A multi-objective resilience-economic stochastic scheduling method for microgrid

Highlights

• Developing a multi-objective economic-resilience scheduling model for Microgrid.

• Analyzing the behavior of renewable energy resources in resilience program.

• Analyzing the impact of resilience/economic indices through the Pareto front.

• Using mixed-integer linear programing to bound the optimal balance of indices.

Abstract

In this paper, the applicability of Microgrids (MGs) is reviewed for power system resilience against low-probability high-impact (LPHI) events. Financial issues have been always one of the major priorities in the scheduling of MGs. Although these systems can feed their loads in islanding mode, resilient operation of them under critical situations caused by LPHI events is a challenging problem. Improving resilience increases MG costs, therefore it is necessary to establish a trade-off between resilience and economic metrics. Therefore, the main purpose of this paper is to develop a novel multi-objective resilience-economic stochastic MG scheduling model. The proposed bi-level resilience-oriented stochastic scheduling integrates the economic perspective along with resilience function simultaneously using a multi-objective mixed-integer linear programming approach. The considered MG resilience function includes various metrics such as the ability to withstand, quick recovery, and the technical criteria in the face of low-probability high-impact events. The proposed method is tested on the modified IEEE 33-bus power system with a set of distributed energy resources, energy storage systems, and electric vehicle parking lots. The results outlined that, although, the integration of the resilience metrics in the MG scheduling problem has increased the operation cost of the MG approximately 25%, but improved the MG resilience more than 70%. On the other hand, the proper management of the independent distributed energy resources enhanced the resilience of the MG approximately 16% while decreased the operation cost of the MG by at least 28%.

Introduction

Micro energy grid facilities can be considered in the front lines against darkness and perhaps the only reachable solutions to prevent widespread power system outages around the world due to low-probability high-impact (LPHI) events [1]. LPHI events refer to severe natural disasters such as thunderstorms, hurricanes, blizzards, and floods [2], which are occurred more increasingly due to climate change. The devastating impact of these events on the infrastructure of human life is undeniable. In the meantime, particularly, the power distribution systems are more vulnerable in the face of these events due to their intrinsic breadth [3]. This issue emphasizes the topic of resilience that addresses the power grids ability to withstand against LPHI events [1]. In recent decades, various researchers have been proposed to improve power system resilience [4], [5]. The use of microgrid (MG) potential in islanding mode and its operational flexibility and self-healing capabilities have been extensively underlined by researchers for improving power system resilience [6], [7].

Microgrid describes a set of loads and distributed energy resources (DERs) connected through a medium-voltage network within a specified electrical boundary, which can feed its loads in both islanding and grid-connected modes [8]. Reference [9] has presented a mechanism for determining the resilience-oriented optimal decisions associated with an MG subject to disruptions in its power lines, intending to minimize system degradation.

The different perspectives developed by researches for utilizing the benefits of MGs for power system resilience can be classified into five categories [10] such as: Converting power systems into MGs, Dynamic MG establishment, Networked MG establishment, Multi-microgrids, and Other methods. The literature review is summarised in Fig. 1 and explained at the following.

The optimal sizing and allocation of switches in the power system to ensure optimum performance through network transformation to MGs during critical situations have been presented in [11]. Yuan in [12] has proposed a method for decomposing the power distribution system to community MGs by integrating local DERs and neighbouring load centres. A method for the transformation of the distribution system into autonomous MGs has been presented in [13]. Qi et al. in [14] designed a reconfiguration method for power systems during events considering faulty equipment.

In [15], a load shedding approach has been proposed for dynamically forming multiple MGs from the radial distribution system. Authors in [16] proposed a comprehensive self-healing strategy based on dividing the on-outage area into MGs. Simonov in [17] described a real-time metering computerized tool for distributed monitoring, dynamic reconfiguration, and control of the double bar bus DC system by dynamically dividing loads. Ding et al. in [18] proposed a master–slave load restoration model to coordinate topology reconfiguration and MG formation dynamically while satisfying various operational constraints. Self-organization and decentralized energy management of the islanded MG cluster via dynamic clustering of MGs has been proposed in [19].

A resilience-oriented optimization strategy has been proposed in [20] by considering feasible islanding in regular operation and survivability of critical loads during the emergency period. Wu et al. in [21] proposed an operation algorithm for collaboration of neighbouring MGs in a community of MGs to enhance resilience during critical situations. Flexible division and unification control strategies have been proposed in [22] to enhance the system resilience by helping networked MGs prepare adequately for extreme events. The optimal scheduling of networked MGs considering resilience constraints is proposed in [23], where an attempt has been made to mitigate the damaging impacts of electricity interruptions by effectively exploiting MG capabilities. Ref. [24] has introduced a nested energy management system for the day-ahead scheduling of networked MGs by forming subgroups during emergencies. Authors in [25] have empirically compared various algorithms for electricity sharing by networked MG clustering in terms of self-sufficiency, sharing the cost, and stability.

In [26], the resilience of an interdependent multi-energy system is assessed in the presence of MGs. This model ignored the economic aspects of MG. Reference [27] seeks enhancement of power system resilience through hierarchical outage management of multi-microgrids. This model has ignored the detailed security constraints associated with the AC optimal power flow. Weber and Shah in [28] developed a tool for evaluation of combined heat and power systems considering MG resilience and emissions. A methodology to identify the vulnerable components, and ensure the resilient operation of the coordinated power and natural gas infrastructures considering multiple outages within the MG has been investigated in [29]. Hussain et al. in [30] developed an autonomous community MG through optimal sizing and siting of tri-generation equipment to deploy the energy hub.

Khodaei in [31] followed the objective of minimizing load shedding by suggesting a robust scheduling method for MG. The stability and economic analysis of MG while supplying critical loads in islanding mode are investigated in [32], [33], respectively. Authors in [34] calculated the MG efficiency curve (MEC) with jointly using the overhead lines fragility model and LPHI event profile. The obtained MEC has been then used to assess the resilience criteria. Ref. [35] investigated the effects of the resilience of communication systems along with power system dynamics on MG stability. A bi-level model for reserve capacity and reliable power supply in coupled MGs has been introduced in [36]. Schneider et al. in [37] evaluated the feasibility of using MGs as a resiliency resource, including their possible benefits and the associated technical challenges. Ref. [38] developed an optimization algorithm for the scheduling of residential urban districts with consideration of hybrid-renewables and water harvesting integration. The integration of distributed energy resources into MG is suggested in [39] for enhancing power systems resilience. Authors in [40] represented a comprehensive mathematical model for the resilient operation of the MG. The proposed model assumes the MG is the owner of DERs; therefore, the economic relations of MG with the owner of DERs for the provision of ancillary services have not taken into account in the final objective function. As a weakness, this assumption is only valid for military-type MGs; thereby, it can not be considered for analysis of the other type of MGs. Further, the resilience perspective has ignored in this paper.

According to the above studies, although the definition and evaluation of resilience have been considered in several papers, most studies have considered a simple definition of resilience. Also, the integration of resilience criteria in MG planning objective function has not been previously reported. Therefore, the main purpose of this paper is to address the challenge of ensuring the resilient operation of MG in an emergency due to destructive events while optimizing the costs of MG operation through the direct integration of resilience criteria in the objective function of MG scheduling.

The resilience of a power system consisting of multi-MGs is highly dependent on the resilience of individual MGs. Fig. 2 shows the strategy of the power system operator in the face of the LPHI event. The MGs that are affected by the LPHI event are disconnected from the main network and try to deal with the event in islanding mode. After the event, the recovery process begins, and then the MG can be reconnected to the upstream network. The presented work in this paper focuses on steps 2 and 3 presented in Fig. 2.

The independent assessment of the MG resilience due to LPHI event and its enhancement simultaneously with optimizing the operating costs have been considered by limited researches. Most papers have either simply defined resilience or evaluated resilience criteria in general based on the reliability criteria. Researchers have also paid less attention to the coordinated optimization of operating costs and the MG resilience function. Therefore, a two-stage MG scheduling method is proposed to address this challenge. The first-stage economic operation of the MG is intended to make an optimal price decision on the day-ahead marginal electricity sale price for customers while maintaining the total operational cost for the next 24-h operation. The idea of establishing the first stage decision is motivated by the essential need of a regular management structure for the next day’s operation from the perspectives of price and energy. At the second stage, the idea of establishing a resilience-oriented real-time operation of MG under uncertainties is motivated by the increasing difficulties due to LPHI events considering uncertainties and various DER behaviours. In this stage, corrective and timely decisions are taken to reduce the destructive effects of LPHI events and improve resilience.

The proposed resilience-oriented stochastic scheduling (ROSS) approach tries to use the charging/discharging potential of energy storage systems (ESSs) and electric vehicle parking lots (EVPs) along with renewable and dispatchable distributed energy resources (DERs) to improve the MG resilience while optimizing the operational costs.

To incorporate the resilience-based objective function to the proposed ROSS method, first, the MG resilience function (RF) is obtained considering vital features underlined through standard resilience definitions. The first resilience metric is timely awareness capability concerning the event occurrence ($\vartheta$), which shows the delay in applying corrective action during the event. The second used metric for resilience is the fragility index (FI), which refers to the withstand ability of the MG against the event. The restoration efficiency index (REI), which indicates the speed of the recovery phase after the LPHI event is the third metric used for proposed MG. Further, the MG voltage index (MVI) and lost load index (LLI) are the last metrics used in the proposed MG resilience function, which show the technical quality of the MG after experiencing the LPHI event. To obtain the FIand REImetrics, the MEC is obtained based on the percentage of loads fed before, during, and after the LPHI event.

The suggested ROSS method assumes the MG is not the owner of all DER units; therefore, they will participate in the resilience program based on the real-time market information to improve operating resilience, particularly, in islanding mode. In fact, the proposed method establishes a balance of economic-resilience indices by integrating resilience criteria into the formulation of the MG stochastic scheduling problem. Besides, it is easy to calculate for any system and improves resilience in the face of LPHI events without spending a lot of time and money.

Fig. 3 describes the proposed resilience -oriented MG two-stage scheduling model. At the first stage, day-ahead analysis is considered without the system uncertainties. At the second stage, the balance of the economic and resilience metrics is obtained according to the real-time market information considering the system uncertainties facing an extreme event.

The modified IEEE 33-bus test system with a set of renewable and dispatchable DERs, ESSs, and EVPs is used to test the effectiveness of the proposed ROSS method. Simulations are carried out in two cases. In the first simulation case, independent DERs that are not owned by the MG do not participate in power generation. In the second case, the independent DERs share their power with the MG based on real-time market information to improve MG resilience. Following the LPHI event, it is assumed that the line limits are decreased based on the event duration, lines 3–4, 6–26, and 10–11 tripped, and the MG is placed in islanding mode. In this critical situation, MG is trying to reduce its load curtailments using the power of DERs and the flexible charging/discharging potential of ESSs as well as EVPs. Since the MG covers a small geographic area, it is assumed the LPHI event affects all the MG components. To guarantee the finding of the global optimum operating point, the presented mixed-integer linear MG ROSS model is handled by GAMS CPLEX 24.1.2 solver of GAMS software. The novel contribution of this paper are summarized as follows:

• Developing a multi-objective model for the optimal economic-resilient operation of MG including renewable and dispatchable DERs.

• Analysing the behaviour of storage and electric parking lot systems during the resilience program.

• Modelling and analysing the participation of independent power producers into the proposed ROSS method.

• Employment of the hardware viewpoint, restoration perspective, and technical aspects for assessing the MG resilience.

• Utilizing lp-metric method for solving the proposed multi-objective resilience-economic MG scheduling problem.

• Employing mixed-integer linear programming to guarantee an optimal balance between economic-resilience indices.

The rest of the paper is organized as follows: The methodology of the proposed ROSS method is provided in Section 2. Section 3 represents the case studies and numerical simulations. Finally, Section 4 concludes the results of this paper.