Three-phase Unbalanced Power Flow Research Articles

A comparison on power flow models for optimal power flow studies in integrated medium-low voltage unbalanced distribution systems

The uptake of distributed energy resources has led to new challenges in distribution system operation. These challenges include voltage and congestion issues along with a higher degree of unbalance due to the installation of mostly single-phase resources. This calls for more accurate distribution system modelling to perform three-phase power flow and optimal power flow analysis to ensure a safe operation. This paper provides a comparison of four unbalanced three-phase power flow formulations to be utilised in optimal power flow-based studies. To adapt these formulations to realistic-sized integrated medium and low voltage unbalanced distribution networks, we propose a linear model for low voltage transformers that is suitable to apply in convex power flow models. The accuracy of these models is compared to the non-linear model considering voltage and current magnitude errors, as well as voltage unbalance factor as performance indices. Our results show that out of the convex formulations, the linear approximated model, which takes the couplings between phases into account, combined with our transformer linearisation, is the most accurate at capturing voltage and current magnitudes. The voltage error of this model in our 5336-node and 3148-node medium-low voltage test networks remains less than 0.38% under a variety of loading and generation scenarios.

Four objective techno-economic generation expansion planning integrated with renewable sources using a novel power flow solution

The use of renewable resources such as wind turbines, solar power, and fuel cells is prevalent in microgrids. However, the environmental constraints and uncertainties associated with renewable sources, along with the restructuring of the electricity industry, present challenges for planners and investors, particularly in economic dimension. This article focuses on investigating the impact of environmental pollution limits and system uncertainties in a restructured environment on the development planning of electric energy production. The aim is to address the economic aspects while considering environmental considerations and uncertainties related to renewable sources. Additionally, network renovation or reconfiguration is explored to balance the load on feeders and minimize areas without electricity, thereby improving service reliability. In this paper four objective function include cost, emission pollution, power losses and voltage profile are considered. In order to find the best solution a novel three-phase unbalanced power flow approach for planning the development of power systems' production using a two-layer iteration algorithm in microgrids with Distributed Generators (DGs) is introduced. The proposed method considers investment, maintenance, operation, and decommissioning costs of units, as well as environmental and economic indicators as objective functions. To select the best solution after multi-objective optimization, a fuzzy decision-making method is employed. The proposed methodology is tested on the IEEE 33-bus system in a restructured environment, considering uncertainties, and its efficiency is demonstrated. The results showcase the effectiveness of the approach in addressing the complexities of planning electric energy production, considering environmental factors, and achieving optimal solutions in the presence of uncertainties.

Time sequence three-phase probabilistic power flow calculation for power system including traction station load of high-speed railway

The increasing traction station load of high-speed railway with single-phase, high-power, spatiotemporal mobility, and uncertainty has brought major impacts and challenges to the power system. The non-negligible characteristics are the spatial distribution of traction stations on high-speed railway lines, the time sequence of traction load moving with EMUs, as well as the nonparametric probabilistic features and correlation of traction load. A method of time sequence three-phase probabilistic power flow (3PPF) calculation for power system including traction station load of high-speed railway is proposed in this paper. Firstly, through the port transformation of traction power supply system (TPSS), the three-phase equivalent model of TPSS is established to construct an unbalanced three-phase power flow calculation model of grid with traction station load. Secondly, considering the spatial correlation, time sequence and non-parametric probabilistic feature of traction load, the time sequence probabilistic models of multiple traction station loads are built based on diffusion-based kernel density estimator (DKDE). Then, the algorithm of time sequence 3PPF calculation based on three-point estimation method (3PEM) is applied to deal with the computational efficiency and accuracy problems of 3PPF considering correlation and timing. Finally, the two modified three-phase power systems are employed for case studies in combination with the measured data of traction station of a high-speed railway. The validity and computing efficiency of the proposed method are verified.

Exact Modeling of Non-Gaussian Measurement Uncertainty in Distribution System State Estimation

In power systems, state estimation is a widely investigated method to collate field measurements and power flow equations to derive the most-likely state of the observed networks. In the literature, it is commonly assumed that all measurements are characterized by zero-mean Gaussian noise. However, it has been shown that this assumption might be unacceptable, e.g., in the case of the so-called pseudo-measurements. In this paper, a state estimator is presented that can model (pseudo-)measurement uncertainty with any continuous distribution, without approximations. This is possible by reformulating state estimation as a maximum-likelihood estimation-based constrained optimization problem, in a more generic fashion than conventional implementations. To realistically describe distribution networks, three-phase unbalanced power flow equations are used. Trade-offs between accuracy and computational effort of different uncertainty modeling methods are presented using the IEEE European Low Voltage Test Feeder.

Resilient Distribution Networks by Microgrid Formation Using Deep Reinforcement Learning

Resilience becomes vital for power grids facing the increasingly frequent extreme weather events. Microgrid formation is a promising way to achieve resilient distribution networks (RDN) when the utility power is unavailable. This paper proposes a RDN-oriented microgrid formation (RoMF) method based on the deep reinforcement learning (DRL) technique, which integrates the OpenDSS as an interaction object and searches for optimal control policies in a model-free fashion. Specifically, we formulate the microgrid formation problem as a Markov decision process, taking into account complex factors such as unbalanced three-phase power flow and microgrid operation constraints. Next, a simulator-based RoMF environment is constructed and integrated into the OpenAI Gym, providing a standard agent-environment interface for applying DRL algorithms. Then, the deep Q-network is used to search for optimal microgrid formation strategies, and an offline-training and online-application framework of the DRL-based RoMF is given. Finally, extensive numerical results validate the effectiveness of our proposed method.

A Two-Level Energy Management Strategy for Multi-Microgrid Systems With Interval Prediction and Reinforcement Learning

Setting retail electricity prices is one of the significant strategies for energy management of multi-microgrid (MMG) systems integrated with renewable energy. Nevertheless, the need of privacy preservation, the uncertainties of renewable energy and loads, as well as the time-varying scenarios, bring challenges for pricing problems. In this paper, a two-level pricing framework is proposed based on interval predictions and model-free reinforcement learning to address these challenges. In particular, at the higher level, the distribution system operator (DSO) is viewed as an agent, which sets retail electricity prices without detailed user information for privacy protection to maximize the total revenue from selling energy with reinforcement learning. For time-varying scenarios with intermittent photovoltaic power generation and diverse loads, a differentiable trust region layer is considered in reinforcement learning to improve the robustness of the policy updating process. While at the lower level, operators in microgrids solve three-phase unbalanced optimal power flow (OPF) problems to minimize generation cost and network power loss. Additionally, to deal with the challenges from the uncertainties of renewable power generation and user loads, interval predictions are chosen to quantify prediction errors and improve the flexibility of pricing policies. Finally, a set of experiments are conducted to validate the effectiveness of the proposed method for pricing problems in MMG systems.

Integrating Transactive Energy Into Reliability Evaluation for a Self-Healing Distribution System With Microgrid

Non-utility owned distributed energy resources (DERs) are mostly untapped currently, but they can provide many grid services such as voltage regulation and service restoration, if properly controlled, and can improve the distribution system's reliability when coordinated with utility-owned assets such as self-healing control and microgrids. This paper integrates transactive energy control into the distribution system reliability evaluation to quantitatively assess the impact of non-utility owned DERs on reliability improvement. A transactive reactive power control strategy is designed to incentivize the DERs to provide reactive power support for improving voltage profiles thus enabling additional customer load restoration during an outage. Also, an operational sequence to coordinate the non-utility owned DERs with the utility owned self-healing control and utility owned microgrids is designed and integrated into the service restoration process with the operational constraints guaranteed by checking the three-phase unbalanced power flow for post-fault network reconfiguration. The reliability indices are then calculated through a Monte Carlo simulation. The transactive reactive power control strategy is tested on a four-feeder distribution system operated by Duke Energy in the U.S. Results demonstrate that the non-utility owned DERs with the transactive control improve the reliability of both the system and critical loads by more than 30%.

Multi-conductor Line Models for Harmonic Load-flow Calculations in LV Networks with High Penetration of PV Generation

Low-voltage (LV) distribution networks are unbalanced and present loads with nonlinear behavior, which introduce harmonics in the networks. The predictable increase in photovoltaic microgeneration (PV µG) accentuates this unbalanced characteristic, as well as poses new technical problems, namely voltage rise and reverse power flow. To accurately account for the distributed PV and loads in the LV network, unbalanced three-phase power flow algorithms should be utilized, where different approaches may be used to represent lines with various degrees of accuracy. The more accurate algorithm considers the electromagnetic coupling between the line conductors, whereas the simpler algorithm represents each conductor of the line as a single-phase line with pure resistive behavior. This paper aims to analyze the influence of the line model on the load flow in a highly unbalanced LV network with a high penetration of PV production, and considers the impact of the harmonics produced by nonlinear loads. Based on the results obtained, it is possible to identify the most suitable model to be used, depending on the study to be performed. Different scenarios of PV generation and loads are addressed in this paper.

A novel three-phase unbalanced power flow solution for islanded microgrids with distributed generations under droop controls

With the increasing penetration rate of distributed generations (DGs) in the distribution network, microgrids are widely applied for the benefits of efficiency and flexibility. The demands of power flow analysis for microgrids are increasing. However, the traditional power flow algorithms cannot be utilized directly when microgrids operate in islanded modes and the DGs are adjusted by a droop control scheme. To increase the effectiveness and generalization of the power flow, a novel two-layer iteration method for microgrids is proposed. First, the three-phase unbalanced power flow is calculated by the power-injection algorithm in the inner iteration. Then, the node admittance matrix of the transmission line, the loads, the power generations and voltage of DGs are updated directly through the power flow results in the outer iteration. Finally, the processes of calculating convergence solutions with inner and outer iterations are presented. The proposed method was implemented on the CloudPSS platform and tested with a modified IEEE-13 bus microgrid system. The power flow results of the proposed method are compared with the electromagnetic transient (EMT) simulation. The comparison results demonstrate the practicability and effectiveness of the proposed algorithm.

TPCPF: Three-Phase Continuation Power Flow Tool for Voltage Stability Assessment of Distribution Networks With Distributed Energy Resources

This work presents a three-phase unbalanced continuation power flow algorithm for voltage stability assessment of distribution systems with high penetration of distributed energy resources (DERs). Analyzing distribution system voltage stability with DER will allow high penetration of renewable energy necessary for the sustainability goals. The developed algorithm can analyze voltage stability for both the meshed and radial systems and the balanced and unbalanced three-phase distribution systems. The developed tool allows the voltage stability analysis to facilitate the planning, operation, control, and distribution system management. The impact of DER on the voltage stability of several test cases has been analyzed considering constant power (PQ) and regulated-voltage (PV) modes of operation for DER units. Moreover, different voltage stability case studies are presented to demonstrate the impact of unbalance, load increment, and network topology on the maximum loading capacity. Results using the IEEE 13-node feeder, the 18-bus balanced shipboard system, the 13-node CIGRE benchmark system, and the 136-bus redial distribution feeder demonstrate that the developed continuation power flow tool can efficiently perform voltage stability analysis for active distribution systems.

Stratified Control Applied to a Three-Phase Unbalanced Low Voltage Distribution Grid in a Local Peer-to-Peer Energy Community

This paper presents control relationships between the low voltage distribution grid and flexibilities in a peer-to-peer local energy community using a stratified control strategy. With the increase in a diverse set of distributed energy resources and the next generation of loads such as electric storage, vehicles and heat pumps, it is paramount to maintain them optimally to guarantee grid security and supply continuity. Local energy communities are being introduced and gaining traction in recent years to drive the local production, distribution, consumption and trading of energy. The control scheme presented in this paper involves a stratified controller with grid and flexibility layers. The grid controller consists of a three-phase unbalanced optimal power flow using the holomorphic embedding load flow method wrapped around a genetic algorithm and various flexibility controllers, using three-phase unbalanced model predictive control. The control scheme generates active and reactive power set-points at points of common couplings where flexibilities are connected. The grid controller’s optimal power flow can introduce additional grid support functionalities to further increase grid stability. Flexibility controllers are recommended to actively track the obtained set-points from the grid controller, to ensure system-level optimization. Blockchain enables this control scheme by providing appropriate data exchange between the layers. This scheme is applied to a real low voltage rural grid in Austria, and the result analysis is presented.

Energy management in unbalanced low voltage distribution networks with microgeneration and storage by using a multi-objective optimization algorithm

The ongoing increase of PhotoVoltaic (PV) microgeneration, pointing to high levels of penetration, can lead to the occurrence of overvoltages. Moreover, the inherent unbalanced nature of the LV distribution grid is a difficulty that must be considered when designing countermeasures. On the other hand, storage systems are suitable devices that can help the process of voltage control. This paper proposes a control system for a real-time energy management system, using Multi-Objective Particle Swarm Optimization (MOPSO) on a highly unbalanced LV distribution network, with batteries and a high share of PV. The purpose of the control system is the optimization of four objectives: Voltage Unbalance Factor (VUF), voltage deviation, active power losses and PV curtailment, wherein four scenarios were considered for assessment. This study is conducted using an unbalanced three-phase power flow algorithm. A comparison of residential and community storage is performed. The results show that the inclusion of storage devices near the prosumers’ PV systems is the recommended solution to enhance voltage stability and balance. Moreover, a significant reduction of active power losses in the LV network is observed.

Distribution optimal power flow

Increased availability of controllable devices and overall visibility means that distribution systems can now be planned and operated in a more optimal way. However, to achieve this, it is crucial to have the underlying tools for determining these optimal decisions and settings. The work in this study discusses the formulation for a three-phase unbalanced distribution optimal power flow. The methodology is developed in Python using the optimisation package Pyomo, and interfaces with OpenDSS to import the distribution system models. Optimal settings for various distribution system control equipment can be calculated to achieve a distribution wide objective. A real-world test case is used to highlight the capabilities of the method and results are demonstrated and discussed.

Linear Single- and Three-Phase Voltage Forecasting and Bayesian State Estimation With Limited Sensing

Implementing state estimation in low and mediumvoltage power distribution is still challenging given the scale of many networks and the reliance of traditional methods on a large number of measurements. This paper proposes a method to improve voltage predictions in real-time by leveraging a limited set of real-time measurements. The method relies on Bayesian estimation formulated as a linear least squares estimation problem, which resembles the classical weighted least-squares (WLS) approach for scenarios where full network observability is not available. We build on recently developed linear approximations for unbalanced three-phase power flow to construct voltage predictions as a linear mapping of load predictions constructed with Gaussian processes. The estimation step to update the voltage forecasts in real-time is a linear computation allowing fast high-resolution state estimate updates. The uncertainty in forecasts can be determined a priori and smoothed a posteriori, making the method useful for both planning, operation and post-hoc analysis. The method outperforms conventional WLS and is applied to different test feeders and validated on a real test feeder with the utility Alliander in The Netherlands.

Distributed Load Restoration in Unbalanced Active Distribution Systems

The resilience of modern power systems has been constantly threatened by various natural disasters and man-made attacks. Under those threats, fast and automatic restoration actions are critical for restoring impacted systems to normal operating conditions and preventing from additional disastrous consequences. Smart grid technologies, such as distributed energy resources (DERs) and microgrids, provide both opportunities and challenges for distribution system restoration. In this paper, distributed load restoration (DLR) in unbalanced active distribution networks is developed using the alternating direction method of multipliers (ADMMs) algorithm. The step-by-step restoration actions are provided to schedule the output of DERs and distribution system control devices, as well as the power consumption from transmission system restoration. The nonlinearities from three-phase unbalanced power flow and distribution components modeling are relaxed into a convex quadratic programming model. Then, the problem is decomposed into subproblems for each node by applying ADMM-DLR; and solves through each agent by exchanging limited information with neighboring nodes in an iterative procedure. The developed models and algorithms are validated and demonstrated through testing of the IEEE 13-node and 123-node test feeders. Simulation results demonstrate the effectiveness of restoring unbalanced distribution system with the hybrid bottom-up and top-down restoration strategies.

Optimal Placement and Dispatch of LV-SVCs to Improve Distribution Circuit Performance

In this paper, a two-stage optimization framework is proposed for optimal placement and centralized real-time control of low-voltage static var compensators (LV-SVCs) in unbalanced distribution circuits to achieve feeder level benefits namely voltage regulation and energy loss minimization. The number, locations, and the optimal real-time reactive power injections from the LV-SVCs are determined from a proposed three-phase unbalanced ac optimal power flow (ACOPF). The ACOPF is formulated as a multi-objective optimization with operating constraints written in rectangular coordinates. The resulting nonlinear nonconvex problem is solved using the predictor-corrector primal-dual interior point method. The proposed approach is scalable for application to large distribution circuits, treats the constraints of physical space limitations effectively, and can take advantage of communication capabilities of LV-SVCs for centralized real-time control. The benefits of the proposed real-time control of LV-SVCs as compared to their operation with local autonomous voltage-based distributed control is demonstrated. The results show that, the proposed approach addresses the LV-SVC placement and control problem effectively to minimize energy losses while maintaining the voltage regulation.

Probabilistic load elasticity analysis in low voltage distribution networks with high penetration of photovoltaic micro generation

Microgeneration PV units connected to the LV distribution network is contributing to a paradigm change on the planning and operation. The proliferation of electric and electronic devices in residential houses, principally nonlinear loads, can be observed and is a result of the evolution of technology. These nonlinear devices may generate a number of harmonics, therefore disturbing and degrading the power quality of the network. This paper intends to give a contribution to the subject by investigating the static load modelling in a LV radial distribution network. For this purpose, a three-phase unbalanced power flow algorithm is used, with the capability of handling static load models variations, through the well-known concept of elasticity. The research is made by using stochastic variations, typifying the residential load segment. The Monte Carlo approach is applied for the stochastic computations, considering the uncertainty in the composition of loads. The obtained probabilistic results are compared to the typical load modelling through ZIP models. The obtained results indicate that overvoltages may occur in summer days at around noon, independently of the behaviour of the loads. On the other hand, voltages at the lower acceptable band can be expected at night during winter, when the peak load occurs.

A modified backward/forward sweep-based method for reconfiguration of unbalanced distribution networks

<span lang="EN-US">A three-phase unbalanced power flow method can provide a more realistic scenario of how distribution networks operate. The backward/forward sweep-based power flow method </span><span lang="EN-AU">(BF-PF)</span><span lang="EN-US"> has been used for many years as an important computational tool to solve the power flow for unbalanced and radial power systems. However, some of the </span><span lang="EN-AU">few </span><span lang="EN-US">available research tools produce many errors when </span><span lang="EN-AU">they </span><span lang="EN-US">are used for </span><span lang="EN-AU">network </span><span lang="EN-US">reconfiguration </span><span lang="EN-AU">because the </span><span lang="EN-US">topology change</span><span lang="EN-AU">s</span><span lang="EN-AU">after multiple switch actions</span><span lang="EN-US"> and the nodes are disorganized continually. </span><span lang="EN-AU">T</span><span lang="EN-US">his paper presents </span><span lang="EN-AU">a modified</span><span lang="EN-AU">BF-PF for </span><span lang="EN-US">three-phase unbalanced radial </span><span lang="EN-AU">distribution networks</span><span lang="EN-US"> that is capable </span><span lang="EN-AU">of arranging</span><span lang="EN-US"> the system topology when reconfiguration changes the branch connections. A binary search is used to determine the connections between nodes, allowing the algorithm to avoid those problems when reconfiguration is carried out, regardless of node numbers. Tests are made to verify the usefulness of the proposed algorithm in both the IEEE 13-node test feeder and the 123-node test feeder, converging in every run where constraints are accomplished. This approach can be used easily for a large-scale feeder network reconfiguration.</span><span lang="EN-AU"> The full version of this modified </span><span lang="EN-US">backward/forward sweep</span><span lang="EN-AU"> algorithm is available for research at MathWorks</span><span lang="EN-US">.</span>

Coordinating Multiple Sources for Service Restoration to Enhance Resilience of Distribution Systems

When a major outage occurs on a distribution system due to extreme events, microgrids, distributed generators, and other local resources can be used to restore critical loads and enhance resiliency. This paper proposes a decision-making method to determine the optimal restoration strategy coordinating multiple sources to serve critical loads after blackouts. The critical load restoration problem is solved by a two-stage method with the first stage deciding the post-restoration topology and the second stage determining the set of loads to be restored and the outputs of sources. In the second stage, the problem is formulated as a mixed-integer semidefinite program. The objective is maximizing the number of loads restored, weighted by their priority. The unbalanced three-phase power flow constraint and operational constraints are considered. An iterative algorithm is proposed to deal with integer variables and can attain the global optimum of the critical load restoration problem by solving a few semidefinite programs under two conditions. The effectiveness of the proposed method is validated by numerical simulation with the modified IEEE 13-node test feeder and the modified IEEE 123-node test feeder under plenty of scenarios. The results indicate that the optimal restoration strategy can be determined efficiently in most scenarios.

Resilience-Oriented Distribution System Restoration Considering Mobile Emergency Resource Dispatch in Transportation System

After major outages, local power sources, including mobile power sources (MPSs), can be coordinated to serve critical loads in distribution systems (DSs). Repair crews (RCs) are sent to repair faulted components. Both mobile emergency resources, i.e., MPSs and RCs, need to travel through the transportation system (TS) before they reach the destination for service. However, traffic congestion may happen after natural disasters and impact the dispatch of the MPSs and RCs. Therefore, the dynamic traffic state in the TS should be considered for efficient dispatch of mobile emergency resources. This paper proposes a framework to determine critical load restoration strategy for the DS, considering the dispatch strategy of the MPSs and RCs in the TS. The cell transmission model (CTM) is used to formulate the weighted dynamic traffic assignment problem (WDTA) in the TS as a linear program (LP), aiming at minimizing the total prioritized travel time of the MPSs and RCs. For the DS, the multi-period critical load restoration problem (CLR-DS) is formulated as a mixed-integer linear program (MILP) to maximize the cumulated service time to critical loads. Unbalanced three-phase power flow and time-varying topological constraints are considered. Case studies validate the effectiveness of the proposed method.