Fortescue Transformations for three-phase power flow analysis in distribution networks

The traditional power flow and fault analysis methods fail to meet the requirements in both performance and accuracy aspects in the distribution network applications. This is due to the unbalanced multiphase nature of the distribution network and also due to the emerging penetration of renewable generation at the distribution level. This paper proposes a comprehensive method for power flow solution and fault analysis of multiphase unbalanced distribution networks with high penetration of inverter-interfaced DERs. Also, the self-protection scheme employed for the inverter of the DERs is also formulated in the proposed method. Performance of the proposed method has been assessed by simulations on a sample distribution network.

A modified Gauss–Seidel algorithm of three-phase power flow analysis in distribution networks

This paper presents the results of power flow calculations in unbalanced three-phase radial distribution networks with nonlinear loads obtained using the decoupled harmonic power flow (DHPF) method. The method is based on three-phase models of distribution network components and the current injection technique. Performances of the method are evaluated on the standard IEEE 13-bus test network. The DHPF method is verified by comparing its results with those generated by the software tool for the analysis of transmission, distribution, and industrial electrical power systems (i.e., DIgSILENT PowerFactory). It is shown that the DHPF method for solving the harmonic power flow (HPF) problem in unbalanced three-phase distribution networks provides effective and high-quality solutions.

In terms of characteristics in urban active power distribution networks and trend of increasing penetration in distributed power, loss reduction problems in urban power distribution networks are studied in this paper. Considering not only random fluctuations of distributed power sources and loads, but also energy efficiency load management technology, air conditioning load, lighting load, and water heater load in controllable energy efficiency load are focused as research objects in this paper where its sensitivity to various influencing factors is analyzed. Moreover, mathematical models of controllable energy efficiency loads for air conditioning, lighting, and water heaters are established to implement mathematical modules for comprehensive damage reduction measures and improved harmony search algorithm is adopted. In addition, optimized load management is performed on the basis of it. Besides it, according to analysis and calculation of actual distribution network in certain city, correctness and superiority of research method are verified, and impact of optimized energy management technology on network loss of distribution network is analyzed as well.

The Colombian power system is being modified by the large-scale integration of renewable energy resources and energy storage systems, in conjunction with the microgrid concept that originates the possibility of alternating and direct current grids or hybrid between them. Here, we propose a classical gradient conjugate method to solve linear algebraic equations without matrix inversions, to address the power flow problem in electrical direct current networks with constant power loads, to contribute with the paradigm of microgrids operated in direct current. This methodology can be applied to the power flow equations since the admittance matrix is positive definite and diagonal dominant which guarantees convergence of the power flow problems. Numerical simulations evidence the applicability of the gradient conjugate method to solve power flow problems in direct current networks with radial and mesh topologies. All the simulations are conducted in MATLAB software version 2017a licensed by the Universidad Tecnológica de Bolivar, Colombia.

The use of distributed optimization for solving optimal power flow (OPF) problems in distribution networks is increasing as the number of controllable devices and the span of service areas increase. However, the performance of the distributed optimization algorithm largely depends on the availability and quality of communication links between the computing entities. In this paper, we evaluate the performance of the alternating direction method of multipliers (ADMM) for solving the OPF problem for volt-VAr optimization (VVO) under non-ideal communication. The overall problem is formulated by considering the unbalanced operation of multi-phase distribution networks. The algorithm's performance is first analyzed, assuming there is an ideal communication between computing entities, which serves as a benchmark for further analysis. Then, two non-ideal communication models, namely (1) sporadic communication failure and (2) communication under a noisy transmission, are applied to the information exchange architecture of the ADMM. Extensive numerical experiments are conducted with two test systems, the IEEE 123-bus feeder and a 2522-bus network scaled down from the IEEE 8500-bus system; these are used to evaluate the performance of the algorithm. The results indicate that the ADMM-based distributed VVO algorithm has deteriorated performance under high levels of communication failure and high levels of noise injection. Additionally, although the centralized-VVO counterpart has some computational superiority when the overall problem is convex and no communication impairments exist, the distributed-VVO has superior immunized solution performance under realistic communication constraints.

In this chapter, a three-phase power-flow and harmonic-converter model are combined and solved using both the sequential and unified Newton's methods. Interaction between the three-phase power flow and a three-phase harmonic converter model has been solved using both decoupled and full Newton methods. The decoupled method displays good convergence if a linearising shunt is present but is slow because the Jacobian matrices need to be recalculated and factorised at every iteration. The full Newton method (with constant Jacobian), is faster and displays more robust convergence. The decoupled method is compatible with any existing three-phase power flow, including a polar fast-decoupled type. A special but simple three-phase power flow is required for the unified method as the converter model must be framed in real variables. Overall, code for the unified method is shorter and less complicated, as there is only one set of sparse storage, mismatch evaluation, convergence checking, etc. The effect of not modelling the power-flow/distortion interaction is a moderate underestimate of unbalance in the power-flow solution, and a large underestimate of distortion at low order noncharacteristic harmonics in the converter model. The AC-DC iterative algorithm can easily be extended into a general purpose model with the capability of including several AC systems, DC systems, possibly with multiple terminals in each system, and all integrated with the power-flow equations. This is essentially a software engineering task, as each half pole contributes a block to the main diagonal of the system Jacobian matrix, with diagonal matrices coupling to other harmonic sources in the same system. The main task is to code the program so as to be versatile, easy to use and modular.

Low voltages and high power loss are two main problems in distribution network especially in remote area. To solve these problems, typical events of low voltage in distribution network need to be analyzed and identify the similarities. Furthermore, building general optimization model for low voltage in distribution network and proposing improved strategies related to such problems are also necessary. This paper proposes optimization model and strategies against low voltage using Matlab as the main platform with objective functions and several constraints. The particle swarm optimization (PSO) is used to solve the problem. With the open DSS COM interface connected to Matlab, the open DSS are called to calculate distribution network 3-phase power flow repeatedly. Finally, the optimizing strategy, including transformer tap positions and capacitors in each node are obtained. Results from simulations verify the effectiveness and feasibility of the proposed model.

In this paper, load modelling has been done in electrical distribution system using local real time test data. This distribution system supplies base loads, residential, industrial, commercial and composite loads. Using power and current-mismatch functions in polar form, a comprehensive framework for applying the Newton–Raphson method to solve power flow problems is presented. The Newton–Raphson approach for solving power flow problems can be applied in six different ways using these two mismatch functions. For load (PQ)buses and generator (PV) buses, we propose a theoretical framework for analyzing these versions. In addition, we compare newly created versions of the Newton power flow method to current variants in this study. Numerical studies on distribution networks are used to study the convergence behavior of all approaches. The measurements are formed for short term load forecasting with different types of realistic loads such as base loads, residential, industrial, commercial and composite loads. The long-term load forecasting and their losses also has been performed along with short term load forecasting. The results are obtained and validated through MATLAB.

小水电以分布式发电的形式在配电网并网发电，改变了传统的配电网的运行方式，引起配电网枯水期电压偏低、丰水期电压偏高、线路末端电压随季节波动较大等问题。本文对含小水电配电网电压问题分析得出，小水电的接入使配电网从无源网络变为有源网络，由原来的单向潮流变为双向潮流，当丰水期小水电发电量较大时潮流反送到主网中，引起配电网电压升高。同时提出了通过改变网络结构并结合并联补偿的方法对电压进行控制，改善配电网的电压质量。 Traditional operation mode of distribution network was altered with the integration of small hy-dropower in it, which causes the problem that the voltage of distribution network drops in dry season, increases in wet season, and the voltage fluctuates greatly with seasons especially at the end of the line. Analysis on voltage problem in distribution network in this paper draws the conclusion that in wet season, the voltage rises since the power flow contrary sends to the main network when the small hydropower station’s generating capacity increases. This paper also presents a method of voltage control by changing the distribution network structure, combining the method of installing parallel compensating devises, which can improve the quality of voltage in distribution network.

The voltage rise problem in distribution networks has been discussed as the foremost concern against the penetration of large amounts of photovoltaics (PVs). As a solution of such a problem, using voltage regulation facilities such as SVC (Static Var Compensator) or Loop power flow controller has been proposed. However, this might require major investments in the distribution network and that means the cost would be imposed on the nation. In this paper, the authors focus on the latent ability of the present distribution network and PVs to find solutions to the problem and propose a low‐cost solution to mitigate the voltage rise by using constant leading power factor operation of PVs. The distribution voltages are calculated in the case of increasing highly penetrated PVs, where it is very important to make an aggregated model of the distribution networks including loads and PVs. The authors aggregate many loads and PVs by using an aggregation method called “Y‐connection.” As a result of simulation with the aggregated realistic model of distribution networks, the authors confirmed that using a combination of leading power factor operation with $Q = - 0.2P$ and the LDC of the distribution transformer makes it possible to maintain adequate voltage without voltage regulation facilities such as SVC. © 2012 Wiley Periodicals, Inc. Electr Eng Jpn, 180(3): 46–54, 2012; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/eej.21276

The integration of distributed generators (DGs) into distribution networks is one of the main issues facing distribution networks. This paper presented a detailed analysis of the impacts of the renewable DGs allocation on system steady state and transient performance of distributed networks. An oscillatory particle swarm optimization (OPSO) algorithm was used to find the optimal locations and sizes of DGs for achieving the objectives of minimizing total transmission losses, system voltage regulation or real power performance as a single- and multi-objective optimization problem in distribution networks. The effectiveness of the method is demonstrated with the IEEE14 bus as a distribution network with 50% increase in system loading considering several penetration scenarios to evaluate concentrated and distributed DGs. Also, the impact of DGs penetration on system transient performance was obtained using detailed non-linear models of both synchronous machines and DGs sources (Photovoltaic and wind) when the system was subjected to a symmetrical three-phase short circuit fault for 6 cycles. The obtained results will help in planning the system with high penetration levels of renewable DG sources and identifying the critical penetration levels for the studied system.

The widespread installation of distributed generation systems is crucial for making optimal use of renewable energy. However, local distribution networks face voltage fluctuation problems if numerous photovoltaic (PV) systems are connected. Recently, energy storage systems that can be installed at commercial customers have been developed. This paper proposes a concept that solves the voltage fluctuation problem in distribution networks with high penetration of PV systems by using customer-side energy storage systems. The distribution network operator (DNO) is allowed to control the output of the energy storage systems of customers during a specific time period in exchange for a subsidy covering a portion of the initial cost of the storage system. The cost effectiveness of the cooperative operation for both customer and DNO is discussed by numerical simulations based on minute-by-minute solar irradiation data. Our results have clarified the possibilities of making voltage management more economical in distribution networks.

In this paper, a communication assisted multi-agent system (MAS) is proposed for improving the voltage profile of distribution systems through proper estimation and control of reactive power. Since renewable energy sources (RESs) connected to distribution networks are highly unpredictable in nature, it is more important to maintain the voltage profile within the permissible limits during this atmospheric changes. The agents in the designed MAS improve the voltage stability which is mostly dominated by reactive power and coordinate their tasks through online information and power flow. The agents effectively estimates the adequate amount of reactive power from the topology of distribution network and maintain voltage stability where distributed static synchronous compensators (DSTATCOMs) are used to supply this reactive power. The main control approach is based on designing a linear quadratic regulator (LQR) with an integrator within the agent framework to control the DSTATCOM. The proposed scheme is validated by comparing it with the conventional PI controller and the simulation results show that the proposed scheme performs in a much better and smarter way even with communication delay.

The integration of renewable energies requests smart power grids to be capable of supporting various power flow patterns, and thus urgently needs the development of smart and robust power flow solvers. However, there are several great challenges, as the problem of power flow divergence and the issue of multi-solution. Homotopy methodology is commonly utilized to deal with these issues. This paper proposes a set of sufficiently conditions for the uniqueness of power flow solution, by showing the uniqueness of continuation path in a homotopy method, which can serve as the condition for controlling when to apply the costly global-searching techniques for finding multiple power flow solutions. Theoretical results are illustrated by simulations on the IEEE 1123-bus distribution network with distributed generation.