Three-phase Power Flow Research Articles

Volt–var curves for photovoltaic inverters in distribution systems

Photovoltaics (PV) are a technology that is becoming increasingly prevalent in the residential sector. The impacts of this new type of generation are not always desirable from a distribution system standpoint, as large penetration levels can lead to voltage increases, considerable unbalance, and excessive tap operations. Recent standard changes have allowed the inverters that are used to grid connect PV systems, to utilise their reactive power capability for voltage regulation. Although this new capability is desirable, it is important to ensure that it is being applied in the most beneficial way. The work in this study makes use of a three-phase optimal power flow method to find optimal volt-var curves for grid-connected rooftop PV inverters, which can perform autonomous voltage control. A number of scenarios are applied to produce a sufficient range of voltages, and the resulting reactive power settings are utilised to determine the volt-var curve for each PV system on a test feeder. An active control scheme is also presented, and the results are compared with the proposed autonomous scheme for a test 24 h period.

Three-Phase Optimal Power Flow for Study of PV Plant Distributed Impact on Distribution Systems

Three-Phase Optimal Power Flow for Study of PV Plant Distributed Impact on Distribution Systems

Load Balancing of Modern Distribution Networks by Genetic Algorithm

The main purpose of this paper is to establish a multi-objective function for optimal load balancing in modern distribution networks. The proposed approach can reduce the three-phase voltage unbalance ratio and system power loss; furthermore, the system operation performance will be improved. The genetic algorithm and three-phase power flow algorithm are coded in Matlab. Finally, the IEEE 37-Bus test system is used as the sample system to verify the accuracy of the proposed approach. The simulation results demonstrate that the proposed approach is systematic and efficient for solving the load balancing problem in active distribution networks.

A Linear Power Flow Formulation for Three-Phase Distribution Systems

Power flow analysis is one of the tools that is required in most of the distribution system studies. An important characteristic of distribution systems is the load unbalance in the phases and a three-phase power flow analysis is needed. In this paper, a three-phase linear power flow (3LPF) formulation is derived based on the fact that in a typical distribution system, voltage angles and magnitudes vary within relatively narrow boundaries. The accuracy of the proposed 3LPF is verified using several test cases. Potential applications of the proposed method are in distribution systems state estimation and volt-VAR optimization.

Three‐phase harmonic power flow by direct Z BUS method for unbalanced radial distribution systems with passive power filters

In this study, a three-phase harmonic power flow method using graph theory, injection current and sparse matrix techniques for unbalanced radial distribution systems is proposed. In the bus frame of reference, a direct iterative method is adopted. The proposed method can be used for both fundamental and harmonic power flow studies. Four three-phase IEEE test feeders are used to prove the accuracy and efficiency of the proposed method. The test results show that the proposed method is robust and reliable for passive power filter design, especially for full-scale distribution systems.

Simplified Modeling of Low Voltage Distribution Networks for PV Voltage Impact Studies

Distributed generation is increasingly being integrated into distribution networks worldwide, presenting new challenges for network operators and planners. In particular, the introduction of photovoltaic (PV) generation at the low voltage (LV) level has highlighted the ongoing need for more extensive and detailed modeling to quantify the full extent and nature of potential impacts. While a number of approaches have been developed to address the size of this problem, the most accurate and comprehensive approach is to carry out simulations for the entire network across multiple scenarios. However, this task is computationally complex and requires significant amounts of data. To address this challenge, this paper presents a simplified and computationally efficient methodology based around a two-bus equivalent model, which may be used to estimate the maximum voltage in an LV area due to PV generation over time. The developed model is validated against a full three-phase power flow approach for a real-world distribution network comprising 10 213 LV network areas. Furthermore, to highlight its utility, the model is used in a case study examining the effectiveness of reactive power injection for mitigating overvoltage due to PV generation.

Editorial

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

Probabilistic simulation framework for balanced and unbalanced low voltage networks

In Low Voltage (LV) distribution networks, the high volatility of distributed photovoltaic (PV) generation has a severe impact on the variation of operation indices, in steady state conditions. During periods with high PV injection and low demand, LV feeders are more and more subject to overvoltage events and temporary PV units’ cut-offs. As a result, the delivered power quality is affected and network operational expenses increase. Moreover, the income of the PV owner is decreased due to the loss of generated energy. For efficiently addressing such operational issues, long term observability analytics of the LV network are required. Distribution System Operators (DSOs) currently deploy such studies in a deterministic manner, focusing on “worst-case” hypothesis, without considering the uncertainty of nodal power injection and consumption. This approach can lead to over restrictive decisions and costly technical solutions. For refining DSO strategies to the variability of network states, probabilistic methods are highly recommended. In this context, this paper presents a Monte-Carlo (MC) framework that simulates the steady operation of the LV network by elaborating user-specific smart metering (SM) measurements. The presented framework integrates a complete three-phase power flow algorithm that can analyse most possible LV network configurations, balanced and unbalanced, considering nodal power injections and consumptions as random variables of each network state. Such unbalanced power flow algorithms had not up to now been linked with probabilistic analysis using network-specific SM readings. For demonstrating the interest of the proposed framework, the latter is used to simulate several configurations in an existing LV feeder with high PV integration and SM deployment.

Voltage Control of PV-Rich LV Networks: OLTC-Fitted Transformer and Capacitor Banks

Due to the increasing adoption of domestic photovoltaic (PV) systems, the use of technologies such as on-load tap changer (OLTC)-fitted transformers, capacitor banks, and remote monitoring are being considered to mitigate voltage issues, particularly in European-style low voltage (LV) networks. Depending on the control strategy, however, the effects on customer voltages and control actions (e.g., tap changes or capacitor switching) can vary significantly. This work presents a framework to assess the performance of different OLTC-based control strategies in terms of voltage compliance with the standard BS EN50160 and the number of control actions. Three control strategies are proposed: constant set-point (CSC), time-based (TBC) and remote monitoring-based (RMC). A week-long Monte Carlo analysis is carried out considering a real UK LV network, three-phase power flows, different PV penetrations and seasonality. Results show that the TBC outperforms the CSC but at the expense of more tap changes. Due to the enhanced visibility, the RMC significantly increases the PV hosting capacity whilst limiting tap operations. Finally, when feeders have contrasting voltage issues, capacitor banks are found to provide additional flexibility and allow higher PV penetrations. These findings are expected to help the industry determining the benefits from OLTC-based solutions in future LV networks.

Comparative Evaluation of Methods for Attributing Responsibilities Due To Voltage Unbalance

This paper presents the results of a comparative analysis among three methods for attributing responsibilities of voltage unbalance in the electrical network, namely, the IEC, three-phase power flow, and conforming and nonconforming currents methods. To do this, computational and experimental simulations are carried out based on employing a system comprised of a perfectly transposed transmission line and two loads that are not always balanced. The cases selected for this study also permit the identification of the main advantages and disadvantages of each method under evaluation. This work is characterized as a topic of great interest to the regulatory agencies responsible for establishing regulations, and for utilities and consumers. It is relevant because by using the methods investigated in this paper, the identification of the sources, which generates unbalance, the division of responsibilities, and the application of penalties due to limit transgression will be possible.

Three‐phase power flow calculations using direct Z BUS method for large‐scale unbalanced distribution networks

In this study, a three-phase power flow solution method using graph theory, injection current, and sparse matrix techniques for large-scale unbalanced distribution networks is proposed. In the bus frame of reference, a direct iterative method is adopted. To integrate the electric characteristics of transformers and step voltage regulators into the proposed method, the existing component models are modified by equivalent injected currents. To validate the performance and effectiveness of the proposed method, four three-phase IEEE test systems and random test systems are used for comparison purposes. As the size of the network increases, the proposed direct Z BUS method drastically shows its superiority over the other methods. The results reveal that the proposed method has good potential for improving the computational efficiency of optimal planning and design as well as real-time power dispatch applications in large-scale distribution systems.

A Three-phase Hybrid Power Flow Algorithm for Meshed Distribution System with Transformer Branches and PV Nodes

Aiming at analyzing the power flow of the distribution systems with distribution transformer (DT) branches and PV nodes, a hybrid three-phase power flow methodology is presented in this paper. The incidence formulas among node voltages, loop currents and node current injections have been developed based on node-branch incidence matrix of the distribution network. The method can solve the power flow directly and has higher efficiency. Moreover, the paper provides a modified method to model DT branches by considering winding connections, phase shifting and off-nominal tap ratio, and then DT branches could be seen like one transmission line with the proposed power flow method. To deal with the PV nodes, an improved approach to calculate reactive power increment at each PV node was deduced based on the assumption that the positive-sequence voltage magnitude of PV node is fixed at a given value. Then during calculating the power flow at each iteration, it only needs to update current injection at each PV node with the proposed algorithm. The process is very simple and clear. The results of IEEE 4 nodes and the modified IEEE 34 nodes test feeders verified the correctness and efficiency of the proposed hybrid power flow algorithm.

Estimation of Voltage-Driven Reinforcement Cost for LV Feeders Under 3-Phase Imbalance

Three-phase imbalance causes uneven voltage drops along low-voltage feeders. Under long-term load growth, the phase with the lowest terminal voltage will trigger network reinforcements, which are earlier than if the three phases were balanced. This leads to a higher voltage-driven reinforcement cost (VRC) than the balanced case. Three-phase power flow analyses are not suitable for VRC estimations under serious data deficiency (without customers’ phase connectivity and smart metering data), and are not scalable due to the iterative nature, which brings a prohibitively high computation burden on a utility level with millions of feeders. To overcome the challenges, this paper proposes a novel scalable methodology for VRC estimations that is applicable from an individual feeder to millions of feeders, where the level of information is insufficient to support accurate three-phase power flow studies. The key is to use five types of load current distributions to represent customers’ phase allocations and individual demands, and to incorporate these distributions into an equivalent impedance matrix, which allows a straightforward VRC estimation without iterations. This paper applies this methodology to an individual feeder, showing that: 1) the VRC decreases (increases) with the increase of the K (beta) factor of the trapezoid (triangular–rectangular) distribution, given that other conditions remain the same; 2) the VRC is more sensitive to voltage imbalance than to current imbalance; and 3) if the three phases are balanced, the change of any single variable results in an increase of the VRC, given that all other input variables remain constant.

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

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

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.

Hierarchical management for integrated community energy systems

Due to the presence of combined heat and power plants (CHP) and thermostatically control loads, heat, natural gas, and electric power systems are tightly coupled in community areas. However, the coordination among these systems has not yet been fully researched, especially with the integration of renewable energy. This paper aims to develop a hierarchical approach for an integrated community energy system (ICES). The proposed hierarchical framework is presented as day-ahead scheduling and two-layer intra-hour adjustment systems. Two objectives, namely the operating cost minimization and tie-line power smoothing, are integrated into the framework. In the intra-hour adjustment, a master–client structure is designed. The CHP and thermostatically controlled loads are coordinated by a method with two different time scales in order to execute the schedule and handle uncertainties from the load demand and the renewable generation. To obtain the optimal set-points for the CHP, an integrated optimal power flow method is developed, which also incorporates three-phase electric power flow and natural gas flow constraints. Furthermore, based on a time priority list method, a three-phase demand response approach is proposed to dispatch thermostatically controlled loads at different phases and locations. Numerical studies confirm that the ICES can be economically operated, and the tie-line power between the ICES and external energy network can be effectively smoothed.

A three-phase optimal power flow applied to the planning of unbalanced distribution networks

Abstract This paper models a three-phase optimal power flow applied to distribution networks. The objective function is to minimize electrical losses, the restrictions of which are the maximum and minimum levels of active and reactive power supplied the voltage magnitudes, and taps of voltage regulators with consideration of the mutual impedances of cables. In order to gain numerical stability, the voltage phasor is represented by the rectangular form. The optimization problem is solved by the Interior Points Method version Primal–Dual, whose importance to the planning of distribution networks is tested using the IEEE-123 system bus.

Metaheuristic and probabilistic techniques for optimal allocation and size of biomass distributed generation in unbalanced radial systems

In this study, a method for solving a probabilistic three-phase power flow in radial distribution networks and taking into account the technical constraints of the system is presented. Regulation of voltage is one of the main problems to be taken into account in networks with distributed generation. The present study introduces a probabilistic model to determine the performance of the distribution system. This study considers the random nature of lower heating value of biomass and loads. This study presents a new hybrid technique combining the shuffled frog leaping algorithm with probabilistic three-phase power flow that is solved by Monte Carlo method. Feasible results are achieved in a few iterations. The results show that the proposed technique can be applied to keep the voltages within the limits specified at each node of a distribution network with biomass power plants. The outcomes are attained using the unbalanced distribution system IEEE-13 node and connecting biomass power plants at some nodes. This study shows that the power losses and voltage unbalance are reduced as a result of the inclusion of distributed generation.

Grid-tie three-phase inverter with active power injection and reactive power compensation

This paper proposes a methodology for the active and reactive power flow control, applied to a grid-tie three-phase power inverter, considering local and/or regionalized power flow control necessity in the forthcoming distributed generation scenario. The controllers are designed by means of robust pole placement technique, which is determined using the Linear Matrix Inequalities with D-stability criteria. The linearized models used in the control design are obtained by means of feedback linearization, aiming to reduce system nonlinearities, improve the controller's performance and mitigate potential disturbances. Through multi-loop control, the power loop uses active and reactive power transfer adapted expressions to obtain the magnitude of the voltage and power transfer angle to control the power flow between the distributed generation and the utility grid. The methodology main idea is to obtain the best controllers with the lowest gains as possible placing the poles in the left-half s-plane region, resulting in fast responses with reduced oscillations. In order to demonstrate the feasibility of the proposal a 3 kVA three-phase prototype was implemented and a comparison with conventional controller is performed to demonstrate the proposed methodology performance. In addition, anti-islanding detection and protection against over/under voltage and frequency deviations are demonstrated through experimental results.

Point Estimate Method for Voltage Unbalance Evaluation in Residential Distribution Networks with High Penetration of Small Wind Turbines

Voltage unbalance (VU) in residential distribution networks (RDNs) is mainly caused by load unbalance in three phases, resulting from network configuration and load-variations. The increasing penetration of distributed generation devices, such as small wind turbines (SWTs), and their uneven distribution over the three phases have introduced difficulties in evaluating possible VU. This paper aims to provide a three-phase probabilistic power flow method, point estimate method to evaluate the VU. This method, considering the randomness of load switching in customers’ homes and time-variation in wind speed, is shown to be capable of providing a global picture of a network’s VU degree so that it can be used for fast evaluation. Applying the 2m + 1 scheme of the proposed method to a generic UK distribution network shows that a balanced SWT penetration over three phases reduces the VU of a RDN. Greater unbalance in SWT penetration results in higher voltage unbalance factor (VUF), and cause VUF in excess of the UK statutory limit of 1.3%.