Three-phase Unbalanced Distribution Systems Research Articles

Optimal Restoration/Maintenance Switching Sequence of Unbalanced Three-Phase Distribution Systems

This paper presents a mixed-integer non-linear programming (MINLP) model for the optimal restoration/maintenance switching sequence of unbalanced three-phase electrical distribution systems. Once the protection coordination has identified and cleared a faulty zone, the proposed MINLP model determines the status of remotely controlled switches and the dispatchable distributed generation (DG) units, used to de-energized the troubled section of the network and supply as much load as possible. The restoration considers the switching sequence over a discrete horizon, guaranteeing that the operational constraints of the distribution system are not violated in every step of the sequence. Furthermore, a set of linearization strategies are presented to transform the proposed MINLP model into a mixed-integer linear programming (MILP) model. The use of MILP models guarantees convergence to optimality by applying convex optimization techniques. Tests are performed on an unbalanced three-phase radial distribution system consisting of 123 nodes, 12 switches, and three dispatchable DG units. The obtained results show that the proposed optimization model is a holistic procedure that can be used to efficiently manage power restoration or to minimize isolated areas in case of scheduled maintenance in modern electrical distribution systems.

An inclusive methodology for Plug-in electrical vehicle operation with G2V and V2G in smart microgrid environments

Smart initiative concepts as smart grids, cities, and microgrids are redefining the electrical power system. This new scenario enables a completely new perspective of applications that lead to a path of general improvement of grid performance, in which the participation of plug-in electric vehicles has great importance. In this view, this work proposes a comprehensive operation strategy of plug-in electric vehicles for unbalanced smart microgrid environments. The first contribution is the grid-to-vehicle strategy based on buses availability of power whose primary objective is the maintenance of satisfactory operating conditions for the grid while controlling the plug-in electric vehicles charging. The second contribution relates to a holistic vehicle-to-grid coordinated approach, which is triggered in the event of microgrid islanding. The goal, in this case, is to assist the network by using the plug-in electric vehicles available stored energy. At last, the main contribution is obtained by the combination of both methodologies providing a comprehensive operation of plug-in electric vehicles for smart microgrids environments. The proposed method is designed for general three-phase unbalanced distribution systems with a wide range of resources and present versatility in the communication requirements. For validation, simulations are performed in a comprehensive unbalanced three-phase distribution system considering different disruptive scenarios faced by microgrids. The results indicate that the proposed methodology is satisfactory and ensure the operation of the microgrid within acceptable limits in both connected and islanded situations.

Sequential Service Restoration for Unbalanced Distribution Systems and Microgrids

The resilience and reliability of modern power systems are threatened by increasingly severe weather events and cyber-physical security events. An effective restoration methodology is desired to optimally integrate emerging smart grid technologies and pave the way for developing self-healing smart grids. In this paper, a sequential service restoration (SSR) framework is proposed to generate restoration solutions for distribution systems and microgrids in the event of large-scale power outages. The restoration solution contains a sequence of control actions that properly coordinate switches, distributed generators, and switchable loads to form multiple isolated microgrids. The SSR can be applied for three-phase unbalanced distribution systems and microgrids and can adapt to various operation conditions. Mathematical models are introduced for three-phase unbalanced power flow, voltage regulators, transformers, and loads. The SSR problem is formulated as a mixed-integer linear programming model, and its effectiveness is evaluated via the modified IEEE 123 node test feeder.

CONTINUATION POWER FLOW OF AN UNBALANCED THREE-PHASE FOUR-WIRE DISTRIBUTION SYSTEM


 A continuation power flow algorithm for an unbalanced three phase four wire distribution system is presented. The proposed algorithm is used to trace the loci of the voltage of the different phases of an unbalanced three-phase distribution system. The locus of the neutral voltage for a wide range of loading conditions is also obtained. The proposed technique is applied on a typical unbalance three phase radial Iraqi distribution system. The results obtained reveal the effectiveness of the continuation technique for exploring all the possible solutions and the determination of maximum loadability of the distribution feeder.
 

Optimally Allocation of Distributed Generators in Three-Phase Unbalanced Distribution Network

Increasing energy demand can be compensated with integration of distributed energy resources in the three-phase distribution system. Load flow analysis of the unbalanced three-phase distribution system requires a tool and algorithm to manage the multiple sources. In this study, Jaya algorithm is applied and interfaced with open source software openDSS to solve the unbalanced three-phase optimal power flow. Further, co-simulation framework is used to obtain the optimal allocation of two types of multiple distributed generators in unbalanced radial distribution system. The effectiveness of the approach is validated on IEEE 123 node distribution system. For a realistic study, mixes of all type of loads and configuration of the actual distribution system are considered. The results are compared with already published results obtained from established particle swarm optimization.

Distributed Computing Architecture for Optimal Control of Distribution Feeders With Smart Loads

This paper presents a distributed computing architecture for solving a distribution optimal power flow (DOPF) model based on a smart grid communication middleware (SGCM) system. The system is modeled as an unbalanced three-phase distribution system, which includes different kind of loads and various components of distribution systems. In this paper, fixed loads are modeled as constant impedance, current and power loads, and neural network models of controllable smart loads are integrated into the DOPF model. A genetic algorithm is used to determine the optimal solutions for controllable devices, in particular load tap changers, switched capacitors, and smart loads in the context of an energy management system for practical feeders, accounting for the fact that smart loads consumption should not be significantly affected by network constraints. Since the number of control variables in a realistic distribution power system is large, solving the DOPF for real-time applications is computationally expensive. Hence, to reduce computational times, a decentralized system with parallel computing nodes based on an SGCM system is proposed. Using a “MapReduce” model, the SGCM system runs the DOPF model, communicates between master and worker computing nodes, and sends/receives data among different parts of parallel computing system. Compared to a centralized approach, the proposed architecture is shown to yield better optimal solutions in terms of reducing energy losses and/or energy drawn from the substation within adequate practical run-times for a realistic test feeder.

Harmonic state estimation for distribution networks using phasor measurement units

This paper presents a novel approach for harmonic state estimation for unbalanced three-phase distribution systems using Phasor Measurement Units (PMUs), considering the presence of harmonic sources connected to the system. Harmonic branch currents in rectangular coordinates are the state variables to be estimated by the proposed methodology. Harmonic voltages and branch currents phasors are measured at monitored buses by PMUs. For the non-monitored buses, load pseudomeasurements are considered as inequality constraints in a proposed optimization problem solved via Safety Barrier Interior Point Method. The main contribution of the method is providing satisfactory estimation results considering non-fully observable power distribution networks with long feeders, requiring a small number of field measurements. Tests on the modified Baran and Wu's 33-bus test system are used to validate the methodology and demonstrate its effectiveness on evaluating power quality indexes, identifying harmonic sources and monitoring harmonic components and their propagation through the network.

A Developed Voltage Control Strategy for Unbalanced Distribution System During Wind Speed Gusts Using SMES

The fast response, high efficiency and long lifetime of superconducting magnetic energy storage (SMES) compared to other energy storage systems make it a preferable selection for energy storage solution for wind power generation. SMES has attracted many researchers to study its potential applications in power systems. This paper discusses a scheme of fuzzy logic controlled SMES to minimize the voltage fluctuations of three-phase unbalanced radial distribution systems connected to wind energy conversion system (WECS) with large scale penetration level of 30% during wind speed gusts. In this paper, wind turbine used is of squirrel cage induction generator (SCIG) with shunt connected capacitor bank for power factor improvement. SMES unit consists of superconducting coil, DC-DC chopper, step down transformer, power conditioning system, and cryostat/vacuum vessel. The control technique is based on fuzzy logic controller (FLC). The studied system is 33-bus three-phase unbalanced radial distribution system. The SMES and WECS were connected to weakest buses in the system, namely Buses18 and 33. The control strategy is discussed in details and the proposed system is evaluated by simulation in MATLAB/SIMULINK package. The simulation results demonstrate the performance of the proposed fuzzy-logic-controlled SMES in mitigating the voltage fluctuations under wind speed gusts.

Coordinated control of distribution grid and electric vehicle loads

Electric vehicle (EV) charging results in unusual power peaks during low energy prices, which can have adverse impacts on distribution grid operation. Therefore, coordinated dispatch of EV loads including the operational constraints of distribution grid is essential. However, a centralized approach to solve this problem is computationally challenging task. This work proposes a bi-level hierarchical vehicle-grid (VG) optimization framework. In the hierarchy, optimal operation of the distribution grid is considered in one level, while the optimal operation of EVs is carried out in another level. The proposed framework consists of comprehensive mathematical modelling of distribution system components, EVs, and operational constraints. The proposed framework is applied to coordinate charging of hundreds of EVs in the IEEE 34-node three-phase unbalanced distribution system. Case studies demonstrate that the hierarchical VG optimization framework provides benefits to the distribution grid operations as well as to the EV owners.

Hierarchical Architecture for Integration of Rooftop PV in Smart Distribution Systems

This paper presents a novel hierarchical multilevel decentralized optimal power flow (OPF) for power loss minimization in three-phase unbalanced large-scale distribution systems via optimal reactive power scheduling of rooftop photovoltaics generators. The system is decomposed into three levels corresponding to: 1) the primary; 2) the lateral; and 3) the secondary feeder subnetworks of distribution systems. A distributed sequential coordination scheme based on analytical target cascading method is developed to minimize power losses while considering the operational constraints. Results based on the proposed method are compared with centralized OPF for validation. Control based on the proposed method is compared with no reactive power control and local reactive power control to identify its effectiveness. Further, a virtual feeder is introduced to separate the coupled subnetworks into decomposed layers, which enables parallel processing of the optimization problems to reduce computational complexity and provide faster solution. A 559-node large-scale distribution network built based on the IEEE 37 node test system is used to demonstrate performance of the proposed algorithm.

Uncertainty Tracing of Distributed Generations via Complex Affine Arithmetic Based Unbalanced Three-Phase Power Flow

Variations of load demands and generations bring multiple uncertainties to power system operation. Under this situation, power flows become increasingly uncertain, especially when significant distributed generations (DGs), such as wind and solar, are integrated into power systems. In this paper, a Complex Affine arithmetic based unbalanced Three-phase Forward-Backward Sweep power flow model (CATFBS) is proposed to study the impacts of uncertainties in unbalanced three-phase distribution systems. An index of Relative Influence of Uncertain Variables on Outcomes (RIUVO) is proposed for quantifying the impacts of individual uncertain factors on power flows and bus voltages. The CATFBS method is tested on the modified IEEE 13-bus system and a modified 292-bus system. Numerical results show that the proposed method outperforms the Monte Carlo method for exploring the impacts of uncertainties on the operation of distribution systems. The proposed CATFBS method can be used by power system operators and planners to effectively monitor and control unbalanced distribution systems under various uncertainties.

Optimal Reactive Power Dispatch for Voltage Regulation in Unbalanced Distribution Systems

In this paper, we propose a method to optimally set the reactive power contributions of distributed energy resources (DERs) present in distribution systems with the goal of regulating bus voltages. For the case when the network is balanced, we use the branch power flow modeling approach for radial power systems to formulate an optimal power flow (OPF) problem. Then, we leverage properties of the system operating conditions to relax certain nonlinear terms of this OPF, which results in a convex quadratic program (QP). To efficiently solve this QP, we propose a distributed algorithm based on the Alternating Direction Method of Multipliers (ADMM). Furthermore, we include the unbalanced three-phase formulation to extend the ideas introduced for the balanced network case. We present several case studies to demonstrate the method in unbalanced three-phase distribution systems.

Multi-objective optimal charging of plug-in electric vehicles in unbalanced distribution networks

Plug-in electric vehicles (PEVs) as new generations of transportation systems have recently become a promising solution to mitigate emissions of greenhouse gases produced by petroleum-based vehicles. Existing power systems may face serious reliability and power quality problems in supplying emerging PEV charging loads unless the charging task is coordinated. In addition, in real world applications, most PEVs are single-phase loads supposed to be charged from residential or commercial outlets. In this paper, a multi-objective optimization framework is proposed to optimally coordinate the charging of single-phase PEVs with dynamic behavior in unbalanced three-phase distribution systems employing smart grid facilities. Objective functions include total cost of purchasing energy in a multi-tariff pricing environment as well as grid total energy losses over charging span. The objective functions are optimized subject to network security, power quality, and PEV constraints. Fuzzy memberships are used to transform differently-scaled objective functions into a same range in order to ensure the Pareto optimality of the multi-objective solution. The proposed method is tested on an unbalanced three-phase distribution system and obtained results, which are discussed in detail, confirm its efficiency in getting a solution satisfying both objective functions as well as in the speed.

Smart Distribution System Operations With Price-Responsive and Controllable Loads

This paper presents a new modeling framework for analysis of impact and scheduling of price-responsive as well as controllable loads in a three-phase unbalanced distribution system. The price-responsive loads are assumed to be linearly or exponentially dependent on price, i.e., demand reduces as price increases and vice versa. The effect of such uncontrolled price-responsive loads on the distribution feeder is studied as customers seek to reduce their energy cost. Secondly, a novel constant energy load model, which is controllable by the local distribution company (LDC), is proposed in this paper. A controllable load is one that can be scheduled by the LDC through remote signals, demand response programs, or customer-end home energy management systems. Minimization of cost of energy drawn by LDC, feeder losses, and customers cost pertaining to the controllable component of the load are considered as objectives from the LDCs and customers' perspective. The effect of a peak demand constraint on the controllability of the load is further examined. The proposed models are tested on two feeders: 1) the IEEE 13-node test feeder; and 2) a practical LDC feeder system. Detailed studies examine the operational aspects of price-responsive and controllable loads on the overall system. It is observed that the LDC controlled load model results in a more uniform system load profile, and that with a reduction in the peak demand cap, the energy drawn decreases, consequently reducing feeder losses and LDC's and customers' costs.

Unbalanced Power Flow in Distribution Systems With Embedded Transformers Using the Complex Theory in <formula formulatype="inline"> <tex Notation="TeX">$\alpha \beta 0\;$</tex></formula> Stationary Reference Frame

This paper presents three new contributions to power flow analysis of unbalanced three-phase distribution systems. First, a complex vector based model in <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\alpha \beta 0\;$</tex> </formula> stationary reference frame is developed to state the power flow equations using a compact matrix formulation. The proposed model is based on Kirchhoff's current law (KCL) and Kirchhoff's voltage law (KVL). Then, a general and exact power transformer model in the <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$\alpha \beta 0\;$</tex></formula> reference frame is proposed. Finally, this transformer model is incorporated into the power flow problem. It will be shown that the use of an orthogonal reference frame simplifies the modeling of the distribution network components. In this work, both the network and the power transformer, as well as PQ type loads, PQ and PV type generators and a slack bus are modeled. By using the node incidence matrix instead of the admittance matrix, the information about the grid topology and the grid parameters (including power transformers) is separately organized. As it will be demonstrated, the proposed formulation is ready to incorporate other complex models of loads, generators or storage devices. The model is tested by using the IEEE 4-Node and the IEEE 123-Node Test Feeders with different transformer connections and balanced and unbalanced lines and loads.

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.

Fluxo de potência trifásico probabilístico para redes de distribuição usando o método de estimação por pontos

Neste artigo é aplicado o método de estimação por pontos para resolver o problema do fluxo de potência trifásico probabilístico para sistemas de distribuição trifásicos desbalanceados. Através da aplicação deste método são determinadas as funções de distribuição de probabilidade das tensões nas barras (magnitude e ângulo) e os fluxos potência ativa e reativa nos ramos da rede. Dois esquemas do método de estimação por pontos são apresentados (2m e 2m+1 pontos). Para testar os métodos propostos são empregados os sistemas IEEE de 4, 34 e 123 barras. Os resultados obtidos através dos esquemas são comparados aos obtidos por uma simulação de Monte Carlo. Esta análise permite avaliar as potencialidades do método em termos de precisão e tempos de simulação.

Estimation of Parameters of a Three-Phase Distribution Feeder

For meaningful distribution system analysis, correct information of the feeder parameter is necessary. However, in many cases (especially in the developing countries), these parameters are not known accurately. To address this issue, a methodology for estimating the feeder parameters from the measured values of power flow and node voltages is proposed in this paper. It is shown that the resulting system of equations is extremely ill-conditioned in nature and to solve this ill-conditioned system of equations, an optimization-based procedure is developed. The feasibility of the proposed methodology has been validated on the IEEE 123-bus three-phase unbalanced radial distribution system.

Distribution systems fault analysis considering fault resistance estimation

Fault resistance is a critical component of electric power systems operation due to its stochastic nature. If not considered, this parameter may interfere in fault analysis studies. This paper presents an iterative fault analysis algorithm for unbalanced three-phase distribution systems that considers a fault resistance estimate. The proposed algorithm is composed by two sub-routines, namely the fault resistance and the bus impedance. The fault resistance sub-routine, based on local fault records, estimates the fault resistance. The bus impedance sub-routine, based on the previously estimated fault resistance, estimates the system voltages and currents. Numeric simulations on the IEEE 37-bus distribution system demonstrate the algorithm’s robustness and potential for offline applications, providing additional fault information to Distribution Operation Centers and enhancing the system restoration process.

A Simple Method for Optimal Capacitor Placement in Unbalanced Radial Distribution System

This article presents a simple method for investigating the problem of contemporaneously choosing optimal location and size of shunt capacitors in three-phase unbalanced radial distribution systems. The main objective function formulated consists of two terms: cost of energy loss and cost related to capacitor purchase and capacitor installation. The problem of choosing optimal locations and sizes for shunt capacitors in an unbalanced radial distribution system is addressed with the two algorithms in this article—one is for selecting the best locations of capacitor placement and candidate node identification algorithm; the second is for the sizing of capacitors, a variational technique algorithm according to available standard size of capacitors. The objective function used in this article is to maximize the net savings in the distribution system. This article presents the results of simulations for 25-bus and IEEE 37-bus unbalanced radial distribution systems.