Multiphase Distribution Networks Research Articles

Phase Identification in Unobservable Distribution Systems

Accurate network and phase connectivity models are crucial to distribution system planning, operations, and situational awareness. In this regard, this paper proposes a novel phase identification approach for unbalanced distribution networks where phases are insufficiently labeled and measurements are limited (i.e., system is unobservable). The proposed approach utilizes the nodal voltage magnitude measurements for clustering the graph representing the phase connectivity information. The proposed approach consists of an optimization formulation that infers the connectivity of the entire multi-phase distribution network in a single shot. Simulation results on IEEE 37, IEEE 123 and EPRI Ckt5 bus test system illustrate the ability of the proposed approach to accurately identify the phase labels under varying availability of data, phase labels errors, and unknown phase connectivity information. The accuracy of the proposed approach is above 90% under these different scenarios and offers gain over 70% over existing state of the art spectral clustering based approaches for phase identification.

Multi-threaded power flow of large-scale active multiphase distribution networks

Multi-threaded power flow of large-scale active multiphase distribution networks

Distributed Optimal Power Flow in Unbalanced Distribution Grids With Non-Ideal Communication

The use of distributed optimization for solving optimal power flow (OPF) problems in distribution networks is increasing as the number of controllable devices and the span of service areas increase. However, the performance of the distributed optimization algorithm largely depends on the availability and quality of communication links between the computing entities. In this paper, we evaluate the performance of the alternating direction method of multipliers (ADMM) for solving the OPF problem for volt-VAr optimization (VVO) under non-ideal communication. The overall problem is formulated by considering the unbalanced operation of multi-phase distribution networks. The algorithm's performance is first analyzed, assuming there is an ideal communication between computing entities, which serves as a benchmark for further analysis. Then, two non-ideal communication models, namely (1) sporadic communication failure and (2) communication under a noisy transmission, are applied to the information exchange architecture of the ADMM. Extensive numerical experiments are conducted with two test systems, the IEEE 123-bus feeder and a 2522-bus network scaled down from the IEEE 8500-bus system; these are used to evaluate the performance of the algorithm. The results indicate that the ADMM-based distributed VVO algorithm has deteriorated performance under high levels of communication failure and high levels of noise injection. Additionally, although the centralized-VVO counterpart has some computational superiority when the overall problem is convex and no communication impairments exist, the distributed-VVO has superior immunized solution performance under realistic communication constraints.

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.

Decoupled load flow for large-scale multiphase distribution networks

The load flow procedure is the base procedure for various power applications in the distribution management systems. The modern distribution networks are significantly larger than the old ones and the need for the accurate and fast load flow calculation is understandable. This paper presents a decoupled model of consumers, line sections, and three-phase transformers which are integrated in the proposed backward–forward sweep procedure. The radialization procedure for the multi-phase weakly-meshed distribution networks has also been introduced. The decoupled load flow procedure has been presented in detail with its performance evaluated when applied on large-scale distribution networks. The results show that the speedup of the decoupled backward–forward procedure compared to the traditional coupled based one is up to 90%. The decoupled solution is more suited for the concurrent approach which will be analyzed in the future work.

Optimal pump scheduling in multi-phase distribution networks using Benders decomposition

With the growing adoption of renewable energy resources in the power grid, co-optimizing the operation of water and power distribution networks (WDNs and PDNs) increases the flexibility of both systems. The optimal water power flow problem (OWPF) is formulated to manage resource utilization across the WDNs and multi-phase PDNs. The nonlinear WDN hydraulic constraints and PDN ac power flow equations render the OWPF problem nonconvex. This paper formulates a convex optimal water power flow (C-OWPF) problem adopting successive approximations in WDNs and branch-flow relaxations in PDNs. The C-OWPF problem is a mixed-integer semidefinite program, which is computationally challenging even for small instances. Additionally, privacy considerations of WDN and PDN operators motivate the need for solving the C-OWPF in a distributed fashion. This paper develops a C-OWPF solver based on Benders decomposition that overcomes computational complexity challenges and preserve the privacy of the respective operators. The merits of the Benders decomposition-based solver are demonstrated on the IEEE 4-bus PDN coupled with a 3-node WDN and the IEEE 123-bus PDN coupled with the 36-node WDN.

Measurement-based prediction-correction online distributed optimal power flow algorithm for multi-phase active distribution networks

Online algorithms have shown great potential in solving time-varying optimal power flow (OPF) problems emerging in active distribution networks (ADNs) with numerous power-electronics-interfaced distributed energy resource (DER) integrations. However, existing online algorithms have the following limitations: 1) Correction-only algorithms ignore the time-varying characteristics of the optimization problem; 2) Prediction-correction algorithms cannot handle nonlinear OPF problems; 3) Most algorithms only consider the application of single-phase cases. This paper addresses the above limitations by proposing a novel measurement-based prediction-correction online distributed OPF algorithm for multi-phase ADNs. This algorithm is based on an improved multi-phase linearized alternating current (AC) power flow model that takes advantage of the voltage measurements to improve the approximation accuracy. In each sampling period, the proposed algorithm first performs a limited number of correction steps, iterating the incremental variable based on the current outputs of DERs and the voltage measurements to track the optimal solution. The DERs then execute the resultant incremental output powers. After forecasting the time-varying parameters, the proposed algorithm performs a few prediction steps to seek a better starting point for the correction steps before the next sampling. Numerical test results of the modified IEEE 37-bus and 123-bus distribution systems demonstrated that the proposed algorithm can track the optimal solution of the time-varying nonlinear OPF problem more accurately than existing online algorithms, even in extra-high penetration scenarios (≥200%).

Optimal power scheduling of seaport microgrids with flexible logistic loads

Seaports are progressively electrified to harness various energy resources to provide green logistic services to ships. They essentially act as multi-energy microgrids to enhance the energy efficiency and environmental sustainability of the maritime industry. This trend necessitates the coordinated operation of multiple sectors in seaport microgrids, which is a challenging problem due to the complex couplings of power, thermal, and fluid flows and the heterogeneity of logistic loads. An optimal power scheduling framework for seaport microgrids is developed. Specifically, a non-linear, non-convex optimisation problem is formulated to integrate various logistic loads, including cold ironing, quay and yard cranes, and reefer areas, in an unbalanced multi-phase power distribution network connected with a thermal network. The optimisation problem is solved in a scalable decomposed manner based on iterative convex relaxation and approximation. Simulation results on a real-world port model verify the efficacy of the proposed framework, as well as the potential of the flexible logistic loads in improving port energy efficiency.

A Linear AC Power Flow Model for Unbalanced Multi-Phase Distribution Networks Based on Current Injection Equations

A realistic and practicable modeling of unbalanced distribution networks (DNs) is the missing link in most studies undertaken in these networks, e.g., optimal power flow (OPF), energy markets, etc. To address the issue, this letter proposes an unbalanced linear three-phase four-wire power flow (PF) model based on current injection equations at nodes. Also, the ZIP representation is considered for loads. The model can be easily generalized for unbalanced three-wire networks with minor changes and assumptions. Hence, the scope of the proposed method can be extended to cover both low-voltage and medium-voltage DNs. The performance of the proposed model is verified through simulations on two IEEE test feeders.

A new power flow for multi-phase distribution networks with simultaneous phase interruptions

A new power flow for multi-phase distribution networks with simultaneous phase interruptions

OPEN: An open-source platform for developing smart local energy system applications

This paper presents OPEN, an open-source software platform for integrated modelling, control and simulation of smart local energy systems. Electric power systems are undergoing a fundamental transition towards a significant proportion of generation and flexibility being provided by distributed energy resources. The concept of ‘smart local energy systems’ brings together related strategies for localised management of distributed energy resources, including active distribution networks, microgrids, energy communities, multi-energy hubs, peer-to-peer trading platforms and virtual power plants. OPEN provides an extensible platform for developing and testing new smart local energy system management applications, helping to bridge the gap between academic research and industry translation. OPEN combines features for managing smart local energy systems which are not provided together by existing energy management tools, including multi-phase distribution network power flow, energy market modelling, nonlinear energy storage modelling and receding horizon optimisation. The platform is implemented in Python with an object-oriented structure, providing modularity and allowing it to be easily integrated with third-party packages. Case studies are presented, demonstrating how OPEN can be used for a range of smart local energy system applications due to its support of multiple model fidelities for simulation and control.

Optimal Power Flow With Step-Voltage Regulators in Multi-Phase Distribution Networks

This paper develops a branch-flow based optimal power flow (OPF) problem for multi-phase distribution networks that allows for tap selection of wye, closed-delta, and open-delta step-voltage regulators (SVRs). SVRs are assumed ideal and their taps are represented by continuous decision variables. To tackle the non-linearity, the branch-flow semidefinite programming framework of traditional OPF is expanded to accommodate SVR edges. Three types of non-convexity are addressed: (a) rank-1 constraints on non-SVR edges, (b) nonlinear equality constraints on SVR power flows and taps, and (c) trilinear equalities on SVR voltages and taps. Leveraging a practical phase-separation assumption on the SVR secondary voltage, novel McCormick relaxations are provided for (c) and certain rank-1 constraints of (a), while dropping the rest. A linear relaxation based on conservation of power is used in place of (b). Numerical simulations on standard distribution test feeders corroborate the merits of the proposed convex formulation.

Bus injection relaxation based OPF in multi-phase neutral equipped distribution networks embedding wye- and delta-connected loads and generators

A novel Optimal Power Flow (OPF) model, based on Semi-Definite Programming approach, for multi-phase active Distribution Networks (DNs) equipped with neutral conductor(s) and both wye- and delta-connected loads/Distributed Generators (DGs) is proposed in this paper. The coupled power injection across phase-neutral and phase-phase conductors is decoupled by modelling of a shunt load/DG through a correction current injection approach and, consequently, explicit power injections are obtained for each conductor of a node. Furthermore, the complete ZIP load representation is considered in the OPF model and two approximations, based on the first-order Taylor series and approximation of the first-order Taylor series, are introduced for the modelling of constant current component of a ZIP load in terms of an optimization variable. Simulations are carried out on several medium and low voltage active DNs under various parameters of the ZIP models for the minimization of either slack-bus power or network losses objective functions. It is successfully demonstrated that the proposed relaxation recovers the global optimal solution of the original OPF problem for both load types (wye and delta) under various combinations of ZIP parameters in the case of lightly or moderately unbalanced DNs, whereas in the case of highly unbalanced DNs, a rank-2 solution is obtained when constant current component dominates the other load components. Furthermore, the impact of unrealistic assumption of Kron reduction approach on the quality of the proposed relaxation for a single or multiple point grounded DNs is also discussed. From a computational point of view, the proposed methodology can be realized on a real-time basis for small DNs. However, for medium and large DNs, the incorporation of additional sparsity exploitation or distributed algorithm techniques are required for its real-time implementation.

Multi‐objective planning model for multi‐phase distribution system under uncertainty considering reconfiguration

In this study, multi-objective particle swarm optimisation (MOPSO) and preference order (PO) ranking-based multi-objective planning model is presented for placement and sizing of wind and solar-based distributed generators (DGs), and capacitors in the multi-phase distribution network, under uncertainty considering network reconfiguration. Uncertainty in solar irradiance, wind speed, and load are considered using Monte Carlo simulation (MCS) with suitable probabilistic models. The planning problem is formulated considering different scenarios generated using MCS. For objective function formulation with varying demand and generation conditions, a dynamic load generation model is developed. A priority vector is proposed for DG and capacitor placement using the analytic hierarchy process to reduce the search space and computational time. The key benefits of the proposed DG placement algorithm are that it gives a single solution that is nearly optimal for all the possible network topologies and it works well for both unbalanced and balanced conditions. The proposed technique has been applied to IEEE 34-bus and IEEE 123-bus systems. The result shows a significant reduction in power losses, current unbalancing and improvement in reliability after the placement of DGs and capacitors.

Electromagnetic transient studies of large distribution systems using frequency domain modeling methods and network reduction techniques

This paper presents the practical application of frequency domain methods to perform detailed electromagnetic transient analysis on very large multi-phase power distribution networks. The proposed technique demonstrates substantial computational gain offering an attractive complement or alternative to widely available time domain tools. This work provides modeling guidance and procedures to derive the system matrix, perform system reduction using network equivalent techniques, and obtain the time domain response. The basic network elements include lumped and distributed parameter lines, transformers, circuit breakers, sources, and loads. In-depth methodology verification confirms great agreement for steady-state and transient simulations when compared with results from ATP/EMTP for two well-known IEEE test feeders (13-bus and-34 bus). Moreover, substantial testing using two large-scale three phase power systems, the IEEE 123-bus and a synthetic 1188-node system emulating a densely meshed urban distribution network, confirm the accuracy of implementing network reduction to solve large networks. The flexibility and adaptability of the proposed methodology can provide considerable time savings to utility companies and engineering firms assessing system wide transients resulting from symmetrical and unsymmetrical faults, network upgrades, and switching schemes.

Placement and Sizing of Inverter-Based Renewable Systems in Multi-Phase Distribution Networks

This paper develops a tractable formulation for optimal placement and sizing of inverter-based renewable systems in multi-phase distribution networks. The goal of the formulation is to minimize the cost of inverter installation, average power import, and average distributed generation curtailment. Three-phase and single-phase inverter models are presented that preserve the underlying mappings between renewable uncertainty to power injection. The uncertainty of distributed generators (DGs) and loads are characterized by a finite set of scenarios. Linear multi-phase power flow approximations are used in conjunction with scenario reduction techniques to arrive at a tractable two-stage stochastic formulation for optimal DG placement and sizing. First-stage decisions are locations for DG deployment and capacity sizes, and second-stage decisions include DG real power curtailment, reactive power support, as well as feeder voltage profile. The resulting formulation is a mixed-integer second-order cone program and can be solved efficiently either by existing optimization solvers or by relaxing the binary variables to the [0,1] interval. Simulation studies on standard multi-phase IEEE test feeders promise that optimal stochastic planning of DGs reduces costs during validation, compared to a scheme where uncertainty is only represented by its average value.

Accelerated Voltage Regulation in Multi-Phase Distribution Networks Based on Hierarchical Distributed Algorithm

We propose a hierarchical distributed algorithm to solve optimal power flow (OPF) problems that aim at dispatching controllable distributed energy resources (DERs) for voltage regulation at minimum cost. The proposed algorithm features unprecedented scalability to large multi-phase distribution networks by jointly exploring the tree/subtrees structure of a large radial distribution network and the structure of the linearized distribution power flow (LinDistFlow) model to derive a hierarchical, distributed implementation of the primal-dual gradient algorithm that solves OPF. The proposed implementation significantly reduces the computation loads compared to the centrally coordinated implementation of the same primal-dual algorithm without compromising optimality. Numerical results on a 4,521-node test feeder show that the designed algorithm achieves more than 10-fold acceleration in the speed of convergence compared to the centrally coordinated primal-dual algorithm through reducing and distributing computational loads.

Beyond Relaxation and Newton–Raphson: Solving AC OPF for Multi-Phase Systems With Renewables

This paper focuses on the AC Optimal Power Flow (OPF) problem for multi-phase systems. Particular emphasis is given to systems with high integration of renewables, where adjustments of the real and reactive output powers from renewable sources of energy are necessary in order to enforce voltage regulation. The AC OPF problem is known to be nonconvex (and, in fact, NP-hard). Convex relaxation techniques have been recently explored to solve the OPF task with reduced computational burden; however, sufficient conditions for tightness of these relaxations are only available for restricted classes of system topologies and problem setups. Identifying feasible power-flow solutions remains hard in more general problem formulations, especially in unbalanced multi-phase systems with renewables. To identify feasible and optimal AC OPF solutions in challenging scenarios where existing methods may fail, this paper leverages the Feasible Point Pursuit - Successive Convex Approximation algorithm—a powerful approach for general nonconvex quadratically constrained quadratic programs. The merits of the approach are illustrated using single- and multi-phase distribution networks with renewables, as well as several transmission systems.

Real Time Multiphase State Estimation in Weakly Meshed Distribution Networks With Distributed Generation

Recent research has presented a load scaling based real time state estimation (SE) approach for radial and multiphase distribution networks; the approach makes use of successive weighted least squares estimation and power flow to adjust forecasted load values so that they conform with the available real time measurements. This paper extends the load scaling based SE approach along two directions, while maintaining performance that is commensurate with real time computing requirements. First, the approach is extended to allow for meshes that are practically available in some distribution systems; this is achieved by embedding the power flow equations of the nodes that are part of the loops within the load scaling formulation. Second, a sensitivity-based technique is introduced to handle isolated line-to-ground voltage magnitude measurements in radial feeders; this technique is compatible with load scaling and is timely as many utilities have increased the monitoring of voltage measurements at pilot nodes to guard against voltage problems that are associated with distributed generation. The efficiency of the proposed estimator is demonstrated by comparison with the three-phase voltage based normal equations approach that handles both voltage magnitudes and meshes.

Improve Distribution System Energy Efficiency With Coordinated Reactive Power Control

In the distribution management system (DMS), an essential application for the energy efficiency improvement is loss reduction. Loss reduction often involves the control of reactive power (var) resources to optimize the var flow in the network. Traditionally, most available var resources in the distribution network have been switchable shunt capacitor banks. Today distributed energy resources (DER) are becoming another significant var resource due to their increasing penetration, which brings new opportunities as well as challenges for loss reduction. This paper proposes an advanced loss reduction approach to achieve the optimal control coordination among multiple capacitors and DERs. The proposed approach and solution are developed on the basis of the detailed multi-phase distribution network modeling and the state-of-the-art optimization technology. This work also investigates the impact of the DER var control on the loss reduction improvement and voltage violation correction. The effectiveness of the proposed approach is demonstrated on practical utility distribution circuits with varying degree of unbalance and model complexity. The performance of the solution method proves the capability of online solution speed for large and complex distribution systems.