Distribution System Power Flow Research Articles

A Flexible Mixed-Integer Linear Programming Approach to the AC Optimal Power Flow in Distribution Systems

In this paper, we propose a flexible mixed-integer linear programming formulation of the AC OPF problem for distribution systems, using convexification and linearization techniques. The proposed formulation allows the representation of discrete decisions via integer decision variables, captures the nonlinear behavior of the electrical network via approximations of controllable accuracy, and can be solved to global optimality with commercial optimization solvers. The formulation is based on conventional variables that describe network behavior, which ensures its flexibility and the possibility of application to various distribution system problems, as we indicate with case studies.

Interval Reactive Power Optimization for Distribution System with DGs

A reactive power optimization method based on interval arithmetic is presented to solve the uncertainty of the output of distributed generation (DG) and the effects of load fluctuation. The concept of interval number and interval arithmetic is introduced to model the interval power flow of distribution system, which is iterated by using the Krawczyk-Moore operator. The objective function is to minimize the interval midpoint value of system’s power loss, with taking the interval voltage constraints into consideration for the interval reactive power optimization model. A modified IEEE 14-bus system is used to validate the proposed model and its Particle Swarm Optimization (PSO) algorithm. The simulation results show that the proposed method is effective.

Analysis on Affecting Factors of Harmonic Power Flow

This paper aims to study on the main factors which influence harmonic power flow in the power system with high power nonlinear loads. Firstly, the mathematical model of harmonic power is derived theoretically. Secondly, the simulation model of a parallel operation within two nonlinear rectifier loads is established in the Matlab/Simulink. The method of active power statistical curve is utilized to analyze the harmonic power flow of the distribution system at different operation modes for rectifier loads. The simulation results show that the main factor that affects the harmonic power flow distribution is the control angle in the rectifier load. Therefore, harmonic active power statistical method proposed in this paper is of great significance to determine the location of the main harmonic sources in the power system.

Distribution System Fault Recovery with Undispatchable Distributed Generations

Considering the probabilistic of the wind power and the solar power, a fault recovery method for distribution systems with the wind power and the solar power is presented in this paper. For the wind power, a simplified steady-state equivalent model of an asynchronous wind generator is added into the Jacobian matrix to consider the impact of the wind power on systems. For the solar power, its output is considered as an injected power which is related with solar irradiance. Three-point estimate is employed to solve the probabilistic power flow of distribution systems with the wind power and the solar power. The restoration is described as a multi-objective problem with the mean of the system loss and the number of switch operations. Fast elitist non-dominated sorting partheno-genetic algorithm is used to solve this multi-objective problem. IEEE 33-bus system is used as an example and the results show that the models and algorithms in this paper are efficient.

Point estimate method for probabilistic load flow of an unbalanced power distribution system with correlated wind and solar sources

Context: The electric parameters of the power networks are usually analysed through deterministic power flows; however, the variation in load demands and power fluctuation of renewable generators cannot be considered with the deterministic power flows because it uses specific power values. The probabilistic power flow methods are better for this purpose since they apply techniques to include and reflect the uncertainty of input variables on the results obtained.Objective: This paper extends the Point Estimate Method (PEM) applied to the probabilistic power flow of an unbalanced power distribution system with dispersed generation and variable power factors. This method is applied to include uncertainties of loads and power sources such as wind and solar. As PEM requires independent input random variables, but usually there is spatial correlation between loads or power sources; therefore, Cholesky decomposition is applied to deal with this situation.Method: In this paper are combined the scheme 2m+1 of the Point Estimate Method with the Cholesky decomposition and some approximation methodologies to estimate the cumulative distribution function of some electrical parameters.Results: The results obtained are the moments about the mean of the output variables, which are used in conjunction with some approximation methodologies to obtain an estimation of the Cumulative Distribution Function for nodes or branch parameters. The proposed methodology is tested on the three-phase unbalanced IEEE 123-node test system, and results are compared with those obtained from the benchmark Monte Carlo simulation.Conclusions: There are comments on some pertinent information about Point Estimate Method performance on this kind of power systems.

An affine arithmetic-based algorithm for radial distribution system power flow with uncertainties

This letter presents an algorithm for radial distribution system power flow in the presence of uncertainties. To reduce the overestimation of bounds yielded by correlation of variables in interval arithmetic (IA), affine arithmetic (AA) is applied in this study to carry out tests of distribution system power flow. Compared with the algorithm based on IA, the proposed algorithm narrows the gap between the upper and lower bounds of the power flow solution. IEEE 33-bus and 69-bus test systems are used to demonstrate the effectiveness of the proposed algorithm.

Optimal Allocation of Energy Storage System for Risk Mitigation of DISCOs With High Renewable Penetrations

Along with the increasing penetration of renewable energy, distribution system power flow may be significantly altered in terms of direction and magnitude. This will make delivering reliable power, on demand, a major challenge. In this paper, a novel battery energy storage system (BESS) based energy acquisition model is proposed for the operation of distribution companies (DISCOs) in regulating price or locational marginal price (LMP) mechanisms, while considering energy provision options within DISCO controlled areas. Based on this new model, a new battery operation strategy is proposed for better utilization of energy storage system (ESS) and mitigation operational risk from price volatility. Meanwhile, optimal sizing and siting decisions for BESS is obtained through a cost-benefit analysis method, which aims at maximizing the DISCO's profit from energy transactions, system planning and operation cost savings. The proposed energy acquisition model and ESS control strategy are verified on a modified IEEE 15-bus distribution network, and risk mitigation is also quantified in two different markets. The promising results show that the capacity requirement for ESS can be reduced and the operational risk can also be mitigated.

Modeling of doubly fed induction generators for distribution system power flow analysis

Large-scale integration of Wind Generators (WGs) with distribution systems is underway right across the globe in a drive to harness green energy. The Doubly Fed Induction Generator (DFIG) is an important type of WG due to its robustness and versatility. Its accurate and efficient modeling is very important in distribution systems planning and analysis studies, as the older approximate representation method (the constant PQ model) is no longer sufficient given the scale of integration of WGs. This paper proposes a new three-phase model for the DFIG, compatible with unbalanced three-phase distribution systems, by deriving an analytical representation of its three major components, namely the wind turbine, the voltage source converter, and the wound-rotor induction machine. The proposed model has a set of nonlinear equations that yields the total three-phase active and reactive powers injected into the connected bus by the DFIG as a function of the bus voltage and wind speed. This proposed model is integrated with a three-phased unbalanced power flow method and reported in this paper. The proposed DFIG model is verified using Matlab–Simulink. IEEE 37-bus test system data from the IEEE Distribution System sub-committee is used to benchmark the results of the power flow method.

Power flow in PME distribution systems during an open neutral condition

The open neutral condition, in distribution networks, can cause significant damage to customer installations. Due to this, the continuity of the neutral conductor is important to the power utilities. In this paper, a power flow algorithm for three-phase four-wire distribution networks with protective multiple earthing (PME), during an open neutral condition, is presented. This algorithm is based on a modified backwards-forwards technique. Additionally, the return current flow is explicitly modeled. Results from three different distribution feeders with different load unbalance and topology are presented and discussed. Furthermore, the effects of the grounding resistances, the load model (constant admittance or constant power), and the neutral breakage point (abruption point) on the voltage levels, are investigated.

A benefits analysis for wind turbine allocation in a power distribution system

This paper proposes an algorithm to analyze the long-term benefits of Wind Turbine (WT) allocation at the demand side of a power distribution system. The benefits are evaluated based on the wind electricity generation and the avoidance of CO2 emissions. The objective function includes the investment cost, maintenance cost, and the cost of loss reduction, subjective to operating limits and line flow constraints. Taking load growth into account, Particle Swarm Optimization (PSO) with a power flow algorithm is proposed to solve this problem. To enhance the performance of the optimization approach, a load flow model with Equivalent Current Injection (ECI) is used to analyze the power flow of distribution systems. By considering the power generation of WTs, electricity prices, and carbon trading prices, the long-term benefits of the installation of wind turbines in different scenarios are evaluated. Examples of IEEE 69-bus systems are presented to illustrate the efficiency and feasibility of the proposed algorithm. Simulation results can help decision makers in selecting the proper installation sites for WTs, as well as in determining the tradeoff between optimal investment and environmental policy for future electricity and carbon markets.

Application of BFNN in power flow calculation in smart distribution grid

Power flow study is performed to ensure the whole electricity system operating safely, stably and reliably. A back/forward sweep neural network (BFNN) algorithm is put forward based on numbering all nodes using breadth first search plan. All neurons use the same excitation function. The BFNN has a clear structure with a high approximation speed and high precision. Each neuron acts as the threshold to its adjacent neuron in front. In BFNN method weights adjusting means voltage adjusting, hence, when the learning process according to BP algorithm ended, the desired voltages are acquired. And then the power flow can be derived. In this paper the convergence of BFNN has also been validated. The proposed BFNN algorithm is proved to have a better approximation effect than using conditional back/forward method by computing power flow in Tongliao 16-bus distribution system in Inner Mongolia.

Application of cascaded H-bridge distribution-static synchronous series compensator in electrical distribution system power flow control

In this study, the power flow control of the electrical distribution network using multilevel converter-based distribution-static synchronous series compensator is presented. The conventional radial distribution network can be changed into a meshed grid because of this device. Using multilevel converter topology, the device can be installed directly in series with the line, connecting two separate feeders from different substations together. Two control methods are proposed to control the power flow in the line. The first control strategy uses a fixed DC bus voltage. Enhancing the performance of the multilevel converter, a novel control strategy using variable DC bus voltage is introduced while maintaining the appropriate dynamic response. The new strategy can reduce the total harmonic distortion (THD) of the injected voltage and losses of the power converter compared with the fixed DC bus method. A new soft start method is also proposed to connect the separate feeders together safely. The feasibility of the control strategies is investigated through simulation and experimental results.

Improvement Of Loadability In Distribution System Using Genetic Algorithm

Generally during recent decades due to development of power systems, methods for delivering electrical energy to consumers, and because of voltage variations is a very important problem ,the power plants follow this criteria. The good solution for improving transfer and distribution of electrical power majority of consumers prefer to use energy near loads .So small units that are connected to distribution system named Decentralized or Dispersed Generation. Deregulated in power industry and development of renewable energies are most important factors in developing this type of electricity generation. Today DG has a key role in electrical distribution systems. For example we can refer to improving reliability indices, improvement of stability and reduction of losses in power system. One of key problems in using DG’s, is allocation of these sources in distribution networks. Load ability in distribution systems and its improvement has an effective role in operation of power systems. However, placement of distributed generation sources in order to improve distribution system load ability index was not considered, we show DG placement and allocation with genetic algorithm optimization method maximize load ability of power systems .This method implemented on IEEE Standard bench marks. The results show effectiveness of proposed algorithm .Another benefits of DG in selected positions are also studied and compared. KeywordsVoltage Profile, Electric Power Losses, Distributed Generation (DG), Distribution System. 1-INTRODUCTION As predicted distributed generation will have a growing role in future of power systems, and also in recent years, this role has been slowly increasing [1]. Atomic Energy Agency (IAEA), offers following definition for distributed generation: The units of generation that give service to customer in place[2]. Council on Large Electric Systems(CIGRE), offers following definition for distributed generation[1]: Advanced Computing: An International Journal ( ACIJ ), Vol.3, No.3, May 2012 2 1 -Not to be planned centrally 2 Not to be transferred centrally 3Usually is connected to distribution network 4 Capacity between 50 to100 MW However, best definition for DG is, the source of electric energy is connected to distribution networks or directly to consumer side. The nominal amounts of these generations varied, but usually their generation capacity range from a few KW to 10 MW. These units are in substations and in distribution feeders, near loads. The effects of DG on voltage profile, line losses, short circuit current, amount of harmonic injection, stability and reliability of network before installation should be evaluated. DG placement and size are very important, because it’s non-optimal installation increases losses and rises costs. Therefore to considering above items and consumption patterns application of an efficient and powerful optimization method is a suitable solution for system planning engineering. 2APPROACH TO QUANTIFY THE BENEFITS OF DG In order to evaluate and quantify benefits of distributed generation, suitable mathematical models must be employed along with distribution system models and power flow calculations to arrive at indices of benefits. Among many benefits three major ones are considered: Voltage profile improvement, line loss reduction and line transmission apparent power improvement index. 2-1-LINE LOSS REDUCTION INDEX (LLRI) Another major benefit offered by installation of DG is reduction in electrical line losses [3]. By installing DG, line currents can be reduced, thus helping reduce electrical line losses. The proposed line loss reduction index (LLRI) is defined as: (1) Where, is total line losses in system with employment of DG and is total line losses in system without DG and it can be: (2) Where, Ii is per unit line current in distribution line i with employment of DG, Ri is line resistance (pu/km), Di is distribution line length (km), and M is number of lines in system. Similarly, is expressed as:

A generalized power flow analysis for distribution systems with high penetration of distributed generation

In this paper, the element incidence matrix has been extended to develop a comprehensive three-phase distribution system power flow program for radial topology. Three-phase overhead or underground primary feeders and double-phase or single-phase line sections near the end of the feeder laterals have been considered. Unbalanced loads with different types including constant power, constant current and constant impedance are modeled at the system buses. Substation voltage regulator (SVR) consisting of three single phase units connected in wye or two single-phase units connected in open delta are modeled to satisfy the desired voltage level along the feeder. The mathematical model of distributed generation (DG) connected as PQ and PV buses are integrated into the power flow program to simulate the penetration of DGs in the distribution systems. The proposed method has been tested and compared with different IEEE test feeders result. The developed algorithm has been used to study the impact of both SVR and high penetration of DG on voltage profile and system power losses.

A robust decoupled power flow for distribution systems

This paper presents a robust decoupled power flow technique based on line current flows in rectangular coordinates for radial distribution systems. The functions of line current flows and their equivalent values, which are computed from the specified load powers, are linearised around a known operating point and transformed through a constant matrix with a view to eliminate the off-diagonal blocks of the Jacobian. The transformation enables perfect decoupling of the power flow problem into two sub-problems without making any assumptions on voltage magnitudes, angles and r/ x ratios. The approach is simple and uses a sparse constant sub-Jacobian matrix that needs to be factorised only once for both real and reactive sub-problems; and is solved iteratively similar to FDPF technique. Test results of 15, 29 and 69 node systems indicate that the proposed method is efficient, robust, accurate and exhibits potential for on-line applications.

Loop frame of reference based three-phase power flow for unbalanced radial distribution systems

This paper introduces a novel three-phase power flow approach for unbalanced radial distribution systems. The proposed approach is developed based on the loop frame of reference, rather than the traditional bus frame of reference. On the basis of the loop frame of reference, a simple direct iterative method in impedance form is applied. Basic graph theory and injection current technique are also applied in the proposed approach. The clear theoretical foundation and the simple topology of the radial distribution network make the proposed method efficient and reliable. To demonstrate the better convergence performance and the efficiency of the proposed approach, four three-phase IEEE test feeders are used for comparisons. The test results show that the proposed method has robust convergence characteristics and high performance, especially for large-scale radial distribution systems.

다수 PV 시스템 배전계통 연계 시 개선된 전압조정 방법

현재의 배전계통의 전압은 변전소에서 단방향 조류를 고려하여 LDC에 의한 전압조정방법으로 ULTC 변압기의 랩을 변환하여 공급전압을 적정범위 내에서 유지되도록 운전하고 있다. 그러나 현재의 배전계통 운용은 소용량에서 대규모 용량에 이르기까지 다양한 용량의 PV 시스템이 배전계동에 연계되어 운전되는 것을 반영하지 못하고 있는 실정이다. 때문에 다수의 PV 시스템이 계통에 연계되어 양방향 조류가 발생하고 이로 인해 연계점의 전압변동이 발생하여도 이를 효과적으로 조정하지 못하여 계통의 전압이 적정범위 내에서 운용되지 못하는 경우가 발생할 수 있다.<BR> 따라서 본 논문에서는 다수 PV 시스템의 연계에 따른 양방향 조류의 발생을 고려하고 연계점의 전압변동에 따른 계통의 전압을 효과적으로 제어할 수 있도록 실시간 감시가 이루어지는 PV 시스템의 특정을 이용하고 기존의 LDC 전압조정방법을 개선하여 PV 시스템 연계 시에도 변전소에서 계통의 전압을 적정범위 내에서 조정할 수 있는 개선된 전압조정방법을 제안하였다.

A Novel Method Mixed Power Flow in Transmission and Distribution Systems by Using Master-Slave Splitting Method

Traditionally, transmission and distribution power flows are studied and developed separately. In order to face keen competition in the market, the coordinated operation between transmission and distribution systems is required. Therefore, in order to balance the boundary mismatch between the transmission and distribution system models existing in the results of traditional power-flow methods, the transmission and distribution systems are studied as a whole in this article. A novel master–slave splitting iterative method is developed for solving the hybrid mixed power-flow problem. Several case studies are carried out, and the accuracy, convergence, efficiency, and reliability of the proposed method are validated.

STATCOM Controls for a Self-Excited Induction Generator Feeding Random Loads

Voltage and frequency fluctuations due to random load variation are the most important power-quality problem in a self-excited induction generator (SEIG) system. Traditionally, instantaneous voltage regulation can be achieved using static synchronous compensators (STATCOMs) to condition the reactive power flow in a power distribution system. However, their widespread use might be limited by temporary loss of synchronization owing to system frequency fluctuations. In this paper, an advanced, laboratory STATCOM was constructed based on the relative rotation speed theory, which is essential in estimating the frequency deviation and assisting the STATCOM in synchronism with system frequency. As a result, the stator voltage fluctuation due to random load variations can be eliminated and effective regulations in generator speed and mechanical power are thus able to be guaranteed. Both simulation and experimental results are in agreement with the proposed controller, leading to the conclusion that simultaneous voltage and frequency control for SEIG feeding the balanced three-phase loads is feasible.

Calculation of distribution system voltage and power flow state using measured values

AbstractThis paper describes a techique of calculating voltage and power flow state of a distribution system using the information measured with two or more switches with sensors installed in a distribution system. In the proposed technique, a set of the power distribution section where two or more switches with a sensor are connected is defined as the large section, and the active power and reactive power consumption in the large section are calculated based on measurement information, voltage (RMS), current (RMS), and power factor. Using the simple distribution system model consisting of the large sections, the power consumption of the large section is calculated by the power flow calculation to separate power consumption and power distribution loss. It is distributed to the small sections that constitute the large section, and detailed power flow calculation is performed. Verification of the proposed technique and basic estimation of the calculation error were performed using the simple power distribution system model. © 2008 Wiley Periodicals, Inc. Electr Eng Jpn, 164(4): 33–42, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20416