Radial Topology Research Articles

Efficient handling of radiality constraints for large-scaled power distribution networks

Power distribution networks are usually characterized by a radial topology and therefore the related optimization problems require radiality constraints in their formulations. However, practical instances may have very large size, and the number of radiality constraints may grow faster than the size of the instance. Hence, the arising optimization models may become computationally intractable due to their huge dimension. This work proposes a combinatorial optimization approach to overcome this issue. Our approach is based on the combinatorial formulation of the radiality constraints and their delayed and efficient generation in the model, following a separation-optimization scheme. We find an optimal acyclic spanning subgraph subject to both technical side constraints and topological radiality requirements on a graph representing the distribution network. This can be done without considering all the exponentially many radiality constrains from the beginning of the model solution, but introducing only the ones that are needed to make the solution feasible. It turns out that the number of required constraints is much smaller than the number of all possible radiality constraints, also because some of the electric constraints already favor the elimination of infeasible configurations. Computational experiments on reconfiguration benchmarks from the literature show the effectiveness of the proposed approach.

Adaptive Static Equivalences for Active Distribution Networks With Massive Renewable Energy Integration: A Distributed Deep Reinforcement Learning Approach

Active distribution networks (ADNs) with 100% renewable energy sources (RESs) penetration are essential in the net-zeros emission power sector. As an efficient analysis tool, the equivalent model for ADNs (EMADNs) can be leveraged to expedite the lengthy analysis and preserve data privacy. Nevertheless, volatile RESs, along with their active management techniques, e.g., voltage regulation schemes (VRSs), deteriorate the fidelity of the developed EMADNs derived from historical data. This paper proposes an adaptive EMADN with tunable network scales and adaptive parameters to address the above challenges. A leaves-trimming network topological reduction algorithm is utilized to preserve the radial topology, the nodes of interest, and VRSs. Upon the derived network topology and components, a distributed Proximal Policy Optimization (DPPO)-based deep reinforcement learning agent is employed to adjust the parameters periodically to maintain the fidelity of EMADNs over time. The distributed training scheme extends the ordinary PPO to boost exploration and training efficiency by exploiting the multi-processors in a synchronous way. Case studies on the IEEE-33 bus and IEEE 123-bus ADNs with massive photovoltaic and wind generation demonstrate the superior accuracy and efficiency of the proposed agent-based EMADNs in various scenarios, especially when the production of RESs exceeds the load amount.

Natural logarithm particle swarm optimization for loss reduction in an island power system

In an island power system, optimizing energy management is fundamental since there are renewable sources with their limitations. This management includes the allocation and capacity of energy sources to supply the loads. In this context, optimizing losses in the system contributes to improve the efficiency of this management. This paper proposes the losses optimization and energy management in the island power system. The authors propose the Natural Logarithm Particle Swarm Optimization to solve the problem and compare it with the Attractor Point Algorithm and Evolutionary Particle Swarm Optimization. And with that, we also propose a particle initialization for the studied particle-based algorithms to guarantee convergence in radial power systems. This is because the system configuration influences the response of the algorithm convergence. These techniques were applied to the IEEE-34 unbalanced radial island system.•Natural Logarithm Particle Swarm Optimization differs from classical PSO in that it does not calculate the velocity of the particles. Therefore, the method considers a cloud of particles with a natural logarithmic trajectory to solve the reduction of losses in a power system with a radial topology.•Natural Logarithmic Particle Swarm Optimization uses an initialization equation to minimize the initial estimation process, which is relevant to the convergence process.

Unlocking responsive flexibility within local energy communities in the presence of grid-scale batteries

The transition towards a decentralized, decarbonized, and distributed energy infrastructure necessitates techno-economic initiatives to empower local energy communities (LECs) to achieve self-reliance and evolve into self-sustained electricity networks. It is crucial to underscore the significance of network resilience, especially in the context of local power generation, battery storage, and the radial topology of low-voltage (LV) networks. While contemporary LV networks have made significant attempts to integrate distributed energy resources (DERs), the notable deficiency lies in their lack of network redundancy, posing a substantial challenge in the occurrence of high-impact, low-probability (HILP) events. Therefore, to enhance LV network resilience and leverage its capability to withstand unexpected disruptions, the network operator needs to unlock the potential contributions of end-users within the active distribution networks (ADNs). In this paper, a comprehensive model is developed based on multi-temporal optimal power flow (MTOPF) for unbalanced LV networks addressing the technical issues in islanded microgrid operational planning. The contributions of the grid-scale batteries in forming islanded microgrids and the flexibility that can be provided by the end-users in the LEC have been considered in this paper. To demonstrate the performance of the proposed model, the simulation studies have been carried out on a part of medium and low voltage networks, consisting of network reconfiguration and load transferring capability to reduce the service interruptions during HILP events. The energy-not-served (ENS) is chosen as one of the key performance indicators (KPIs) in this study. With the unlocking flexibility potentials and contribution of the DERs, including grid-scale energy storage (GES) units and Photovoltaic (PV) panels, the ENS has been reduced from 700.8 kWh to 447.5 kWh by activating the local resources, proper switching action, and contribution of the flexible loads, for one of the severe HILP events, i.e., the main grid outage. In this case, the full load curtailment index is reduced from 180 to 106 client hours.

Exploring discrete space–time models for information transfer: Analogies from mycelial networks to the cosmic web

Fungal mycelium networks are large scale biological networks along which nutrients, metabolites flow. Recently, we discovered a rich spectrum of electrical activity in mycelium networks, including action-potential spikes and trains of spikes. Reasoning by analogy with animals and plants, where travelling patterns of electrical activity perform integrative and communicative mechanisms, we speculated that waves of electrical activity transfer information in mycelium networks. Using a new discrete space–time model with emergent radial spanning-tree topology, hypothetically comparable mycelial morphology and physically comparable information transfer, we provide physical arguments for the use of such a model, and by considering growing mycelium network by analogy with growing network of matter in the cosmic web, we develop mathematical models and theoretical concepts to characterise the parameters of the information transfer.

Capacity contributions of Southern Oregon offshore wind to the Pacific Northwest and California

Variable renewable energy generation poses unique capacity challenges, which increasingly depend on weather events at varying timescales. Facilitated by transmission planning, geographic and technological diversity of the generation fleet may provide a mitigation to capacity shortfalls. In this work, offshore wind (OSW) energy is sited in the areas off the West Coast between Coos Bay, Oregon, and Crescent City, California. Three generation and transmission scenarios are modeled within the Western Interconnection: (i) 3.4 gigawatts (GW) of installed OSW capacity connected to Southern Oregon through a High Voltage Alternating Current (HVAC) Radial Topology in 2030; (ii) 12.9 GW of installed OSW capacity connected to Washington, Oregon, and California through a High Voltage Direct Current (HVDC) Radial Topology post-2030, and (iii) the same 12.9 GW connected to the same locations through a Multi-terminal DC (MTDC) Backbone Topology post-2030. Zonal dispatch simulations assuming coincident wind, solar, and hydropower production and loads over 18 meteorological years, accounting for temperature-dependent equipment derating and forced outages, serve as inputs to the Associated System Capacity Contribution (ASCC) methodology. The capacity credit is 33%, 25% and 34% for the 2030 HVAC Radial Topology, 2030+ HVDC Radial Topology, and 2030+ MTDC Backbone Topology, respectively. Transmission design is shown to mitigate the typical erosion of marginal capacity contribution as more OSW is developed, underscoring the opportunity for grid modernization while decarbonizing the generation mix.

A DC fault current fast-computing method of MMC-HVDC grid with short circuit protection equipment

The multi-terminal modular multi-level converter-based high voltage direct current (MMC-HVDC) grid with short circuit protection equipment (SCPE) is so complex that it is difficult to estimate its fault current and analyze the performance of SCPE by conventional time-domain numerical calculation method, it meets three big obstacles. This paper has made significant progress in overcoming these obstacles. 1). By applying the modern electrical circuit theory, a systematic formulation of the differential equation set for fault current calculation is developed to avoid a lot of complex and cumbersome matrix manual calculations. 2). A novel Y-Delta transformation in the s-domain is proposed to develop an eliminating virtual node approach for a complex MMC-HVDC grid, including the ring, radial, and hybrid topologies. 3). It is difficult to solve the equivalent circuit of MMC-HVDC grid with SCPE since SCPE is a time-variable-nonlinear circuit. A canonical voltage source model of SCPE is established to transform the time-variable-nonlinear circuit into a piecewise linear circuit. Based on the three significant progresses, a DC fault current fast-computing method of MMC-HVDC grid with SCPE is put forward to deal with all kinds of MMC-HVDC grids with several kinds of SCPEs. Then, the performance of several kinds of SCPE is analyzed and compared by this method. Consequently, the proposed DC fault current fast-computing method is a new powerful tool to estimate the fault current of MMC-HVDC grid and analyze the performance of SCPE.

Deep-Learning-Aided Voltage-Stability-Enhancing Stochastic Distribution Network Reconfiguration

Power distribution networks are approaching their voltage stability boundaries due to the severe voltage violations and the inadequate reactive power reserves caused by the increasing renewable generations and dynamic loads. In the broad endeavor to resolve this concern, we focus on enhancing voltage stability through stochastic distribution network reconfiguration (SDNR), which optimizes the (radial) topology of a distribution network under uncertain generations and loads. We propose a deep learning method to solve this computationally challenging problem. Specifically, we build a convolutional neural network model to predict the relevant voltage stability index from the SDNR decisions. Then we integrate this prediction model into successive branch reduction algorithms to reconfigure a radial network with optimized performance in terms of power loss reduction and voltage stability enhancement. Numerical results on two IEEE network models verify the significance of enhancing voltage stability through SDNR and the computational efficiency of the proposed method.

Novel protection method for AC microgrids with multiple distributed generations using Unscented Kalman filter

Traditional protection methods were inadequate in multiple distributed generations (MDG) microgrids due to the bidirectional power flow/high fault current in the grid-connected (GC) mode, and reduced fault current in the islanded (ID) mode. Therefore, a reliable and robust protection method has become of paramount importance for such MDG-based microgrids. This article suggests an Unscented Kalman filter (UKF) to detect, classify, and locate faults in such MDG-based microgrids. Initially, the harmonic content is generated from the UKF-estimated current signal to compute the total harmonic RMS factor (THRF). Then the changes in the THRF of each phase are cross-checked to a pre-specified threshold level to distinguish the fault conditions. Furthermore, the cumulative covariance-dependent reactive energy (CCDRE) is computed from both the estimated state and covariance matrix of voltage and current signals provided by UKF. Finally, the directional trends in the CCDRE are used to identify the fault zone in the microgrids. The effectiveness of the proposed method is validated through ample simulations on CIGRE and IEC 61,850–7–420 microgrid test system via MATLAB® Simulink. The results illustrate that the presented strategy is robust in both the GC mode and the ID mode of operation in meshed and radial topologies with 99.9% accuracy.

Universal Adaptive Differential Wavelet Energy-Based Protection Scheme for an AC Microgrid

A protection engineer’s top priorities are the detection of faults and the recognition of faulty phases. Modern distribution networks are interconnected; thus, any breakdown poses a hazard to the entire system. One of the challenges with microgrids is developing an effective protection scheme. In this paper, a new scheme has been proposed that effectively detects faults in the grid-connected, as well as off-grid modes also radial and looped topology of the microgrid. The scheme can adapt to the system changes and even detects the high resistance faults in a low-voltage distributed feeder. Moreover, various non-fault events such as load switching, capacitor switching, DG outage, section cutoff, and external faults have also been considered for evaluation. The performance of the scheme has also been tested for changes in fault inception angles, fault types, fault locations, simultaneous, evolving, and composite faults. The suggested method has also been tested using real-time data from the OPAL-RT simulator. The results demonstrate that the suggested scheme is suitable for real-time practical applications for the protection of microgrid feeders. Further, a comparative study has been done to prove that the proposed scheme is better than several existing protection schemes considered in this paper.

Integration of PV systems into low voltage networks using standard load profiles

The impact of a higher share of distributed generation units is shown using the example of PV systems. A LV network with partly meshed and partly radial topology has been examined. Standard load profiles have been applied to obtain results with a resolution of 15 minutes. Feed-in profiles are compared with a data set based on measured values to model PV generation. Two extreme cases for transformer loading and compliance with voltage limits are high load (winter) without PV and low load (summer) with PV feed-in. In the latter case, power flow via the transformer was reversed during certain periods of the day. At the same time, voltage was increased especially at a long electrical distance from the transformer.

A distributed energy resources control method to improve the loading profile of radial distribution feeders using solid-state transformer

The multi-purpose use of distributed energy resources (DER) can bring a lot of income to its owners. For example, the load imbalance of the radial feeders in the distribution network is an old problem that occurs due to the simple structure of the radial topology and the unidirectional power flow in traditional networks. With emerging DERs and the development of power electronic technology, previous concepts are changing continuously. This paper aims to balance the load between two feeders whilst, it yields better voltage profiles and more appropriate utilization of distribution feeders. This paper proposes a new control method for DERs (including PV panels plus battery storage) that makes the radial system pretends a ring topology properties. It is done with the help of a solid-state transformer (SST). The relationships of the DER current controller are formulated based on current passes through the ring connection. Case studies are carried out on improved IEEE 33-node and 13-node systems with DERs and SSTs. The results show that the suggested control method can simulate the real ring topology and operating objective namely, load balancing is reached.

Enhancing resilience by outage management strategy based on semidefinite programming relaxation method in unbalanced microgrids

During electrical power outages caused by extreme events, microgrid operators (MGOs) attempt to restore as much electrical load as possible. This work suggests a strategy for outage management (OM) to improve microgrid resilience by using two optimal actions: distribution feeder reconfiguration (DFR) and scheduling of distributed energy resources (DERs). After a line fault, the radial network topology is determined by the proposed model using the rank of the incidence matrix. The proposed model is formulated by an analytical optimization method created by semidefinite programming (SDP) relaxation. The SDP changes the non-convex and nonlinear model suggested for OM into an approximated convex model, which commercial software applies. The proposed model considers the uncertain behavior of non-dispatchable DERs and the electrical demands that deal with an information gap decision theory (IGDT) based on a risk-averse strategy. To improve the proposed model's flexibility, the shortened electrical demand as a demand response program (DRP) is considered. The aim of optimization is the minimization of the accumulative cost for dispatchable DER operation and load reduction. The suggested SDP model is figured out using the MOSEK solver in GAMS software. Using the offered model in the 69-bus unbalanced test system displays that the SDP model averagely decreases total operation cost and execution time by 1.04% and 61.29% on all scenarios in comparison with the conventional GAMS model.

Adaptability Analysis of Distribution Network Protection Technology Considering Distributed Photovoltaic Power Generation Access

The integration of distributed power sources into the distribution network has transformed the traditional radial topology structure of the distribution network into a multi-source structure, which can lead to a series of problems, such as voltage violations and bidirectional power flow in the lines. This situation presents a significant challenge to traditional distribution network protection technology. Therefore, based on the electrical characteristics of random loads and distributed power sources, the impact of distributed power source integration on fault characteristics and protection is analyzed, and the adaptability of different distribution network protection methods to distributed power source integration is evaluated. Key factors for improving the protection action characteristics of the distribution network are proposed.

Efficient Allocation and Sizing the PV-STATCOMs in Electrical Distribution Grids Using Mixed-Integer Convex Approximation

Photovoltaic (PV) systems are a clean energy source that allows for power generation integration into electrical networks without destructive environmental effects. PV systems are usually integrated into electrical networks only to provide active power during the day, without taking full advantage of power electronics devices, which can compensate for the reactive power at any moment during their operation. These systems can also generate dynamic reactive power by means of voltage source converters, which are called PV-STATCOM devices. This paper presents a convex formulation for the optimal integration (placement and sizing) of PV-STATCOM devices in electrical distribution systems. The proposed model considers reducing the costs of the annual energy losses and installing PV-STATCOM devices. A convex formulation was obtained to transform the hyperbolic relation between the products of the voltage into a second-order constraint via relaxation. Two simulation cases in the two IEEE test systems (33- and 69-node) with radial and meshed topologies were implemented to demonstrate the effectiveness of the proposed mixed-integer convex model. The results show that PV-STATCOM devices reduce the annual cost of energy losses of electrical networks in a more significant proportion than PV systems alone.

Performance Analysis of a Backward/Forward Algorithm Adjusted to a Distribution Network with Nonlinear Loads and a Photovoltaic System

Context: The backward/forward (BF) algorithm is a sweep-type technique that has recently been used as a strategy for the power flow analysis of ill-conditioned networks. The purpose of this study is to evaluate the performance of the BF algorithm compared to that of a computational tool such as Simulink, with both strategies adjusted to the operating conditions of a distribution network with nonlinear components (loads and photovoltaic system), unbalanced loads, and harmonic distortion in the voltage and current signals. Method: The study case is a low-voltage distribution network with a radial topology, unbalanced loads, and nonlinear components. The BF algorithm is adjusted to consider two approaches of the Norton model: a coupled admittance matrix and a decoupled admittance matrix. The latter is also used in the network model created in Simulink. The performance of the algorithm is evaluated by analyzing 18 operation scenarios defined according to the presence and use intensity of the loads and solar irradiance levels (low and high). Results: In general, the three strategies could successfully determine the waveform and RMS values of the voltage signals with errors of less than 0,8 and 1,3%, respectively. However, the performance of the strategies for the estimation of current signals and power parameters shows errors of 5-300% depending on the level of solar irradiance at which the photovoltaic system operates. Conclusions: The results show that the BF strategy can be used to analyze unbalanced power grids with increasing penetration of renewable generation and the integration of nonlinear devices, but the performance of this strategy depends on the load model applied to represent the behavior of nonlinear devices and generation systems.

Evaluation of the efficacy of transient overvoltages suppression measures in different wind farm topologies using SF6 circuit breaker

Various overvoltage mitigation schemes were used in literature in suppression of switching overvoltages in wind farms. However, the evaluation of how the effectiveness of these mitigation techniques would vary with the change of the wind farm topology is still un-explored territory. The main aim of this paper is to study the effectiveness of four mitigation schemes while using SF6 circuit breaker namely; R–L smart choke, R–C snubber circuit, surge capacitor and pre-insertion resistor (PIR) were studied in four different wind farm topologies; radial, single-sided ring, double-sided ring and star topologies. The topologies were based on a real wind farm located in Zaafrana, Egypt. The results showed that R–L choke to be the most effective scheme for all topologies followed by PIR, R–C snubber and surge capacitor schemes respectively. Their percentage of reduction of overvoltage ranged from 62 to 84% for R–L choke, 33–67% for PIR, 8–25% for R–C snubber circuits and 4–15% for surge capacitors. Also, it was shown that the change of the wind farm topology didn’t affect the order of effectiveness of the mitigation schemes such that R–L remained the most effective and surge capacitor the least effective for all topologies.

Design of Radial Flow Channel Proton Exchange Membrane Fuel Cell Based on Topology Optimization

In this paper, the flow channel of the radial proton exchange membrane fuel cell (PEMFC) is optimized by the topological optimization method. Using the SNOPT algorithm, a two-dimensional stable constant temperature model is freely constructed in the cyclic sector design domain. Topology optimization aims to maximize the efficiency of PEMFC and minimize the energy dissipation of reaction gas. We analyze radial topology flow channels’ mass transfer capacity and cell performance with different maximum volume constraints. The results show that under high current density, the performance of the optimized channel is significantly better than that of the traditional channel. Increasing the maximum volume constraint is beneficial for improving the mass transfer of PEMFC. At 0.6 V, the cell performance of Scheme 4 is 14.9% higher than the serpentine flow channel and 9.5% higher than the parallel flow channel. In addition, in the optimal selection, 3D simulation modeling is carried out for more accurate verification.

ML-Based Intermittent Fault Detection, Classification, and Branch Identification in a Distribution Network

The accurate detection and identification of intermittent cable faults are helpful in improving the reliability of the distribution system. This paper proposes intermittent fault detection and identification for distribution networks based on machine-learning (ML) techniques. For this reason, the IEEE 33 bus system is simulated in the radial and mesh topologies by considering all possible single- and three-phase electrical faults and limitations to collect high-resolution voltage and current waveforms. Moreover, this simulation investigates and considers various cases including low-impedance faults (LIFs) and high-impedance faults (HIFs) with a short and long duration. The collected data from the simulation are used for high-impedance intermittent fault detection, classification, and branch identification using eight supervised learning methods. A comparison between the accuracy and error of these ML classifiers shows that gradient booster (GB) and K-nearest neighbors (KNN) have the best performance for all three objectives. However, GB has a very high computation time compared to KNN.

Planning of an LVAC Distribution System with Centralized PV and Decentralized PV Integration for a Rural Village

Energy demand is continuously increasing, leading to yearly expansions in low-voltage (LV) distribution systems integrated with PVs to deliver electricity to users with techno-economic considerations. This study proposes and compares different topology planning strategies with and without PVs in a rural area of Cambodia over 30 years of planning. Firstly, the optimal radial topology from a distribution transformer to end-users is provided using the shortest path algorithm. Secondly, two different phase balancing concepts (i.e., pole balancing and load balancing) with different phase connection methods (i.e., power losses and energy losses) are proposed and compared to find the optimal topology. Then, the integration of centralized (CePV) and decentralized PV (DePV) into the optimal topology is investigated for three different scenarios, which are zero-injection (MV and LV levels), no sell-back price, and a sell-back price. Next, the minimum sell-back price from CePV and DePV integration is determined. To optimize phase balancing, including the location and size of PV, an optimization technique using a water cycle algorithm (WCA) is applied. Finally, an economic analysis of each scenario based on the highest net present cost (NPC), including capital expenditure (CAPEX) and operational expenditure (OPEX) over the planning period, is evaluated. In addition, technical indicators, such as autonomous time and energy, and environmental indicator, which is quantified by CO2 emissions, are taken into account. Simulation results validate the effectiveness of the proposed method.