Resilient-enhancing critical load restoration using mobile power sources with incomplete information

doi:10.1016/j.segan.2020.100418

Sustainable Energy, Grids and Networks

Volume 26, June 2021, 100418

https://doi.org/10.1016/j.segan.2020.100418 Get rights and content

Highlights

•
The proposed model boosts the system resilience via scheduling MPSs and forming MGs.
•
A two-stage robust optimization formulation is adopted to manage problem uncertainty.
•
A receding horizon framework is developed to model the dynamic nature of field data.
•
The charging capability of MPSs is modeled to improve the recovery process.

Abstract

Mobile power sources (MPSs) have great potentials to enhance the resilience of distribution system due to mobility and flexibility. However, because of incomplete and asynchronous data after a natural disaster, decisions may lead to under-utilization of MPS and weak recovery performance. This paper proposes a robust receding horizon recovery strategy that dispatches MPSs and forms multiple microgrids (MGs) to maximize the restored critical loads (CLs). The receding horizon framework is utilized to update the system information dynamically and re-optimize the problem until accomplishment of the recovery process. A two-stage robust optimization formulation is adopted to take into account the problem uncertainty, i.e. unknown status of branches in damaged areas. Due to long-lasting duration of the recovery process, charging capability for re-chargeable MPSs is added to the proposed approach. Several case studies are carried out on IEEE 33-node distribution test system and IEEE 123-node test feeder to verify the effectiveness of proposed framework. The benefits of the new model are remarkable when there is a significant level of incomplete information, which is a likely case after high impact natural disasters.

Introduction

Natural disasters over the last years have triggered significant power outages with high-impact and long-lasting effects [1]. The catastrophic consequences for the economy and society have underlined the significance to reinforce power system resilience [2]. Since distribution systems remain in danger in the case of natural events and could leave numerous customers without electricity for days, immediate and effective response is one of crucial requirements of a resilient distribution system [3]. As conventional recovery strategies cannot restore loads fast enough [4], distribution systems would require an enhanced strategy for resilience. Microgrids (MGs) not only enhance the level of social welfare and the reliability of distribution systems [5], [6], [7], but also are deemed as one of the prominent solutions to boost the resilience of distribution systems [8], [9]. Ref. [10] introduced a hierarchical scheme for outage management in a smart grid with multiple MGs. In [11], an advanced distribution system recovery method was proposed to restore critical loads (CLs). The method optimally allocates available distributed energy resources to CLs and forms resilient MGs.

Mobile power sources (MPSs) offer spatiotemporal mobility for immediate electrical service restoration over distribution systems [4]. This feature is particularly attractive when customers have partial access to the main grid, which is prevalent in natural disasters [12]. A two-stage MPS positioning framework was introduced in [12], consisting of pre-positioning and real-time allocation of resources. The charging capability is excluded in this work. Ref. [13] proposed a novel method for the adaptive formation of multi-MGs as one of the operational features for improving the critical service restoration strategy. Nonetheless, the model is not multi-period and MPSs are dispatched once at the first stage of disasters. Therefore, it is unable to fully utilize the MPS versatility and flexibility. In [14], a combined post-disaster load restoration strategy was developed for MPS pre-positioning and routing, MG generation scheduling, and grid reconfiguration. Ref. [15] introduced a resilient scheme for post-disaster recovery logistics that include network reconfiguration, coordinating repair crews, and MPSs. Ref. [16] investigated a load restoration framework that would optimize the dispatch of MPSs and the travel times of repair crews.

Uncertainties in real time operations could have a major impact on the resilience enhancement problem. In [4], an innovative two-stage framework was introduced, in which a robust optimization model is used to pre-position MPSs at the first stage (ex-ante) to improve the system survivability. At the second stage (ex-post), MPSs are dispatched and network topology is reconfigured under the assumption of complete information about the damages. This assumption might not hold in prevailing disasters. Ref. [17] introduced a stochastic post-hurricane recovery framework that uses both MPSs and reconfiguration plan to improve the resilience of networked MGs. The uncertain parameters include MPS travel times and active/reactive load demand; the status of branches in damaged areas are however considered to be known right after the event.

Using the Monte Carlo simulation method, uncertainties representing the status of roads, branches, and load demands were captured by scenario trees in [18]. However, calculating the probability of each scenario, due to the lack of sufficient historical data pertaining to natural disasters, is hardly possible. An innovative approach was proposed in [19] to tackle the uncertainties of switches status and asynchronous information during the distribution system recovery process. However, the incorporated energy sources are not mobile and this feature notably restricts the problem flexibility.

Another essential facet of the ex-post load restoration problem is the dynamic nature of field data. After a disaster, various types of field data [18], which are employed in order to enhance the restoration performance, needs to be updated progressively for the real-time decision-making.

In the light of literature review, there is a research gap to model the dynamic nature of field data and uncertainty of branches status in damaged zones during the distribution system recovery process. For this purpose, a robust receding horizon based recovery process is proposed in this paper. The proposed recovery process optimally dispatches MPSs and forms MGs to maximize the restored CLs in a resilient distribution system. In order to manage the uncertainty of branches status in damaged areas of distribution network, a two-stage robust optimization method is devised. Since the decisions are immunized against the worst-case scenario, the final recovery process is utterly robust for the given uncertainty budget. Furthermore, a receding horizon framework is adopted to exploit the progressively updated data in the favor of solution optimality. This framework continuously updates the unknown status of branches and re-optimizes the decisions to restore more CLs. The charging capability of mobile energy storage systems is also incorporated in the model to enhance the flexibility of recovery process. Accordingly, the major contributions of this paper are as follows:

•
In order to optimally dispatch MPSs and form multiple optimal MGs after the natural disaster, the uncertainty of branches status in damaged areas of distribution system is managed by a two-stage robust optimization model.
•
A receding horizon framework is applied to exploit the gradually updated branches status data in damaged areas. This framework re-optimizes the decisions after field crew’s inspections so as to restore more weighted CLs.

Section snippets

Proposed problem statement

Fig. 1 illustrates a typical resilience curve following to an event [18]. R refers to a system performance metric. System states include resilient pre-event state ( $t_{0}$ , $t_{e}$ ), event progress ( $t_{e}$ , $t_{p e}$ ), degraded post-event state ( $t_{p e}$ , $t_{r}$ ), recovery state ( $t_{r}$ , $t_{p r}$ ), post-recovery state ( $t_{p r}$ , $t_{i r}$ ), and infrastructure recovery ( $t_{i r}$ , $t_{p i r}$ ).

As recovery state starts at $t_{r}$ , DSO schedules resources and forms multiple MGs [1]. Due to credible damages to the monitoring system or its original limited

Proposed model

The objective function in this paper is maximizing the sum of weighted restored CLs. The proposed multi-period two-stage robust optimization formulation identifies branches of unknown zones with the worst effect on the objective function. Using the proposed formulation, the DSO can dynamically schedule MPSs and form MGs, while taking the uncertainty of branches status in unknown zones into account. At first, the proposed formulation is presented for a specific time duration of the recovery

Scheme overview and solution methodology

The outline of the proposed multi-period robust receding horizon-based recovery is shown in Fig. 3. It is consisting of three main stages, initialization, preparation, and receding horizon recovery process. In the first stage, which is before the event, distribution system configuration data, CL demand and priorities, MPSs characteristics and locations are initialized. Proactive management, such as pre-positioning of MPSs and line hardening, can be considered at this stage. Ref. [22] have

Case Study 1: IEEE 33-node distribution test system

The IEEE 33-node distribution test system [25] is used to validate the proposed MPS scheduling and MG forming. Numerical experiments are implemented in GAMS on a computer with an Intel i7-9750H, 2.59 GHz processor, and 16 GB of memory. The MILP master and sub-problems are solved by CPLEX solver.

As shown in Fig. 4, DSO faces 4 known branch damages after the disaster. Also, there are 3 unknown zones which are shown by rectangular boxes in the distribution system. According to the field crews’

Conclusion

In this paper, a robust receding-horizon based recovery framework was presented for scheduling MPSs and forming MGs while maximizing the weighted sum of restored CLs. Simulation results showed that incomplete information in the deterministic approach led to MPS underutilization and weak recovery performance. However, considering unknown zones and re-optimizing the decision variables with respect to the updated data received from field crews’ inspections can significantly increase the sum of

CRediT authorship contribution statement

Seyed Amin Sedgh: Writing - original draft, Software, Conceptualization. Meysam Doostizadeh: Methodology, Formal analysis, Software, Visualization. Farrokh Aminifar: Validation, Writing - review & editing, Supervision. Mohammad Shahidehpour: Validation, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Resilient-enhancing critical load restoration using mobile power sources with incomplete information

Highlights

Abstract

Introduction

Section snippets

Proposed problem statement

Proposed model

Scheme overview and solution methodology

Case Study 1: IEEE 33-node distribution test system

Conclusion

CRediT authorship contribution statement

Declaration of Competing Interest

Sustain. Energy. Grids Netw.

Sustain. Energy. Grids Netw.

Sustain. Energy. Grids Netw.

Appl. Energy

Inf. Sci. (Ny).

Oper. Res. Lett.

Toward a consensus on the definition and taxonomy of power system resilience

IEEE Access

The grid: stronger bigger smarter?

IEEE Power Energy Mag.

Modernizing distribution system restoration to achieve grid resiliency against extreme weather events: an integrated solution

Proc. IEEE

Routing and scheduling of mobile power sources for distribution system resilience enhancement

IEEE Trans. Smart Grid

Provisional microgrid planning

IEEE Trans. Smart Grid

Enhancing power system resilience through hierarchical outage management in multi-microgrids

IEEE Trans. Smart Grid

Critical load restoration using distributed energy resources for resilient power distribution system

IEEE Trans. Power Syst.