Newton-Raphson Power Flow Method Research Articles

Optimal Allocation of Photovoltaic Distributed Generations in Radial Distribution Networks

Photovoltaic distributed generation (PVDG) is a noteworthy form of distributed energy generation that boasts a multitude of advantages. It not only produces absolutely no greenhouse gas emissions but also demands minimal maintenance. Consequently, PVDG has found widespread applications within distribution networks (DNs), particularly in the realm of improving network efficiency. In this research study, the dingo optimization algorithm (DOA) played a pivotal role in optimizing PVDGs with the primary aim of enhancing the performance of DNs. The crux of this optimization effort revolved around formulating an objective function that represented the cumulative active power losses that occurred across all branches of the network. The DOA was then effectively used to evaluate the most suitable capacities and positions for the PVDG units. To address the power flow challenges inherent to DNs, this study used the Newton–Raphson power flow method. To gauge the effectiveness of DOA in allocating PVDG units, it was rigorously compared to other metaheuristic optimization algorithms previously documented in the literature. The entire methodology was implemented using MATLAB and validated using the IEEE 33-bus DN. The performance of the network was scrutinized under normal, light, and heavy loading conditions. Subsequently, the approach was also applied to a practical Ajinde 62-bus DN. The research findings yielded crucial insights. For the IEEE 33-bus DN, it was determined that the optimal locations for PVDG units were buses 13, 25, and 33, with recommended capacities of 833, 532, and 866 kW, respectively. Similarly, in the context of the Ajinde 62-bus network, buses 17, 27, and 33 were identified as the prime locations for PVDGs, each with optimal sizes of 757, 150, and 1097 kW, respectively. Remarkably, the introduction of PVDGs led to substantial enhancements in network performance. For instance, in the IEEE 33-bus DN, the smallest voltage magnitude increased to 0.966 p.u. under normal loads, 0.9971 p.u. under light loads, and 0.96004 p.u. under heavy loads. These improvements translated into a significant reduction in active power losses—61.21% under normal conditions, 17.84% under light loads, and 33.31% under heavy loads. Similarly, in the case of the Ajinde 62-bus DN, the smallest voltage magnitude reached 0.9787 p.u., accompanied by an impressive 71.05% reduction in active power losses. In conclusion, the DOA exhibited remarkable efficacy in the strategic allocation of PVDGs, leading to substantial enhancements in DN performance across diverse loading conditions.

Quasi-static Power Flow and Fault Analysis of Photovoltaic Farm

This report first analysis quasi static power flow for photovoltaic power plant. Then, fault analysis for different symmetrical and asymmetrical fault is done. The system used is IEEE 39 bus New England system that a Photovoltaic farm with 500 MW power is connected to bus 24. Newton-Raphson Power flow method is used with Gauss-Jordan elimination method for matrix inversion in this power flow analysis. Different operation condition including faults are also considered for fault at bus 16. The results are validated with simulation in MATLAB software.

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.

Quality Improvement of 20 KV Voltage Profile Of PT. PLN (Persero) Ketapang According to SPLN No.72 Of 1987

This study aims to determine the magnitude of the increase in the voltage profile of the 20.kV distribution network system of PT. PLN (Persero) Ketapang with the installation of reactive power injection equipment. The research method used is the Newton Raphson power flow method with MATLAB simulation program. From the results of these calculations, Pawan 2 and Pawan 6 load buses each have a voltage drop above 5%, which is found on 42 buses. To overcome this, reactive power injection (Qc) was carried out: 150 KVAR on bus 26 of Pawan 2, and 900 KVAR on bus 40 and 46, and 600 KVAR on bus 51 of Pawan 6. This leads to the increase in voltage drop percentage on Pawan 2 and Pawan 6, thus, the profile meets SPLN No. 72 of 1987, which is below 5%.

Optimal short-term operation of pumped-storage power plants with differential evolution algorithm

In this study, the optimal short-term operation of the lossy electric power system which included the pumped-storage power generation unit (Ps) was carried out. The problem is quite complex in terms of its constraints and being a mathematically difficult problem. Therefore, in order to obtain optimal solutions of the problem, differential evolution algorithm (DE) was used. In this study, one day operation of a system, which includes thermal and Ps units, solved with different optimization algorithms in the literature was addressed. The addressed system was solved in two different ways. First of all, the solution is made assuming that the system consists only of thermal generation units. Then, a Ps unit was added to a bus in the system and it was solved again and the benefit obtained was discussed. In the solution of the sample system, transmission line losses are taken into consideration and Newton-Raphson power flow method was used to calculate these losses. The sample system was solved 30 times with DE and the optimal solution values were determined. All possible constraints in problem solving were provided through the punishment method. The results obtained from the solutions of the sample systems were compared and discussed.

Power flow modeling of islanded AC microgrids with hierarchical control

This paper presents the power flow modeling of droop-controlled distributed generation units with secondary frequency and voltage restoration control for hierarchically controlled islanded microgrids. These models are incorporated in the conventional Newton-Raphson power flow method as a new bus, without the necessity of a slack bus, and include the gains of the control systems that influence the steady-state solution. Two case studies are addressed. In the first case study, comparisons of the proposed models against the steady-state solutions obtained with PSCAD and Simscape Power System of Simulink, where the closed-loop controls are explicitly modeled, are presented. In the second case study, the proposed method is contrasted against the droop-based approach. The results obtained exhibit low computing effort, reliability, and effectiveness of the proposed models since quadratic convergence behavior is maintained independently of the size and topology of the microgrid. Besides, it is demonstrated that hierarchical and droop controllers lead to different solutions, which confirms the necessity of including the hierarchical control in the power flow model.

Current-based Newton-Raphson power flow calculation for AT-fed railway power supply systems

This paper proposes a current-based Newton-Raphson power flow method for an autotransformer (AT)-fed railway power supply system. The power flow formulation based on the NR method for such a multi-conductor system is revised. The train’s position variation and load variation cases were studied on the impacts of a dynamically moving train to the performance of the proposed power flow method. The Nakhon Ratchasima – Nong Khai railway line was used to study the convergence characteristics of the proposed method when implementing in a practical situation. The results of the proposed NR method were compared with those of the Gauss-Seidel (GS) and sequential linear power flow (SLPF) method for the same power system. The analysis and comparison of convergence behaviour of all three methods have been done in details. By varying train’s position, the GS method showed the great drop in the number of iterations and execution time at the AT’s positions but it appeared to be the maximum execution time for the SLPF method, while the proposed NR did not show substantial changes. For the case of load variation, GS and SLPF method showed an increase in the number of iterations and execution time with the load while the proposed NR was almost unchanging with the load. Regardless of memory usage, the proposed NR showed better convergence for both train position and load variation cases.

Optimal location strategy for distributed generation to maximize system voltage stability based on line sensitivity factors

This paper presents a combination strategy to determine the optimal location of PV distributed generation units (PV-DGs) in terms of maximizing the power system voltage stability level. The voltage collapse power indices (VCPIs) is chosen to access the voltage stability level of a system. To eliminate the need of iterations, a new line power flow calculation method based on the line sensitivity factors (LSFs) is developed. It could precisely compute out VCPI without executing AC power flow program. Combined with the economic optimization software HOMER to determine the sizes and quantities of PV-DGs, the optimal buses to connect PV-DGs are selected by minimizing the sum of VCPIs. The proposed location strategy is validated by multiple IEEE test systems. The numerical simulation results demonstrate that the proposed method is accurate on VCPI calculations and has the decreased computation time compared with the Newton-Raphson power flow method. Through the continuous power flow results, it is verified that the optimal DG configuration selected by the proposed strategy could maximize the overall voltage stability margin of the system.

Influence and Strategy of Electric Vehicle Charging on Distribution Network Voltage Based on Uncertainty Charging Habit

With the increasing scale of the use of electric vehicles, impact of electric vehicle charging on the distribution system cannot be ignored. Considering uncertainty in the charging behavior, large-scale disorderly charging will cause the voltage deviation of distribution network exceeds the specified value. In the paper, based on the IEEE33 node as an example, the goal is to minimum each node voltage deviation by to controlling charge power, considering the constraints of the charging energy and the charging time, and optimized by the genetic algorithm. By using Newton Raphson power flow method, the voltage offset of each node before and after optimization is obtained, and the effectiveness of the charging load optimization model is verified by comparing and analyzing.

Contingency Analysis of South Bandung Electric Power System

Electric power transmission system must operate reliably and continuously, but in fact there are many disturbance that affect the reliability and stability of the power system. This study aims to determine the weak elements of power system when release of components occur. This study uses simulation with Newton Raphson power flow method for contingency analysis. The study is located in South Bandung electric power system with voltage of 150 kV. In this study, the object of contingency analysis is IBT-II 500/150 KV at peak periods load in 2013 to evaluate the system reliability when release of the Inter bus Transformer (IBT). Selection of the component is based that IBT is the most important component in the power supply that should be maintain continuously. The results of the study and analysis show that in the event of contingency almost all bus voltage has decreased below the limit allowable voltage and IBT-I get overloaded, then the maneuver is performed according to the procedures of specified load. The results of this study can be use as a reference for the electric power operating system which has conditions similar to the simulated cases.

Estimating the saddle-node bifurcation point of static power systems using the holomorphic embedding method

Voltage stability studies have been progressively gaining importance in the power engineering community. Predicting the saddle-node bifurcation point (SNBP) of a power system has become more critical as the power-system loading has increased in many places without a concomitant increase in transmission resources. Since a Newton–Raphson power-flow method is inherently unstable near the SNBP, adaptations such as continuation methods have been used as stabilizers. A new class of nonlinear equation solvers known as the holomorphic embedding method (HEM) is theoretically guaranteed to find the high-voltage solution to the power-flow problem, if one exists, up to the SNBP, provided sufficient precision is used and the conditions of Stahl’s theorem are satisfied by the equation set. In this paper, four different HEM-based methods to estimate the saddle-node bifurcation point of a power system, are proposed and compared in terms of accuracy as well as computational efficiency.

Large-scale power system controlled islanding based on Backward Elimination Method and Primary Maximum Expansion Areas considering static voltage stability

This paper proposes a novel approach for separation of bulk power system into several stable subsystems following a severe disturbance. An interconnected power system may become unstable due to wide area contingency when it is operated close to the stability boundaries as a result of increased demand, power industry restructuring and competition in the deregulated electricity markets. Meanwhile, large-scale power system controlled splitting is the last resort to prevent catastrophic cascading outages and wide area blackout. The proposed method of this paper reduces the huge initial search space of the islanding strategy to only interface boundary network by clustering the coherent generators and simplifying the network graph. Then, Backward Elimination Method (BEM) based on Primary Maximum Expansion Areas (PMEAs) has been proposed to generate all proper islanding scenarios in the simplified graph. The Newton–Raphson power flow method and Q–V modal analysis have been used to evaluate the steady state stability of the islands in each generated scenario. Binary Imperialistic Competitive Algorithm (BICA) has then been applied to minimize total load-generation mismatch considering no-isolated bus, voltage permitted range and static voltage stability constraints. Comprehensive discussions have been provided using the simulations on NPCC 68-bus test system. The results demonstrate the speed, effectiveness and capability of the proposed strategy to generate fast feasible splitting solutions considering static and dynamic stability.

Development of a New Model of IPFC for Power Flow in Multi-Transmission Lines

Interline Power Flow Controller (IPFC) is one of series series controlled Flexible Alternating Current Transmission System (FACTS) devices, which has the capability of controlling the power flow in multi transmission lines. In this paper, Power Injection Model (PIM) is proposed by using voltage source converters (VSCs). The proposed model is incorporated in Newton-Raphson (NR) power flow solution method and analyzed with a MATLAB program. A study on variation of power flow, bus voltages in all transmission lines and buses for different values of IPFC parameters has been carried out on standard 2 machine 5 bus system. General Terms FACTS, Newton-Raphson power flow method, multi transmission lines.

A simple implementation of power mismatch STATCOM model into current injection Newton–Raphson power-flow method

This paper presents a simple implementation of Static Shunt Compensator (STATCOM) into Newton–Raphson current injection load flow method. The controlled STATCOM bus in the network is represented by voltage-controlled bus with zero active power generation at the required voltage magnitudes. The power mismatch equation of the connected STATCOM bus is included in Newton–Raphson current injection load flow algorithm, while the other PQ buses are represented by current mismatch equations. Moreover, the parameters of STATCOM can be calculated during iterative process and the final value will be updated after the convergence is achieved. This representation of generator buses reduces the number of required equations with respect to the classical and improved versions of the current injection methods. In addition of that the developed model reduces the complexities of the computer program codes and enhances the reusability by avoiding modifications in the Jacobian matrix. The performance of the developed STATCOM model has been tested using standard IEEE systems.

Harmonic Propagation and Interaction Evaluation between Small-Scale Wind Farms and Nonlinear Loads

Distributed generation is a flexible and effective way to utilize renewable energy. The dispersed generators are quite close to the load, and pose some power quality problems such as harmonic current emissions. This paper focuses on the harmonic propagation and interaction between a small-scale wind farm and nonlinear loads in the distribution grid. Firstly, by setting the wind turbines as P – Q(V) nodes, the paper discusses the expanding Newton-Raphson power flow method for the wind farm. Then the generalized gamma mixture models are proposed to study the non-characteristic harmonic propagation of the wind farm, which are based on Gaussian mixture models, improved phasor clustering and generalized Gamma models. After the integration of the small-scale wind farm, harmonic emissions of nonlinear loads will become random and fluctuating due to the non-stationary wind power. Furthermore, in this paper the harmonic coupled admittance matrix model of nonlinear loads combined with a wind farm is deduced by rigorous formulas. Then the harmonic propagation and interaction between a real wind farm and nonlinear loads are analyzed by the harmonic coupled admittance matrix and generalized gamma mixture models. Finally, the proposed models and methods are verified through the corresponding simulation models in MATLAB/SIMULINK and PSCAD/EMTDC.

New network sensitivity-based approach for real-time complex power flow calculation

This study proposes a novel network sensitivity-based approach to solving complex power flow calculation problems in real time. A new sensitivity factor, named Jacobian-based distribution factor (JBDF), is used for the calculation of active and reactive power flow in transmission systems. It is derived from the Jacobian matrix of the base case Newton–Raphson power flow solution, and kept constant during real-time line flow calculation. Unlike well-known distribution factors, such as generation shift distribution factor (GSDF), generalised generation shift distribution factor (GGDF) and Z-bus distribution factor (ZBD), this approach reflects changes in complex injection power. Changes in load conditions from base case loads, with either conforming or non-conforming changes in complex power in each bus, can be used to rapidly compute active and reactive power flow without iterations. The proposed approach was tested on IEEE 14-Bus and 30-Bus systems. Numerical results demonstrate that the proposed approach is not only superior to previous distribution factors, but also compares favourably with the Newton–Raphson power flow method. It is well suited to real-time applications in steady-state security control and optimal dispatch.

Improvement of Power System Security under Network Contingency with Static VAR Compensator

SVC is incorporated in Newton Raphson method in which Power Flow Solution is a solution of the network under normal operation as well as network contingency, the model of SVC i.e. SVC Susceptance Model is discussed. Newton Raphson Power flow method has been developed for the steady behavior of large complex power systems, it allows the study of power flow under abnormal conditions as well as normal conditions. It is shown that how the system power losses are decreased after incorporating the SVC in this model. It is also shown that how the SVC is useful in network contingency. The results are generated for 5-Bus system.

Voltage Stability of Medium and Low Voltage Distribution Networks with Wind Generation Based on Hilbert-Huang Transform

Nowadays the voltage instability problems occur in the distribution grid due to the integration of more and more fluctuant distributed generators. This paper focuses on voltage stability of distribution networks with wind generation. A voltage stability index is presented, and calculated by an expanding Newton-Raphson power flow method in which the wind power generation nodes are modified according to the P-Q(V) character. In order to obtain the key components of fluctuant wind power, the Hilbert-Huang transform algorithm is utilized to reveal the inherent characteristics of wind power. The extrema extending method based on the mirror periodic is used in the empirical mode decomposition and can handle the end effects. According to the Hilbert spectrum and instantaneous energy of each intrinsic mode functions, the components with lower instantaneous frequency are selected to rebuild the wind power. The new rebuilt series consist of stationary and monotonic components which are smoother, and the rebuilt series can reflect the main fluctuant characteristic of the initial wind power data by comparing the index.

Avaliação da confiabilidade composta sob o enfoque do bem estar utilizando simulação Monte Carlo não-seqüencial

A avaliação da confiabilidade de sistemas de potência compostos têm sido realizada utilizando critérios e métodos determinísticos e probabilísticos. A avaliação da confiabilidade sob o enfoque do bem estar é uma nova proposta que combina critérios determinísticos com metodologias probabilísticas e define os estados do sistema como saudáveis, marginais ou de risco. Este trabalho apresenta a avaliação da confiabilidade composta sob o enfoque do bem-estar utilizando simulação Monte Carlo Não-Seqüencial. É assumida a hipótese de coerência do sistema e os índices de freqüência são calculados utilizando o método da probabilidade condicional. A avaliação do desempenho do sistema é feita através da solução do fluxo de potência pelo método de Newton-Raphson e da solução do fluxo de potência ótimo pelo método dos Pontos Interiores. São apresentados resultados para o sistema IEEE-RTS com e sem curva de carga. Demonstra-se que tanto a método escolhido como a hipótese assumida são válidos e fornecem uma alternativa eficiente para a análise do bem-estar de sistemas de grande porte.

Assessment of available transfer capability for practical power systems with combined economic emission dispatch

This paper describes the assessment of available transfer capability (ATC) with capacity benefit and transmission reliability margins of practical power systems with combined economic emission dispatch (CEED). ATC is a measure of unutilized capability of transmission system subjected to wheeling transactions without violating transmission constraints at given time and load. In this paper, capacity benefit margin (CBM) is incorporated in the test systems by reserving powers in transmission lines. The transmission reliability margin (TRM) is implemented either by making any one of the transmission lines as out of order or by making a generator out at a time. CEED problem has been formulated as a multi-objective problem by considering both economy and emission simultaniously. This bi-objective CEED problem is converted into single objective function using price penalty factor approach. In the proposed approach, Newton Raphson power flow method and Evolutionary Programming (EP) algorithm have been combined used for ATC calculation considering CBM, TRM and economic emission dispatch respectively. A novel modified price penalty factor is proposed in this paper to solve the CEED problem. A non-linear scaling factor is also included in EP algorithm to improve the convergence performance. Assessment of ATC in combined economic emission environment has been tested both on IEEE-30 and Indian utility-62 bus systems with line flow constraints. Simultaneous bilateral and multilateral wheeling transactions have been carried out in the test systems for the assessment of ATC. The solutions obtained are quite encouraging and useful in the present deregulated environment.