Unbalanced Active Distribution Networks Research Articles

Robust network topology for unbalanced active distribution networks with uncertain injections

AbstractThis research paper introduces a comprehensive formulation for robust dynamic network reconfiguration (NR) of unbalanced active electric distribution networks (DNs). Network reconfiguration is a potent strategy to minimise active power loss in DN as it involves altering network topology through sectionalising (normally closed) and tie‐line switches (normally open). However, NR is usually a mixed integer NP‐hard non‐linear optimisation problem due to the discrete nature of the switches. Hence, including variable injection uncertainties (from generation or load) for an unbalanced active DN with all its attributes further poses a significant challenge in solving NR. The proposed formulation addresses these challenges in a robust optimisation (RO) framework to get a robust topology and power and voltage set points for dispatchable Distributed Generators (DGs). Also, Chance‐Constrained robust formulations are proposed to regulate the conservatism of RO. Numerical analyses demonstrate the impact of conservative robust NR on DG set points compared to the non‐robust NR method. Tests on a modified unbalanced IEEE 34‐bus system and comparison with previous formulations verify the efficacy of the proposed approach, showcasing its effectiveness.

An Efficient Modular Optimization Scheme for Unbalanced Active Distribution Networks With Uncertain EV and PV Penetrations

Integrated control strategies with Network Reconfiguration (NR), Demand Response (DR), and voltage control can reduce peak demand, energy loss, and system-wide unbalances in modern three-phase active Electric Distribution Networks (EDNs). However, simultaneous handling of these strategies is computationally complex and challenging. This paper presents a stochastic optimization formulation that slices the problem, solves the sub-problems separately, and splices them back to find optimal solutions efficiently. At the outset, all constraint-violating configurations are eliminated using a graph-theory-based edge traversal search developed from the classic Knuth’s Algorithm-S. Subsequently, deploying suitable indices, cyclic NR-DR assignments are performed to find near-optimal topologies and load schedules concerning the minimum loss, peak load, and unbalances. Further, Voltage Regulators (VRs) are set to achieve loss and unbalance reduction with minimal tap operations. The proposed scheme is tested on the modified IEEE 123-node test feeder with extensive EV and PV penetrations. The results show that this modular scheme provides superior solutions with an almost 75% reduction in time than the conventional co-optimization method. Various other case studies illustrate the effectiveness of the proposed scheme.

Loop Analysis and Angle Recovery Based Reactive Power Optimization for Three-Phase Unbalanced Weakly-Meshed Active Distribution Networks

This paper presents a loop analysis and angle recovery (LAAR) based reactive power optimization for three-phase unbalanced and weakly-meshed active distribution networks (ADNs). For each loop, the width first search (WFS) method is used to find the breakpoint bus of each tie line, and then all loops are broken up at these breakpoint buses by disconnecting tie lines, placing added buses, and adding compensation powers, so that the original weakly-meshed ADN can be precisely converted into an equivalent radial ADN. Furthermore, the traditional second-order cone programming can be employed for the equivalent radial networks to find the global optimal solution. However, the compensation powers are not constant values but related to the bus voltages, which are unknown before opening the loops. To address this problem, we design an iterative method to dynamically update the values of compensation powers until the convergence criterion is met. Moreover, the voltage angles are recovered for all loops at each iteration. The effectiveness of the proposed LAAR method is demonstrated by 9 cases, and the results show that the LAAR method can achieve a better convergence performance than the traditional method.

Two-stage Stochastic Programming for Coordinated Operation of Distributed Energy Resources in Unbalanced Active Distribution Networks with Diverse Correlated Uncertainties

This paper proposes a stochastic programming (SP) method for coordinated operation of distributed energy resources (DERs) in the unbalanced active distribution network (ADN) with diverse correlated uncertainties. First, the three-phase branch flow is modeled to characterize the unbalanced nature of the ADN, schedule DER for three phases, and derive a realistic DER allocation. Then, both active and reactive power resources are co-optimized for voltage regulation and power loss reduction. Second, the battery degradation is considered to model the aging cost for each charging or discharging event, leading to a more realistic cost estimation. Further, copula-based uncertainty modeling is applied to capture the correlations between renewable generation and power loads, and the two-stage SP method is then used to get final solutions. Finally, numerical case studies are conducted on an IEEE 34- bus three-phase ADN, verifying that the proposed method can effectively reduce the system cost and co-optimize the active and reactive power.

Optimal Micro-PMU Placement in Distribution Networks Considering Usable Zero-Injection Phase Strings

Real-time monitoring tools and their optimal measurement infrastructure are expected to play a critical role in smart grid applications. These applications require greater measurement precision and speed, which is not possible with conventional measurement devices. Due to their high economic burden and superseded technology, transmission level phasor measurement units (PMUs) are inappropriate for unbalanced active distribution networks (ADNs). Micro-synchrophasor technology is faster, less expensive with tighter accuracy tolerances. However, large-scale implementation of real-time monitoring instrumentation is economically unfeasible due to the size of ADNs, and successful deployment requires a new meter placement approach. In this paper, a micro-phasor measurement unit ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> PMU or micro-PMU) placement technique is proposed considering the unique traits of ADNs, which establishes a new concept of usable zero-injection phase strings (UZIP Strings). The method is evaluated using the IEEE-13, IEEE-34, and IEEE-123 node distribution test feeders. The fidelity of the placement algorithm is further verified via a fault detection and localization study. The results indicate better performance than previous literature with minor placement variations between deterministic and meta-heuristic algorithms for the presented holistic and UZIP String reduction methods.

A Hierarchical Service Restoration Framework for Unbalanced Active Distribution Networks Based on DSO and VPP Coordination

Modern active distribution networks (ADNs) have become more resilient to service interruptions due to the flexibility offered by integrated distributed energy resources (DERs). Compared to network-owned DERs, directly controlled by the distribution system operator (DSO), a vast majority of DERs controlled by independent virtual power plants (VPPs) are much more difficult to coordinate. The coordination with the VPPs and the management of uncertainty are the two major obstacles in the utilization of these DERs in the ADN restoration (ADNR). This article proposes a hierarchical framework for the sequential ADNR to overcome these two obstacles. The proposed framework adaptively integrates the sequential ADNR planning and the VPP scheduling models based on a comprehensive DSO and VPP coordination scheme to quantify and include the flexibility of VPPs in the ADNR. Furthermore, to address the uncertainty of renewable DERs and loads, a chance-constraint (CC) approach is used in these models. As the probability distributions of the uncertain parameters are not fully known, a distributionally robust reformulation for CCs is proposed that ensures that the solution is robust to any uncertainty distribution defined within a moment-based ambiguity set. The DR reformulation is further linearized to achieve DRCC mixed-integer linear-programming models for ADNR planning and VPP scheduling. Finally, its effectiveness is evaluated on the IEEE 123 node ADN.

Probabilistic Assessment of PV Hosting Capacity Under Coordinated Voltage Regulation in Unbalanced Active Distribution Networks

The increasing penetration of photovoltaic (PV) generators has led to a shift of the operational policy of the distribution system operator (DSO) from passive to active intervention in distribution networks (DNs), where a centralized controller governs the operation of voltage regulation devices. However, the PV output uncertainty hinders the verification of the impact of PVs on DNs. Therefore, the hosting capacity (HC) analysis framework for PV penetration should reflect both the operational benefit of the DSO and the PV output uncertainty. Thus, in this study, a two-stage optimization-based framework is proposed to analyze the probabilistic HC for PV under active network management (ANM) of DNs. In the first stage, the optimal PV base capacity (PVBC) to maximize the sum of the HC for PVs is determined based on a heuristic optimization method; in the second stage, using the predefined load and PV output profile, the maximum available power generation curve for PVBC is calculated, and the maximum HC for PV is derived by the calibration of PVBC through a comparison with the actual PV generation profile curve. The proposed method considers the time-series-based load flow results, reflecting the time-scheduling strategy by the DSO. Moreover, the uncertain characteristics of PV output are stochastically considered using a Monte Carlo simulation-based repetitive calculation approach. Case studies were implemented using the modified IEEE-123 test system, and the simulation results provided a quantitative comparison of the effect of the probabilistic HC improvement on the utilization of controllable resources and the centralized ANM by the DSO.

Optimal Management of Unbalanced Active Distribution Networks Using Model Predictive Control in a Stochastic Environment

Optimal Management of Unbalanced Active Distribution Networks Using Model Predictive Control in a Stochastic Environment

Sequential and Comprehensive BESSs Placement in Unbalanced Active Distribution Networks Considering the Impacts of BESS Dual Attributes on Sensitivity

<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-</i> The placement of battery energy storage system (BESS) determines whether its capabilities can be effectively exploited. However, existing BESS placement studies are commonly based on a balanced network model while practical distribution networks are essentially unbalanced. Besides, the power injection-based loss sensitivities are widely used to reduce the computation and memory burdens for complicated placement applications, which nevertheless cannot fully consider the impacts of both the BESS charging and discharging attributes and tends to generate less cost-effective clustered solutions. To address the challenges above, this study firstly proposes a multi-objective BESS placement optimization model for unbalanced active distribution networks, considering the time-varying load and renewable profiles as well as electricity prices, to minimize the cost of primary investment and operation/maintenance while maximizing the saving by loss reduction and load shifting. Then, a sequential BESS placement strategy is presented, based on the definition of a comprehensive loss sensitivity index (CLSI) considering the dual attributes of BESS charging and discharging, for more cost-effective and reasonable placement solutions. Finally, the proposed CLSI based sequential BESS placement is tested by detailed simulations on a real Australian distribution network of high PV penetrations.

Block-Sparse Bayesian Learning Method for Fault Location in Active Distribution Networks With Limited Synchronized Measurements

Timely and accurate fault location techniques can reduce power outages and improve power supply reliability. This paper proposes a new fault location method for active distribution networks (ADNs) which utilizes limited synchronized measurements (μPMUs). The proposed method formulates the fault location problem as the estimation of a block-sparse fault injection current signal which can inherently reveal fault types and locations. A modified block-sparse Bayesian learning (BSBL) algorithm is utilized to estimate this block-sparse signal by exploiting its both block structure and intra-block correlation. In addition, the proposed method provides a strategy for the optimal placement of much fewer μPMUs that will not yield a complete observable system. The proposed method is able to pinpoint the fault position accurately, and is applicable to both balanced and unbalanced ADNs. The effectiveness of the proposed method is examined on the IEEE 123-node distribution network with DGs and the results are discussed thoroughly.

Active Distribution Network Modeling for Enhancing Sustainable Power System Performance; a Case Study in Egypt

The remarkable growth of distributed generation (DG) penetration inside electrical power systems turns the familiar passive distribution networks (PDNs) into active distribution networks (ADNs). Based on the backward/forward sweep method (BFS), a new power-flow algorithm was developed in this paper. The algorithm is flexible to handle the bidirectional flow of power that characterizes the modern ADNs. Models of the commonly used distribution network components were integrated with the developed algorithm to form a comprehensive tool. This tool is valid for modeling either balanced or unbalanced ADNs with an unlimited number of nodes or laterals. The integrated models involve modeling of distribution lines, losses inside distribution transformers, automatic voltage regulators (AVRs), DG units, shunt capacitor banks (SCBs) and different load models. To verify its validity, the presented algorithm was first applied to the unbalanced IEEE 37-node standard feeder in both passive and active states. Moreover, the algorithm was then applied to a balanced 22 kV real distribution network as a case study. The selected network is located in a remote area in the western desert of Upper Egypt, far away from the Egyptian unified national grid. Accordingly, the paper examines the current and future situation of the Egyptian electricity market. Comparison studies between the performance of the proposed ADNs and the classical PDNs are discussed. Simulation results are presented to demonstrate the effectiveness of the proposed ADNs in preserving the network assets, improving the system performance and minimizing the power losses.

Coordinated optimisation of PEV charging with the support of reactive discharging and phase switching in unbalanced active distribution networks

Plug-in electric vehicles (PEVs) are being widely deployed, especially in the residential premises. Random PEV charging causes negative impacts on the power grid, a coordinated PEV charging is essential. Currently, PEV charging studies mainly focus on the active power control of PEVs while there is a risk of worse operation, due to the transferring of charging load instead of eliminating. Besides, existing PEV charging studies are commonly based on a three-phase balanced network model, but practical distribution networks, especially on the low-voltage level, are unbalanced. This study proposes a novel coordination strategy of PEV charging in unbalanced distribution networks, with the support of reactive discharging and phase switching. The optimisation model of PEV charging is firstly proposed to minimise the network loss and charging cost while maximising users’ benefit from ancillary reactive service. The optimal power flow problem defined above is solved by a combined solver of discrete particle swarm optimisation and direct load flow. Then, a coordination strategy of PEV charging, reactive discharging and phase switching is presented to apply the proposed optimisation over 24 h. Finally, detailed simulations are conducted on a real Australian distribution network, to test the feasibility and effectiveness of the proposed optimisation and coordination strategy of PEV charging in unbalanced distribution networks.

Optimized Two-Time Scale Robust Dispatching Method for the Multi-Terminal Soft Open Point in Unbalanced Active Distribution Networks

To alleviate the impact of output uncertainty of renewable energy sources (RESs) in unbalanced active distribution networks (ADNs), this paper proposed a two-time scale robust optimization method for the multi-terminal soft open point (SOP). In the long-term scale, the operation points of the SOP were optimized by semidefinite programming (SDP) model to minimize system loss and mitigate voltage unbalance. An improved iterative cutting plane (ICP) method was proposed to strengthen the exactness of the SDP rank-one relaxation. In the short-term scale, V 2- P and V 2- Q droop control mode was implemented in the SOP to better respond to the output uncertainty of RESs. Then a slope robust optimization model was established based on long-term operation points and short-term forecast data to improve system robust security. To coordinate these two time scales, a co-optimization re-dispatch strategy was proposed in the short-term model so that the robust safety margin could be further expanded in extreme conditions. Case studies show that the proposed method can fully utilize the flexible power flow regulation ability of the multi-terminal SOP to reduce system loss, mitigate voltage unbalance and guarantee system robust security in the presence of RES output uncertainty.

Optimization framework for coordinated operation of home energy management system and Volt-VAR optimization in unbalanced active distribution networks considering uncertainties

This study proposes an optimization framework that coordinates the operations of a home energy management system (HEMS) in a low-voltage (LV) distribution network and Volt/VAR optimization (VVO) in a medium-voltage (MV) distribution network through flexible electricity consumption and production of prosumers. The proposed framework consists of a three-level optimization problem, which corresponds to the HEMS for a prosumer at the first level, HEMS aggregator at the second level, and VVO at the third level. The optimal operations of home appliances and distributed energy resources are scheduled in the HEMS according to the prosumer’s preferred appliance scheduling and comfort level. Given the optimal energy consumption schedules from multiple HEMSs, the HEMS aggregator recalculates them while interacting with the VVO, which monitors and controls the MV distribution network efficiently. Furthermore, to incorporate the uncertainty for the predicted errors of residential solar photovoltaic generation and outdoor temperature into the proposed framework, the deterministic optimization (DO)-based HEMS aggregator model is reformulated into a chance constrained optimization (CCO)-based model. Numerical examples tested in IEEE 13-node MV and CIGRE 18-node LV distribution systems show that, in contrast with a method without coordination of HEMS and VVO, the proposed DO-based approach reduces the total energy losses, active energy consumption, and reactive energy consumption by 21.03%,7.62%, and 115.51%, respectively, in the LV system, and 2.34%,1.36%, and 4.07%, respectively, in the MV system. In addition, the performance of the proposed CCO-based approach was validated in terms of probability level of chance constraints.

Data-driven stochastic service restoration in unbalanced active distribution networks with multi-terminal soft open points

Service restoration is critical in ensuring the reliability of distribution networks after the isolation of faults. Multi-terminal soft open points (MTSOPs) can realize power flow among multiple feeders and provide voltage support for power outage areas. This mechanism can help improve the restoration ability of distribution systems. A distribution network is typically unbalanced when the load, distributed generation, and line parameters are unbalanced. This study proposes accordingly a service restoration model for unbalanced active distribution networks (UADNs) with MTSOP. The power control principles of MTSOP in the fault condition and a service restoration strategy in MTSOP-based UADN are first analyzed. Then, a deterministic service restoration model is established. The maximized weighting restored load and the minimized voltage unbalance are used as the objective functions. The original optimization model is converted into a mixed integer second-order cone programming problem by linearizing the three-phase power flow equation, the big-M method, and the second-order cone relaxation, which can be solved by commercial solvers. A two-stage data-driven stochastic optimization model for service restoration in UADN is established by considering the uncertainty of load demand and the generation of renewable energy. The IEEE 33-node, Taiwan Power Company, and modified IEEE 123-node systems are used to verify the proposed model.

A deep learning-based general robust method for network reconfiguration in three-phase unbalanced active distribution networks

By connecting deep learning and robust optimization, this paper proposes a general robust method (GRM) for distribution network reconfiguration (DNR) while hedging against the risk brought by uncertainties in active distribution networks (ADNs). The method is general in the way that it is applicable for both loss minimization and load balancing in three-phase unbalanced distribution systems with few a priori assumptions on the distributions of the uncertain distributed generator (DG) output and loads. An uncertainty set construction network based on deep neural networks is first proposed to adaptively construct the uncertainty set from historical data for DGs and loads. Then the robust DNR for three-phase unbalanced networks is formulated as a two-stage mixed-integer quadratic programming (MIQP) problem considering the worst-case scenario within this uncertainty set. Finally, based on the column-and-constraint generation (C-CG) method and duality theory, an iterative algorithm is devised to solve the GRM. Numerical tests on two unbalanced IEEE benchmarks have validated the effectiveness of the proposed method.

Vulnerability Assessment of Conservation Voltage Reduction to Load Redistribution Attack in Unbalanced Active Distribution Networks

This article proposes a new type of load redistribution attack on a closed-loop conservation voltage reduction (CVR) in an unbalanced three-phase distribution network having voltage regulators (an on-load tap changer (OLTC) and capacitor bank), smart inverters for solar photovoltaic and energy storage systems, and smart meters. The objective of the proposed attack strategy using a bilevel optimization problem is to maximize three-phase active power flow from the substation (upper level) while guaranteeing normal CVR operation (lower level) through the injection of malicious data into smart meters. The bilevel optimization problem is finally transformed into a single-level optimization problem based on Karush-Kuhn-Tucker conditions of the lower level optimization problem. An IEEE 13-node distribution feeder is used to quantify the performance of the proposed attack in terms of voltage level, OLTC tap position, PV penetration rate, and attack effort.

Coordinated optimal dispatch of VPPs in unbalanced ADNs

To manage and control massive distributed energy resources (DERs) integrated into active distribution networks (ADNs), dispersed DERs are aggregated as virtual power plants (VPPs). This study introduces a distributed optimal dispatch strategy of VPPs considering operational constraints in unbalanced ADN. First, a practical multi-VPP coordination optimal dispatch model considering P–Q coupling characteristics in unbalanced ADN is proposed. Then, the primal–dual interior-point algorithm is employed to transform the original model into a Karush–Kuhn–Tucker equation, where afterwards distributed quasi-Newton method is developed to solve the equation. Under the proposed distributed strategy, each VPP only communicates limited boundary information with utility grid. With the advantage of quasi-second-order information, the proposed method outperforms the popular distributed gradient-based algorithm, alternating direction method of multipliers. The distributed method provides merits such as efficient calculation and privacy protection for multi-VPP operation in ADN. Numerical tests evaluate the efficiency and accuracy of the proposed method.

Distributed Load Restoration in Unbalanced Active Distribution Systems

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

An Online Coordinated Charging/Discharging Strategy of Plug-in Electric Vehicles in Unbalanced Active Distribution Networks with Ancillary Reactive Service in the Energy Market

The global acceptance and off-grid charging of plug-in electric vehicles (PEVs) are expected to grow tremendously in the next few years. Uncoordinated PEV charging can cause serious grid issues such as overloading of transformers and unacceptable voltage drops. Single-phase residential charging can also initiate or contribute to voltage unbalance conditions in the distribution networks. A potential solution and key challenge for PEV integration is shifting of the charging activities to off-peak periods. This paper proposes a new PEV coordination approach based on genetic algorithm (GA) optimization to perform online centralized charging and discharging considering transformer loading and node voltage magnitude and unbalance profiles. It allows PEV as source of active and reactive power to participate in energy market based on different prices during a day, without any degradation. Finally, the impacts of uncoordinated and the proposed GA coordinated PEV charging/discharging strategy are simulated for a real unbalanced Western Australian distribution network in the Perth solar city over 24 h.