Distribution System Power Flow Research Articles

New approach for the probabilistic power flow of distribution systems based on data clustering

The growing popularity of renewable-based generations along with loads fluctuation and network topology variation has exposed distribution systems to high uncertainties, causing difficulties in operating and planning decisions. In addition, the correlation among various uncertain variables has introduced more complexity to this problem. The probabilistic assessment of power systems with various uncertain variables and with any correlation between them can be efficiently handled by Monte–Carlo simulation (MCS) method, but the calculation burden in this method is heavy and thus it is not appropriate in online applications. Keeping the accuracy of the results, data clustering techniques can be efficiently substituted for this method with much less calculation time and burden. In this study, two methods based on data clustering which can consider the correlation between different variables in a straightforward manner are presented for the probabilistic power flow of distribution systems. In order to demonstrate the efficiency of the proposed methods, IEEE 37 node test feeder and IEEE 123 node test feeder were selected as the case study. The results obtained by the proposed methods were compared with those of the MCS method in terms of accuracy and calculation time.

Decentralized saddle-point dynamics solution for optimal power flow of distribution systems with multi-microgrids

Since various types of distributed renewable energy resources are integrated into distribution systems in the form of microgrids, how to implement the coordinated operation between a distribution system and microgrids is a major concern. This paper focuses on solving the optimal power flow of a distribution system with multiple microgrids based on the decentralized saddle-point dynamics approach. First, the distribution system and the microgrids are regarded as separate entities and their external networks are replaced by Ward equivalent circuits. Hence, the distribution system and microgrids are decoupled so that their linearized power flow models can be built separately. Then, a decentralized quadratic programming model for optimal power flow with the distribution system and microgrids as separate entities is established to achieve low active power loss and high utilization of renewable energy resources. Next, the decentralized saddle-point dynamics approach is applied to solve this model from the viewpoint of the dynamic system control, which transforms the solution of Karsh-Kuhn-Tucker conditions into an asymptotically stable process. The proposed method only needs to exchange the border-bus voltages and equivalent injection powers between the distribution system and each microgrid, which can protect the privacy of different entities and possesses plug-and-play features. Finally, case studies on a real distribution system with two real microgrids are carried out to verify the effectiveness of the proposed method.

An Interval Arithmetic-Based Power Flow Algorithm for Radial Distribution Network with Distributed Generation

This paper presents a primary distribution system power flow analysis in the presence of uncertainties in distributed generation and loads. The algorithm is based on a backward/forward sweep power flow algorithm with power flow updates. The uncertainties are modelled by real compact intervals based on interval arithmetic. A simple and interactive method is used to consider the generator bus voltage controls and reactive power limits. Simulations are presented on a 69-bus, a 104-bus and a 282-bus test distribution system to verify the effectiveness of the proposed method. The power flow solution bounds obtained by the proposed algorithm are compared to those calculated using a Monte Carlo simulation. The results confirm the efficiency of the proposed method which makes it promising to solve real problems of power flow analysis in distribution feeders.

Power flow in radial distribution systems in the presence of harmonics

This paper presents the results of power flow calculations in the presence of harmonics in radial distribution systemsobtained using the decoupled harmonic power flow (DHPF) algorithm. In this algorithm, the interaction among the harmonicfrequencies is assumed to be negligible and hence the calculations are separately performed for every harmonic order of interest. Adetailed methodology for calculating current and voltage high order harmonics, harmonic losses and total harmonic distortion ofvoltage of the electrical distribution networks in the frequency domain is presented. The standard backward/forward sweep method isused for solving the power flow problem at the fundamental frequency. Furthermore, some practical and approximated models ofnetwork components in harmonic analysis are given. The performance of the DHPF approach is studied and evaluated on two standardtest systems with nonlinear loads, the distorted IEEE 18-bus and IEEE 33-bus. Nonlinear loads are treated as harmonic current sourcesthat inject harmonic currents into the system. The DHPF algorithm is verified by comparing its results with those generated bysoftware tools for the analysis of transmission, distribution and industrial power systems (i.g. ETAP and PCFLO). Simulation resultsshow the accuracy and efficiency of the applied procedure for solving the harmonic power flow problem.

A modified affine arithmetic-based power flow analysis for radial distribution system with uncertainty

In a distribution system, the loads and distributed generators connected at a bus have lot of uncertainty due to which the power injections at that bus become uncertain. These uncertainties need to be incorporated in distribution system power flow analysis to get an idea of the uncertainty in the power flow solution. One of the methods used for finding solution intervals for power flow is Monte Carlo simulations. However, Monte Carlo simulations approach suffers from the drawback of large time consumption due to repeated power flows. To overcome this limitation, affine arithmetic based power flow analysis is introduced in literature which is capable of generating solution intervals to the interval power flow problem without the need of repeated power flow analysis. Multiplication operation between two affine terms in conventional affine arithmetic generates an extra noise term in the affine product. In affine based power flow analysis for distribution system, multiplication operation is used repeatedly since backward/forward sweep algorithm is iterative in nature. This generates a large number of noise terms in certain affine parameters which ultimately leads to larger solution intervals for the problem. In the present work, a new formulation of complex affine multiplication is introduced for the affine arithmetic based distribution power flow analysis which does not generate any extra noise term for the resulting complex affine product. The proposed modified affine arithmetic based distribution power flow analysis is tested on IEEE 33, 69, 202 and 874 bus radial distribution systems. All the four test systems are assumed to have distributed generation. The solution intervals obtained are compared with the solution intervals of conventional affine arithmetic based distribution power flow analysis. Results show that the solution intervals of the proposed method are closer to Monte Carlo solution intervals as compared to conventional affine arithmetic based distribution power flow analysis.

Fast Computation of Power Flow in Distribution Systems by Renumbering Nodes

Fast Computation of Power Flow in Distribution Systems by Renumbering Nodes

An optimal reactive power control method for distribution network with soft normally-open points and controlled air-conditioning loads

The paper proposes an optimal reactive power control method for distribution systems with soft normally-open points (SNOP) and considering the direct load control (DLC) of thermostatically controlled air-conditioning loads. The starting voltage constraints of aggregate air-conditioning loads connected into a distribution network is studied according to the direct control mode and the starting characteristic of air-conditioning load. Using the flexible regulating capacity of power flow of SNOP, an optimal model of reactive power flow for distribution systems with SNOP is established to meet the voltage quality of sensitive loads and the starting requirements of aggregate air-conditioning loads. In the model, the load balancing commands of different DLC aggregators, the on/off status of thermostatically controlled air conditioner, the power regulating command of SNOP, the voltage adjusting and reactive power compensation devices are comprehensively controlled in the constraints of reduction balance and starting voltage of air-conditioning loads, as well as the conventional network and voltage constraints. And a multi-objective functions are developed for the objectives of solving the low-voltage problems, minimizing the comfort impacts on users of air-conditioning and minimizing the active power loss of distribution systems. Finally, the simulation results of a practical 53-bus 10 kV distribution system demonstrate the accuracy and effectiveness of the proposed method.

A Novel Direct Power Flow for Distribution Systems with Voltage-Controlled Buses

Large-scale distribution systems (DSs) require an efficient power flow algorithm which can explicitly exploit their characteristics. This paper presents a novel power flow algorithm for radial and weakly meshed distribution systems (WMDSs) using a direct method (DM). The paper also develops a novel approach to simulate the voltage-controlled buses which is becoming increasingly important due to the introduction of distributed generations in DSs. The proposed power flow algorithm is constructed based on simple electrical circuit rules so that only a Z matrix expressing common impedances between loads is required for simulation. For WMDSs, only modification is to use the current divider rule to solve meshes. The simulation of PV-buses is presented using the Newton–Raphson solution algorithm. The validation and comparison of results in different systems show the simplicity and low computations of the proposed method which make it time-saving and very efficient for large-scale DSs.

Chordal Relaxation Based ACOPF for Unbalanced Distribution Systems With DERs and Voltage Regulation Devices

In emerging distribution systems with a proliferation of distributed energy resources (DERs) and flexible demand assets, operation characters of the unbalance network and voltage regulation devices need to be accurately addressed for ensuring the secure and economic operation. This paper focuses on the modeling and solution approach of AC optimal power flow (ACOPF) for unbalanced distribution systems with DERs and voltage regulation transformers (VRT). The ACOPF problem is formulated as a chordal relaxation based semidefinite programming (SDP) model, and a tighter convexification model of VRTs is proposed for mitigating solution inexactness. Analytical conditions are presented and proved to determine whether global optimal solution to the original ACOPF problem can be retrieved from solutions of the chordal relaxation based SDP model. Numerical studies on modified IEEE 34-bus and 8500-node systems show that the proposed approach presents a better computational performance as compared to rank relaxation based SDP approaches and general nonlinear solvers.

Influence of Distributed Generation on Relay Protection in Distribution Network and Protection Scheme

The access of distributed generation to changes the structure, power flow and failure modes of traditional power distribution systems, which may lead to the decrease of sensitivity, malfunction and reclosing of traditional three-stage current protection.etc. Aiming at this problem, this paper based on analyzes the influence of distributed power supply on the relay protection of distribution network, and puts forward the protection scheme of circuit breaker, direction module and inverse time overcurrent protection. Finally, the PSCAD/EMTDC is used to simulate a 10 KV distribution system with distributed generation to verify the effectiveness of the proposed protection scheme.

Taguchi's method for probabilistic three-phase power flow of unbalanced distribution systems with correlated Wind and Photovoltaic Generation Systems

Abstract In this paper, we address the problem of the probabilistic steady-state analysis of an electrical distribution system that includes wind and photovoltaic power plants. We propose a new method that takes into account the uncertainties due to the time variations of power load demands and the random nature of solar and wind energy. The new method extends a probabilistic approach proposed in the relevant literature for balanced electrical distribution systems to unbalanced electrical distribution systems, and it also takes into account the correlation among the random input variables. The method is based on Taguchi's orthogonal arrays. Numerical applications based on an IEEE test system provide evidence of the probabilistic performance of the proposed approach. The results obtained with the proposed method are compared with the results obtained using non-linear Monte Carlo simulation and the Point Estimate Method.

Integrated Transmission and Distribution System Power Flow and Dynamic Simulation Using Mixed Three-Sequence/Three-Phase Modeling

The interactions between distribution and transmission systems have increased significantly in recent years. However, in traditional power system simulation tools, transmission and distribution systems are separately modeled and analyzed. Hence, it is difficult to analyze the impacts of distribution systems on transmission systems and their interactions in detail. To facilitate the analysis of integrated transmission and distribution (T&D) systems, a novel modeling framework is proposed in this paper, where the transmission system is modeled as one subsystem in three-sequence detail, while each distribution system connected to it is represented as a subsystem and modeled in three-phase detail. With this modeling approach, unbalanced conditions at the boundary between T&D systems and within the transmission system can be represented. The integrated T&D power flow is solved by iteratively solving a three-sequence power flow for the transmission system and a three-phase power flow for each distribution system. Furthermore, a new dynamic simulation algorithm for integrated T&D system is proposed. The main challenge in developing this integrated T&D dynamic simulation is associated with different network representations in the transmission and distribution systems. With a partitioned solution approach adopted for dynamic simulation, the multi-area Thevenin equivalent approach is utilized in the network solution step to address this challenge. The proposed algorithms have been tested against an all electromagnetic transient simulation.

Multi-objective distributed wind generation planning in an unbalanced distribution system

In addition to increasing penetration of distributed generation (DG), the distribution system power flow may be significantly impacted by direction and magnitude. This paper proposes a method for optimal placement of wind DG considering the unbalanced operation of distribution systems. The objective function includes static voltage stability index, three-phase unbalance index, system reliability index, and DG investment cost. The untransposed distribution lines and unbalanced load are modelled, and corresponding static voltage stability index and system reliability considering DG penetrations are derived. The expected and stochastic daily distributed generation and demand profiles in four seasons are calculated to improve the accuracy. To solve this multi-objective optimization model, a fuzzy membership function is used to integrate the four individual objectives, and a sensitivity-based method is proposed to solve the model efficiently. Case study on IEEE 13-bus distribution 3-phase networks and 123-node test feeder successfully verifies the performance of the proposed approach.

The initial guess estimation newton method for power flow in distribution systems

With the increasing integration of distributed generations U+0028 DGs U+0029, there is a demand for DGs to play a more important role on the voltage regulation. Meanwhile, the high penetration of DGs could raise a technical problem that the distribution system may operate with bi-directional power flow, leading to the inadequacy of the traditional power flow. Considering this new scenario in distribution system power flow, the convergence theorem is proposed, which contributes to develop a novel selection method of the initial guess closed to the convergent solution. Moreover, to ensure the fast rate of power flow convergence, the theorem of the maximum iterations estimation is also proposed. Based on the two proposed theorems, an Initial Guess Estimation Newton method is proposed, considering different operational status of DGs and initial guess sensitivity simultaneously. Based on the standard node systems, Tongliao grid, and 69 system of USA, three simulation examples are provided to illustrate the effectiveness of the proposed method.

Research on probabilistic optimal power flow of distribution system with multilayer structure based on energy router

The core connotation of global energy interconnection is to realise the large-scale utilisation and sharing of renewable energy, especially distributed renewable energy. In order to realise energy sharing over a wide area and stabilise the impact of intermittent and random output distributed renewable energy on distribution network (DN) under global energy interconnection, a multilayer structure based on energy router for DN is proposed first. Then a multi-objective optimal power flow (OPF) model for the multilayer structure DN is established, which is aimed at the lowest cost of power generation, the minimum pollutant treatment cost and the minimum active power loss. This paper proposes the steady-state power flow model of the energy router embedded DN and formulates the model of OPF problem. Case studies are carried out on a modified IEEE 33-bus distribution system. The role of the energy router on improving the system voltage level is discussed. The results show that the energy router is able to regulate bus voltages of the system, and system operation status is greatly improved.

Cutting planes based relaxed optimal power flow in active distribution systems

Optimal power flow (OPF) has played a significant role in the design, planning and operation of active distribution systems (ADSs). Due to its ability to achieve the optimality with higher computational efficiency, the second order cone programming (SOCP) based on branch flow model (BFM) has received an increasing attention in recent years. However, various sufficient conditions and assumptions are required to ensure the relaxation exactness in the existing literatures. In this study, we introduce the cutting planes to tackle this exactness challenge for general distribution networks especially the ADS with high renewable penetration. Firstly, a typical operation optimization model is presented as an example of OPF in ADS. A general branch flow model based relaxed optimal power flow (BFM-ROPF) model is then formulated as a SOCP problem after conic relaxation. According to these conditions with the objectives which are not monotonously increasing in power injections or branch currents, a total power loss cut (TPLC) is introduced to ensure the conic relaxation exactness. Moreover, a leaf branch current cut (LBCC) is incorporated to prevent the inexactness of SOCR in some leaf branches. Afterwards, the proof of the cutting planes is given to guarantee the optimality and the relaxation exactness of the BFM-ROPF model even though power loss is not included in the objectives. Numerical results based on 33-bus and 69-bus systems are given to verify the effectiveness of the proposed method.

A Study on Cooperative Voltage and Frequency Control Method Using Distributed Generations Considering Large Penetration of Renewable Energy Sources

SUMMARYIn order to solve energy and environmental issues, the introduction of photovoltaics (PVs) has been progressed in recent years. Due to the uncertain PV output fluctuation depending on the weather conditions, the proper frequency management becomes an important issue when a large amount of PVs are included in power systems. On the other hand, since the voltage increase in the end of feeder lines can be caused by the reverse power flow in distribution systems with PVs, it is needed to enhance the voltage controllability. When gas engine generators are included in distribution systems, they can contribute to both frequency and voltage control issues. However, the coordination between those control purposes will be another problem because the frequency and voltage controls have interactions each other. Hence, in this paper, we developed a distributed frequency control method taking into account the voltage constraint in distribution systems.

Loop frame of reference based harmonic power flow for unbalanced radial distribution systems

Abstract In this paper, a three-phase harmonic power flow method for unbalanced radial distribution systems is proposed. The proposed method is based upon the loop frame of reference, rather than the conventional bus frame of reference. In addition, an injection current technique is also applied in the proposed method. The proposed method can be used for both fundamental and harmonic power flow studies. Four three-phase IEEE test feeders are used to prove the accuracy and efficiency of the proposed method. The test results show that the proposed method is robust and reliable for passive power filters set design, especially for full-scale distribution systems.

A quadratic approximation for the optimal power flow in power distribution systems

This paper presents a quadratic approximation for the optimal power flow in power distributions systems. The proposed approach is based on a linearized load flow which is valid for power distribution systems including three-phase unbalanced operation. The main feature of the methodology is its simplicity. The accuracy of the proposed approximation is compared to the non-linear/non-convex formulation of the optimal power flow using different optimization solvers. The studies indicate the proposed approximation provides a very accurate solution for systems with a good voltage profile. Results over a set of 1000 randomly generated test power distribution systems demonstrate this solution can be considered for practical purposes in most of the cases. An analytical solution for the unconstrained problem is also developed. This solution can be used as an initialization point for a more precise formulation of the problem.

Simplified probabilistic voltage stability evaluation considering variable renewable distributed generation in distribution systems

This study investigates the evaluation of static voltage stability using a two-point estimation method (2PEM) and continuation power flow (CPF) in distribution systems. The stochastic distribution generation (DG) units have been considered with their respective probability density function (PDF). The proposed static voltage stability evaluation method first chooses several sample points to replace the PDFs using 2PEM. Then, based on each sample point, the critical static voltage stability value is calculated by CPF. On the basis of the critical values corresponding to all selected sample points, Cornish–Fisher series are used to evaluate the PDF of the critical static voltage stability, and then the static voltage stability state can be obtained. The proposed method has been tested on IEEE 33-bus, PG&E 69-bus and a real case with two stochastic DG units. Comparisons have been made with the Monte Carlo simulation and the first-order second-moment method. The results show that the proposed method has better efficiency and accuracy.