Three-phase Distribution Network Research Articles

A Complex-Valued Stationary Kalman Filter for Positive and Negative Sequence Estimation in DER Systems

In medium- and low-voltage three-phase distribution networks, the load imbalance among the phases may compromise the network voltage symmetry. Inverter-interfaced distributed energy resources (DERs) can contribute to compensating for such imbalances by sharing the required negative sequence current while providing active power synchronized with the positive sequence voltage. However, positive and negative sequences are conventionally defined in a steady state and are not directly observed from the instantaneous voltage and current measurements at the DER unit’s point of connection. In this article, an estimation algorithm for sequence separation based on the Kalman filter is proposed. Furthermore, the proposed filter uses a complex vector representation of the asymmetric three-phase signals in synchronous coordinates to allow for the implementation of the Kalman filter in its stationary form, resulting in a simple dynamic filter able to estimate positive and negative sequences even during transient operation. The proposed stationary complex Kalman filter performs better than state-of-the-art techniques like DSOGI and very similarly to other Kalman filter implementations found in the literature but at a fraction of its computational cost (23.5%).

Harmonics Assessment of Distribution Transformer with Photovoltaic Integration and Unbalanced Loads

Harmonic distortion is one of the monumental power quality problems in an electrical power system. It frequently originated from non-linear loads generating non-sinusoidal steady state waveforms, which may lead to various undesirable effects on distribution transformers such as increased losses, overheating and lifetime reduction. In previous works, the harmonic current contributions from non-linear loads from consumers have been appointed as the main contributor of harmonic issues in the distribution transformers. However, since the integrations of renewable energy as a distributed generation (DG) have exponentially increasing in recent years, the impact of solar photovoltaic (PV) system implementation into distribution system on amplifying additional harmonic contents also needs to be addressed. Therefore, this paper conducts a comparative analysis of voltage and current harmonic profiles within the distribution transformer in three-phase distribution network and three-phase grid-connected photovoltaic (GCPV) system, with both subjected to supply unbalanced non-linear loads. The simulation is carried out using MATLAB Simulink 2021a software and the results are compared according to standards. As a result, the distribution transformer in the GCPV system is proven to contain higher levels of voltage and current harmonic distortion compared to a normal distribution grid.

Multiple-node model of wind turbine generating system for unbalanced distribution system load flow analysis

This paper discusses a method to integrate a wind turbine generating system (WTGS) into a three-phase unbalanced distribution system load flow (DSLF) analysis. The proposed method is based on the single-phase multiple-node model. In the present work, the single-phase multiple-node model is extended to a three-phase multiple-node model to facilitate the load flow analysis of a three-phase unbalanced power system network. The multiple-node model (i.e., three-node model) will only modify the load flow analysis by introducing two lines and two load buses to the distribution system network where the WTGS is installed. Thus, a standard three-phase load flow program can be employed to compute the unknown quantities in the DSLF problem formulation. The proposed method is verified by incorporating the model into the load flow analysis of three-phase distribution networks. The investigation uses two representative distribution networks (i.e., 19-bus and 25-bus networks). The results of the study confirm the validity of the proposed method.

Allocation of power losses and energy in the distribution network

The goal is to determine methods for calculating power losses in a three-phase four-wire low voltage distribution network using measurements of a balance smart meter and consumer smart meters, and to establish the factors influencing the power losses and their allocation among individual network wires, loads, and consumers. The study involved examining three methods for determining power losses for current measurement snapshot. The first method suggests calculating losses as the difference between the power supplied to the network and the total power consumed. The second method calculates power losses using the contribution method. The third method, which in addition to measurement information requires knowledge of the topology and parameters of the network components, determines power losses based on the results of the state estimation method. The research proposes an algorithm for transition from a four-wire distribution network modeling to a three-wire one. The algorithm allocates power losses of the neutral wire among the phase wires. The findings indicate that the negative losses in the network with unbalanced phase loads are caused by the presence at the nodes of the least loaded phase of higher voltage than the voltage at the power supply node. The reason for higher losses in phases with minimal load is the uneven allocation of loads in the phases. In addition, the study reveals that the power loss values obtained by the contribution method, i.e. directly from the measurements of smart meters, are closer to the losses determined from the readings of the balance meter and consumer meters, compared to the losses found from the state estimation results. The considered methods for calculation and allocation of power losses are illustrated by an example of a real-world distribution network equipped with smart meters. The paper demonstrates the examples of allocating total power losses between phase wires and a neutral wire, among phase wires only, and between total loads at phase nodes and individual consumers in phases.

Loss Allocation in Three-phase Distribution Network using $\tau$-value

Loss Allocation in Three-phase Distribution Network using $\tau$-value

Line parameter, topology and phase estimation in three-phase distribution networks with non-[formula omitted]PMUs

The increasing penetration of distributed energy sources demands higher observability of the distribution networks for better scheduling, operation, dispatching and control. However, the huge amounts of nodes in the distribution networks implies that any additional measuring instrument would be of huge costs burden for DSO. In this paper, we proposes a full-scale framework for line parameters, topology, phase label estimation and angle recovery utilizing smart meter measurements only for the non-μPMU distribution networks. Firstly, we linearize the three-phase power flow model and induce the relationship of nodal voltage magnitudes and power injections. Then, a joint estimation method based on linear regression and topology characteristics is proposed to find line parameters, topology, and phase label. Finally, the nodal angle information is recovered by non-linear regression based on the estimation result. Simulations on both single-phase and three-phase networks are implemented. The results suggest that the proposed framework can provide an accurate estimation result with limited measurements.

Algorithm for passive reactive power compensation of an unbalanced three-phase four-wire system using capacitors ensuring minimum line losses

Currently in three-phase distribution networks, especially low-voltage networks, there are some inefficient powers. These are defined as reactive power, unbalanced power owing to linear loads, power owing to supply unbalanced voltage, and harmonic power. This has given rise to the concept of power quality. To improve power quality, devices called active filters have been developed. These devices eliminate all the inefficient power. However, for most processes, the elimination of reactive power needs to be from a price/performance perspective because the use of active filters is very expensive. Therefore, the use of capacitor banks in any of their versions (single-phase, three-phase, scalable battery, SVC, etc.) is the most economical and sufficient solution. In this study, a calculation algorithm is proposed to obtain compensators for the inductive reactive power of the load, consisting only of single-phase capacitor banks. These capacitors are designed to minimise losses in the supply line, which are lower than those obtained using the minimum loss line (MLL) strategy. The resulting compensator consists of three, two, or one capacitor, depending on the load characteristics.

Holomorphic Embedding Load Flow Method in Three-Phase Distribution Networks With ZIP Loads

The Holomorphic Embedding Load flow Method (HELM) employs analytic continuation of complex analytic functions to calculate the practical (high voltage) load flow solution and provides promising convergence guarantees. Although HELM has been applied to various types of power systems, the literature has not thoroughly investigated three-phase distribution networks with common load types/connections. In this paper, we extend HELM to three-phase distribution networks with ZIP loads, while preserving its prominent convergence promises. Specifically, we introduce a HELM formulation, which emphasizes on accurate modeling of constant-current loads (and the voltage dependence of current injections) for both wye and delta connections. We perform extensive numerical experiments on standard test systems with various equipment/connection types to demonstrate the accuracy and efficacy of the proposed HELM compared with the existing literature.

Second-Order Cone Programming (SOCP) Model for Three Phase Optimal Power Flow (OPF) in Active Distribution Networks

With the high penetration of distributed generations (DGs), modern distribution systems require novel and efficient optimal power flow (OPF) models. This paper proposes a second-order cone programming (SOCP) based AC-OPF model for three-phase radial power distribution networks. Mutual coupling effects are generally ignored in the existing multi-phase SOCP AC-OPF models. To overcome this critical issue, the proposed SOCP-OPF model introduces a coupling coefficient for the mutual coupling effects on the three-phase unbalanced lines. The derivation of the coupling coefficients has been illustrated with the required proof that the relaxation is tight and the solution from the proposed OPF model is optimal for an unbalanced multi-phase distribution network. The SOCP-OPF model is evaluated on several IEEE standard distribution networks without and with high penetration of Distributed Energy Resources (DERs). It has been shown that the proposed OPF model provides an optimal global solution for convex objective functions. Also, this OPF model is scalable and computationally efficient compared to Nonlinear Programming (NLP) and other convex OPF models.

A novel estimation method for maximum PV hosting capacity in radial distribution networks using bus voltage and electrical distance

Large-scale photovoltaics (PV) generation at the distribution network causes overvoltage problems. These large PV systems are generally connected to the distribution network in three-phase configurations to ensure that power is balanced across all phases. At the same time, radial distribution networks are a common configuration of power systems worldwide as it is simpler and more cost-effective than meshed networks. In such a context, this paper proposes a novel method to estimate PV hosting capacity (PHC) for connection points in a radial and three-phase balanced distribution network. Different from existing methods that normally require power flow solutions of the network, the proposed method only needs line parameters and the historical voltage at the connection point. In addition, the proposed method features conservative estimation for PHC and thus can ensure the safety of network voltage compared with existing methods. The accuracy is tested on the IEEE 33 bus system and the estimation error is within 6%. Furthermore, the proposed method can be easily extended to consider branch losses that can reduce the estimation error to be within 1%. The obtained results have confirmed the feasibility and effectiveness of the proposed method.

Use of Inverter-Based Air Conditioners to Provide Voltage Regulation Services in Unbalanced Distribution Networks

The large-scale integration of photovoltaic generation and electric vehicles results in over-voltage, under-voltage, and voltage unbalance problems in three-phase distribution networks. The power consumption of the air conditioners (ACs) is large among the daily electrical appliances and can be regulated to provide voltage regulation services. To protect occupants' privacy and utilize the existing dispatch strategy of the battery, we propose a thermal battery equivalent model of the inverter-based AC to regulate the active power and provide a voltage regulation service. Moreover, an improved Newton-Raphson power-flow algorithm is developed to reduce the computational burden. The affinity propagation method is applied to cluster ACs according to different operating states. Thus, the ACs' operating frequencies are adjusted to reset the corresponding operating power. The feasibility of the thermal battery equivalent model and voltage regulation algorithm is verified based on case studies utilizing the revised IEEE 33-node three-phase power distribution network.

Local Electricity Market operation in presence of residential energy storage in low voltage distribution network: Role of retail market pricing

Local Electricity Market (LEM) appears as a promising consumer-centric market-based approach that extends the self-consumption method, widely implemented in residential households, to collective self-consumption in the local energy communities, enabled through peer-to-peer (P2P) transactions. To facilitate the integration of LEM in the wholesale electricity market (WEM), it is paramount to comprehend the synergy of retail electricity pricing on the LEM operation hosted in the low-voltage distribution network (LVDN). The paper presents a co-simulation framework consisting of a local electricity market model coupled with a three-phase distribution network simulator to perform a holistic case study for a smart energy community in Ireland. The novel contribution of the work is to explore the potential of local electricity trading in the presence of residential energy storage (ES), under different retail pricing schemes existent in Ireland, by evaluating economic benefits to the energy community and network performance of three-phase LVDN. Extensive simulation studies indicate that the presence of residential ES significantly boosts P2P transactions under static time-of-use (SToU) pricing. These P2P transactions are primarily contributed by energy arbitrage (among customers in LEM) in the winter and surplus PV-generated electricity in the summer. On the other hand, the scheduling of ES under SToU pricing deteriorates the network performance of LVDN in winter, showing the highest active power loss and under-voltage scenario among all the cases. Another unique aspect of LVDN is the voltage unbalance studied and found to be highly correlated with ES operation under SToU pricing. Recommendations have been made to the relevant stakeholders and market actors, identifying key aspects necessary to roll out the LEM under retail electricity pricing schemes.

An Indirect Procedure for Real-Time Monitoring the Neutral Conductor Deterioration in Three-Phase Distribution Networks

An indirect procedure for real-time monitoring the neutral conductor condition in three-phase distribution networks, based on watching over the growth of a novel parameter (∆τ), has been described in this paper. The parameter ∆τ has been defined as the relationship between the neutral-displacement power and Buchholz’s apparent power measured at the fundamental frequency in the loads of the distribution networks for any condition of the neutral conductor and in its nominal conditions. The effectiveness of this procedure has been compared with other traditional indirect procedures, such as the surveillance of the RMS values of the line-to-neutral load voltages or their zero-sequence component. The practical application on a real distribution network reveals that the growth of the parameter ∆τ in the early stages of the breaking process of the neutral conductor follows a straight line whose equation is known for each length and section of that conductor, regardless of the loads and the voltage regulation of the transformer of the distribution network. This characteristic of the ∆τ parameter shows that the proposed procedure is suitable for monitoring neutral conductor deterioration and can be used for preventive maintenance of distribution networks.

Measurement of power effects caused by the deterioration of the neutral conductor in three-phase distribution networks

Measurement of power effects caused by the deterioration of the neutral conductor in three-phase distribution networks

Application of the Generalized Normal Distribution Optimization Algorithm to the Optimal Selection of Conductors in Three-Phase Asymmetric Distribution Networks

This article addresses the problem of the optimal selection of conductors in asymmetric three-phase distribution networks from a combinatorial optimization perspective, where the problem is represented by a mixed-integer nonlinear programming (MINLP) model that is solved using a master-slave (MS) optimization strategy. In the master stage, an optimization model known as the generalized normal distribution optimization (GNDO) algorithm is proposed with an improvement stage based on the vortex search algorithm (VSA). Both algorithms work with discrete-continuous coding that allows us to represent the locations and gauges of the different conductors in the electrical distribution system. For the slave stage, the backward/forward sweep (BFS) algorithm is adopted. The numerical results obtained in the IEEE 8- and 27-bus systems demonstrate the applicability, efficiency, and robustness of this optimization methodology, which, in comparison with current methodologies such as the Newton metaheuristic algorithm, shows significant improvements in the values of the objective function regarding the balanced demand scenario for the 8- and 27-bus test systems (i.e., 10.30% and 1.40% respectively). On the other hand, for the unbalanced demand scenario, a reduction of 1.43% was obtained in the 27-bus system, whereas no improvement was obtained in the 8-bus grid. An additional simulation scenario associated with the three-phase version of the IEEE33-bus grid under unbalanced operating conditions is analyzed considering three possible load profiles. The first load profile corresponds to the yearly operation under the peak load conduction, the second case is associated with a daily demand profile, and the third operation case discretizes the demand profile in three periods with lengths of 1000 h, 6760 h, and 1000 h with demands of 100%, 60% and 30% of the peak load case. Numerical results show the strong influence of the expected demand behavior on the plan’s total costs, with variations upper than USD/year 260,000.00 between different cases of analysis. All implementations were developed in the MATLAB® programming environment.

Line Parameter, Topology and Phase Estimation in Three-Phase Distribution Networks with Non-Μpmus

Line Parameter, Topology and Phase Estimation in Three-Phase Distribution Networks with Non-Μpmus

Techniques for compensation of unbalanced conditions in LV distribution networks with integrated renewable generation: An overview

An increasing number of single-phase loads and renewable energy resources (RESs), such as single-phase rooftop PV units, are unevenly distributed in low voltage (LV) distribution networks. This exacerbates unbalanced conditions in the network which in turn adversely affects the power quality, stability and reliability. This paper presents a comprehensive review of the state-of-the-art techniques for alleviation of the unbalanced conditions in both three-wire and four-wire LV three-phase distribution networks. Technical issues arising from the unbalanced conditions are highlighted. Several definitions of the unbalance indicators and standards that are widely used for unbalance analysis are also given. Furthermore, recent unbalance compensation techniques based on three devices; namely, power electronic converters, electric vehicles (EVs) and energy storage systems (ESSs) are critically reviewed. It is found that the power electronic converters with suitable control strategies and management of EV chargers and plug-in electric vehicles (PEVs) have been intensively studied so far. However, based on the literature survey, there is currently no work on applying cutting-edge methods, such as the distributed cooperative control strategy and multi-agent deep reinforcement learning (MADRL), to utilize distributed single-phase ESSs to mitigate the unbalanced conditions. Therefore, key challenges, possible unbalance mitigation techniques and future research directions are recommended and discussed. • Techniques for alleviating unbalanced conditions in LV systems are reviewed. • Three devices with recent techniques for compensation are presented. • Indicators and standards for analysis of unbalanced conditions are provided. • 1-phase ESSs is recommended with new strategies for future research directions.

Optimal Phase-Balancing in Three-Phase Distribution Networks Considering Shunt Reactive Power Compensation with Fixed-Step Capacitor Banks

The black hole optimization (BHO) method is applied in this research to solve the problem of the optimal reactive power compensation with fixed-step capacitor banks in three-phase networks considering the phase-balancing problem simultaneously. A master–slave optimization approach based on the BHO in the master stage considers a discrete codification and the successive approximation power flow method in the slave stage. Two different evaluations are proposed to measure the impact of the shunt reactive power compensation and the phase-balancing strategies. These evaluations include a cascade solution methodology (CSM) approach and a simultaneous solution methodology (SSM). The CSM approach solves the phase-balancing problem in the first stage. This solution is implemented in the distribution network to determine the fixed-step capacitor banks installed in the second stage. In the SSM, both problems are solved using a unique codification vector. Numerical results in the IEEE 8- and IEEE 27-bus systems demonstrate the effectiveness of the proposed solution methodology, where the SSM presents the better numerical results in both test feeders with reductions of about 32.27% and 33.52%, respectively, when compared with the CSM. To validate all the numerical achievements in the MATLAB programming environment, the DIgSILENT software was used for making cross-validations. Note that the selection of the DIgISLENT software is based on its wide recognition in the scientific literature and industry for making quasi-experimental validations as a previous stage to the physical implementation of any grid intervention in power and distribution networks.

Expansion planning of joint medium- and low-voltage three-phase distribution networks considering the optimal integration of distributed energy resources

This article proposes a novel hybrid approach based on the three-phase bus impedance matrix to solve the medium and low voltage planning problem of three-phase distribution systems considering the optimal integration of battery energy storage systems (BESSs) and different renewable energy sources (RESs). The mathematical formulation to describe the problem involves a mixed-integer non-linear model that considers the allocation and selection problem of distribution substations and transformers, medium and low voltage branches, RESs, and BESSs. Furthermore, the optimal operation of BESSs, the load balancing among low voltage system phases, the upgrading of existing elements, and the uncertainty of RESs, demands, and energy prices are considered. To solve the investment problem, an Iterated Local Search algorithm with neighborhood structures is applied, which uses the electrical information from the three-phase bus impedance matrix to generate new solutions. In addition, a two-step decomposition stochastic optimal power flow is proposed to solve the operational problem considering the stochastic scenarios. The performance of the new methodology is tested on a real distribution system. The numerical results show that integrating RESs and BESSs in the planning problem minimizes the cost of energy losses by 14.16% and the energy purchased from substations by 18.78%.

Design and Analysis of the Shunt Active Power Filter with the ε-NSRLMMN Adaptive Algorithm for Power Quality Improvement in the Distribution System

In this article, an adaptive normalized Sign Regression Least Mean Mixed Norm (ε-NSRLMMN) algorithm-based control technique is developed for the Shunt Active Power Filter (SAPF) to compensate for the grid current harmonics and reactive power under balanced and unbalanced loading conditions. The adaptive ε-NSRLMMN control algorithm improves power quality and makes the source current sinusoidal and power factor (PF) close to unity. It is used for load compensation in a three-phase distribution network. The fundamental active component is extracted from the distorted load current using an adaptive technique. This control algorithm has the advantages of improved convergence, better stability, lower harmonic distortion, less complexity and less steady-state error than the Sign regressor least mean mixed norm (SRLMMN), Least mean square (LMS) and least mean fourth (LMF). Adaptive ε-NSRLMMN is used for learning the fundamental active weight components of the load current. The parameters of the proposed algorithm are trained in real-time. A traditional PI controller has been used to regulate the dc-link voltage of the Voltage Source Converter (VSC). The performance of the proposed algorithm has been justified by simulation and experimental results.