Load Flow Formulation Research Articles

A new method to incorporate three-phase power transformer model into distribution system load flow analysis

This paper proposes a new and simple method to incorporate three-phase power transformer model into distribution system load flow (DSLF) analysis. The objective of the present work is to find a robust and efficient technique for modeling and integrating power transformer in the DSLF analysis. The proposed transformer model is derived based on nodal admittance matrix and formulated by using the symmetrical component theory. Load flow formulation in terms of branch currents and nodal voltages is also proposed in this paper to enable integrating the model into the DSLF analysis. Singularity that makes the calculations in forward/backward sweep (FBS) algorithm is difficult to be carried out. It can be avoided in the method. The proposed model is verified by using the standard IEEE test system.

The Equivalence between Successive Approximations and Matricial Load Flow Formulations

This paper shows the equivalence of the matricial form of the classical backward/forward load flow formulation for distribution networks with the recently developed successive approximations (SA) load flow approach. Both formulations allow solving the load flow problem in meshed and radial distribution grids even if these are operated with alternating current (AC) or direct current (DC) technologies. Both load flow methods are completely described in this research to make a fair comparison between them and demonstrate their equivalence. Numerical comparisons in the 33- and 69-bus test feeder with radial topology show that both methods have the same number of iterations to find the solution with a convergence error defined as 1×10−10.

On the design of three-dimensional mechanical metamaterials using load flow visualization

Mechanical metamaterials have generated considerable interest due to their unique attributes such as light weight, high strength, enhanced energy absorption, high impact, and fracture resistance. However, most of the design methodologies in literature are predominantly computational and provide limited user-insight (especially for three-dimensional designs). This paper presents an alternative two-phase design methodology for the conceptual synthesis of three-dimensional tunable mechanical metamaterials. In the first phase, we obtain a kinematically feasible conceptual topology using a building block-based design approach. In the second phase, the conceptual topology is refined using shape/size optimization to meet specific elastic properties and conform to manufacturing requirements. The building block-based approach uses a unique visualization formulation that represents the deformation behavior as ‘load flow’ in the constituent members. An immersive virtual reality tool is developed to mitigate the visual difficulty in the design of three-dimensional microstructures. Furthermore, the load flow formulation is used to propose a qualitative classification scheme for negative Poisson’s ratio elastic metamaterials based on relative values of shear moduli and bi-axial elastic stiffnesses. The efficacy of the framework is illustrated through the design of microstructures with negative Poisson’s ratios in spatial directions and the ability to achieve isotropic microstructures from a qualitative understanding of the conceptual designs. Such a framework can lead to the design of synthetic materials that have potential applications in multifunctional structures, shape morphing structures, and soft robotics.

Conceptual Insightful Synthesis of Spatial Compliant Mechanisms Using the Load Flow Formulation

Abstract Conceptual design of spatial compliant mechanisms with distinct input and output ports may be hard because of its complex interconnected topology and is currently accomplished by computationally intensive automated techniques. This paper proposes a user insightful method for generating conceptual compliant topology solutions. The method builds on recent advances where the compliant mechanism deformation is represented as load flow in its constituent members. The nature of load flow enables functional decomposition of compliant mechanisms into maximally decoupled building blocks, namely, a transmitter member and a constraint member. The proposed design methodology seeks to synthesize spatial compliant designs by systematically combining transmitter-constraint members first, identifying kinematically feasible transmitter load paths between input(s) and output(s), and then selecting appropriate constraints that enforce the load path. The paper proposes four design steps to generate feasible solutions and four additional guidelines to optimize load paths and constraint orientations. The method is applied with equal ease to three spatial complaint mechanism examples that belong to single-input single-output, multiple-input single output, and single-input multiple-output mechanisms.

An Improved Harmonic Load Flow Formulation

The paper contributes an improved harmonic load flow formulation with fewer convergence problems but the same accurate results as traditional formulations. The proposed formulation approaches the harmonic load flow problem as a single nonlinear equation system where the harmonic bus voltage influence on nonlinear load behavior is considered and harmonic bus voltages at linear buses are not included as unknowns. This formulation allows any sort of nonlinear load to be considered and uses the Newton-Raphson method with true Jacobian matrix to reduce the inherent increase in the number of iterations caused by the presence of highly distorted bus voltages. The numerical results obtained when solving a three-bus network operating under highly distorted bus voltages using traditional harmonic load flow formulations and the improved formulation are comparatively discussed.

Improved load flow formulation for radial distribution networks

This paper aims to provide an improved load flow formulation for solving load flow problem in radial distribution networks. The improved algorithm is formulated from the basic Kirchoff’s voltage law. The proposed method does not need any matrix multiplication, and the voltage equation is derived to compute the voltage at each node. The proposed method is then tested on 28-bus, IEEE-33 and IEEE-69 systems of radial distribution networks with different resistance to reactance ratio and different condition of loads. The simulation results from the suggested algorithm show that the proposed method has fast convergence capability compared with other existing methods. A very good agreement is achieved.

Gauss-Seidel Method for Calculation of Unbalanced Load Flow

Three phase load flow is a study that will provide an overview of the voltage conditions, phase angle, current, power and power losses of each bus in each phase a, b and c. A three-phase load flow study can be used in a three-phase power system control and planning operation. The purpose of this paper is to create a three-phase load flow formulation for unbalanced load conditions. Unbalanced loads on the electric power system will affect consumers, namely a decrease in the voltage received by consumers. Three-phase power flow calculations using the Gauss-Seidel Method (GSM) and computation are done using Matlab software which will be tested on the IEEE 5-bus system. The simulation results show that the unbalanced load flow converges at 32 iterations, the total power on the reference bus (slack bus) is 54.840 MW for phase a, 53.119 MW for phase b, and 64.039 MW for phase c. The IEEE 5-bus system has the largest voltage drop occurring on bus 5 which is 7.7%, 6.9% and 8.9% respectively for phases a, b and c. The biggest power losses occur at line bus 1 to bus 2 at 0.912 MW, 0.854 MW and 1,228 MW or 2.30%, 2.20% and 2.67% respectively for phases a, b and c.

Maximum entropy based probabilistic load flow calculation for power system integrated with wind power generation

Distributed generation including wind turbine (WT) and photovoltaic panel increased very fast in recent years around the world, challenging the conventional way of probabilistic load flow (PLF) calculation. Reliable and efficient PLF method is required to take into account such changing. This paper studies the maximum entropy probabilistic density function reconstruction method based on cumulant arithmetic of linearized load flow formulation, and then develops a maximum entropy based PLF (ME-PLF) calculation algorithm for power system integrated with wind power generation (WPG). Comparing to traditional Gram–Charlier expansion based PLF (GC-PLF) calculation method, the proposed ME-PLF calculation algorithm can obtain more reliable and accurate probabilistic density functions (PDFs) of bus voltages and branch flows in various WT parameter scenarios. It can solve the limitation of GC-PLF calculation method that mistakenly gaining negative values in tail regions of PDFs. Linear dependence between active and reactive power injections of WPG can also be effectively considered by the modified cumulant calculation framework. Accuracy and efficiency of the proposed approach are validated with some test systems. Uncertainties yielded by the wind speed variations, WT locations, power factor fluctuations are considered.

Hybrid real–complex current injection-based load flow formulation

This paper presents a new current injection-based load flow procedure in which the Y-bus matrix becomes the main building block of the Jacobian. Starting from a conventional complex formulation, an augmented incremental model is developed comprising both complex and real unknowns, corresponding to PQ and voltage-regulated buses respectively. Then, details are provided on the incorporation of voltage regulating devices (PV buses and tap changers) into the proposed hybrid model. Test results are presented showing that, when solution adjustments are considered, the proposed approach is competitive with the conventional power mismatch-based Newton's method, and performs much better than sensitivity-based schemes usually adopted in combination with current injection-based load flow solutions.

Application of Particle Swarm Optimization for Transmission Network Expansion Planning with Security Constraints

In this study, a new discrete parallel Particle Swarm Optimization (PSO) method is presented for long term Transmission Network Expansion Planning (TNEP) with security constraints. The procedure includes obtaining the expansion planning with the minimum investment cost using a model based on DC load flow formulation. (N-1) contingency is included in this model. The Particle Swarm Optimization algorithm presented in this study is used to solve the planning problem for two different models: without security constraints and with security constraints. Also to solve the problem of transmission expansion planning for a medium network, new improved particle swarm optimization algorithms, the so called, Parallel Particle Swarm Optimization (PPSO) is proposed in this research. The algorithm presents high performances for such networks. The performances with this new algorithm are shown to be better than the ones with the standard PSO. Simulation results show the effectiveness of the parallel particle swarm optimization algorithm.

Distribution power flow method based on a real quasi-symmetric matrix

This paper presents a new load flow formulation to solve active and passive electric distribution networks. The fundamental idea discussed here is how to obtain the power flow solution by using the elements of a unique quasi-symmetric matrix called TRX in the iterative process. The method is formulated for single-phase balanced and three-phase unbalanced radially operated networks. It works with real variables as opposed to complex variables used in previous backward/forward sweep algorithms discussed in literature. The proposed TRX matrix constitutes a complete database by including information of network topology structure as well as branch impedances of the distribution feeder. Data arrangement is suitable to be exchanged under standard Common Information Model (CIM) under Distribution Management Systems (DMS) environment allowing an efficient computation of the state of the system for on-line and off-line study applications. The proposed methodology was applied on a group of IEEE test systems and a real distribution system of 49,000 nodes.

The Effect of Induction Motor Modeling in theContext of Voltage Sensitivity: Combined Loads and Reactive Power Generation, on Electric Networks Steady State Analysis

This paper presents the steady state induction motor modeling, since these devices have significant impact on voltage stability of Electric Power Systems. This work is carried out in the context of voltage dependency of both: combined loads and reactive power generation. In studies of induction motor voltage stability, the modeling of electrical parameters of this device is as important of the stiffness of electrical system itsef. Besides, the synchronous generator considers voltage reactive power limits due to maximum armature current, maximum and minimum field current as well as under excitation limiters. In this development, the analysis tool is the Jacobian Matrix Minimum Singular Value (MSV) of the load flow formulation and its associated left and right Singular Vectors. This induction motor model is included in an ordinary load flow program and results from studies of a 9 bus system, are presented.

Unbalanced Phase-to-Phase Voltage Compensators Applied to Radial Distribution Feeders

This paper describes an application of a thyristor-controlled reactive power compensator (TCRC), which aims at individually controlling phase-to-phase voltage imbalancing in radial distribution feeders. The compensator model is straightforward included into the classical three-phase load flow formulation. The Newton-Raphson iterative solution is obtained through an algorithm based on the orthogonal Givens rotation. The solution method allows to overcome the usual ill-conditioned Jacobian matrix problem arised from radial networks with high R/X ratios. Large amount of simulations are carried out in order to evaluate the TCRC model robustness.

Determinação do ponto de máximo carregamento de sistemas de potência utilizando o fluxo de carga desacoplado rápido parametrizado

Os métodos de fluxo de carga por Newton-Raphson e fluxo de carga desacoplado rápido convencionais são considerados inadequados para a obtenção do ponto de máximo carregamento de sistemas de potência, devido à problemas de mal-condicionamento neste ponto crítico e na sua vizinhança. Neste ponto a matriz Jacobiana do método de Newton-Raphson torna-se singular e considera-se que não são mais válidas as hipóteses de desacoplamento P-V e Q-teta utilizadas para a formulação do método fluxo de carga desacoplado rápido. No entanto, mostra-se neste trabalho, que com pequenas modificações, as versões XB e BX do fluxo de carga desacoplado rápido tornam-se adequadas para a obtenção do ponto de máximo carregamento. Estas novas versões modificadas são comparadas entre si com o intuito de explicitar suas características, assim como da influência da atuação dos limites de geração de potência reativa e de tap's de transformadores. Os resultados obtidos para os sistemas testes do IEEE (14, 30, 57 e 118 barras) mostram que as características de convergência das versões originais são preservadas. Além disso, durante o traçado das curvas PV, os diversos métodos podem ser comutados entre si possibilitando o cálculo de todos os pontos da curva com um número reduzido de iterações.

Load modelling for analysis of power‐system harmonics under unbalanced conditions

AbstractThis paper analyses the load‐harmonic modelling under unbalanced conditions. It presents a harmonic characterization of linear three‐phase loads (three‐phase P‐Q consumptions) for different impedance configurations and analytical models for an ideal six‐ and twelve‐pulse converter supplied by unbalanced voltages, too. The models of these linear and non‐linear loads are incorporated to the three‐phase harmonic load‐flow formulation. A 15‐bus network is presented to study the different load behaviour.

Fuzzy-logic method for adjustment of variable parameters in load-flow calculation

The paper presents a new approach using fuzzy logic to adjust variable parameters so as to meet constraints during load-flow study. Parameters to be adjusted include transmission-line impedance, phase angle and transformer tap position, and the constraints are transmission-line power flow and bus-voltage magnitude. Versatile apparatus which are used to tune these parameters include the thyristor-controlled series compensator, thyristor-controlled phase shifter, unified power-flow controller and on-load tap changer. The proposed approach is particularly aimed at assisting convergence in load flow programs. The parameters to be adjusted are decoupled from the main body of the load-flow formulation. The methodology for parameter adjustment is conducted by using fuzzy logic.

Neural network load-flow

The paper is devoted to the development of a neural network architecture which implements the Newton-Raphson algorithm for solving the set of nonlinear equations of power-system load-flow analysis. The principal context is that of online network analysis in energy management systems with particular reference to the optimal power-flow function. The author shows that the complete Newton-Raphson load-flow formulation maps into an array of two-layer neural networks. The development starts from a formulation for solving as a minimisation problem the linearised equation system to which the Newton-Raphson sequence leads at each iteration. For that purpose, an objective function in quadratic form is derived. A neural network structure is given which implements the steepest descent method for minimising this objective function. It is shown that the weighting coefficients of neural networks are formed from element values in the Jacobian matrix of Newton-Raphson load-flow analysis. When the Jacobian matrix is nonsingular, the quadratic objective function derived has a unique and global minimum. A principal feature of the extensive parallel processing capability of the architecture developed is that the computing time of load-flow analysis is independent of the number of nodes in the power network for which analysis is carried out. For a sample section of a power network, and by software simulation, the architecture which the paper seeks to report gives solutions which are identical with those from a standard sequential processor load-flow program.

Transformer magnetizing current and iron-core losses in harmonic power flow

The problem of modifying the harmonic power flow analysis to permit the inclusion of nonlinear anisotropic transformers and computation of their iron-core (and copper) losses are discussed. The nonlinear model used for transformers is capable of simulating saturation of iron-cores, anisotropy of laminations, and the iron-core and copper losses associated with anisotropic transformers, but simple enough to be included in the harmonic power flow algorithm without deteriorating its convergence properties. The dependency of iron-core losses on the maximum value of the total (fundamental and harmonic) flux density and the fact that iron-core losses are a function of the waveform of the induced voltage/spl minus/that is its harmonic phase shifts with respect to the fundamental phase angle/spl minus/are included. The induced voltage is transformed from frequency domain to time domain: the instantaneous induced voltage and the computed /spl lambda/-i characteristics are employed to compute the instantaneous magnetizing and core-loss currents. Thereafter a transformation is made from time domain back to frequency domain to compute the fundamental and harmonic components of the above-mentioned currents. Therefore, transformer harmonic couplings are properly modeled and included in the analysis. The modified harmonic load flow formulation is applied to a balanced three-phase feeder consisting of a grounded-wye, grounded-wye nonlinear anisotropic transformer and linear and nonlinear loads. >

Voltage contingency selection technique for security assessment

The paper presents a fast and accurate technique for ranking transmission line outages according to the severity of their effects on busbar voltages. To simulate each contingency case, the proposed technique uses the DC formulation with compensation method to compute the post outage angle and the superdecoupled load flow formulation, and compensation method to derive the post outage voltage. The quadratic voltage performance index for every line contingency is then computed, and the results are subsequently sorted in descending order, according to the severity of effects. Computational results of this technique, applied to different test systems, are presented.

An operations-oriented formulation and solution to the load flow problem

This paper presents an operations-oriented formulation and solution to the load flow problem. In this approach all the unit real power outputs are assumed specified and the objective is to calculate the bus loads. This fundamental change is useful in some power system problems and is also closer to the actual problem facing a load flow user. Different solution approaches, including a decoupled method, are proposed to solve the above problem. The numerical and analytical properties of this new decoupled load flow approach are similar to those of the conventional decoupled method. The main advantages of this proposed approach are: all the bus generations can be specified, a slack or swing bus need not be defined, and losses are independent of a choice of reference bus. This fundamental change in the load flow formulation has various applications. These include transmission loss evaluation, loss penalty factor calculation, and study applications in energy management systems.