Fast Decoupled Power Flow Research Articles

Transformer Outage Contingency in the Southern Interconnected Grid of Cameroon Based on Dynamic Power Flow Simulation

The power system is a network of components having specific operational limits such that any violation of these limits during their operation could lead to more damage in the grid. The grid in Cameroon has been facing several undesired loading events at some sections of the network and the utility company has over the years, employed measures to mitigate these issues. This study has used the ETAP software to conduct a contingency analysis on the largest independent grid in Cameroon, supplying 6 regions in Cameroon. Seventeen transformer outage events in the network were used to conduct the N‐1 scenario‐based contingency, so that the vulnerability of the network can be evaluated. The fast decoupled power flow method was continuously applied on the network, and the different contingency scenarios were ranked using a combination of 4 performance indices. These four performance indices gave information on the impact of the various transformer outage scenarios on the grid. The four indices were added to give a combined value, and the outages were ranked in order of severity based on this combined index. A major contribution of this paper is the use of four scalar indices to classify the critical elements in the grid of a developing country. The initial load flow simulation of the network showed that 12 nodes had under voltages, while 3 transformers and one transmission line were overloaded. The Ngousso corridor suffered one of the worst under voltage situation during the initial power flow study. This is an indication that the utility company needs to undertake intensive network upgrade and implore measures to increase power generation to support the growing loads. It was observed that all the contingency scenarios experienced convergence. The Oyomabang transformer 1 had the highest combined index of 71.20, showing a huge negative impact on the network as a result of the outage of the transformer. This was followed by the Oyomabang transformer 2 with a combined index of 48.63. The results will be very useful to utility operators in prioritizing transformers in the network with high risk of causing huge impact on the network in case of an outage.

Parallel multi-GPU implementation of fast decoupled power flow solver with hybrid architecture

Parallel multi-GPU implementation of fast decoupled power flow solver with hybrid architecture

A Review of State-of-the-Art Techniques for Power Flow Analysis

This paper presents a review of the State-of-the-Art Techniques for Power Flow Analysis (PFA) that are newly proposed. However, some of the existing classical methods for the Power Flow Analysis such as Newton-Raphson method, Gauss-Siedel method, and Fast Decoupled Power Flow Technique were also discussed so as to give a background and a wider view of the improvements recorded so far. From the findings, the State-of-the-Art Techniques such as Particle Swamp Optimization Algorithm for optimal Power Flow Incorporating Wind Farms, Hybrid Firefly and Particle Swamp Optimization Algorithm, Mann Iteration Process Technique for III-Conditioned System, and A New Approach Newton-Raphson Load Flow Analysis in Power System Networks with STATCOM have shown superiority over and above the existing classical methods in terms of accuracy, speed of convergence and overall efficiency. Particularly, there are two newly proposed methods for dc grids: Direct Matrix–Current application (DM-CA) and Direct Matrix-Impedance Approximation (DM-IA) methods that stand out with respect to accuracy, convergence and computational effort which means they can be used for planning, optimization and analysis purposes of practical dc grids.

Alternative Current Injection Newton and Fast Decoupled Power Flow

This article presents an alternative Newton-Raphson power flow method version. This method has been developed based on current injection equations formulated in polar coordinates. Likewise, the fast decoupled power flow, elaborated using current injection (BX version), is presented. These methods are tested considering electrical power systems composed of 57-, 118-, and 300-bus, as well as a realistic system of 787-bus. For the robustness analysis, simulations were performed considering different loading conditions and R/X ratios of the transmission line. Based on the simulations that were realized, there is evidence that the performance of the proposed current injection methods is similar to the power injection methods.

Noise-resilient quantum power flow

Quantum power flow (QPF) offers an inspiring direction for overcoming the computation challenge of power flow through quantum computing. However, the practical implementation of existing QPF algorithms in today's noisy-intermediate-scale quantum (NISQ) era remains limited because of their sensitivity to noise. This paper establishes an NISQ-QPF algorithm that enables power flow computation on noisy quantum devices. The main contributions include: (1) a variational quantum circuit (VQC)-based alternating current (AC) power flow formulation, which enables QPF using short-depth quantum circuits; (2) NISQ-compatible QPF solvers based on the variational quantum linear solver (VQLS) and modified fast decoupled power flow; and (3) an error-resilient QPF scheme to relieve the QPF iteration deviations caused by noise; (3) a practical NISQ-QPF framework for implementable and reliable power flow analysis on noisy quantum machines. Extensive simulation tests validate the accuracy and generality of NISQ-QPF for solving practical power flow on IBM's real, noisy quantum computers.

Data-driven Power Flow Method Based on Exact Linear Regression Equations

Power flow (PF) is one of the most important calculations in power systems. The widely-used PF methods are the Newton-Raphson PF (NRPF) method and the fast-decoupled PF (FDPF) method. In smart grids, power generations and loads become intermittent and much more uncertain, and the topology also changes more frequently, which may result in significant state shifts and further make NRPF or FDPF difficult to converge. To address this problem, we propose a data-driven PF (DDPF) method based on historical/simulated data that includes an offline learning stage and an online computing stage. In the offline learning stage, a learning model is constructed based on the proposed exact linear regression equations, and then the proposed learning model is solved by the ridge regression (RR) method to suppress the effect of data collinearity. In online computing stage, the nonlinear iterative calculation is not needed. Simulation results demonstrate that the proposed DDPF method has no convergence problem and has much higher calculation efficiency than NRPF or FDPF while ensuring similar calculation accuracy.

Fast-decoupled power flow method for integrated analysis of transmission and distribution systems

The growing participation of distributed generation in the electricity supply along with the advances in smart grid technologies have emphasized the active role of distribution systems and their more complex interaction with the transmission system. As a consequence, the operation of the power grid requires closer coordination between transmission and distribution systems. This paper proposes an integrated analysis that allows a unique power flow method to be effectively applied to any voltage level of the power system, from the high-voltage bulk transmission network to the low-voltage distribution feeders. The proposed methodology combines the decoupled power flow approach and complex per unit normalization technique to efficiently deal with the high dimension of unified network analysis and the different characteristics of transmission and distribution networks, regarding line parameters and topological arrangements. Simulations are conducted in an integrated T&D network, and in a large primary-secondary distribution system as well. The results demonstrate the effectiveness of the proposed approach and attest the relevance of integrated power flow analyzes to adequately determine the interrelationships between the different operating levels of the electrical network.

Graph Computing Based Distributed Parallel Power Flow for AC/DC Systems with Improved Initial Estimate

The sequential method is easy to integrate with existing large-scale alternating current (AC) power flow solvers and is therefore a common approach for solving the power flow of AC/direct current (DC) hybrid systems. In this paper, a high-performance graph computing based distributed parallel implementation of the sequential method with an improved initial estimate approach for hybrid AC/DC systems is developed. The proposed approach is capable of speeding up the entire computation process without compromising the accuracy of result. First, the AC/DC network is intuitively represented by a graph and stored in a graph database (GDB) to expedite data processing. Considering the interconnection of AC grids via high-voltage direct current (HVDC) links, the network is subsequently partitioned into independent areas which are naturally fit for distributed power flow analysis. For each area, the fast-decoupled power flow (FDPF) is employed with node-based parallel computing (NPC) and hierarchical parallel computing (HPC) to quickly identify system states. Furthermore, to reduce the alternate iterations in the sequential method, a new decoupled approach is utilized to achieve a good initial estimate for the Newton-Raphson method. With the improved initial estimate, the sequential method can converge in fewer iterations. Consequently, the proposed approach allows for significant reduction in computing time and is able to meet the requirement of the real-time analysis platform for power system. The performance is verified on standard IEEE 300-bus system, extended large-scale systems, and a practical 11119-bus system in China.

Steady-state Security Assessment Based on K-Means Clustering Algorithm and Phasor Measurement Units

Background: The security assessment plays a crucial role in the operation of the modern interconnected power system network. Methods: Hence, this paper addresses the application of k-means clustering algorithm equipped with Principal Component Analysis (PCA) and silhouette analysis for the classification of system security states. The proposed technique works on three principal axes; the first stage involves contingency quantification based on developed insecurity indices, the second stage includes dataset preparation to enhance the overall performance of the proposed method using PCA and silhouette analysis, and finally the application of the clustering algorithm over data. Results: The proposed composite insecurity index uses available synchronized measurements from Phasor Measurement Units (PMUs) to assess the development of cascading outages. Considering different operational scenarios and multiple levels of contingencies (up to N-3), Fast Decoupled Power Flow (FDPF) have been used for contingency replications. The developed technique applied to IEEE 14-bus and 57-bus standard test system for steady-state security evaluation. Conclusion: The obtained results ensure the robustness and effectiveness of the established procedure in the assessment of the system security irrespective of the network size or operating conditions.

An efficient holomorphic embedded based approach for available transfer capability evaluation

Available Transfer Capability (ATC) is the additional power that can be securely and reliably transacted over and above the already committed transactions in a power network. In the electricity market, where every player (power producer and consumer) tries to earn higher profit, quick and accurate assessment of ATC of the power network is a prime concern. Holomorphic Embedding (HE) is a novel and non-iterative way of solving the Power Flow (PF) equations, which guarantees to find the operational High Voltage (HV) solution, in case it exists. Analytic continuation extends the domain of convergence of non-analytic functions to have voltage solutions. This paper, thus, proposes an extremely efficient and accurate approach for evaluation of ATC using the Holomorphic Embedded PF (HEPF) considering the intact system condition and N-1 contingency situations. This approach is successfully tested on IEEE 30 bus, IEEE 118 bus, and IEEE 300 bus systems for various bilateral and multilateral transactions. The results, thus, obtained prove the efficacy of the proposed approach in comparison with those obtained from the repeated Newton-Raphson PF (NRPF), Fast Decoupled PF (FDPF) and Continuation PF (CPF) based methods.

GPU-Based N-1 Static Security Analysis Algorithm With Preconditioned Conjugate Gradient Method

N-1 static security analysis (SSA) is an important method for power system stability analysis that requires solving N alternating-current power flows (ACPF) for a system with N elements to obtain strictly accurate results. Past researches have shown the potential of accelerating these calculations using an iterative solver with graphics processing unit (GPU). This paper proposes a GPU-based N-1 SSA algorithm with the preconditioned conjugate gradient (PCG) method. First, a shared preconditioner is selected to accelerate preprocessing of the iterative method for fast decoupled power flow (FDPF) in N-1 SSA. Second, it proposes a GPU-based batch-PCG solver, which packages a massive number of PCG subtasks into a large-scale problem to achieve a higher degree of parallelism and better coalesced memory accesses. Finally, the paper presents a novel GPU-accelerated batch-PCG solution for N-1 SSA. Case studies on a practical 10828-bus system show that the GPU-based N-1 SSA algorithm with the batch-PCG solver is 4.90 times faster than a sequential algorithm on an 8-core CPU. This demonstrates the potential of the GPU-based high-performance SSA solution with the PCG method under a batch framework.

Negative Reactance Impacts Power Flow Convergence Using Conjugate Gradient Method

It is usually considered in power systems that the B matrices in fast decoupled power flow (B’ and B”) are symmetric and positive-definite. The fast decoupled power flow (FDPF) based on the conjugate gradient (CG) iterative method was well developed, because the CG iterative method has a good convergence property and a lower memory requirement which can be easily implemented in the parallel computation. However, a rare yet important phenomenon hasn’t been well addressed in that “negative reactance” may exist in the practical power system models, which could affect the definiteness of B matrices in FDPF and the CG convergence performance. In this brief, the eigenvalues of B matrices with negative reactance are investigated and the convergence of CG for FDPF is discussed. Several large-scale practical systems are tested, which could provide some insights for the study of the FDPF using the CG method with negative reactances.

Unified Transmission and Distribution Fast Decoupled Power Flow

In this paper, the conventional Newton–Raphson fast decoupled (NRFD) power flow formulation is extended to allow the analysis of transmission and distribution systems (T&D) in a unified approach. The proposed extension associates the well-known computational efficiency of NRFD algorithms to the application of the complex per unit normalization (cpu). Artificial power injections at T&D boundary buses are appended to the power flow formulation as new state variables, in order to maintain the analysis accuracy. The required modifications on NRFD power flow algorithm and an overview of cpu technique are presented. Simulation results attest the relevance of a unified T&D analysis to properly determine the interrelation of active distribution feeders and transmission system operation. In this context, the performance of the proposed approach clearly indicates its effectiveness to deal with different topological and operational power networks.

Extended fast decoupled power flow for reconfiguration networks in distribution systems

This study proposes a power flow methodology focused on the need for reconfiguration analysis in modern distribution networks. The proposal is based on the extended fast decoupled Newton-Raphson method, which uses the information of the network switching equipment status (open or closed). To deal with eventual islanding during a reconfiguration procedure, a numerical observability technique used in state estimation analysis has been adapted for topological processing when network segments are disconnected from voltage references. A complex per unit normalisation technique is employed so that the power flow calculation by the fast decoupled approach is viable, even for networks having high R/X ratio lines. Simulation results considering two distribution feeders, one of large size, with different topological conditions are presented. The performance of the proposed methodology qualifies it as a relevant computational tool to support network reconfiguration studies involving emergent distribution systems.

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 10 000 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.

A New DC Power Flow Model for Q Flow Analysis for use in Reactive Power Market

DC Power Flow method is widely used for active power flow analysis in deregulated power system. DC Power Flow model is a constant matrix, non-iterative model which is built into DC Optimal Power Flow model for market clearing and settlement of real power market. As of now, there are few papers available in DC Power Flow model for reactive power flow analysis .Hence, this paper introduces a pure Q market and proposes a new DC Q flow model (DCQF) which can be built into a DC Optimal Q flow model for market clearing and settlement of pure Q market. In addition to the DCQF method, to obtain accurate result satisfying a specified mismatch tolerance, an Iterative QF method is also proposed whose results match exactly with the solution obtained using FDPF method. The DCQF method and Iterative QF method are tested on Ward and Hale 6-Bus System, IEEE-30 Bus System and Indian Utility 119-Bus System. The bus voltage magnitude computed using the proposed DCQF method is compared with the accurate solution obtained using Iterative QF method (proposed)/Fast Decoupled Power Flow method for a mismatch tolerance of 0.1MVAr. The maximum error value obtained is acceptable even for security analysis. The proposed DCQF and Iterative QF method are faster when compared to FDPF method.

Fast Decoupled Power Flow to Emerging Distribution Systems via Complex pu Normalization

This paper proposes a generalized approach of the per unit normalization, named complex per unit normalization (cpu), to improve the performance of fast decoupled power flow methods applied to emerging distribution networks. The proposed approach takes into account the changes envisaged and also already faced by distribution systems, such as high penetration of generation sources and more interconnection between feeders, while considering the typical characteristics of distribution systems, as the high R/X ratios. These characteristics impose difficulties on the performance of both backward-forward sweep and decoupled-based power flow methods. The cpu concept is centred on the use of a complex volt-ampere base, which overcomes the numerical problems raised by the high R/X ratios of distribution feeders. As a consequence, decoupled power flow methods can be efficiently applied to distribution system analysis. The performance of the proposed technique and the simplicity of adapting it to existing power flow programs are addressed in the paper. Different distribution network configurations and load conditions have been used to illustrate and evaluate the use of cpu.

Fast security risk assessment of the power system with wind power penetration

Security risk assessment difficulties brought about by uncertainties can be solved by probabilistic power flow. A security risk assessment scheme of the power system using fast probabilistic power flow is proposed in this paper. The scheme applied probabilistic power flow on fast decoupled power flow model, considering multi-scenario of wind power and static characteristics of power systems, gaining the probabilistic distribution information of each desired variable by improved Von Mises method based on cumulants. Besides voltages and branch flows, the scheme can also obtain the distribution of frequency to assess the power system completely, which is not concerned in conventional probabilistic power flow calculation. The proposed algorithm was realized by programming based on Matpower 4.0. The examples executed on IEEE RTS-24 system demonstrate the rapidity, validity, and prospect for online application of the proposed scheme.

Security risk assessment using fast probabilistic power flow considering static power-frequency characteristics of power systems

Large scale blackouts in the world have aroused the study of security risk assessment (SRA) urgently. SRA difficulties brought about by uncertainties can be solved by probabilistic power flow (PPF). Conventional methods usually focus on the probabilistic density function (PDF) and the cumulative distribution function (CDF) of node voltages and branch flows only. A SRA scheme of power system using fast PPF is proposed in this paper. The scheme took static power-frequency characteristics (SPFCs) into account, and fast decoupled power flow (FDPF) was used to solve PPF. Besides node voltage and branch flows, the scheme can obtain the PDF and CDF of frequency. The computing speed of the proposed scheme considering wind power multi-scenarios is enhanced compared to conventional method. SRA indices are introduced to evaluate the power system quantitatively. The examples on the IEEE RTS-24 system demonstrate the feasibility, rapidity and validity of the proposed scheme.

An improved fast decoupled power flow model considering static power–frequency characteristic of power systems with large‐scale wind power

AbstractLarge‐scale wind power (LSWP) integration may cause significant impact on power system frequency, so it is necessary to take frequency regulation issues into account in power system steady‐state operation analysis. An improved fast decoupled power flow model considering static power–frequency characteristic of power systems with LSWP is proposed in this paper. In this scheme, the active power of generators and loads are presented with their static power–frequency characteristics. The slack bus degenerates to the nodal voltage phase angle reference bus of the system, and all the generators with frequency regulation capability participate in unbalanced power regulation. The power flow calculation results can reveal the impact to the system frequency of operation mode change and load variation, and present the output adjustment of the generators. The proposed model can be solved conveniently by the block solving technology based on the fast decoupled power flow algorithm. The scheme presented in this paper has been tested on the IEEE standard 30‐bus test system by simulating basic operation and primary and secondary frequency regulation of the generators, which demonstrated the validity by the method. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.