Multi-phase Distribution Systems Research Articles

Neutral-to-Earth Voltage (NEV) and state estimation for unbalanced multiphase distribution systems based on an optimization model

Neutral-to-Earth Voltage (NEV) and state estimation for unbalanced multiphase distribution systems based on an optimization model

Discontinuities and unstable solutions beyond the maximum load point of nonlinear unbalanced distribution systems

• Discontinuities in the PV curves are inherent to the power flow formulation of distribution systems. • Discontinuities may change the operational point between two or more PV curves. • Defining if the maximum loading point is not part of a fully unstable curve is challenging. • A false maximum loading point may be used inappropriately when analyzing multiphase distribution systems. • Discontinuities may occur around the loading level that is related to when the eigenvalues of multiple Jacobians are on the same attraction area. Distribution feeders are usually modeled by a set of nonlinear equations that likely leads to multiple solutions on power flow tools if an adequate nonlinear mathematical model for multi-grounded unbalanced feeders is considered. Specifically, this work presents a study about these solutions through the analysis of PV curves obtained by using the multiphase continuation power flow tool. Herein, the paper discloses discontinuities on the PV curves, which are related to the occurrence of multiple Jacobians with several eigenvalues on the same attraction area. The results revealed the possibility of unstable solutions presenting greater maximum loading levels (around 29.5% higher) than the stable solution. Moreover, a power factor variation study has also indicated that unstable solutions might occur for a broad range of reactive power values. Finally, it is shown that, in some distribution systems, the maximum loading point found is not a global one and, most importantly, stable curves can be confused with unstable ones, leading users and researchers to wrong conclusions in their studies.

Injected Current Sensitivity Based Load Flow Algorithm for Multi-Phase Distribution System in the Presence of Distributed Energy Resources

This paper presents an injected current sensitivity (ICS) based multi-phase load flow (LF) methodology with minimal Jacobian computation for the three-phase unbalanced distribution system with multiple Distributed Energy Resources (DERs). In the proposed approach, first, a generalized bus admittance and Jacobian matrix have been formulated that include various distribution system components such as lines, shunt capacitors, voltage control devices such as regulators, different transformer connections, and load models. Second, DERs are modeled as a PV bus and incorporated into the proposed LF algorithm by formulating a reactive power injection-based sensitivity matrix that iteratively computes its net power injections. Unlike the traditional Jacobian matrix-based LF methods where an update of Jacobian (size and element) is required for each PV bus, this method does not require any update, hence, making it faster and more flexible to include a large number of DERs. From the various tests performed on the standard IEEE three-phase distribution network and their derivatives, it has been observed that the proposed approach is accurate, efficient, computationally less complex, and scalable.

Optimum allocation of multiple type and number of DG units based on IEEE 123-bus unbalanced multi-phase power distribution system

The increasing demand for clean energy has resulted in the growth of renewable energy-based distributed generation (DG) penetration in the power distribution networks (PDN). The crucial point here is to find the optimum allocation of DGs to minimize the power loss and enhance the system performance overall. In this study, the Equilibrium Optimizer (EO) algorithm-based method is proposed to determine the location, size, connection type, and power factor of three different types of multiple DGs based on a three-phase 123-bus unbalanced PDN. The complex 123-bus UPDN has been very little studied to date, and most existing research works on the DG allocation problem have been conducted using a co-simulation platform. In this work, an unbalanced three-phase backward forward load flow (UBFLF) algorithm is written and executed under the MATLAB environment. This approach has decreased the complexity of co-simulation and provided advantages like optimizing the power factor value and the connection type (Delta/Wye) of DGs easily. Six more recent and well-established optimization algorithms such as PSO, JFO, BO, SMA, FDA, and GBO are also applied under the same test conditions to solve the Type-III DGs allocation problem. The results obtained are compared with the proposed method to show the effectiveness of the method in terms of elapsed time, statistical variables (such as standard deviation, median, variance and so on), converge speed, and best/worst case active power loss values. The efficacy of the presented method is also validated by comparing the results obtained using three distinct platforms as MATLAB/Simulink, IEEE-PES data, and OpenDSS. The detailed and comprehensive analyses show that the proposed approach demonstrates the lowest power loss, more enhancement in voltage profile, and the superiority of the EO algorithm in the application of a 123-bus unbalanced power distribution network.

Three-phase voltage stability analysis in an integrated transmission-distribution network

The transmission–distribution interaction is not generally considered in the voltage stability analysis of power systems. Moreover, the load-ability assessment of power system with considering of the penetration level of distributed generation (DG) resources and the performance of on-load tap changers (OLTCs) need to be further analysed. In this study, unstable regions in integrated transmission–distribution networks (ITDNs) were detected in terms of voltage stability and maximum load-ability. A new voltage stability index was also proposed based on the Thevenin equivalent circuit observed from distribution buses. The proposed method was exactly proportional to the active and reactive powers of each bus in the multi-phase distribution system. Accordingly, the static voltage stability of an integrated test system can be accurately analysed. Two IEEE transmission test systems (3 buses and 14 buses) connected to the distribution systems were utilized to simulate the proposed method. The simulation results were analysed in detail to find the maximum load-ability. The results strongly suggested the significance of the voltage stability analysis in ITDNs.

Coordination of OLTC and smart inverters for optimal voltage regulation of unbalanced distribution networks

Photovoltaic (PV) smart inverters can improve the voltage profile of distribution networks. A multi-objective optimization framework for coordination of reactive power injection of smart inverters and tap operations of on-load tap changers (OLTCs) for multi-phase unbalanced distribution systems is proposed. The optimization objective is to minimize voltage deviations and the number of tap operations simultaneously. A novel linearization method is proposed to linearize power flow equations and to convexify the problem, which guarantees convergence of the optimization and less computation costs. The optimization is modeled and solved using mixed-integer linear programming (MILP). The proposed method is validated against conventional rule-based autonomous voltage regulation (AVR) on the highly-unbalanced modified IEEE 37 bus test system and a large California utility feeder. Simulation results show that the proposed method accurately estimates feeder voltage, significantly reduces voltage deviations, mitigates over-voltage problems, and reduces voltage unbalance while eliminating unnecessary tap operations. The robustness of the method is validated against various levels of forecast error. The computational efficiency and scalability of the proposed approach are also demonstrated through the simulations on the large utility feeder.

Gradient-Based Multi-Area Distribution System State Estimation

The increasing distributed and renewable energy resources and controllable devices in distribution systems make fast distribution system state estimation (DSSE) crucial in system monitoring and control. We consider a large multi-phase distribution system and formulate DSSE as a weighted least squares (WLS) problem. We divide the large distribution system into smaller areas of subtree structure, and by jointly exploring the linearized power flow model and the network topology, we propose a gradient-based multi-area algorithm to exactly and efficiently solve the WLS problem. The proposed algorithm enables distributed and parallel computation of the state estimation problem without compromising any performance. Numerical results on a 4,521-node test feeder show that the designed algorithm features fast convergence and accurate estimation results. Comparison with traditional Gauss-Newton method shows that the proposed method has much better performance in distribution systems with a limited amount of reliable measurement. The real-time implementation of the algorithm tracks time-varying system states with high accuracy.

Complex Variable Multi-phase Distribution System State Estimation Using Vectorized Code

With the advent of advanced energy management systems in distribution systems, there is a growing interest in rapid and reliable code for distribution system state estimation (DSSE) in large-scale systems. Fast DSSE methods employed in the industry are based on load scaling as they are well suited to the abundance of pseudo-measurements. Due to the paucity of real-time measurements in DSSE, phasor measurement units (PMUs) have been proposed as a potential solution to increase the estimation accuracy. However, load scaling methodologies are not extendable for exploiting PMUs. This paper proposes a high-performance DSSE method that can handle the PMUs together with all common measurement types in industrial DSSE. By using Wirtinger calculus, the method operates entirely in complex variables and employs the latest version of advanced vector extensions (AVX-2) to reap the maximum potential of computer processing units. The paper highlights the derivation of complex DSSE in matrix form, from which one can infer the implications on code reliability and maintenance. Numerical results are reported on large-scale multi-phase distribution systems, and they are contrasted with a publicly available code for DSSE in real variables. The simulation results show that loop unrolling in AVX-2 contributes about a two-fold increase in the solving speed.

Lossy DistFlow Formulation for Single and Multiphase Radial Feeders

A line loss approximation via parametrization is developed to improve performance of the simplified Baran and Wu DistFlow method, while maintaining a linear set of equations. The approach is evaluated on thousands of training feeders that are created to determine a numerically optimal setting for the parameterization. Feeders are generated using recent advances in synthetic network test case generation. The problem is formulated with the same structure as the simplified DistFlow, yet is more accurate given that line losses are explicitly expressed and quantified. The single-phase methodology is extended to multiphase systems by formulating matrix-vector equations that maintain an analogy to their single-phase counterpart. Results with approximated line losses are shown to also improve the accuracy of multiphase distribution system calculations.

False Data Injection Attacks Against State Estimation in Multiphase and Unbalanced Smart Distribution Systems

In power transmission systems, the false data injection (FDI) attacks against state estimation (SE) have been well studied. However, due to the unique features of power distribution systems including: the low x/r ratio, existence of one-and/or two-phase branches, unbalanced load distributions, and unsymmetrical line parameters; the research on FDI attacks against distribution system SE (DSSE) is still open. In this paper, we investigate the vulnerability of DSSE to FDI attacks. In particular, we first propose a local state-based linear DSSE for multiphase and unbalanced smart distribution systems, which can facilitate the construction of FDI attacks numerically with the least information of system states. Then, the construction of three-phase coupled FDI attacks is introduced. The consideration of the coupling among phases by the three-phase coupled FDI attacks may require the modification of a large number of measurements by the attackers. To reduce the number of required measurements, the perfect three-phase decoupled FDI attacks, which consider the weak couplings among phases, is investigated. The probabilities of successful three-phase decoupled FDI attacks in strongly three-phase coupled systems are also derived numerically. The performance of the proposed FDI attacks against DSSE is evaluated based on IEEE test feeders. The case study results indicate the feasibility of the FDI attacks against DSSE in practical multiphase and unbalanced smart distribution systems. Future research directions including potential countermeasures are also highlighted.

Sparsity-Based Short-Circuit Analysis of Power Distribution Systems With Inverter Interfaced Distributed Generators

This paper proposes a method for calculating short-circuit current in distribution systems with inverter interfaced distributed generators (IIDG). It is capable of calculating the short circuit in a multi-phase distribution systems based on the symmetrical components without obtaining the complete impedance matrix. Furthermore, it considers the load effect and the pre-fault state of the system for the fault analysis and is able to handle unbalanced systems with mutually coupled phases. The problem is formulated as an iterative linear system calculation and is solved by generalized minimal residual (GMRES) approach. The validity of the proposed algorithm is verified through the simulation of IEEE 13-node, 123-node, 478-node, 954-node, and 1430-node distribution systems. Simulation results demonstrate the effectiveness of the proposed algorithm and the advantages of using the GMRES method to calculate the short circuit current in a distribution system with IIDG.

Exact Optimal Power Dispatch in Unbalanced Distribution Systems With High PV Penetration

Smart inverters provide additional control capability to help optimize the operation of distribution systems. This paper proposes a framework for exact optimal active and reactive power dispatch of distributed photovoltaic (PV) generation, switched capacitors, and voltage regulators in large multi-phase unbalanced distribution systems. The objectives of the optimal dispatch are minimization of the energy loss, PV active power curtailment, and operations of capacitors and voltage regulators, in addition to elimination of voltage violations and reverse power flow. The optimization problem is formulated in rectangular coordinates as a nonlinear, nonconvex problem. Effective computational strategies are proposed to allow the application of predictor-corrector primal-dual interior point method to solve optimization problems in real-time with a large number of constraints and variables, including discrete variables corresponding to switched capacitors and voltage regulators. The accuracy of the numerical solution and the ability to implement the proposed framework are validated using the unbalanced multi-phase IEEE 34-bus and EPRI 2,998-bus distribution systems with 15-minute load and PV data. The results show a significant loss reduction and elimination of both voltage violations and reverse power flow.

Load Flow in Multiphase Distribution Networks: Existence, Uniqueness, Non-Singularity and Linear Models

This paper considers unbalanced multiphase distribution systems with generic topology and different load models, and extends the $Z$ -bus iterative load-flow algorithm based on a fixed-point interpretation of the AC load-flow equations. Explicit conditions for existence and uniqueness of load-flow solutions are presented. These conditions also guarantee convergence of the load-flow algorithm to the unique solution. The proposed methodology is applicable to generic systems featuring i) wye connections; ii) ungrounded delta connections; iii) a combination of wye-connected and delta-connected sources/loads; and iv) a combination of line-to-line and line-to-grounded-neutral devices at the secondary of distribution transformers. Further, a sufficient condition for the nonsingularity of the load-flow Jacobian is proposed. Finally, linear load-flow models are derived, and their approximation accuracy is analyzed. Theoretical results are corroborated through experiments on IEEE test feeders.

HPC-Based Intelligent Volt/VAr Control of Unbalanced Distribution Smart Grid in the Presence of Noise

The performance of Volt/VAr optimization has been significantly improved due to the integration of measurement data obtained from the advanced metering infrastructure of a smart grid. However, most of the existing works lack: 1) realistic unbalanced multi-phase distribution system modeling; 2) scalability of the Volt/VAr algorithm for larger test system; and 3) ability to handle gross errors and noise in data processing. In this paper, we consider realistic distribution system models that include unbalanced loadings and multi-phased feeders and the presence of gross errors such as communication errors and device malfunction, as well as random noise. At the core of the optimization process is an intelligent particle swarm optimization-based technique that is parallelized using high performance computing technique to solve Volt/VAr-based power loss minimization problem. Extensive experiments covering the different aspects of the proposed framework show significant improvement over existing Volt/VAr approaches in terms of both the accuracy and scalability on IEEE 123 node and a larger IEEE 8500 node benchmark test systems.

Faulted Segment Identification in Multi-phase Distribution Systems Using Sequence Component Modeling

This article discusses the potential for identifying faulted segment(s) on multi-phase distribution primaries using sequence component modeling and standard three-phase short-circuit solvers. Identifying faulted segments in a timely manner speeds up fault isolation and restoration processes, contributing to greater feeder reliability. The methodology utilizes fundamental frequency current magnitudes from the feeder head in conjunction with an approximate sequence model of the multi-phase feeder including single-phase and double-phase line segments augmented with dummy lines. Under certain fault conditions, multiple faulted segments may be yielded for which a new faulted segment reduction method based on voltage sag data is proposed. The Saskpower network simulated in MATLAB/Simulink (The MathWorks, Natick, Massachusetts, USA) environment was used to evaluate the faulted segment identification and reduction methods. The evaluation studies show quite promising results in uniquely identifying the actual faulted segment with reduced measurement and modeling requirements.

Voltage Security Assessment on Unbalanced Multiphase Distribution Systems

This paper presents a multiphase continuation power flow (MCPF) methodology to perform voltage security analyses on unbalanced multiphase distribution systems. The proposed tool includes comprehensive models of most network components, and allows for explicit representation of neutral cables and grounding connections. The methodology has been validated through comparisons with a commercial software and with results available in the literature. Additional analyses are presented using the IEEE 4-bus, the Neutral-to-Earth (NEV) and the IEEE 8500 Test Systems. These systems have been developed to present several challenges to distribution systems analytical tools. In particular, the influence of the 3-phase transformer connections on the PV curves have been demonstrated and has been useful to stress the importance of a complete system representation.

Renewable Distributed Generation Models in Three-Phase Load Flow Analysis for Smart Grid

The paper presents renewable distributed generation (RDG) models as three-phase resource in load flow computation and analyzes their effect when they are connected in composite networks. The RDG models that have been considered comprise of photovoltaic (PV) and wind turbine generation (WTG). The voltage-controlled node and complex power injection node are used in the models. These improvement models are suitable for smart grid power system analysis. The combination of IEEE transmission and distribution data used to test and analyze the algorithm in solving balanced/unbalanced active systems. The combination of IEEE transmission data and IEEE test feeder are used to test the the algorithm for balanced and unbalanced multi-phase distribution system problem. The simulation results show that by increased number and size of RDG units have improved voltage profile and reduced system losses.

Improving Service Restoration of Power Distribution Systems Through Load Curtailment of In-Service Customers

Load curtailment programs including direct load control and demand response allow system operators to directly and/or indirectly reduce a portion of total customer demand. One system application which can be improved by implementation of load curtailment is service restoration. As such, this work presents a problem formulation, solution algorithm, and simulation results for service restoration of power distribution systems incorporating load curtailment of in-service customers via direct load control. It is shown that the addition of load curtailment allows for one or more of the following: a reduction of the total number of switch operations required, an increase to the number of customers served, and/or an increase to the total amount of load restored. These improvements are demonstrated through simulation results from a 416-bus multiphase distribution system.

Fault Analysis of Multiphase Distribution Systems Using Symmetrical Components

The paper presents a new approach for performing the fault analysis of multiphase distribution networks based on the symmetrical components. The multiphase distribution system is represented by an equivalent three-phase system; hence, the single-phase and two-phase line segments are represented in terms of their sequence values. The proposed technique allows the state of the art short-circuit analysis solvers to analyze unbalanced distribution networks. The fault currents calculated using the proposed technique is compared with the phase components short-circuit analysis solver. The obtained results for the IEEE radial test feeders show that the proposed technique is accurate. Based on the proposed method, the existing commercial grade short-circuit analysis solvers based on sequence networks can be utilized for performing unbalanced distribution systems.

The Effects of Mutual Coupling and Transformer Connection Type on Frequency Response of Unbalanced Three Phase Electrical Distribution System

In this paper, a novel harmonic modeling technique by utilizing the concept of multi-terminal components is presented and applied to frequency scan analysis in multiphase distribution system. The proposed modeling technique is based on gathering the same phase busses and elements as a separate group (phase grouping technique, PGT) and uses multi-terminal components to model three-phase distribution system. Using multi- terminal component and PGT, distribution system elements, particularly, lines and transformers can effectively be modeled even in harmonic domain. The proposed modeling technique is applied to a test system for frequency scan analysis in order to show the frequency response of the test system in single and three-phase conditions. Consequently, the effects of mutual coupling and transformer connection types on three-phase frequency scan responses are analyzed for symmetrical and asymmetrical line configurations.