Fast Decoupled Load Flow Method Research Articles

A Basic AC Power Flow Based on the Bus Admittance Matrix Incorporating Loads and Generators Including Slack Bus

This paper presents an algorithm for solving the AC basic power flow based on some enrichments provided in the bus admittance matrix methods findable in the literature. In particular, the interpretation of the slack bus generator as a current source rather than a voltage one and its inclusion inside an “all-inclusive” admittance matrix allows obtaining strong performances of the algorithm. In fact, this method gives both a well conditioning of the admittance matrix and the reduction of matrix partitioning for each iteration. As a result, a greater precision of the solution, a shorter execution time compared to classical commercial methods, a decreasing number of iterations and optimal convergence properties are obtained. Eventually, in order to show the efficiency of the method, real and fictious networks are tested, by comparing its results and performances with robust open source/commercial software packages that use well-known methods ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i.e.</i> , Newton-Raphson and Fast Decoupled Load Flow methods).

A Novel Fast Hybrid Frequency Domain Approach for Evaluating Harmonic Power Flow in Electricity Networks

Ideally, an AC power supply should constantly provide a perfectly sinusoidal voltage signal at every customer location. Nowadays, many power electronic equipment’s are used in industry in seeking higher system reliability and efficiency and more electronic or microprocessor controllers are used in power system to control AC/DC transmission lines or loads. Moreover, the importance of green energy such as wind and solar is continually growing in our societies not only due to environmental concerns but also to resolve the problem of access to electricity in rural areas. As a result of these issues, power quality problems especially generation of harmonics are on the rise in the distribution network. In electrical power system, harmonics have a number of undesirable effects on power system devices as well as on their operation. It therefore becomes imperative for power system engineers to analyse the penetration of harmonics from the various sources into the network which commonly is known as harmonic power flow evaluation. This paper proposed a novel fast hybrid frequency domain approach (FHA) to evaluate the steady state harmonic power flow with discrete harmonic frequency. The proposed method is applied to IEEE – 14 bus, IEEE New England 39 - bus, IEEE – 57 bus and IEEE 118 - bus power system respectively and compared with Newton – Raphson (NR) load flow method and Fast decoupled load flow method (FDLF) and the results validate the accuracy, robustness and authenticity of the proposed method.

Automatic schemes for including generator Q and transformer tap limits in the fast decoupled load flow method

This study proposes a modified formulation for the popular fast decoupled load flow method to facilitate automatic incorporation of reactive power flow related constraints, i.e. generator reactive power and in-phase transformer tap limits. This formulation has been developed by viewing each device constraint as a set of complementary conditions and adopting the complementarity framework to define one equation to represent this set. The original set of load flow equations is augmented with this set of new equations representing the device constraints and solved to get the adjusted solutions directly. This approach is a significant departure from all the earlier approaches. The earlier approaches generally adopt a two-stage scheme. In the first stage, an approximate unadjusted solution is obtained and in the next stage, adjustments are attempted by ad hoc schemes. The new formulation presented here permits handling both the reactive power related constraints simultaneously. However, it can also be used in situations where only one type of adjustment is needed. Two alternate algorithms in complementarity framework based on mixed complementarity problem and non-linear complementarity problem formulations are presented here. Simulation results are presented to provide evidence of the impressive performance of the new algorithms as compared with the existing ones.

Performance Study of Load Flow Algorithms in Well and Ill-Conditioned Systems

Existing transmission systems are classified as either ill systems or healthy systems. Most of the load flow algorithms works proficiently under well-conditioned systems. However, some of those algorithms fail to produce the accurate results for ill-conditioned systems. This paper investigates the performance of eight load flow algorithms based on the conventional Newton-Raphson, Fast-decoupled and Second-order Load Flow methods for a wide range of electrical bus system sizes. Tests are carried out for each load flow algorithm on six different standard bus systems, each with five different ill-conditioning levels. The results show that improved load flow model with constant Jacobian has advantages over the conventional load flow approach in both well and ill-conditioned system, especially for large-scale system.

Comparative Study of Three Linear System Solver Applied to Fast Decoupled Load Flow Method for Contigency Analysis

This paper presents the assessment of fast decoupled load flow computation using three linear system solver scheme. The full matrix version of the fast decoupled load flow based on XB methods used in this study. The numerical investigations are carried out on the small and large test systems. The execution time of small system such as IEEE 14, 30, and 57 are very fast, therefore the computation time can not be compared for these cases. Another cases IEEE 118, 300 and TNB 664 produced significant execution speedup. The superLU factorization sparse matrix solver has best performance and speedup of load flow solution as well as in contigency analysis. The invers full matrix solver can solved only for IEEE 118 bus test system in 3.715 second and for another cases take too long time. However for superLU factorization linear solver can solved all of test system in 7.832 second for a largest of test system. Therefore the superLU factorization linear solver can be a viable alternative applied in contingency analysis. Keywords : Fast Decoupled Load Flow, Contigency Analysis, and Linear System Solver

Comparative Study of Three Linear System Solver Applied to Fast Decoupled Load Flow Method for Contigency Analysis

Comparative Study of Three Linear System Solver Applied to Fast Decoupled Load Flow Method for Contigency Analysis

An efficient approach to handle the problem of load flow divergence in phasor based simulators

Dynamic behavior and stability of power systems can be studied with phasor-based programs in a reasonable time. Dynamic simulation of power systems needs to be initialized by Load Flow (LF) solutions. However, LF solutions may diverge in some critical conditions. This paper proposes an efficient Transient Stability (TS) based method to overcome the problem of load flow divergence in phasor-based power system simulators. The main idea is using the capability of TS module in such packages in order to overcome the divergence problem in fast-decoupled load flow (FDLF) method. This article focuses on LF convergence in networks with high R/X ratios branches such as distribution systems and microgrids. Suggestions for speeding up the convergence time and preventing of angle instability during TS simulation are described. The proposed methodology can be utilized in TS programs that use FDLF method for solving LF problems. The obtained accurate simulation results in a reasonable time show the efficiency and practical applicability of the proposed method.

Fast and accurate second order load flow method based on fixed Jacobian matrix

This paper presents the second order load flow method (SOLFM) based on the constant Jacobian matrix, with flat initial guesses (1.0∠0°) in polar coordinates. The proposed SOLFM does not need to calculate the Jacobian and Hessian matrix separately; keeping the PV type buses. Accordingly, the solution sped up the proposed SOLFM to a level that is much faster than the classical Newton Raphson Load Flow Method (NRLFM). Moreover, the polar coordinate system can simplify the proposed method's load flow equation. The convergence characteristic of the proposed SOLFM is superior to the NRLFM due to the usage of the Hessian matrix. The validation of proposed SOLFM is proven by testing the Malaysian 664 bus system with respect to NRLFM and the Fast Decoupled Load Flow Method (FDLFM) in the context of computation time and convergence characteristic.

Investigation of schemes for incorporating generator Q limits in the fast decoupled load flow method

Fast Decoupled Load Flow (FDLF) is a very popular and widely used power flow analysis method because of its simplicity and efficiency. Even though the basic FDLF algorithm is well investigated, the same is not true in the case of additional schemes/modifications required to obtain adjusted load flow solutions using the FDLF method. Handling generator Q limits is one such important feature needed in any practical load flow method. This paper presents a comprehensive investigation of two classes of schemes intended to handle this aspect i.e. the bus type switching scheme and the sensitivity scheme. We propose two new sensitivity based schemes and assess their performance in comparison with the existing schemes. In addition, a new scheme to avoid the possibility of anomalous solutions encountered while using the conventional schemes is also proposed and evaluated. Results from extensive simulation studies are provided to highlight the strengths and weaknesses of these existing and proposed schemes, especially from the point of view of reliability.

Research on Fast Decoupled Load Flow Method of Power System

The power flow calculation is study the steady-state operation of the power system as basic electrical calculations. It is given the power system network topology, device parameters and determines system health boundary conditions, draw a detailed operating status of the power system through numerical simulation methods, such as voltage amplitude and phase angle on the bus system the power distribution and the power loss. Flow calculation is the power system operation, planning and safety, reliability analysis, is fundamental to the system voltage regulation, network reconfiguration and reactive power optimization must call the function, so the trend has very important significance to calculate the power system.

Fast decoupled load flow analysis with SSSC power injection model

This paper presents a facile incorporation of a static synchronous series compensator (SSSC) into the fast decoupled (FD) load flow method. The model is based on power injection formulation. The SSSC is represented by a series impedance and two power injection loads at the terminal nodes. These power injection loads are based on the specified power flow and updated during the iterative process. This developed model of SSSC can be implemented easily in the FD load flow method without changing in the basic computational algorithm. The developed model overcomes the problem of power flow SSSC model which exists when only the SSSC links two subnetworks. The FD load flow with the power injection model of SSSC has been validated using standard IEEE data. © 2014 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Identification of Catastrophic Failures in Power System Using Pattern Recognition and Fuzzy Estimation

This paper presents a new approach for finding the sequence of events that may lead to catastrophic failure in a power system. The probable sequences (of events) leading to catastrophic failures are identified using risk indices which incorporate the severity as well as the probability of the contingencies. Probable collapse sequences are identified offline for different possible loading conditions using a modified fast decoupled load flow method which considers the voltage and frequency dependence of loads and generator regulation characteristics and stored in a knowledge base. Pattern recognition method and fuzzy estimation are used for online identification of collapse sequences for any operating condition from the stored database (knowledge base).

Determinação do ponto de máximo carregamento de sistemas de potência utilizando o fluxo de carga desacoplado rápido parametrizado

Os métodos de fluxo de carga por Newton-Raphson e fluxo de carga desacoplado rápido convencionais são considerados inadequados para a obtenção do ponto de máximo carregamento de sistemas de potência, devido à problemas de mal-condicionamento neste ponto crítico e na sua vizinhança. Neste ponto a matriz Jacobiana do método de Newton-Raphson torna-se singular e considera-se que não são mais válidas as hipóteses de desacoplamento P-V e Q-teta utilizadas para a formulação do método fluxo de carga desacoplado rápido. No entanto, mostra-se neste trabalho, que com pequenas modificações, as versões XB e BX do fluxo de carga desacoplado rápido tornam-se adequadas para a obtenção do ponto de máximo carregamento. Estas novas versões modificadas são comparadas entre si com o intuito de explicitar suas características, assim como da influência da atuação dos limites de geração de potência reativa e de tap's de transformadores. Os resultados obtidos para os sistemas testes do IEEE (14, 30, 57 e 118 barras) mostram que as características de convergência das versões originais são preservadas. Além disso, durante o traçado das curvas PV, os diversos métodos podem ser comutados entre si possibilitando o cálculo de todos os pontos da curva com um número reduzido de iterações.

Discussion of "advanced SVC models for newton-raphson load flow and newton optimal power flow studies"

SVC’s normally are connected to the power system through a medium or low voltage transformer [3]. This transformer is modeled together with the equivalent reactance of the SVC regulation characteristic [4] [1]. This implies that an exact model should involve a reactance equivalent of the transformer and the high voltage node should be regulated remotely. However, in your paper this situation is not explained, even though in Section IV-E a control strategy with several devices is explained based on remote voltage control in PQ nodes. Could the authors explain how the Newton‐Raphson method would be modified under this situation? The comparisons between the proposed SVC models in this paper and the generator model are based on the quality of the power flow solution. In this sense, there is not any comparison with the generator/fixed-compensator model. Have the authors some results about this comparison? Also, from the robustness and computational effort points of view, would the proposed models in this paper represent any advantage compared with the generator/fixed-compensator model? On the conclusion section it is pointed out that the proposed model using the firing angle as state variable gives a more complete information. Would you like to explain the content of this information? Even though here it is discussed the Newton‐Raphson method, the generator model of SVC’s does not present any problem when the Fast Decoupled Load Flow (FDLF) method, while their limits are not violated. When the equivalent susceptance and firing angle models are used updating of nodal admittance and B matrices becomes necessary, which will result in some complications to implement these models on the FDLF method. Would the authors like to make some comments about this problem?

Control adjustments in fast decoupled load flow

The fast decoupled load flow (FDLF) method has gained wide acceptance in the power industry owing to its simplicity and computational efficiency. The critical role of control adjustments designed to simulate the control strategies of system operation in load flow solutions has long been recognized. The implementation of standard adjustments, such as area interchange control, bus type switching, transformer-tap/phase-shift control, and switchable shunt control, may lead to oscillations, or even divergence of the FDLF solution. In this paper, this problem is circumvented by introducing a voltage angle or magnitude update solution after every set of adjustments. DC lines, multiterminal DC links and flexible AC transmission systems (FACTS) are also modelled as real power flow adjustments. Test results on several practical systems are presented to demonstrate the effectiveness of the developed FDLF method.

A heuristic linearized line outage contingency ranking of integrated multiterminal AC-DC power systems

This paper presents an efficient noniterative algorithm for the line outage contingency ranking of integrated multiterminal AC-DC systems. The proposed method can be used to obtain the contingency ranking based on the real power overload performance index. The proposed method uses the converter real and reactive powers, obtained by the base-case solution of AC-DC load flow, to transform the original AC-DC system to an equivalent AC system. The post-contingency voltages and angles of the transformed system are obtained either by a hybrid method or by using the first iteration 1 P - 1 Q of the AC fast decoupled load flow method. The hybrid method is based on an improved linearized method and the sensitivity relationship of the equivalent AC power system. The proposed hybrid method was tested on 5-bus, 14-bus and 30-bus AC-DC test systems having a DC link and DC mesh connections. For all the test systems, contingency rankings based on the real power overload performance index and the voltage deviation performance index were obtained by the proposed method and compared with the results obtained by the full sequential AC-DC load flow algorithm. The capture ratios obtained by the proposed method are excellent.

Novel decoupled load flow method

Most of the reported decoupled load flow methods are derived from the Newton method by neglecting the coupling subjacobians. The paper presents a novel decoupled load flow method that does not ignore the coupling subjacobians. The effects of the coupling subjacobians are carefully taken into account by properly modifying the mismatch vectors and coefficient matrices of the proposed decoupled load flow equations. In the absence of PV busbars and for the same R/X ratio of all branches, the performance of the proposed decoupled load flow method may be considered as good as that of the Newton method. The performance of the proposed method was investigated on the IEEE 14-, 30- and 118-busbar systems, in addition to a simple two-busbar system, for various values of the branch resistance R and the R/X ratio. Iterations required by the proposed method to solve the load flow problems were compared with those found in the Newton and conventional fast decoupled load flow methods. >

Phase-shifting transformers in load flow and short-circuit analysis: modelling and control

A new accurate model representing phase-shifting transformers for both load flow and fault analysis is introduced. The model is simple, efficient and numerically stable. The theoretical basis of the model and the practical procedures of implementation for the fast-decoupled load flow method and short-circuit calculation are presented. For load flow implementation the developed model requires no additional storage except for data; the number of iterations and the time per iteration is unchanged. The phase-shifting trans formers have been used for real power control in parallel circuits and the relative analyses and test results are presented. For short-circuit analysis, the asymmetry in the admittance matrix introduced by the phase-shifting transformers is dealt with in two stages. The network is first solved using symmetrical admittance matrix, fully exploiting sparsity, and subsequently the effect of the asymmetry is superposed using the diakoptical approach and effective programming, which optimises the calculation time and storage. To illustrate the process involved a small numerical example is given in Appendix 9.1. The model described was implemented in the Interactive Power System Analysis program [12], and the results of verification for various transformer arrangements in typical practical networks are presented.

Modelling of Nonlinear Nodal Admittances in Load Flow Analysis

A new type of bus for load flow analysis is proposed in this paper; this type of bus, named PX, is particularly suited for modelling elements like static compensators or asynchronous generators. The inclusion of this PX bus in the Fast Decoupled Load Flow method is presented and discussed. Numerical results are reported when applying this approach to solve load flow problems in two standard systems.

Fast decoupled load flow methods in rectangular coordinates

The fast decoupled load flow method of Stott and Alsac in polar co-ordinates (FDLP) is possibly the most popular method used by utilities to date, due to its reduced memory requirement and faster rate of convergence. However, no proper attempts appear to have been made to develop its counterpart in rectangular coordinates. This paper reviews an existing model of the fast decoupled load flow method in rectangular coordinates (FDLR) and presents three new versions. The potential of the new models of FDLR, as compared to its existing model and the FDLP model, have been tested on two IEEE test systems, for well-behaved and ill-conditioned cases.