Continuation Power Flow Method Research Articles

Large scale penetration impact of PMS-WTGS on voltage profile and power loss for 5-bus, 330kV system of the Nigerian grid

In recent times, adverse environmental changes and the gradual reduction in fossil fuel deposits is making integration of renewable energy secure global attention. This paper therefore investigates the effect of high penetration of wind power on power loss and voltage profile of 52-bus, 330kV Nigerian grid. Modeling and simulation of the study were successfully done using the Continuation Power Flow method and Power System Analysis Toolbox in the Matrix Laboratory environment. The Ant Colony Optimization (ACO) technique codes were used to determine the best sites and sizes of Permanent Magnet Synchronous-based Wind Turbine Generators (PMS-WTGs) on the grid as nonoptimal placement and size of PMS-WTGs will result into active power losses and poor voltage profile. The ACO and power flow analysis indicated two load buses, Aladja bus and Yola bus as best sites for PMS-WTGs with optimal sizes of 100MW and 197MW respectively. The result shows a decrease in the system's active (42.1%) and reactive (43.9%) power losses while heightening voltage magnitudes of critical buses to statutory values and enhancing the grid power quality. The overall results indicate that integrating 297MW PMS-WTGs improves voltage stability and power loss reduction by maximizing system loadability and reducing line losses.

Assessment of photovoltaic generation penetration effect on the maximum loadability of the system

This paper proposed a method to investigate the effect of increasing PV penetration on the voltage stability of an IEEE 14-bus test system considering maximum PV penetration and system loadability limit. The critical bus of the test system has been decided based on nose curve analysis. The solar PV system is deployed with the most critical bus of the system. The effect of increasing PV penetration on the improvement in the loading capacity of various power system components like transmission lines, transmission line transformers, and generators is investigated over the adopted test system. Based on solar PV penetration up to 100 MW, the maximum loadability limit of the IEEE 14-bus test system increases, as shown by the results. Bus 14 is found to be the most severe bus of the test system using the continuation power flow (CPF) method. However, in some cases, overloading situations develop after a certain limit of PV penetration in the power system. In this condition, the overloading of the power system equipment is improved by the use of a Static Synchronous Compensator (STATCOM) at bus number 14, a double circuit line in the critical line (9–14), and Static Synchronous Series Compensator (SSSC) in the most severe line (9–14) in the system. The maximum loadability of the system gets maximum enhanced from 4.0349 p.u. to 4.5602 p.u. under simultaneous use of solar PV generation, SSSC, and STATCOM at the most critical bus and in most severe line of the system. As evidence, the enhancement in maximum loadability of the system found using the proposed method has been also compared with the existing research. The maximum system loadability has been also enhanced under normal and (N-1) contingency conditions by the use of PV penetration in the system. PSAT/MATLAB software is used for simulation and maximum loadability has been investigated by continuation power flow (CPF) method.

An Extended Continuation Power Flow Method for Static Voltage Stability Assessment of Renewable Power Generation-Penetrated Power Systems

The continuation power flow method (CPF) has been extensively used for obtaining the static voltage stability limit of power systems, which provides important guidance for the stable operation. However, the conventional CPF cannot account for the dynamic characteristics of renewable power generation, thus resulting in prominent errors for renewable power generation-penetrated power systems. In this paper, we investigate the static voltage stability assessment (SVSA) of power systems with high penetration of rgb0,0,0renewable power generation (RPG). An extended Jacobian matrix is firstly established by considering the dynamic characteristics of synchronous generators (SG) and renewable power generation in constant AC voltage control mode (CVRPG). Based on the extended Jacobian matrix, an extended CPF method is proposed for SVSA of the power system and a reactive power sensitivity index is proposed to indicate the voltage support capability of nodes. Simulation results show that the proposed extended CPF method has higher accuracy than conventional CPF in assessing the static voltage stability of power systems with high penetration of RPG. It is also revealed that that the voltage support capability of each node rises as the proportion coefficient is increases.

Optimal allocation of distributed generation in active distribution power network considering HELM-based stability index

Traditionally, assessment of static voltage stability for distribution power networks with distributed generation (DG) utilizes the continuous power flow (CPF) method by calculating load margin index (LMI) at various load levels, which suffers from slow calculation speed and low accuracy when power flow calculation becomes ill-conditioned. To overcome this issue, this paper presents a novel holomorphic embedding load flow method (HELM)-based approach that calculates voltage stability indices for various types of nodes in a distribution network. Different orders of sensitivity information are calculated using the HELM method, and the criteria for assessing voltage stability are derived, which are used as constraints to optimize the location and capacity of DG. Such formulation of the optimization problem does not need to calculate the maximum load margin using CPF. Moreover, it can be effectively solved using the Genetic Algorithm and easily adaptable to various operating conditions of DG, which improve the calculation speed of the stability index. The effectiveness of the proposed approach is verified on IEEE 33-node and IEEE 69-node distribution power network models. Results show that considering the HELM VSI, the location, and capacity of DG in the distribution network can be better optimized. For the IEEE 33-node model, the total cost is reduced by approximately 2.33%, the network loss is reduced by 1.2%, and the HELM voltage stability criteria index is increased by about 4.23%; while for the IEEE 69-node system, the total cost is reduced by about 2.98%.

Real Time Voltage Stability Estimation under Contingencies by Generalized Curve Fit Method using PMU

An accurate voltage stability monitoring scheme is necessary to take possible remedial action. Recent developments in Phasor Measurement Units (PMUs) technology provide the foundation for online voltage stability monitoring of a power system network. In this paper, the generalized curve fit method using PMUs in the system has been used to access voltage stability of the system and a sensitivity based approach has been used to identify critical buses of the system. Voltage stability margin has been obtained and compared using generalized curve fit method and continuation power flow method using PMUs in the system. Variations in voltage stability margin caused by changing load patterns have also been considered while estimating voltage stability under contingencies. Nose curves obtained using generalized curve fit and continuation power flow methods are also compared. Case studies have been performed on a standard IEEE 14-bus system and practical 246-bus Northern Regional Power Grid (NRPG) system representing power network of nine states of India, with the help of Real Time Digital Simulation (RTDS) and Power System Analysis Toolbox (PSAT) software.

Novel Hybrid Modified Modal Analysis and Continuation Power Flow Method for Unity Power Factor DER Placement

Distributed energy resource (DER) has become an effective attempt in promoting use of renewable energy resources for electricity generation. The core intention of this study is to expand an approach for optimally placing several DER units to attain the most stable performance of the system and the greatest power losses decrease. The recommended technique is established on two analytical methods for analyzing voltage stability: the new modified modal analysis (MMA) and the continuation power flow (CPF) or MMA–CPF methods. The MMA evaluates voltage stability by considering incremental connection relating voltage and active power, which includes the eigenvalue and the related eigenvectors computed from the reduced modified Jacobian matrix. Furthermore, an active participation factor (APF) is computed from the eigenvectors of the reduced modified Jacobian matrix. The CPF method uses a predictor–corrector stepping pattern to reach the solution track and compute the tangent vector sensitivity (TVS). Both APF and TVS indicate each load bus sensitivity in the network. In addition, an objective function regarding losses decrease and eigenvalue is expressed to calculate the best bus position for DER allocation. The proposed MMA–CPF technique has been assessed on a 34-bus RDN and the outcomes demonstrate the effectiveness of the proposed scheme.

Integrated T&D Voltage Stability Assessment Considering Impact of DERs and Distribution Network Topology

Electric distribution systems are going through a major upgrade with increasing penetration of distributed energy resources (DERs) and impacting transmission system operational analysis. Traditionally, the transmission system’s voltage stability margin is computed by performing a continuation power flow (CPF) analysis. In transmission-CPF, loads in distribution systems are aggregated at the transmission-distribution (T&D) interface buses, and the distribution system’s electrical characteristics, like feeder length, increasing penetration of DERs, and associated control, are not considered. The traditional CPF thus considers the distribution network as a purely passive network without active network management and distributed energy resources. In this paper, two integrated T&D CPF methods are implemented using a co-simulation framework that uses individual transmission and distribution solvers. The first method is iteratively-coupled T&D CPF (IC-TDCPF), where the iterative coupling concept forces convergence of boundary variables at T&D PCC (Point of common coupling) at every CPF step. The second method, Loosely Coupled T&D CPF (LC-TDCPF), relaxes the boundary convergence constraints at PCC to achieve faster calculation speed. Moreover, a reduced distribution network equivalent is also developed to enable faster computation of VSM by reducing the number of integrated T&D buses. The developed T&D CPF co-simulation framework uses an open-source platform <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MATPOWER</i> for solving transmission system and open-source software <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OPENDSS</i> for solving distribution system. Three large integrated T&D systems with 4196, 10587, and 12295 buses are developed to demonstrate the impact of DERs, voltage-dependent load models, and distribution network topology on integrated voltage stability margin using the proposed T&D CPF and co-simulation.

Evaluation of EV penetration level limit in distribution system applying charging and scheduling strategies

Traveling by electric vehicles (EVs) instead of conventional fuel cars is strongly supported by a lot of governments for the sustainable development of urban transportation. However, EVs increase the load in the distribution system which impacts the voltage stability in the distribution network. In this paper, a method for evaluation the largest EV number to be accommodated in the distribution system is proposed. First of all, a Monte Carlo charging model for electric vehicles is established. Then the EV charging schedule is determined with the TOU electricity price and the dispatch method to suppress the maximum peak load is presented. Ultimately, Considering the temporal and spatial features of EV charging, the maximum vehicle access capacity of the distribution network is calculated by the continuous power flow method. The developed method was tested in the PG&E 69-bus distribution system, and the results show that the EV penetration level evaluation method proposed is an efficient tool for the distribution system planning, as well as the voltage stability analysis with the fast increasing EVs in the distribution system.

Continuation Power Flow Analysis of Power System Voltage Stability with Unified Power Flow Controller

The rising power demand has forced power systems all over the world to operate very close to their stability limits. When power systems are overloaded, faulty, or in lack of reactive power, voltage collapses would ensue. The capacity of a power system to keep the voltage of every bus constant under disturbances is called voltage stability. This dynamic phenomenon hinges on the load features. It is commonly known that flexible AC transmission systems (FACTS) can improve voltage stability. This paper puts forward a load flow model with the unified power flow controller (UPFC), and relies on the model to investigate the voltage stability of a power system through continuation power flow (CPF) method. The validity of the model was verified through a simulation, using the power system analysis toolbox (PSAT) in MATLAB/Simulink environment.

Calculation of static voltage stability margin under N-1 contingency based on holomorphic embedding and Pade approximation methods

A calculation technique for the static voltage stability margin (SVSM) under N-1 contingency based on the fast and flexible holomorphic embedding (FFHE) and Pade approximation (PA) methods is proposed. The technique can also obtain the approximate analytic function between the post N-1 contingency SVSM and the pre-contingency SVSM. Using the contingency parameter as an embedded variable, the relationship between the post N-1 contingency SVSM and the pre-contingency SVSM is approximately described in the form of power series. By constructing the FFHE matrix equation, the values of state variables at the pre-contingency static voltage stability limit point are taken as the 0th order coefficients. The FFHE matrix equation is solved to obtain the higher order coefficients from the lower order coefficients step by step. Thereby the power series expression of post N-1 contingency SVSM is obtained. In addition, by using the PA method, the approximate rational fraction expression of the post-contingency SVSM which can improve the convergence and accuracy of the power series can be obtained. Test results for the IEEE 39-bus system and an actual 1559-bus power grid demonstrate that the proposed method to calculate the post-contingency SVSM has high accuracy and strong robustness compared with the optimal power flow and continuation power flow methods. The average relative errors of the proposed method in the two cases are 0.58155% and 1.0862%. The strong robustness is reflected in the fact that there is no need to repeatedly select the initial value for calculation under different contingencies.

Improving performance of transmission networks using facts through continuation power flow method

Over the past 50 years, modern electrical systems have become more complex, as they overrun the geographical boundaries of neighboring countries. The problem is that the power system faces many challenges, because it is exposed to difficult operating conditions. The phenomenon of voltage instability is the most frequent phenomenon, and this can lead to the collapse of the power system. To avoid power outages in the system (especially in blackout situations), the power system must be analyzed in order to maintain voltage stability in the expected difficult operating conditions. The main objective is to determine the maximum load capacity of the system and the causes of voltage instability. The voltage instability problem is related to the nature of nonlinear loads, so different load characteristics must be taken into consideration when analyzing voltage stability. This study aims to discover the maximum load capacity required by using the continuous power flow method (CPF) in the studied network. Then, the performance of this network using a Flexible Alternating Current Transmission System (FACTS) will be utilized. FACTS systems present a promising solution in improving the voltage stability by improving the power transmission capacity and controllability of the parameters of the existing power networks. This study will be conducted on a reference network platform under normal working conditions, then installation of one of the FACTS systems will show its effect on improving voltage stability. The continuous power flow method will be used to find PV curves, which in turn will help to determine the conditions of maximum loading while maintaining stability, and identify the bus bar with the smallest voltage, on which the flexible AC systems will be installed. The software environment MATLAB/PSAT will be used for modeling and simulation.

PMU-Based Voltage Stability Measurement Under Contingency Using ANN

An artificial neural network (ANN) is an effective and efficient approach for solving problems, which require fast and complicated computation. The study proposed a PMU measurement-based voltage stability monitoring and assessment using ANN hybrid model for the evaluation of voltage stability margin. Particle swarm optimization (PSO) optimizes the meta-parameter of ANNs for improving its convergence rate. This model helps in real-time monitoring of long-term voltage stability to avoid grid blackout. The power system security is generally defined based on the single contingency “N−1” criterion, meaning normal system minus one element. Separate ANNs are trained and designed for selected worst case “N−1” contingencies along with base case configuration. Phasor Measurement Unit installed at distant locations provide real-time synchronized measurements of voltage phasor, which forms the input feature for the proposed model. Load <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula> margin evaluated by continuation power flow (CPF) method is considered as output feature of the proposed ANN model. The performance indices mean absolute percentage error (MAPE) and maximum percentage error (MPE) with smaller values indicate small deviation between the estimated and the actual values. The proposed approach is effectively tested on IEEE 14-bus and 30-bus test system.

Online Monitoring of Voltage Stability Margin in Kosovo Power System Using Local Measurements

This paper presents an analysis of the voltage stability of the Kosovo power system. The first part of the study has included a detailed analysis of the Kosovo power system by using the continuous power flow method, with an emphasis on the determination of the P–V curve of voltage stability. Thus, it has identified the weak and critical points of the power system in terms of voltage stability and has defined the margin of instability. In order to achieve online monitoring of voltage stability in the power system, it is proposed to place phasor measurement units in the weakest critical buses. Furthermore, the Thevenin equivalent method has been applied to evaluate voltage stability in the critical buses. The maximum transmissible real power to the weak buses in the system can be achieved when load impedance is equal to the Thevenin impedance. The load and Thevenin impedance values have been obtained from the relevant PMU data. Following online monitoring of voltage stability in the power system, the developed voltage stability load bus index can be used as useful information by system operators in order to undertake appropriate countermeasures to prevent voltage collapse.

An adaptive multi-step Levenberg-Marquardt continuation power flow method for voltage stability assessment in the Ill-conditioned power systems

Continuation power flow (CPF) is a well-known way for determining voltage instability point in electrical power systems. In an ill-conditioned power system, solving traditional CPF using the Newton’s method encounters divergence or very slow convergence, because the Jacobian matrix is singular or near singular. This paper presents the application of the adaptive multi-step Levenberg-Marquardt (AMSLM) method to solve the power flow problem in an ill-conditioned power system. In the next step and based on the new proposed AMSLM power flow (AMSLM-PF) method, an AMSLM continuation power flow (AMSLM-CPF) method for voltage stability assessment of the ill-conditioned power systems is presented. Moreover, a fuzzy inference system (FIS) is proposed to optimize the parameters of the new AMSLM-PF method. To demonstrate the effectiveness of the proposed AMSLM-PF and AMSLM-CPF methods, detailed simulation results are presented and analyzedfor IEEE 14-bus, IEEE 43-bus, IEEE 118-bus and 2383-bus power systems.

An Innovatory Method Based on Continuation Power Flow to Analyze Power System Voltage Stability with Distributed Generation Penetration

With the penetration of distributed generation (DG) units, the power systems will face insecurity problems and voltage stability issues. This paper proposes an innovatory method by modifying the conventional continuation power flow (CCPF) method. The proposed method is realized on two prediction and correction steps to find successive load flow solutions according to a specific load scenario. Firstly, the tangent predictor is proposed to estimate the next predicted solution from two previous corrected solutions. And then, the corrector step is proposed to determine the next corrected solution on the exact solution. This corrected solution is constrained to lie in the hyperplane running through the predicted solution orthogonal to the line from the two previous corrected solutions. Besides, once the convergence criterion is reached, the procedure for cutting the step length control down to a smaller one is proposed to be implemented. The effectiveness of the proposed method is verified via numerical simulations on three standard test systems, namely, IEEE 14-bus, 57-bus, and 118-bus, and compared to the CCPF method.

Feasibility study on new energy multi-feed direct current grid connection

To adapt to the characteristics of new energy long-distance transmission, this paper proposes a scheme of multi-fed voltage source converter grid connection and line-commutated converter transmission for a regional large energy base. First, the feasibility of this multi-infeed direct current (DC) transmission scheme is discussed. Then, the performance characteristics of the multi-infeed DC and other traditional transmission technologies are compared and analysed. In addition, the economic benefits of the multi-infeed DC project are evaluated. To study the characteristics of new energy multi-infeed DC power transmission mode, a long-distance energy transmission system based on multi-infeed DC power transmission mode is built using DIgSilent software. On the basis of the continuous power flow method, the static characteristics of the system are studied. Based on the time-domain simulation method, the transient characteristics of the system are studied. The results show that multi-infeed DC has great advantages in large-scale regional new energy long-distance transmission.

Online monitoring of voltage stability margin using PMU measurements

With the growing smart grid concept it becomes important to monitor health of the power system at regular intervals for its secure and reliable operation. Phasor Measurement Units (PMUs) may play a vital role in this regard. This paper presents voltage stability monitoring in real time framework using synchrophasor measurements obtained by PMUs. Proposed approach estimates real power loading margin as well as reactive power loading margin of most critical bus using PMU data. As system operating conditions keep on changing, loading margin as well as critical bus information is updated at regular intervals using fresh PMU measurements. Simulations have been carried out using Power System Analysis Toolbox (PSAT) software. Accuracy of proposed Wide Area Monitoring System (WAMS) based estimation of voltage stability margin has been tested by comparing results with loading margin obtained by continuation power flow method (an offline approach for accurate estimation of voltage stability margin) under same set of operating conditions. Case studies performed on IEEE 14-bus system, New England 39-bus system and a practical 246-bus Indian power system validate effectiveness of proposed approach of online monitoring of loading margin.

Continuous Power Flow and Time Domain Analysis for Assessing Voltage Stability

Voltage instability is considered one of the primary sources of insecurity in power systems. Voltage instability is the phenomenon in which the voltage on the receiver's side is dropping far below the normal value and does not return even after establishing a voltage recovery mechanism, or continue to oscillate due to lack of attenuation. In this study, there will be a voltage stability analysis on the power system in several phases by conducting a power flow analysis, static voltage stability analysis using continuous power flow method, and dynamic voltage stability analysis using the time-domain analysis. The power system tested on this research is the IEEE 6 bus system from Wood & Wollenberg, with the software used for the simulation, which is PSAT. The results show that voltage stability analysis using Continuous Power Flow and Time Domain Analysis can provide a more comprehensive overview of a power system stability level. The highest decrease in voltage with a value of 1.5% appears in Bus 5 which is also suffering the lowest stability level. The system has a load margin (λ) value of 1.6130 a clearing time of under 0.4 seconds

A Dynamized Power Flow Method Based on Differential Transformation

This paper proposes a novel method for solving and tracing power flow solutions with changes of a loading parameter. Different from the conventional continuation power flow method, which repeatedly solves static AC power flow equations, the proposed method extends the power flow model into a fictitious dynamic system by adding a differential equation on the loading parameter. As a result, the original solution curve tracing problem is converted to solving the time domain trajectories of the reformulated dynamic system. A non-iterative algorithm based on differential transformation is proposed to analytically solve the aforementioned dynamized model in form of power series of time. This paper proves that the nonlinear power flow equations in the time domain are converted to formally linear equations in the domain of the power series order after the differential transformation, thus avoiding numerical iterations. Case studies on several test systems including a 2383-bus system show the merits of the proposed method.

The new steady state voltage stability analysis methods with computation loads separation technique in DC power systems

The steady state voltage stability analysis is extremely important to the security of power systems. The continuation power flow (CPF) is one of the important tools for the steady state voltage stability analysis. However, its computation load is very large. To improve the analysis performance in DC power systems, a basic technique is used to explore the exact relationships between injected currents, buses voltages, lines currents and lines voltages. Based on the basic technique, the computation loads can be separated and some repeated computation can be avoided. In this paper, two new methods to calculate critical point are proposed. One is by combining the basic technique and a correctness method for CPF. The method improves the calculation speed by avoiding the repeated computation of same topology and buses types analysis. Another method is a direct method. The direct method is based on the novel view to understand power systems and the physical (and mathematical) essence of critical point and voltage collapse. Most CPF is discussed in AC system. The corresponding CPF in DC system will be studied to get standard results for comparison. Compared with CPF in DC systems, the numerical verification shows that the proposed methods can reduce most computation loads of CPF method in DC systems.