Continuation Power Flow Method Research Articles

Improved Step Size Newton Raphson Method using quadratic equations properties in ill-conditioned power system

SUMMARY The Step Size of the Newton Raphson Method (SSNRM) is based on the optimal multiplier that is used to determine the Multiple Load Flow Solutions (MLFS) for an ill-conditioned power system. However, the SSNRM is incapable of determining the desirable Low Voltage Solution (LVS) from the MLFS at the Maximum Loading Point (MLP), due to the fact that when the load demand increases, the LVSs moves closer to each other at the MLP. Commonly, the smallest optimal multiplier was used to calculate the LVS at the MLP under this condition. However, this paper proves the fact that using the smallest optimal multiplier to determine the most suitable LVS for the systems having multiple solutions at the MLP will not guarantee a favourable outcome. Therefore, this paper investigates the application of the properties of scalar quadratic equations (PSQE) that enhances the function of the SSNRM at the MLP. Thus, an indicator, based on PSQE, is introduced in this work, which amends the existing SSNRM for the purpose of finding the desirable LVS at the MLP. The closest optimal multiplier to the proposed indicator is selected in order to determine the desirable LVS from all possible solutions at the MLP. The proposed method has been tested on a three-bus and IEEE 30-bus systems at the MLP for verification purposes. Additionally, the continuation power flow method is also utilized in order to compare it to the proposed method for the IEEE 30-bus system at the MLP. Copyright © 2013 John Wiley & Sons, Ltd.

Continuation Power Flow Method with Improved Voltage Stability Analysis in Two Area Power System

Power systems operation becomes more important as the load demand increases all over the world. This rapid increase in load demand forces power systems to operate near critical limits due to economic and environmental constraints. The objective in power systems operation is to serve energy with acceptable voltage and frequency to consumers at minimum cost. This paper studies the important power system phenomenon and voltage stability by using continuation power flow method. Voltage collapse scenario is presented which can be a serious result of voltage instability and also the parameters that affected by voltage collapse are discussed. In analysing power system voltage stability, continuation power flow method is utilized which consists of successive load flows. Case studies are carried on 11 bus network in two areas and PV curves for several buses are obtained. Simulation is done with PSAT in MATLAB. Continuation Power Flow is was implemented using Newton Raphson method. In this paper the effect of compensator, placement of generator and variation of line reactance on the voltage stability have been studied and Comparison between performance of installation shunt capacitor, adding generator and variation of line reactance for improve voltage stability has been done. Simulation results show the proper performance of installation shunt capacitor, adding generator and variation of line reactance to improve voltage control and significantly increase the load ability margin of power systems.

A Critical Eigenvalues Tracing Method for the Small Signal Stability Analysis of Power Systems

The continuation power flow method combined with the Jacobi-Davidson method is presented to trace the critical eigenvalues for power system small signal stability analysis. The continuation power flow based on a predictor- corrector technique is applied to evaluate a continuum of steady state power flow solutions as system parameters change; meanwhile, the critical eigenvalues are found by the Jacobi-Davidson method, and thereby the trajectories of the critical eigenvalues, Hopf bifurcation and saddle node bifurcation points can also be found by the proposed method. The numerical simulations are studied in the IEEE 30-bus test system.

Investigation and Comparison of the Effect of Facts Devices, Capacitors and Lines Reactance Variations on Voltage Stability Improvement and Loadability Enhancement in Two Area Power System

This paper studies the important power system phenomenon and voltage stability by using continuation power flow method. Voltage collapse scenario is presented which can be a serious result of voltage instability and also the parameters that affected by voltage collapse are discussed. In analyzing power system voltage stability, continuation power flow method is utilized which consists of successive load flows. In this paper steady-state modeling of Static VAR Compensator (SVC) and Unified Power Flow Controller (UPFC) and effect of compensator and variation of line reactance on the voltage stability have been studied and Comparison between performance of UPFC and SVC and installation shunt capacitor and variation of line reactance for improve voltage stability has been done.Case studies are carried on 11 bus network in two areas. Simulation is done with PSAT in MATLAB. Continuation Power Flow was implemented using Newton Raphson method. Simulation results show the proper performance of UPFC, SVC, installation shunt capacitor and variation of line reactance to improve voltage control and significantly increase the loadability margin of power systems. Full Text: PDF

Saddle Node Bifurcation and Voltage Stability Analysis of Sri Lanka

In electrical power systems, saddle node bifurcation (SNB) is the voltage stability margin at which voltage collapse takes place. It plays an important role in power system planning and operation as economic and environmental pressures force to operate always closer to the limit of stability. Voltage collapse is associated with the reactive power demands not being met because of limitations in the generation and transmission of reactive power. Determination of the SNB point greatly assists planning and operation of power system. Among various voltage stability analysis (VSA) methods, this paper specifies the continuation power flow (CPF) method as it accurately identifies the SNB point and the critical or the weaker bus. In this paper, power system of Sri Lanka is assessed for diverse applications of VSA by concerning about single element outage or (N-1) criterion and the role of voltage compensation devices. Furthermore, the optimum at the SNB point is verified by eigenvalue analysis.

Enhancement of ATC with FACTS devices using Real-code Genetic Algorithm

Determination and enhancement of Available Transfer Capability (ATC) are important issues in deregulated operation of power systems. This paper investigates the use of FACTs devices, like SVC and TCSC, to maximize power transfer transactions during normal and contingency situations. ATC is computed using Continuation Power Flow (CPF) method considering both thermal limits and voltage profile. Real-code Genetic Algorithm (RGA) is used as an optimization tool to determine the location and controlling parameters of SVC and TCSC. The suggested methodology is tested on IEEE 14-bus system and also on IEEE 24-bus reliability test system for normal and different contingency cases.

Algorithm of Continuous Power Flow Considering Auto-Disconnection of Large-Scale Wind Farms

Voltage stability of power grid would be affected greatly by the connection of large-scale wind farms. Conventional continuous power flow method can not accurately simulate the system’s operation when wind farms are connected to power gird. A new continuous power flow method is proposed, considering auto-disconnection of large-scale wind farms. The step-size control segment is improved in this algorithm in order to simulate the operation characteristics of wind farm and determine the precise time when a certain wind farm is cut off.

Continuation power flow with adaptive stepsize control via convergence monitor

A continuation power flow method with adaptive step size is proposed. Two approaches are used to predict the step size. First, convergence monitor is proposed to predict step size. This step size is compared with the step sizes obtained by the first-order sensitivity of Q-generation and voltage with respect to a parameter. Whichever step size is smaller is chosen to reduce the possibility of divergence and to deal with discrete controls. Convergence monitor is capable of detecting possible divergence in corrector within three iterations. The method of detecting limit-induced bifurcation is proposed by means of sensitivity. The proposed approach is tested on a 300 bus system as well as a practical system. The performance shows that it needs much less time and does not need the critical buses preselected.

An innovative technique to evaluate network equivalent for voltage stability assessment in a widespread sub-grid system

The equivalent two-bus network models currently available are obtained by lumping all the series impedances and shunt admittances of transmission lines within a series equivalent impedance, to assess voltage stability of multi-bus power system. This paper reports the development of an equivalent pi-network model using a new methodology considering series and shunt parts of line loss separately obtained from the operational parameters of optimal power flow solution of the original multi-bus power network, which can be applied to assess the overall voltage stability status of the system accurately by developing the concept of a generalized global voltage stability margin (GVSM). Simulation results for a typical longitudinal power supply (LPS) system and a robust practical (Indian Eastern Grid) system establish that the pi-equivalent model obtained by the proposed method is highly promising for assessing voltage stability of any power system at any operating point in global scenario in a better way as compared to available series equivalent model. Continuation power flow (CPF) method has also been adopted here to verify the potential of the proposed method for voltage stability assessment. In the proposed equivalent network the generators have been modeled more accurately considering optimal operating criteria.

Performance analysis of a novel Q -limit guided continuation power flow method

This study presents a new bifurcation point calculation method that is based on the continuation power flow (CPF) method. The algorithmic continuation steps are guided by the prediction of Q-limit breaking points. A Lagrange polynomial interpolation formula is used in this study in order to find the Q-limit breaking point indices that determine when the reactive power output of a generator has reached its limits. The algorithmic continuation steps will then be guided to the closest Q-limit breaking point, consequently reducing the number of continuation steps and saving computational time. The novel method is compared with alternative conventional and enhanced CPF methods. Studies have been undertaken on IEEE 30, IEEE 118, National Grid (NG) 61 and NG 953 bus systems.

Application of continuation power flow method in radial distribution systems

The paper presents a set of equations (SOE) comprising voltage magnitude and nodal real/reactive power balance equations to model a radial distribution system (RDS). The voltage equations in the SOE have dual roots. Then a Newton–Raphson (NR) method is presented to solve the SOE to determine the voltage solution of an RDS. This NR method is extended using the continuation technique to trace the P– V curves and to determine the maximum loading point of an RDS. Implementation of the proposed method on some common RDS and a 5002-bus RDS is demonstrated. An interesting characteristic of the path traced by the minimum singular value of the system Jacobian during the application of the continuation method for a system with shunt capacitors is reported. An analysis of a simple 4-bus system with and without a capacitor demonstrates that the presence of capacitive load creates multiple positive regions of σ min. One positive region exists when the system is healthy (before collapse). The second region exists in between collapse point and the point where an increase in the load creates reactive power flow reversal on the source line.

Voltage security evaluation based on perturbation method

This paper proposes a new algorithm for estimating voltage security margin. The algorithm is based on the perturbation method and has significant computational efficiency. The proposed algorithm can be used for on-line voltage security evaluation. It has been validated using IEEE-14, IEEE-30 and IEEE-57 bus systems. Results from the tests show higher efficiency and smaller error margins compared to continuation power flow (CPF) method. Voltage collapse is a serious threat to the security of stressed power systems; therefore, voltage security (VS) has become a major challenge for management of power systems. The motivation for this research is a direct consequence of the deregulation of electricity industries and markets worldwide.

A new approach for estimating voltage collapse point based on quadratic approximation of PV-curves

The MW-distance to voltage collapse is a good indicator of voltage stability at a given operating condition in power systems. This indicator is determined using PV-curves obtained through continuation power flow (CPF) program. The CPF method performs several power flow runs requiring a large amount of computing time. This method is reliable for off-line voltage stability studies, but not very much suitable for real-time operation of today's stressed power systems. Given that, it is essential for system operators to have quick information about voltage stability, a new method is needed for a fast estimation of voltage collapse point. This is the main thrust of the presented paper. It is well known that PV-curves are approximately quadratic functions and become exactly quadratic in close neighborhood of the collapse point. Some authors used this fact and suggested methods that use two to three power flow solutions for a relatively quick, but approximate, calculation of the collapse point. The present paper, also based on quadratic approach, proposes a new method for the determination of voltage collapse that uses only one power flow solution and gives more accurate estimate of the collapse point when compared with other existing methods. Another advantage of the presented method is that the estimation becomes more accurate for stressed power systems. In addition, application of the presented method for performing the top/stable portion of the PV-curves provides an effective step-size that reduces the number of power flow runs. The method is tested using the New England 39-bus and the IEEE 300-bus test systems. The results confirm the effectiveness of the presented method.

Continuation Power Flow With Nonlinear Power Injection Variations: A Piecewise Linear Approximation

Power injection variations that occur in power systems are generally nonlinear. A continuation power flow method with multiple nonlinear power injection variations is presented in this paper. To model the nature of nonlinear power injection variations, a piecewise-linear model is proposed to approximate the nonlinear model of power injections. The piecewise-linear model is studied and incorporated into continuation power flow, making it capable of handling nonlinear power injection variations. The impacts of linear as well as nonlinear load variations on the P-V curve, Q-V curve, and P-Q-V curve are numerically analyzed on test power systems. Numerical studies indicate that the direction of power injection variation can significantly affect the load margin and that the differences between uniform linear power injection directions and multiple nonlinear power injection variations can be significant. The importance of accurately modeling power injection variations on simulated power system quasi-state behaviors is stressed.

Development of nonlinear predictor with a set of predicted points for continuation power flow

AbstractIn this paper, a new continuation power flow method is proposed to speed up computational time for drawing P– V curves in power systems. The continuation power flow calculation aims at successively evaluating power flow solutions in changing the nodal specified value of power flow calculation. The P– V curves are useful for static voltage instability. The conventional continuation power flow calculation methods are based on the predictor– corrector method. This paper proposes a new nonlinear predictor in the predictor– corrector method. The proposed method simultaneously evaluates a set of solution candidates through the nonlinear predictor. The effectiveness of the proposed method is demonstrated in sample systems. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 163(4): 30–41, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20297

Nonlinear predictors and hybrid corrector for fast continuation power flow

Continuation power flow is a powerful tool to simulate power system steady-state stationary behaviours with respect to a given power injection variation scenario. Although continuation power flow methods have been implemented in several commercial packages, they may be still too slow for online applications. The authors aim to improve the continuation power flow methods, mainly their speed and, to a less extent, their reliability. Nonlinear predictors are developed based on the polynomial interpolations. The authors' numerical studies show that continuation power flow with the proposed nonlinear predictors can be much faster than that with traditional linear predictors such as tangent or secant predictors. Of the nonlinear predictors, second-order polynomial approximation-based and third-order-based nonlinear predictors show their superior performance in speed. Continuation power flow with second-order nonlinear predictors is generally slightly faster than that with third-order nonlinear predictors. In addition, a hybrid corrector is developed and incorporated into continuation power flow. It is numerically shown on several test systems ranging from 118-bus to 1648-bus that continuation power flow with the proposed hybrid corrector can be much faster than that with traditional correctors such as the Newton method and the fast decoupled method. Finally, an improved continuation power flow with the developed nonlinear predictor and hybrid corrector is presented and evaluated.

Voltage security assessment and optimal load shedding of power system using the case-based reasoning approach

This paper presents the case-based reasoning (CBR) technique, a novel approach for voltage security assessment and optimal load shedding plan in a real time environment. CBR extracts the information of voltage security from large sets of possible operating conditions of the power system, which are screened off-line by randomly varying the real and reactive loads at PQ buses. In a real time environment, a database may be created by keeping the record of operating states by state estimation. The severity of the contingency is assessed by the number of insecure operating states caused by that contingency, which is predicted by CBR. Security classes are defined by the threshold value of the maximum loadability margins (MLM), calculated using the continuation power flow (CPF) method. For insecure states, the presented technique also gives an optimal load shedding plan to bring the system into secure mode.

Power Systems Voltage Security Assessment and Optimal Load Shedding by CBR Approach

This paper presents a case-based reasoning (CBR) technique, a novel approach for voltage security assessment and optimal load shedding in real-time environment. The CBR extracts the information of voltage security from large sets of possible operating conditions of the power system, which are screened off-line by randomly varying the real and reactive loads at PQ buses. The severity of contingency is then assessed by the number of insecure operating states, which are predicted by the CBR system under that contingency. Security classes are defined by threshold value of maximum loadability margins (MLM), calculated using continuation power flow (CPF) method. For insecure states, the presented technique also gives optimal load shedding plan to bring the system from insecure to secure region. Decision trees (DT) are used for case indexing to reduce the search time to obtain the set of relevant cases, which are in thousands of numbers. In addition, decision trees also provide the information about those case features, which mostly influence the severity of a given contingency of the power system. Unlike other non-deterministic approaches, the proposed method is easy to understand for operators, easy to modify under the change of topology of the power system and has continuous learning capability. The effectiveness of the proposed approach is tested on IEEE test systems. The proposed CBR approach provides a fast and accurate voltage security assessment for unknown load patterns and a load shedding plan for insecure cases to mitigate the voltage collapse. Hence it found to be suitable for on-line applications of energy management systems.

The CBR-PNN approach to real-time voltage security assessment of power systems

This paper presents the Case-based Reasoning (CBR) technique, a novel approach to voltage security assessment of power system in a real-time environment. The Probabilistic Neural Network (PNN) is used for determining the solution to a new case, using the old cases from the case base of the CBR system. A feature selection technique based on the information gained has been employed to identify the relevant input features for PNN. The CBR technique extracts the information of voltage security from large sets of possible operating conditions of the power system, generated by computer simulation. Also the ranking of contingencies is done by CBR as accurately as the one done by the Continuation Power Flow (CPF) method. Security classes are defined by the threshold value of maximum loadability margins, calculated by the CPF method. The effectiveness of the proposed approach is tested on IEEE test systems. The proposed method gives fast and accurate voltage security information for unknown patterns and it is found to be suitable for real-time monitoring of voltage security in energy management systems.

Tracing PV and QV Curves With the Help of a CRIC Continuation Method

This paper investigates the use of the constraint reactive implicit coupling (CRIC) method for the engine of a continuation power flow program. Full Newton continuation power flow methods are robust and accurate but are computationally expensive. Fast decoupled methods provide accurate results and require less computational time, but their performance worsens at heavy loading conditions, where the system active/reactive power decoupling characteristics are lost. This paper makes use of the CRIC method, which preserves the decoupled power flow solution structure but better models the active/reactive coupling. Effective stopping criteria are proposed for the continuation method, which helps to speed up computation. Such stopping criteria are also applied for tracing QV curves for some practical Brazilian power systems, with all operating limits considered