Distribution System Restoration Research Articles

Routing and Scheduling of Electric Buses for Resilient Restoration of Distribution System

Electric buses (EBs) have been widely adopted in public transit. EBs can feed power back to the distribution system (DS) at a charging station and serve as temporary mobile power sources (MPSs), such as hurricanes. Thus, they have great potential to enhance grid resilience against meteorological disasters. This article proposes a DS restoration method for enhancing resilience considering the routing and scheduling of a group of EBs. To maintain the function of EBs in public transit, we establish an EB scheduling problem (EBSP) with predetermined optional service trips. The schedule must meet a certain public transit demand, and the not-in-service EBs can transfer power among charging stations, unleashing their abilities as MPSs. The proposed model considers the en-route energy consumption of EBs, and the restoration process aims to minimize the losses of loads over time and the energy usage of EBs for supporting the grid. The problem is finally cast as a mixed-integer linear program (MILP), which can be processed by off-the-shelf solvers. The proposed model is tested on two systems with dozens of EBs. The results validate our work’s effectiveness and demonstrate the potential of EBs in enhancing the resilience of DSs.

Robust coordination of repair and dispatch resources for post-disaster service restoration of the distribution system

Since extreme weather events usually severely damage the power grid and lead to widespread power outages, coordinating repair and dispatch resources, such as repair crews (RCs), mobile power sources (MPSs), renewable energy sources (RESs) and energy storage systems (ESSs), is an efficient method to restore the power supply for outage loads. However, the uncertainties existing in RES output and load demand pose significant challenges to the service restoration of distribution systems in terms of security constraints. To address these uncertainties, this paper proposes a robust restoration approach to maximize the restored load in a distribution system by coordinating RCs, MPSs, RESs, ESSs and network reconfiguration. The coordination problem is formulated as a two-stage robust optimization model to generate optimal dispatching and operation schemes of multiple resources with guaranteed robustness against uncertainties. Involving some unexpected changes in topologies and distributed sources during post-disaster repair, the robust coordination model is re-optimized to guarantee the efficiency of repair and operation scheme. Simulation results show that the repair and dispatch resources can be coordinated effectively to accommodate the RES output and load demand uncertainties while maximizing the amount of restored load for service restoration of the distribution system.

A Novel Fault Location Algorithm in Distribution Network Based on Power-on Signal and Power-off Signal

In recent years, with the continuous promotion of clean and low-carbon energy strategy, power system’s operation mode has been transformed gradually. Consequently, the extended time of fault location when it occurs will jeopardize the fault restoration of distribution system and reduce the grid resilience. Hence, this paper proposes a novel fault location algorithm based on the combination of power-on signal and power-off signal, which can improve the efficiency of the fault location. First, the principle of numbering node is presented, making it convenient for computer to identify the relationship between device in the distribution network. Then, some assumptions and principles of the algorithm are shown, together with the termination condition of the proposed algorithm. Finally, case study involving an actual distribution network is carried out. Results show that the proposed algorithm is able to achieve accurate fault location meanwhile improve the efficiency of fault location.

A Two-Level Simulation-Assisted Sequential Distribution System Restoration Model With Frequency Dynamics Constraints

This paper proposes a service restoration model for unbalanced distribution systems and inverter-dominated microgrids (MGs), in which frequency dynamics constraints are developed to optimize the amount of load restoration and guarantee the dynamic performance of system frequency response during the restoration process. After extreme events, the damaged distribution systems can be sectionalized into several isolated MGs to restore critical loads and tripped non-black start distributed generations (DGs) by black start DGs. However, the high penetration of inverter-based DGs reduces the system inertia, which results in low-inertia issues and large frequency fluctuation during the restoration process. To address this challenge, we propose a two-level simulation-assisted sequential service restoration model, which includes a mixed integer linear programming (MILP)-based optimization model and a transient simulation model. The proposed MILP model explicitly incorporates the frequency response into constraints, by interfacing with transient simulation of inverter-dominated MGs. Numerical results on a modified IEEE 123-bus system have validated that the frequency dynamic performance of the proposed service restoration model are indeed improved.

Formation of ad hoc microgrids for prompt critical load pickup during blackouts by leveraging stochastic distributed energy resources

Extreme weather events that are increasing in frequency and impact can cause extended disruptions to power grids. To increase the resilience of power grids, focus is shifting from infrastructure hardening to quickening the restoration of distribution systems after a disaster. One method to achieve this is through the use of microgrids leveraging distributed generation in islanded mode. While much work has been done in using microgrids for system restoration, the stochastic nature of distributed energy resources (DERs) have so far been neglected. Here, a data-driven approach to leverage stochastic DERs to form ad hoc microgrids to supply local critical loads prior to wide-scale system restoration is presented. The proposed method is tested on a modified IEEE European LV Test Feeder. Results show that considering the stochastic nature of the resources during microgrid formation greatly affects their supply adequacy confidence levels.

Optimal Restoration of Distribution Systems Considering Temporary Closed-Loop Operation

This article presents a new mathematical model to solve the restoration problem in balanced distribution systems with distributed generators (DGs) considering closed-loop topology operation during the restorative state. The restorative state is comprised of the interval of time since the permanent fault has been isolated until the time at which the faulted zone is repaired. During this interval of time, switching operations are performed to minimize the negative effects resulting from the occurrence of a permanent fault in the network. In this way, the two main objective functions of the restoration problem are to minimize the amount of load curtailment in the restored system and to minimize the number of switching operations. Conventionally, the network topology is maintained radial throughout the restorative state. In this article, the possibility of forming loops is considered for improving both objective functions. As such, a new mixed-integer second-order cone programming model is proposed, considering the temporary formation of operational loops in the restorative state, and both connected and islanded operation of the DGs. Several tests are carried out using a 53-node test system and a 2313-node system for single and multiple fault scenarios. The results obtained with the proposed model outperform the solutions achieved when only open-loop configurations are considered for the restoration problem. Moreover, it is verified that the islanded operation of the DGs provides more flexibility to the network, allowing more load to be restored.

Robust coordination of multiple power sources for sequential service restoration of distribution systems

When a distribution system encounters a major outage due to extreme events, an efficient sequential service restoration (SSR) strategy is required to restore the outage system. However, uncertainties associated with renewable energy generation and load demands pose significant and complex challenges for the optimization of SSR strategies. This paper proposes a robust multiple power source co-optimization approach for the SSR of an outage distribution system. First, network configuration and sequential switching actions are jointly optimized to sequentially form microgrids (MGs). Second, multiple types of power sources, such as distributed generators and energy storage units, are re-energized and coordinated to pick up critical loads in parallel restored MGs. In addition, uncertainties associated with renewable energy generation and load demands are considered during the restoration process, thereby requiring a robust SSR scheme to increase the reliability of MG operations, The mathematical problem is modelled as a mixed-integer tri-level programming problem with inner-level binary variables. Thus, the extended column-and-constraint generation (EC&CG) algorithm is employed to solve the proposed robust model. The numerical results demonstrate the effective performance of the proposed approach and its robustness and advantages compared to existing models that do not consider uncertainties.

Linear power flow formulations and optimal operation of three-phase autonomous droop-controlled Microgrids

Linear power flow formulations enable the integration of power flow constraints to linearly constrained power system optimization problems in transmission and distribution systems. Typical examples include the application of DC power flow and DistFlow to distribution system reconfiguration and restoration. While non-linear power flow equations and its associated optimal power flow have been developed in the literature, there is no existing linear power flow formulation for islanded droop-controlled microgrids to the best of the authors' knowledge. To address this need, this paper presents two linear power flow approximations for three-phase islanded droop-controlled microgrids. The first approximation was derived based on the current injection method and the second approximation was derived from the three-phase DistFlow formulation. The two approximations were verified using detailed time-domain simulations at steady-state in PSCAD with resulting mean errors of the nodal voltages being under 1%. To demonstrate the application of the proposed power flow formulations, the two approximations were expanded for integration in optimal power flow formulations for islanded droop-controlled microgrids to minimize cost. Unlike the existing non-linear models, the linear power flow formulations presented in this paper can be solved easily using non-iterative linear matrix operation and its optimal power flow extensions are linearly constrained.

Black-Start and Service Restoration in Resilient Distribution Systems With Dynamic Microgrids

The resilience of distribution systems has been challenged by power outages caused by natural disasters, which calls for novel solutions to system restoration. However, the existing black-start (BS) techniques are mainly developed at the transmission level. This problem can be resolved by adopting dynamic microgrids (MGs), i.e., MGs with dynamic and adjustable boundaries nested in the distribution systems. This article proposes a restoration procedure that adopts self-organizing inverters as BS units and achieves distribution system restoration in the context of dynamic MGs. The proposed restoration procedure is structured as a two-stage approach and designed to restore a complete blackout distribution system to the state where the system is ready for seamless main grid reconnection. A framework of dynamic MG operation is developed, which improves the self-healing capability of off-grid distribution systems with automatic sectionalization and flexible reconfiguration. A sequence of actions during restoration is defined, along with distributed controllers designed with considerations of practical operating challenges. The proposed restoration procedure is validated on a 34-bus system using real-time hardware-in-the-loop simulation.

Optimization Decision-Making Method for Distribution System Restoration Considering the Interdependency Between Power and Water Distribution Systems

Optimization Decision-Making Method for Distribution System Restoration Considering the Interdependency Between Power and Water Distribution Systems

Resilient Restoration of Distribution Systems in Coordination With Electric Bus Scheduling

Electric buses (EBs) possess large-capacity batteries and are dispatched by a central operator, exhibiting great potential to enhance the resilience of distribution systems (DSs) against meteorological disasters. This paper proposes an optimization model for joint post-disaster DS restoration, considering coordinated dispatching with EBs. By assuming that the DS can rent some EBs from the bus company, an EB scheduling problem with adjustable timetables is established. Idle buses are placed at designated areas and feed power back to the grid via charging piles or charging stations in case of need. The schedule of the remaining buses should meet the passenger transport demand, which is smaller than usual because of bad weather. The objective is to maximize the total benefits and minimize the EB rental cost of the grid company. Techniques in integer algebra are used to reformulate the proposed restoration problem with bus scheduling constraints as a mixed-integer linear program, which can be processed by off-the-shelf solvers. The proposed method is tested on a modified 15-bus system and IEEE 123-bus system. The results demonstrate that the resilience of the system is enhanced, and the benefits of the grid company increase significantly, because of the flexibility brought by EBs.

Hybrid Modeling Based Co-Optimization of Crew Dispatch and Distribution System Restoration Considering Multiple Uncertainties

Natural disasters could lead to large-scale power outages by causing severe damages to distribution networks (DNs). Developing highly efficient outage management schemes is imperative for expediting service restoration. To this end, a novel multistage co-optimization model is proposed to seamlessly integrate the repair crew dispatch with the distribution system restoration. Furthermore, multiple sources of uncertainties are incorporated. To properly handle these uncertainties, a novel hybrid modeling approach is developed. In particular, the first stage is cast as a deterministic optimization problem to determine the crew route option prior to the realization of uncertainties. The second stage is to reconfigure the DN for forming multimicrogrids considering the uncertainties in crew travel time and repair time, which is formulated as a stochastic program. In the third stage, a robust optimization framework is applied to acquire a scheduling plan of various DERs that is immune to the worst-case realizations of electricity demand and photovoltaic generation. Finally, an advanced solution method is devised to achieve the computational tractability based on constraint and column generation and progressive hedging approaches. Numerical tests on the modified IEEE 37-bus DN show that the computation performance of the proposed solution method well fits the real-time application and also demonstrate that the highest demand curtailment is reduced by 3.3% and the variance of the restoration outcome is lowered by 40.5% compared with a recently proposed benchmark.

Optimal Restoration of Active Distribution Systems With Voltage Control and Closed-Loop Operation

This article presents a new mixed-integer second-order cone programming model for solving the restoration problem in active distribution systems considering the optimal control of distributed generators (DGs), voltage regulators (VRs), on-load tap changers (OLTCs), and capacitor banks (CBs). In contrast to most of the works found in the literature, temporary loops may be formed in the network during the restorative operation state. This operating condition allows restoring the service to more loads. In this way, the objective function of the problem minimizes (i) the total load not supplied, (ii) the number of switching operations, (iii) the changes in the statuses of the voltage control devices and in the dispatch of the DGs, and (iv) the number of basic loops formed in the system. Several tests are carried out using a 53-node system for single-fault and multiple-fault scenarios. The results obtained with the proposed approach outperform the solutions achieved when only radial configurations are allowed in the problem. Moreover, it is also verified that the voltage control allows for more efficient restoration schemes.

Optimal Policy Synthesis from A Sequence of Goal Sets with An Application to Electric Distribution System Restoration

Motivated by the post-disaster distribution system restoration problem, in this paper, we study the problem of synthesizing the optimal policy for a Markov Decision Process (MDP) from a sequence of goal sets. For each goal set, our aim is to both maximize the probability to reach and minimize the expected time to reach the goal set. The order of the goal sets represents their priority. In particular, our aim is to generate a policy that is optimal with respect to the first goal set, and it is optimal with respect to the second goal set among the policies that are optimal with respect to the first goal set and so on. To synthesize such a policy, we iteratively filter the applicable actions according to the goal sets. We illustrate the developed method over a sample distribution system.

Co-Optimization of Supply and Demand Resources for Load Restoration of Distribution System Under Extreme Weather

To deal with the issue of the distribution system (DS) resilience enhancement under extreme weather events, this paper presents a new methodological framework for enhancing the load restoration of DS during a hurricane. As distinct from existing studies, this approach integrates mobile emergency generators (MEGs) and prosumer communities (PCs) incorporating combined heat and power (CHP) units, electric boilers (EBs), photovoltaic (PV) sources, and demand response (DR) resources and comprehensively explores the coordination and flexibility of supply-side and demand-side resources to boost the post-disaster DS recovery. The discussed problem is formulated by using a two-stage robust optimization model. In the first stage, the MEGs are pre-positioned prior to the hurricane with the objective of minimizing the outage cost of the load to promote the capability of DS to resist extreme disturbance. The second stage determines the real-time allocation of MEGs, output power of CHP units and EBs, and the power consumption of electric loads after the hurricane to maximize DS’s load recovery considering the worst-case of the uncertainty realization. Since the fragility analysis of network elements has an essential impact on the efficacy of the optimal strategy, we introduce the Z-number-based approach to scientifically determine the failure probability of components considering the effect of the aging of components and the credibility of the failure information obtained from the fragility. The effectiveness of the proposed methodology is examined based on an IEEE 123-bus distribution test system, and the obtained results confirm the validity of the proposed approach in actual implementations.

Robust Distribution System Load Restoration With Time-Dependent Cold Load Pickup

Service restoration is one of the critical functions to enable the future self-healing distribution system. To restore the distribution system in a timely and reliable manner, the realistic system operating conditions need to be accurately characterized. In this paper, two main factors that have great impacts on distribution system restoration (DSR) in practice are investigated. First, cold load pickup (CLPU), generally caused by thermostatically controlled loads (TCLs), is a common phenomenon after an outage and shaped by the outage duration. However, the time-dependent behaviors of CLPU are rarely considered in literature. In this paper, the operating state evolution of TCLs after an outage is analyzed to characterize time-dependent CLPU. And the time-dependent CLPU is analytically embedded in DSR to accurately represent the actual behaviors of the restored loads. Second, it is difficult to predict loads that fluctuate during DSR due to the lack of real-time measurement data. Accordingly, a robust DSR based on the information gap decision theory (IGDT) is proposed to address this challenge, fully considering the uncertainty of CLPU. The proposed models are tested in IEEE 13-node and 123-node test feeders. Simulation results demonstrate that the time-dependent CLPU model and the uncertainty modeling of CLPU can accurately capture the actual behaviors of loads with TCLs after an outage, which greatly improves DSR decisions in practice.

Collaborative Distribution System Restoration Planning and Real-Time Dispatch Considering Behind-the-Meter DERS

Modern distribution systems are becoming more resilient against power outages thanks to the flexible generation capacity provided by the increasing integration of distributed energy resources (DERs). Compared to utility-scale DERs, which can be directly controlled by system operators, small-scale, behind-the-meter DERs are much more difficult to coordinate despite being the vast majority. Two major obstacles to the implementation of DERs for service restoration are the coordination of behind-the-meter DERs and the management of uncertainty. In this paper, a novel distribution system restoration strategy is proposed to overcome these two obstacles. The flexibility of behind-the-meter DERs is quantified and integrated into the restoration planning models within a hierarchical structure. The model predictive control technique is employed to enable adaptive restoration planning solution adjustments to accommodate fault scenarios and forecast errors. Besides, real-time power dispatch models are proposed to maintain power balance using available DER capability. Comprehensive integration of adaptive restoration planning schemes and real-time dispatch results are achieved through a collaborative restoration framework. The effectiveness of the proposed restoration strategy is verified through a modified IEEE 123-bus system and a real-world utility system.

Distribution system restoration using graph theory after multiple faults

This study presents a novel graph theory-based approach to restore the distribution systems (DSs) after multiple simultaneous faults due to extreme weather conditions. The algorithm promptly finds the switching sequence to energise as many healthy zones as possible in an unbalanced DS. All the resulted topologies are later checked for operating constraints such as line flows and bus voltages. Hierarchy based load curtailment is proposed to remove any existing violations by shedding minimum non-critical loads. The proposed algorithm also gives the order in which the faults have to be cleared, depending on the priority of the disconnected load and inconvenience caused to the public. OpenDSS is used for unbalanced power flow analysis. Studies on the IEEE 37-bus system and the IEEE 123-bus system compared the proposed algorithm with other existing methods in the literature.

A convex model for induction motor starting transients imbedded in an OPF-based optimization problem

Large horsepower induction motors play a critical role in the operation of industrial facilities. In this respect, the distribution network operators dedicate a high priority to the operational safety of these motor loads. In this paper, the induction motor starting is modeled analytically and in a semi-static fashion. This model is imbedded in a convex distribution system restoration problem. In this optimization problem, it is aimed to determine the optimal status of static loads and the optimal dispatch of distributed generators such that: a) the induction motors can be reaccelerated in a safe way and, b) the total power of static loads that cannot be supplied before the motor energization, is minimized. The proposed optimization problem is applied in the case of a distribution network under different simulation scenarios. The feasibility and accuracy of the obtained results are validated using a) off-line time-domain simulations, and b) Power Hardware-In-the-Loop experiments.

Hindcasting the Functional Loss and Restoration of the Napa Water System Following the 2014 Earthquake Using Discrete-Event Simulation

Models that simulate postearthquake functional loss and restoration of water distribution systems support the development and implementation of more informed resilience-enhancing strategies. This study uses pipe damage, repair data, and a discrete-event simulation (DES) model to hindcast the water system damage and functional loss and restoration, following the 2014 South Napa earthquake. The DES model represents the water system as a set of entities (e.g., pipes, tanks, pumps) that interact through a sequence of events (e.g., earthquake damage, inspection) of variable duration that may be triggered at different points in time depending on the entity attributes (e.g., pipe vulnerability), access to resources (e.g., inspection crews), and the completion of other events. In addition to pipe damage and time-dependent inspection and repair processes, the DES model incorporates a pressure-driven analysis (PDA) that captures the restoration of water availability following the event. The tuned DES model is then used to simulate the postearthquake disruption and restoration of the City of Napa’s water supply for a Mw 6.7 event on the West Napa fault. By propagating the uncertainties in the damage to the network components (e.g., pipe) conditioned on the shaking intensity and the temporal (e.g., repair time) and resource-related (e.g., the number of inspection crews) variables, probabilistic descriptions of network component repair and water service restoration are generated.