Distribution System Load Flow Research Articles

Probabilistic load flow for distribution systems with uncertain PV generation

Large integration of solar Photo Voltaic (PV) in distribution network has resulted in over-voltage problems. Several control techniques are developed to address over-voltage problem using Deterministic Load Flow (DLF). However, intermittent characteristics of PV generation require Probabilistic Load Flow (PLF) to introduce variability in analysis that is ignored in DLF. The traditional PLF techniques are not suitable for distribution systems and suffer from several drawbacks such as computational burden (Monte Carlo, Conventional convolution), sensitive accuracy with the complexity of system (point estimation method), requirement of necessary linearization (multi-linear simulation) and convergence problem (Gram–Charlier expansion, Cornish Fisher expansion). In this research, Latin Hypercube Sampling with Cholesky Decomposition (LHS-CD) is used to quantify the over-voltage issues with and without the voltage control algorithm in the distribution network with active generation. LHS technique is verified with a test network and real system from an Australian distribution network service provider. Accuracy and computational burden of simulated results are also compared with Monte Carlo simulations.

Unbalanced Radial Distribution System Load Flow and Voltage Profile Enhancement in the presence of Distributed Generators

Unbalanced Radial Distribution System Load Flow and Voltage Profile Enhancement in the presence of Distributed Generators

A binary SFLA for probabilistic three-phase load flow in unbalanced distribution systems with technical constraints

This paper shows that in order to solve a probabilistic three phase load flow in radial distribution networks, it is necessary to apply effective techniques that take into account their technical constraints. Among these constraints, voltage regulation is one of the principal problems to be addressed in photovoltaic distributed generation. This paper applies a new method utilizing Shuffled Frog-Leaping Algorithm and three phase probabilistic load flow combined with the Monte Carlo method to solve this problem. The objective function used is the power losses expected value. Acceptable solutions are reached in a small number of iterations. Results prove that the proposed method can be applied for the keeping of voltages within desired limits at all load nodes of a photovoltaic grid-connected system. To evaluate the performance of photovoltaic system this paper has developed a probabilistic model that takes into account the random nature of solar irradiance and load. Numerical applications are presented and considered regarding the unbalanced distribution system IEEE 13-nodes and including photovoltaic generators at several nodes. The results obtained show the decrease of the power losses due to the presence of distributed generation.

A nonlinear-hybrid fuzzy/probabilistic load flow for radial distribution systems

Uncertainty analysis of future system operation is the key feature of current study. This paper shows that how subjective differences in representing fuzzy inputs can affect the final outputs. We consider a confined range of forecasted samples in terms of fuzzy membership functions as well as the range of historical forecasting errors in terms of probability density functions. On this basis, this paper proposes a combined fuzzy/probabilistic evaluation of distribution system voltages, considering hybrid fuzzy/probabilistic uncertainties for consumption and generation. The proposed method allows the sampled fuzzy inputs to incorporate in a Monte Carlo-based nonlinear fuzzy load flow including Wind Turbine Generating Units (WTGUs). As a result of hybrid uncertainty representation, the evaluation of fuzzy load flow results will be assessed in probabilistic framework. Numerical simulations are performed on the unbalanced IEEE 34-bus test distribution system equipped with WTGUs.

Three-phase load flow

This paper presents a method for calculating three-phase load flow and voltage conditions in radial distribution systems with unbalanced loads. Asymmetries present in the distribution networks are the result of the unbalanced load and inductive and capacitive coupling between the phases. Therefore, the modeling takes into account loads voltage dependency and lines mutual coupling. The calculation is based on fundamental principles of circuit theory: I and II Kirchhoff's law. In order to apply the Kirchhoff's laws, it was necessary to define the network topology in appropriate way by numbering the branches in the network. The accuracy of the algorithm is demonstrated on the IEEE 13 test network.

DSPFAP: Distribution systems power flow analysis package using Matlab graphical user interface (GUI)

AbstractThis paper describes a software package whose purpose is to provide a tool to be used for load flow analysis in Power System Analysis courses. The software package which is called Distribution Systems Power Flow Analysis Package (DSPFAP) uses the graphical user interface (GUI) capabilities of Matlab. The main advantage of the developed package is that the load flow analysis can be achieved in both transmission and distribution levels. The package facilitates different forward/backward sweep‐based algorithms to be used for the distribution systems and conventional Newton–Raphson, Gauss–Seidel algorithms for the transmission system load flow analysis. In addition to that, effect of voltage dependent load models and effects of DGs on the distribution systems load flow solution can be investigated using the program. It is also possible to use conventional algorithms for distribution system load flow analysis in the package. The package can freely be downloaded from the website: http://www.gyte.edu.tr/Dosya/102/power/. © 2009 Wiley Periodicals, Inc. Comput Appl Eng Educ 18: 1–13, 2010; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20209

Incorporation of Uncertainties in Radial Distribution System Load Flow with Voltage-dependent Loads

In this article, application of interval arithmetic is proposed for considering the uncertainties of the input parameters in the power flow solution of a balanced radial distribution system with voltage-dependent loads. The uncertainties in both the feeder parameters and the load demands have been considered. The feasibility of the proposed method has been tested on two different balanced radial distribution systems by comparing the results obtained by this technique with those obtained by repeated power flow solutions. Further, it is also shown that the use of voltage-dependent loads (as compared to constant power loads) in an interval load flow solution provides more accurate estimation of the bus voltage limits.

Fuzzy load flow in balanced and unbalanced radial distribution systems incorporating composite load model

This paper presents a fuzzy approach load flow for balanced and unbalanced radial distribution systems with incorporating load model. Fuzzy set theory proposes an appropriate way to model inexactly expressed information and data which have uncertainty. In this paper the combination of fuzzy models and techniques for electrical distribution systems is presented. The theories relating to the fuzzy numbers are simplified into a form suitable for practical application. The utilization of fuzzy approach is demonstrated by a radial load flow method where the voltage in the substation and the power demands are represented by fuzzy numbers.

Modeling of unified power quality conditioner (UPQC) in distribution systems load flow

This paper presents modeling of unified power quality conditioner (UPQC) in load flow calculations for steady-state voltage compensation. An accurate model for this device is derived to use in load flow calculations. The rating of this device as well as direction of reactive power injection required to compensate voltage to the desired value (1 p.u.) is derived and discussed analytically and mathematically using phasor diagram method. Since performance of the compensator varies when it reaches to its maximum capacity, modeling of UPQC in its maximum rating of reactive power injection is derived. The validity of the proposed model is examined using two standard distribution systems consisting of 33 and 69 nodes, respectively. The best location of UPQC for under voltage problem mitigation in the distribution network is determined. The results show the validity of the proposed model for UPQC in large distribution systems.

Distribution Systems Forward/Backward Sweep-based Power Flow Algorithms: A Review and Comparison Study

Because of different characteristic features of distribution networks, such as radial structure and high R/X ratio, distribution system load flow analysis differs significantly from transmission systems. Accordingly, a number of methods that are specially designed for the solution of the power flow problem in radial distribution systems are found in the literature. Most of the developed methods are based on the forward/backward sweep processes for the solution of the ladder networks. In this article, various distribution system load flow algorithms, based on the forward/backward sweeps, are reviewed, and their convergence ability is quantitatively evaluated for different loading conditions, R/X ratios, and sub-station voltage levels. Moreover, the effects of static load modeling on the convergence characteristics of algorithms are also investigated.

Incorporation of a new wind turbine generating system model into distribution systems load flow analysis

AbstractThis paper describes a new model for wind turbine generating systems (WTGSs) that is widely used as distributed generation sources. The model is developed by using the bi‐quadratic equation, which is generally used for the calculation of the line voltages in distribution systems' load flow analysis, and facilitates computation of real and reactive power outputs of the WTGSs for a specified wind speed and terminal voltage. The developed model is validated with an experimental setup composed by an induction generator coupled with an induction motor as a prime mover. In addition to that, measured values are also compared with the calculated values, obtained by using the turbine models found in the literature. The incorporation of the developed model into some well‐known distribution systems' load flow algorithms is detailed. The effect of WTGSs on the power losses, voltage profile of radial distribution systems are evaluated for the sample test systems. Additionally, the performance of the load flow algorithms with the new model are examined and found to be robust and reliable. Copyright © 2008 John Wiley & Sons, Ltd.

Modeling of D-STATCOM in distribution systems load flow

This paper presents modeling of Distribution STATCOM (D-STATCOM) in load flow calculations for the steady-state voltage compensation. An accurate model for D-STATCOM is derived to use in load flow calculations. The rating of this device as well as the direction of required reactive power injection for voltage compensation in the desired value (1 p.u.) is derived and discussed analytically and mathematically by the phasor diagram method. Furthermore, an efficient method for node and line identification used in load flow calculations is presented. The validity of the proposed model is examined by using two standard distribution systems consisting of 33 and 69 nodes, respectively. The best location of D-STATCOM for under voltage problem mitigation approach in the distribution networks is determined. The results validate the proposed model for D-STATCOM in large distribution systems.

Probabilistic three-phase load flow for unbalanced electrical distribution systems with wind farms

A probabilistic method is proposed to take into account the uncertainties of loads and wind production in electrical unbalanced distribution systems. The proposed method is based on Monte-Carlo simulation applied to the nonlinear three-phase load flow equations including wind farms, thereby taking into account all load and line unbalances that can characterise the distribution systems. The method allows the evaluation of phase-voltage and unbalance factor probability functions and in particular the maximum values and 95th percentiles, being the statistical measures of greatest interest in many international standards for power quality. Numerical applications are presented and discussed with reference to the three-phase unbalanced IEEE 34-bus test distribution system in presence of wind farms connected at different busbars.

A Unified Three-Phase Transformer Model for Distribution Load Flow Calculations

This paper provides a unified method to model three-phase transformers for distribution system load flow calculations, especially when the matrix singularity caused by the transformer configuration arises. This paper shows that the singularity appears only in certain transformer admittance submatrices and only in certain transformer configurations. The unified method presented in this paper can solve the voltage/current equations in the forward/backward sweep algorithm for various types of transformer configurations, whether or not the corresponding admittance submatrices are singular. Comprehensive comparisons have been made between the proposed approach and other methods. Test results demonstrate the validity and effectiveness of the proposed method.

A direct approach for distribution system load flow solutions

A direct approach for unbalanced three-phase distribution load flow solutions is proposed in this paper. The special topological characteristics of distribution networks have been fully utilized to make the direct solution possible. Two developed matrices-the bus-injection to branch-current matrix and the branch-current to bus-voltage matrix-and a simple matrix multiplication are used to obtain load flow solutions. Due to the distinctive solution techniques of the proposed method, the time-consuming LU decomposition and forward/backward substitution of the Jacobian matrix or Y admittance matrix required in the traditional load flow methods are no longer necessary. Therefore, the proposed method is robust and time-efficient. Test results demonstrate the validity of the proposed method. The proposed method shows great potential to be used in distribution automation applications.

Data structure for radial distribution system load flow analysis

Owing to the radial nature and high R/X ratio, radial distribution systems (RDS) employ a special recursive technique for distribution load flow (DLF). An efficient method for DLF plays a critical role in automation algorithms of RDS whose scope encompasses fault isolation, network reconfiguration and service restoration. The ability of automation algorithms to handle these complex tasks that require frequent topology changes in the RDS demands a dynamic topology processor based on a well-defined data structure. The purpose of this paper is to formulate a dynamic data structure (DDS) and an algorithm that generates the DDS of the RDS as an R-tree. The proposed DDS algorithm generates the DDS and is used as a topology processor in the DLF algorithm. The resulting DLF algorithm is computationally efficient and can handle rapidly changing topology by updating the R-tree. The pseudocodes for the DDS algorithm and the overall recursive algorithm for DLF are presented. Various RDS have been tested with the proposed method and the results demonstrate its efficiency over other known methods of DLF.

A novel and fast three-phase load flow for unbalanced radial distribution systems

A novel and fast three-phase load flow algorithm for unbalanced radial distribution systems is proposed in this paper. The proposed method uses branch voltages as state variables and employs the Newton-Raphson (NR) algorithm to solve the load flow problem. By utilizing branch voltages as state variables, a constant Jacobian matrix can be obtained, and a building algorithm for Jacobian matrix is then developed from the observation of the constant Jacobian matrix. A solution technique, which takes the network structure into account to avoid the time-consuming lower and upper triangular (LU) factorization, is also developed. Since the factorization procedure can be avoided, the proposed method can save computation time. For any power system equipment, if its equivalent current injection or admittance matrix can be obtained, it can be integrated into the proposed method. Test results demonstrate that by integrating the Jacobian building algorithm and efficient solution technique, the proposed method is an effective three-phase load flow method and has great potential for real-time use.

A Novel and Fast Three-Phase Load Flow for Unbalanced Radial Distribution Systems

A novel and fast three-phase load flow algorithm for unbalanced radial distribution systems is proposed in this paper. The proposed method uses branch voltages as state variables and employs the Newton-Raphson algorithm to solve the load flow problem. By utilizing branch voltages as state variables, a constant Jacobian matrix can be obtained and a building algorithm for Jacobian matrix is then developed from the observation of the constant Jacobian matrix. A solution technique, which takes the network structure into account to avoid the time-consuming LU factorization, is also developed. Since the factorization procedure can be avoided, the proposed method can save computation time. For any power system equipment, if its equivalent current injection or admittance matrix can be obtained, it can be integrated into the proposed method. Test results demonstrate that by integrating the Jacobian building algorithm and efficient solution technique, the proposed method is an effective three-phase load flow method and has great potential for real-time use.

Probabilistic load flow in distribution systems containing dispersed wind power generation

A probabilistic model for the active power produced and the reactive power absorbed by wind turbines (WTs) equipped with induction generators is developed which takes into account the probabilistic nature of short-term wind velocity forecasts. The model is incorporated in a radial distribution load flow program which allows probabilistic modeling of loads at the MV/LV substation level and of voltage regulator effects at the beginning of the MV distribution feeder. Using this program probabilistic short- and medium-term predictions of the power flows at the various sections of the feeder and of voltage profiles at all nodes of the network are obtained.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Distribution system load flow calculation with microcomputer implementation

In this paper, a load flow calculation method for a radial distribution system is developed. The proposed method, which is derived from a Z-loop analysis, is very straightforward and simple without unnecessary mathematical approximations. It requires the same storage size as the Gauss-Seidel method, but less computation time than the conventional Newton-Raphson program. It is attractive for accurate or approximate off-line and on-line routines and contingency calculations for radial systems. The proposed solution algorithm can be implemented directly and efficiently into microcomputers with limited storage capacities. To examine the effectiveness, three normal radial distribution systems for 13-, 22-, and 58-bus systems were studied by the proposed method, and the convergence characteristics of a 43-bus ill-conditioned system are compared with the Newton-Raphson method. The proposed method is recommended for distribution system load flow analysis.