converts factorization of sparse matrix to a series of dense matrix operations, which are the most computational intensive part of multifrontal method. Our work develops these dense kernel computations in GPU. Example systems from MATPOWER and random matrices are tested. Results show that performance improvement is highly related to the quantity and size of dense kernels appeared in the factorization of multifrontal method. Overall performance, quantity and size of dense kernels from both cases are reported.

Mitigate overestimation of voltage stability margin by coupled single-port circuit models

Wide-area measurement-based voltage stability assessment (VSA) by coupled single-port circuit models has been widely discussed recently. This method models the coupling effects of load buses within a meshed network into extra impedance of a single-port model for each load bus. In simulation studies, overestimations of voltage stability margin using this approach have been observed when critical load bus or buses are decoupled from other load buses. In this paper, the overestimations are reported for the first time through examples and are further analyzed in details. Moreover, to mitigate such overestimations, two methods are proposed: one method uses a mitigation factor based on actual system reactive power response; the other method changes the types of certain weak generation buses when forming the coupled impedance. Both approaches are applied to a sample 4-bus system as well as the IEEE 118-bus system and successfully mitigate the overestimations.

GPU-based two-step preconditioning for conjugate gradient method in power flow

With the development of the modern power system and the computational hardware, the industrial and research communities are more interested in simulating larger and more complicated power grids. Various iterative solvers for linear systems have been investigated with power system applications for its parallel potential in large scale linear computations. They usually require preconditioning to improve their convergence rate. This work will discuss three preconditioners: Jacobi preconditioner, Chebyshev preconditioner, and a two-step preconditioner with Jacobi first and then Chebyshev. The results show that the two-step preconditioner provides better preconditioning effects than using any of them alone. Besides, the GPU implementation of the iterative solver and preconditioners shows performance improvement over Matlab implementation. The improvement can reach up to 8.9× with the two-step preconditioner for the largest test system. These results demonstrate great potential for both preconditioned iterative solver and GPU application in power system simulations.

GPU-Based Fast Decoupled Power Flow With Preconditioned Iterative Solver and Inexact Newton Method

Power flow is the most fundamental computation in power system analysis. Traditionally, the linear solution in power flow is solved by a direct method like LU decomposition on a CPU platform. However, the serial nature of the LU-based direct method is the main obstacle for parallelization and scalability. In contrast, iterative solvers, as alternatives to direct solvers, are generally more scalable with better parallelism. This study presents a fast decouple power flow (FDPF) algorithm with a graphic processing unit (GPU)-based preconditioned conjugate gradient iterative solver. In addition, the Inexact Newton method is integrated to further improve the GPU-based parallel computing performance for solving FDPF. The results show that the GPU-based FDPF maintains the same precision and convergence as the original CPU-based FDPF, while providing considerable performance improvement for several large-scale systems. The proposed GPU-based FDPF with the Inexact Newton method gives a speedup of 2.86 times for a system with over 10xa0000 buses if compared with traditional FDPF, both implemented based on MATLAB. This demonstrates the promising potential of the proposed FDPF computation using a preconditioned iterative solver under GPU architecture.

An impact increments-based state enumeration reliability assessment approach and its application in transmission systems

This paper proposes an impact increments-based state enumeration (IISE) reliability assessment approach, specially designed for transmission systems. Firstly, the reliability index calculation formula of the traditional state enumeration technique is transformed into an impact increments-based formation. With the derived formula, the calculation of state probability is simplified and the weight of low order contingency states is increased. Moreover, it is proved in this paper that impact increments of mutually independent high order contingency states, whose outage components are with remote distances, can be eliminated. Due to this fact, the calculation of impacts of most high order contingencies can be reduced without decreasing the precision of reliability indices. When applied to electrical power transmission systems, load variations can also be considered by replacing impact increments by their expectations under various load levels. Thus, annual reliability indices can be obtained by the proposed method. Case studies are performed on the IEEE-118 bus system and a 1354-bus portion of European transmission system from PEGASE project. Results indicate that annual reliability indices can be efficiently obtained with IISE method. Comparing with the traditional state enumeration and Monte Carlo simulation methods, the proposed method is more precise and efficient in various kinds of transmission systems.

Volt-VAR interaction evaluation in bulk power systems

This paper presents a novel method to evaluate the Volt-VAR interactions among the buses using relative gain (RG). Following the viewpoint of a multi-input-multi-output system, the Volt-VAR coupling RG is calculated based on the QV matrix which is extracted from power flow Jacobian matrix to evaluate the Volt-VAR interactions among the buses. The voltage stability weak buses are identified through a modified loading margin, and considered as voltage stability critical buses. The proposed evaluation method has great significance for partitioning Volt-VAR control areas in power systems. New England 39-bus system and Polish power system are used to test the performance of the proposed approach. The simulation results verify the effectiveness of the proposed approach in evaluating the Volt-VAR interactions.

Partitioning voltage stability critical injection regions via electrical network response and dynamic relative gain

In this paper, a new approach based on dynamic relative gain is proposed for partitioning voltage control areas in bulk power systems. The critical nodes of voltage stability are determined using voltage stability index, “L index”. The cross relative gain between the critical nodes and other nodes are calculated based on the concept of dynamic transfer function (DTF) and dynamic cross relative gain (DRG). The principle of identifying the strong coupling load nodes and generator nodes are proposed according to the characteristics of DTF and DRG. Then the voltage control regions are constructed based on the critical node and its strong coupled nodes. Furthermore, the practical voltage control regions are obtained through merging different control areas according to the voltage coupling relationships of the critical node. Finally, the effectiveness of the proposed method is demonstrated in the New England 39-bus system with multi-scenario and comparison study. Besides, the method is applied in the Polish power grid, which verifies its feasibility and practicality in bulk power system.

A two-stage MILP formulation for source-load coordinated dispatch with wind power considering peak-valley regulation and ramping requirements

In this paper, a two-stage mixed integer linear programming (MILP) formulation for source-load coordinated dispatch with wind power considering peak-valley regulation and ramping requirements is proposed. First, the peak-load regulation and ramping requirements of the net load curve are analyzed. Second, the first stage optimization model considering incentive-based demand response (IDR) is formulated to optimize the net load curve, in which the objective function is to minimize the compensation costs of IDR. Several constraints are taken into account to reduce the peak-valley regulation needs and meet the ramping requirements. Then, based on the optimized load curve, the second stage day-ahead dispatch optimization model is proposed to optimize the allocation of generation sources, taking the total costs of power generation minimization as the objective function considering thermal unit reserve costs. The proposed model is applied to a 10-unit system with a wind power farm with 600MW installed capacity. Simulation results demonstrate the effectiveness and feasibility of the proposed model.

A volt-var optimal control for power system integrated with wind farms considering the available reactive power from EV chargers

In order to fully take advantage of the available reactive power from EV chargers (EVCs), a volt-var optimal control (VVOC) strategy for power system integrated with wind farms is proposed. The VVOC strategy consists of two steps: day-ahead optimal scheduling and intra-day optimal adjustment. In the first step, on-load tap changers (OLTCs) and capacitor banks (CBs) are scheduled to minimize the power losses based on the day-ahead forecasted loads and wind power outputs. The second step consists of two scenarios: normal operation and breakdown operation. Under normal operation, only the EVCs are scheduled for the within-day adjustment of reactive power compensation. The breakdown operation is implement when the bus voltage violation occurs, and the CBs are scheduled with the minimum switching numbers for fast voltage recovery. A time-adaptive delay method is applied to the breakdown operation to avoid overcompensation. An IEEE-30 bus system is used to verify the effectiveness of the VVOC strategy for power system integrated with wind farms.