Three-phase Unbalanced Distribution Research Articles

A Generalized Framework for Service Restoration in a Resilient Power Distribution System

An electric power grid is one of the complex infrastructures, and because of its complex nature, there is simply no way that outages can be completely avoided. Thus, a modern society that depends on reliable electric supply requires a resilient electric system that can recover from disruptions while integrating emerging smart grid technologies. This article presents a novel approach for service restoration in a modern power distribution system with controllable switches and distributed generation (DG) resources for any kind of outage. The proposed framework supports both the traditional service restoration using feeder reconfiguration and the grid-forming DG-assisted intentional islands that are dynamically sized using algorithms based on the fault scenario, available resources, and priority of loads. The problem is formulated as a mixed-integer linear program that incorporates critical system connectivity and operating constraints. Simulations are performed to demonstrate the effectiveness of the proposed approach using a large-scale four-feeder 1069-bus three-phase unbalanced distribution test system. It is demonstrated that the framework is effective in utilizing all available resources in quickly restoring the power supply to improve resiliency during extreme events and is scalable for a large-scale unbalanced power distribution system.

Investment Deferral of Feeder Upgrades Revealed by System-Wide Unbalanced Dynamic Rating: Harvesting the Hidden Capacity of Distribution Systems Discovered by Thermal Map Technology

Dynamic thermal rating for underground cables with balanced phase currents has been extensively studied in the literature. Paradoxically, distribution feeders operate inherently unbalanced and no publications are available for unbalanced thermal rating. Because of the lack of technology, utilities operate with very conservative margins using the maximum of the three-phase currents to determine the line loading. This practice leads to the significant underutilization of underground cables. To fill the gap this paper presents a physically sound and accurate transient electro-thermal model of unbalanced three-phase distribution cables considering variations in the load and environment. Moreover, the model proposed in this paper allows harvesting the large hidden capacity of distribution systems trapped in the thermal inertia of underground cables. A convenient visual tool is developed to uncover hot spots and underutilized energy routes. This facilitates real-time network reconfiguration based on predicted load graphs and dynamic thermal conditions. The proposed model is also useful to study load growth, perhaps eliminating or deferring capital investments needed to upgrade the capacity of the existing underground feeders. The IEEE 37-bus distribution network is used as a case study. The results show that the proposed methodology has a high potential to defer investments, for instance, one could save $5M for a small system like the IEEE 37-bus distribution network which would have been necessary under current conservative practice.

Detecting False Data Injection Attacks in Smart Grids: A Semi-Supervised Deep Learning Approach

The dependence on advanced information and communication technology increases the vulnerability in smart grids under cyber-attacks. Recent research on unobservable false data injection attacks (FDIAs) reveals the high risk of secure system operation, since these attacks can bypass current bad data detection mechanisms. To mitigate this risk, this paper proposes a data-driven learning-based algorithm for detecting unobservable FDIAs in distribution systems. We use autoencoders for efficient dimension reduction and feature extraction of measurement datasets. Further, we integrate the autoencoders into an advanced generative adversarial network (GAN) framework, which successfully detects anomalies under FDIAs by capturing the unconformity between abnormal and secure measurements. Also, considering that the datasets collected from practical power systems are partially labeled due to expensive labeling costs and missing labels, the proposed method only requires a few labeled measurement data in addition to unlabeled data for training. Numerical simulations in three-phase unbalanced IEEE 13-bus and 123-bus distribution systems validate the detection accuracy and efficiency of this method.

Robust distribution system state estimation with hybrid measurements

With growing connection of distributed energy resources, availability of demand side response technologies, deployment of smart meters, the distribution system needs advanced network automation for running the system efficiently. State estimation is the core driver of network automation. While the output from SMs will make the state estimation more accurate, advanced metering infrastructures come with several challenges such as noisy, erroneous measurement including lost or missed measurements, exposure to cyber attack and so on. This study proposes a three-phase unbalanced distribution system state estimation which is robust against noisy distribution system measurements, bad data attacks and missing or delayed measurements. This method considers measurement from hybrid sources such as SCADA, micro-phasor measurement units (${\mu}$μPMUs) and SMs. Kalman smoother is used to fill the missing measurements and expectation-maximisation based forecasting is used to interpolate the hybrid measurements to a common timestamp and compensate for the delay in SM measurements. Extensive numerical comparisons are made on IEEE 13, 37 and 123 bus systems to test the robustness of the proposed DSSE against delayed SM measurements and bad or noisy data. An IEEE 24 bus system is modelled and real-time measurement devices are interfaced to it in Hypersim. The data from the hybrid measurement devices of IIT Kanpur smart grid is also used to test the robustness of the proposed method.

Conic Optimization for Electric Vehicle Station Smart Charging With Battery Voltage Constraints

This article proposes a new convex optimization strategy for coordinating electric vehicle charging, which accounts for battery voltage rise and the associated limits on maximum charging power. Optimization strategies for coordinating electric vehicle charging commonly neglect the increase in battery voltage, which occurs as the battery is charged. However, battery voltage rise is an important consideration since it imposes limits on the maximum charging power. This is particularly relevant for dc fast charging, where the maximum charging power may be severely limited, even at the moderate state of charge levels. First, a reduced-order battery circuit model is developed, which retains the nonlinear relationship between the state of charge and maximum charging power. Using this model, limits on the battery output voltage and battery charging power are formulated as the second-order cone constraints. These constraints are integrated with a linearized power flow model for three-phase unbalanced distribution networks. This provides a new multiperiod optimization strategy for electric vehicle smart charging. The resulting optimization is a second-order cone program and, thus, can be solved in polynomial time by standard solvers. A receding horizon implementation allows the charging schedule to be updated online, without requiring prior information about when vehicles will arrive.

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.

Multiobjective Framework for Optimal Integration of Solar Energy Source in Three-Phase Unbalanced Distribution Network

Recently, there is a global consent regarding the high penetration of solar energy (SE) resources to mitigate technical and environmental concerns. SE is intermittent in nature and if its incorporation is not properly planned, a multitude of serious technical issues will arise in the network. In this perspective, considering the energy industry's practical aspects, a comprehensive robust practical planning model is presented in this article to optimally integrate intermittent SE source with battery and DSTATCOM to maximize reliability and financial, environmental, and technical benefit of the system. Voltage unbalance in the system creates varieties of problems, such as poor power quality, higher power loss, and lesser system efficiency. However, owing to the lack of proper industrial real data, researchers were unable to judge and incorporate the voltage unbalance issues, which are significant for the planning engineers to provide efficient solutions. Keeping this into view, the proposed method is tested on the real three-phase unbalanced 240-node network of the USA where the customers are equipped with smart meters to provide real power data for realistic analysis. K-means clustering algorithm is utilized to generate the appropriate number of scenarios that can accurately include the intermittency of solar power generation and load. A multiobjective algorithm, namely the extended version of NSGA II (E_NSGA II), is utilized for the optimal allocation of the devices. Compare to other algorithms, results reveal the competence and robustness of the proposed planning methodology for the optimal allocation of SE with battery storage and DSTATCOM in order to maximize the overall benefits of the three-phase network.

A Novel PSOS-CGSA Method for State Estimation in Unbalanced DG-Integrated Distribution Systems

This paper proposes a novel optimization method, namely, hybrid PSOS-CGSA for state estimation in three-phase unbalanced DG-integrated distribution systems. The distribution system state estimation (DSSE) is formulated as a nonlinear optimization problem with constraints where loads and DG outputs are considered as the control variables, while real-time measurements are treated as dependent variables. The proposed DSSE model estimates the loads and DG outputs at each bus by minimizing the difference between the measure and calculated values of the variables monitored in real-time. A novel hybrid algorithm of particle swarm optimization with sigmoid-based acceleration coefficients and chaotic gravitational search algorithm (PSOS-CGSA) is proposed and applied for the DG-integrated DSSE. The feasibility of the proposed approach is verified on the IEEE 13-bus test system, the IEEE 37-bus test system, and the IEEE 123-bus test system. These simulations show that the proposed DSSE model provides reliable and accurate state estimation of DG-integrated distribution systems with a very limited number of real-time measurements at the source substation. The results obtained by proposed hybrid PSOS-CGSA are evaluated by comparing with other methods under the same test conditions, and the obtained results demonstrate the merits of the proposed scheme.

Distribution optimal power flow

Increased availability of controllable devices and overall visibility means that distribution systems can now be planned and operated in a more optimal way. However, to achieve this, it is crucial to have the underlying tools for determining these optimal decisions and settings. The work in this study discusses the formulation for a three-phase unbalanced distribution optimal power flow. The methodology is developed in Python using the optimisation package Pyomo, and interfaces with OpenDSS to import the distribution system models. Optimal settings for various distribution system control equipment can be calculated to achieve a distribution wide objective. A real-world test case is used to highlight the capabilities of the method and results are demonstrated and discussed.

Allocation and sizing of single tuned passive filters in three-phase distribution systems for power quality improvement

This paper presents an optimization problem formulation for allocation and sizing of single tuned passive filters in power distribution systems with the objective of minimizing total harmonic distortion. Inequality constraints are considered to determine upper and lower bounds for power factor correction, tuned frequency, voltage unbalance factor, voltage magnitudes and harmonic distortion based on power quality standard limits. The optimization problem is solved using genetic algorithm in which the filters locations, their connection types and parameters for each phase of the system are determined. Simulations are carried out using three-phase unbalanced 33-bus and 69-bus distribution test feeders to demonstrate the viability and efficiency of the proposed formulation to obtain results with total harmonic distortion lower than 5%, voltage unbalance factor lower than 1%, power factor greater than 0.92 and voltage magnitudes between acceptable limits. The main contributions of this paper are the formulation considering multiple power quality indexes in three-phase unbalanced distribution systems, the possibility of the filters to be connected in Y or Δ to satisfy the objective function and the constraints of the optimization problem. Additionally, security constraints related to the operation of the capacitor banks of the filters are considered in this paper.

Joint Estimation of Operational Topology and Outages for Unbalanced Power Distribution Systems

An electric power distribution system is operated in several distinct radial topologies by opening and closing of system's sectionalizing and tie switches. The estimation of the system's current operational topology is a precursor to implementing any optimal control actions (during normal operation) or restorative actions (during outage condition). This paper presents a mathematical programming approach to estimate the operational topology of a three-phase unbalanced power distribution system under both outage and normal operating conditions. Specifically, a minimum weighted least absolute value estimator is proposed that uses the line flow measurements, historical/forecasted load data, and ping measurements and solves a mixed-integer linear program (MILP) to estimate the operational topology and any outaged sections simultaneously. We thoroughly validate the accuracy of the proposed approach using IEEE 123-bus and a 1069-bus three-phase multi-feeder test system with the help of numerous simulations. It is observed that the approach performs well even at high percentages of measurement errors.

Holomorphic embedding load flow for unbalanced radial distribution networks with DFIG and tap‐changer modelling

In this study, the holomorphic-embedding method as a linear and non-iterative method is developed and implemented to solve the load flow of the three-phase unbalanced radial distribution networks. Previously, this method was used to solve the load flow problem of balanced transmission networks. The proposed methodology could be applied for a variety of unbalanced radial distribution networks with any number of buses and branches. The characteristics of unbalanced radial distribution networks including line coupling effects, unbalanced loads and unsymmetrical phases are considered in this study. The proposed method uses an unbalanced network structure and modifies the calculation approach of the admittance matrix. In this manner, an unbalanced network is modelled the same as the balanced networks. The tap-changer, doubly-fed induction generator (DFIG), and photovoltaic system are modelled in the admittance matrix or current injection vector. The performance of the proposed method is validated on the 19-bus unbalanced radial distribution network. Finally, the effectiveness of the proposed method in solving the load flow problem is investigated.

Bayesian Learning-Based Harmonic State Estimation in Distribution Systems With Smart Meter and DPMU Data

This paper studies the problem of locating harmonic sources and estimating the distribution of harmonic voltages in unbalanced three-phase power distribution systems. We develop an approach for harmonic state estimation utilizing two types of measurements from smart meters and distribution-level phasor measurement units (DPMUs). It involves regression analysis for power flow calculation, prediction of demands using recurrent neural networks, and sparse Bayesian learning for state estimation. The proposed approach requires fewer DPMUs than nodes, making it more applicable to existing distribution grids. We show the effectiveness of the proposed estimator through extensive numerical simulations on an IEEE test feeder. We also investigate how the increased penetration of distributed energy resources could affect the performance of our state estimator.

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.

Distributed CVR in Unbalanced Distribution Systems With PV Penetration

In this paper, a distributed multi-objective optimization model is proposed to coordinate the fast-dispatch of photovoltaic (PV) inverters with the slow-dispatch of on-load tap changer and capacitor banks for implementing conservation voltage reduction in unbalanced three-phase distribution systems. In existing studies, PV inverters and voltage regulation devices are generally dispatched by fully centralized control frameworks. However, centralized optimization methods are subject to single point of failure and suffer large computational burden. To tackle these challenges, a distributed dispatch method is developed to coordinate PV inverters and conventional voltage regulation devices in distribution systems. The proposed method is based on a modified alternating direction method of multipliers algorithm to handle non-convex optimization problems without relaxing the original formulation, which could lead to sub-optimality. Numerical results from simulations on modified IEEE 13-bus, 34-bus, and 123-bus unbalanced three-phase systems have been used to verify the proposed method.

HEMS-enabled transactive flexibility in real-time operation of three-phase unbalanced distribution systems

This paper proposes a coordinated two-stage real-time market mechanism in an unbalanced distribution system which can utilize flexibility service from home energy management system (HEMS) to alleviate line congestion, voltage violation, and substation-level power imbalance. At the grid level, the distribution system operator (DSO) computes the distribution locational marginal prices (DLMP) and its energy, loss, congestion, and voltage violation components through comprehensive sensitivity analyses. By using the DLMP components in a first-stage optimization problem, the DSO generates two price signals and sends them to HEMS to seek flexibility service. In response to the request of DSO, each home-level HEMS computes a flexibility range by incorporating the prices of DSO in its own optimization problem. Due to future uncertainties, the HEMS optimization problem is modeled as an adaptive dynamic programming (ADP) to minimize the total expected cost and discomfort of the household over a forward-looking horizon. The flexibility range of each HEMS is then used by the DSO in a second-stage optimization problem to determine new optimal dispatch points which ensure the efficient, reliable, and congestion-free operation of the distribution system. Lastly, the second-stage dispatch points are used by each HEMS to constrain its maximum consumption level in a final ADP to assign consumption level of major appliances such as energy storage, heating, ventilation and air-conditioning, and water heater. The proposed method is validated on an IEEE 69-bus system with a large number of regular and HEMS-equipped homes in each phase.

Multi-Timescale Three-Phase Unbalanced Distribution System Operation With Variable Renewable Generations

This paper proposes a multi-timescale operational approach for a three-phase unbalanced distribution system containing hourly scheduling at substation level and minutes power flow operation at feeder level. In the substation scheduling model, the objective is to minimize the system cost with variable renewable generations. The given error distribution model of renewable generation is formulated as a chance constraint and derived into a deterministic form by Gaussian mixture model with genetic algorithm-based expectation-maximization. In the feeder scheduling model, the system cost is further reduced with the optimal power flow (OPF) at a timescale of minutes. Considering the nonconvexity of the three-phase unbalanced OPF problem in distribution systems, the semidefinite programming is used to relax the problem into a convex problem and a distributed computation approach is built based on alternating direction method of multiplier. The IEEE 123-bus distribution system, University of Denver campus distribution system, and the IEEE 8500-bus distribution system are used as the test bench for the proposed approach. The numerical results demonstrate the effectiveness and validity of the proposed method.

A sparse recovery model with fast decoupled solution for distribution state estimation and its performance analysis

This paper introduces a robust sparse recovery model for compressing bad data and state estimation (SE), based on a revised multi-stage convex relaxation (R-Capped-L1) model. To improve the calculation efficiency, a fast decoupled solution is adopted. The proposed method can be used for three-phase unbalanced distribution networks with both phasor measurement unit and remote terminal unit measurements. The robustness and the computational efficiency of the R-Capped-L1 model with fast decoupled solution are compared with some popular SE methods by numerical tests on several three-phase distribution networks.

Optimal Dispatch of Battery Energy Storage System Using Convex Relaxations in Unbalanced Distribution Grids

This paper presents second-order cone programming (SOCP) and semidefinite programming (SDP) models to solve the multiperiod optimal control problem of unbalanced three-phase distribution grids with battery energy storage systems. The decision variables are the active and reactive power of the battery energy storage system. The objective is to minimize the power loss and energy purchase cost from the distribution substation. The optimal dispatch problem requires solution by volt/VAR optimization. The SOCP and SDP models ensure global optimum of original nonconvex nonlinear programming problem. Multiobjective volt/VAR optimization is performed and the benefits of reactive power support from battery energy storage systems are explored. A simulation-based heuristic to extract rank-one solution from the higher rank solution of SDP model is also proposed. Empirical results show the numerical stability and exactness of the proposed three-phase SOCP and SDP models.