Two-stage economic, reliability, and environmental scheduling of multi-microgrid systems and fair cost allocation

https://doi.org/10.1016/j.segan.2021.100546Get rights and content

Highlights

  • Cooperative energy management for renewable MMG systems.

  • Proposing the HLCP approach to considers the preferences between objectives.

  • Presenting a two stage energy management that considers cost, emissions, and ENS.

  • Ensuring that the cost of the MMG remains at its optimum.

  • Presenting a fair cost allocation to divide the overall gain of coalition among MGs.

Abstract

Microgrids (MGs) play a critical role to enhance the flexibility and efficiency of the distribution systems as well as reliability and environmental problems. In this paper, we propose a two-stage multi-objective optimization framework for optimal energy management of multi-microgrid systems (MMG). The proposed model considers the total cost, energy not supplied (ENS), and greenhouse gas emissions to determine the best plan for the MMG system. We propose a hybrid lexicography-compromise programming (CP) to handle non-homogeneous objective functions by the two-stage technique. At the first stage, the operation cost of the MMG system is minimized to determine the best plan from the economic perspective. At the second stage, the ENS and greenhouse gas emissions have been considered objective functions using CP method. The main advantage of the proposed model is that it remains the operation cost of the MMG system at its optimum. The proposed model is based on the cooperation of MGs to provide a stable and reliable solution, where the total cost of the MMG system has been allocated among MGs based on their contributions. The simulation results show the cost of the multi-microgrid system, ENS, and CO2 emissions are improved by 33.72%, 83.5%, and 8%, respectively.

Introduction

With the penetration of renewable generation, microgrids (MG) have been turned into alternatives to enhance the safety and stability of distribution networks [1], [2]. Microgrids are low voltage and small-scale active distribution networks that can be used in the connected or isolated modes [3], [4], [5]. Renewable generations, energy storage systems, and small-scale dispatchable resources are the main resources that can be used to supply the required demand of MGs [6], [7]. A large and growing body of literature had been conducted on the energy management of MGs in the distribution systems.

Farinis et al. [8] proposed a hierarchical multi-agent system to determine the best plan for MGs in both grid-connected and autonomous modes. The battery energy management system for renewable MGs had been studied in [9]. The role of the power station of electric vehicles in the MGs had been formulated as the bi-level model in [10]. Li et al. [11] proposed a distributed control approach for optimal scheduling of DC MGs. Refs. [12], [13] studied the role of MGs in the resilience of distribution systems. The authors in [14] developed a power management strategy to enhance the power quality of hybrid AC/DC MGs. Although the energy storage systems (ESS) are integrated into the model to cover the uncertainty of renewable generations, the role of demand response (DR) programs was not studied. The dynamic optimal scheduling of a water-energy MG considering the customer’s temperature comfort range had been investigated in [15], where the ESS and renewable generation integrated into the model to enhance the flexibility of MG. Nasr et al. [16] presented a multi-objective optimization that considered the generation contingency and voltage stability for MGs. However, the impacts of uncertain behavior of renewable generations and market prices were not deliberated.

With the rapid development of MGs, the interaction among them in the distribution systems introduced the multi-microgrid (MMG) concept. Various research works had been studied the energy management of the MMG system. For example, the authors in [17] studied the optimal energy scheduling of the MMG systems in both normal and emergency conditions. The proposed model used the chance-constrained model to handle the uncertain nature of renewable generation. Nevertheless, the efficiency of the proposed model on the emission of greenhouse gases was not investigated. Park et al. [18] evaluated penetration of the renewable generation on the performance of the isolated MMG system. However, the cost allocation among MGs, emission of greenhouse gases, and energy not supplied (ENS) were not considered. In [19], Pakdel et al. suggested a multi-objective optimization for water management of the MMG system, where the MMG system had been modeled as the multi-energy hub. The authors employed the epsilon constraint technique and fuzzy approach to define the best plan for the energy hubs. However, the uncertainty of renewable generation and DR programs had not been studied. However, the emission of greenhouse gases and ENS are not applied to the model as the objective functions. In addition, the proposed model cannot ensure the optimal economic solution for the studied system because it needed a trade-off between the objective functions. A cooperative energy scheduling framework had been proposed in [20] to model the internal interaction among MGs, where the renewable generation and ESS integrated into the model to enhance the flexibility of the system. However, the uncertainty of renewable generation was not applied to the model. Also, the cost allocation among MGs, ENS, and emission of greenhouse gases were not investigated.

Hakimi et al. [21] presented a stochastic planning problem to consider the uncertain behavior of renewable generation and electric vehicles on the MMG operation scheduling, where the DR programs, energy storage systems, fuel cells, electrolyzer were integrated into the model to enhance the flexibility of the MMG system. The suggested model in [22] tried to minimize the amount of load-shedding in the MMG system, where the worst scenario had been evaluated to supply the required demand in the islanded mode. A stochastic two-level framework had been developed in [23] to manage the transactive energy among MGs. At the first level, local energy management had been performed to determine the shortage and surplus capacity of MGs. Also, central energy management had been implemented to ensure the optimal solution at the second level. Nevertheless, the efficiency of the cooperation MGs were not studied.

The cooperative games are commonly studied in [24], [25], [26], [27] to model the energy management of MMG systems. In these strategies, the MGs cooperate to ensure the global optimum by centralized control. Ref. [24] suggested a cooperative game for short-term energy scheduling of the MMG systems considering the uncertain behavior of renewable generation. Although the cooperative games ensure the global optimum for the MMG system, this operating cost should be divided among sub-systems. Therefore, one of the important issues in cooperative games is fair cost allocation. Du et al. [25] employed the concept of core in the cooperative game to allocate the total operation cost of the MMG system for each autonomous grid-connected MG. Ref. [26] developed an Aumann–Shapley to consider the efficiency, and bargaining power of each MG to allocate the economic cost of MMG system. Bahmani et al. [27] proposed cooperative energy management for networked multi-carrier systems considering electrical and thermal DR programs. The proposed model integrated the electrical, thermal, and ice storage into the system to enhance its flexibility. Finally, the authors utilized the Shapley value to determine the contribution of each sub-system. Nevertheless, the probabilistic behavior of renewable generation had not been considered. The optimal energy scheduling of the hybrid MMG system was formulated as a bi-level problem in [28] considering the congestion in the point of common coupling. The authors employed a cooperative game to fairly divide profit between MGs. The authors in [29] designed an energy trading mechanism based on the cooperative game, where the Shapley value had been utilized to define the cost of each MG. However, the impacts of different uncertainties were not applied to the model.

According to the literature, most of the research works focused on the energy scheduling of MMG systems from the economic perspective, where the reliability and environmental issues had been neglected. In this paper, we propose a multi-objective optimization that considers the operating costs, the amount of energy not supplied, and the emission of greenhouse gases simultaneously. The local energy management system (LEMS) of each MG sends the generation capacity, marginal cost of resources, and load demand to the central energy management system (CEMS). The CEMS considers the uncertain nature of renewable generation and market prices to determine the best scheduling for the MMG system. At the first stage, the CEMS only optimizes the operating cost of the MMG system to ensure the optimal economic solution for the MGs. Then, the amount of energy not supplied and emission of greenhouse gases have been minimized simultaneously at the second stage given that the operating cost of the MMG system remains at its optimum. The CEMS uses the proposed two-stage model to remain the operating cost at its optimum and simultaneously improves the amount of energy not supplied and the emission of greenhouse gases. The CEMS sends the results of two-stage optimization as well as generating power of local resources, energy storage planning, and the responsive loads to each LEMS. The proposed model is based on the cooperative game that provides the opportunity for cost reduction, where the MGs share their resources to utilize the surplus capacity of the MMG system as the backup. In addition, the Shapley value is developed to consider the contribution of MGs in the coalition and allocates the fair costs based on their bargaining powers. Table 1 compares the related research works with the proposed model.

Nevertheless, the main contributions of the work are listed as follows:

1. Proposing a multi-objective optimization for energy scheduling of the MMG systems considering economical, reliability, and environmental aspects simultaneously. The responsive loads, energy storage systems, and various controllable resources have been integrated into the model to cover the uncertain behavior of renewable generation and enhance the flexibility of the MMG system.

2. Presenting a hybrid of lexicography and compromise programming techniques to handle the multi-objective energy scheduling. The operating cost of the MMG system is the main objective and minimizes at the first stage of the lexicography approach. At the second stage of the lexicography approach, we optimize ENS and emission by compromise programming that is appreciated to combine the non-homogeneous objective functions. The main advantage of the proposed hybrid lexicography and compromise programming approach is that it optimizes the ENS and emission, while remains the operating cost of the MMG system at its optimum. Actually, in the proposed model, the trade-off is performed only between ENS and emission.

3. The proposed model is based on the cooperative game and the MMG system has been managed by a centralized structure to ensure the best response for the MMG system. Besides, the total operating cost of the system is fairly divided among MGs based on their contributions and bargaining powers. Therefore, it can be easily applied to single and multi-owner systems.

The rest of this paper is organized as follows: the mathematical formulation of the proposed energy management as well as objective functions and constraints are modeled in Section 2. The proposed hierarchical energy management has presented in Section 3. Section 4 evaluates the results of the suggested method on a general test system. The fair cost allocation is presented in Section 5. Finally, the conclusion has described in Section 6.

Section snippets

Mathematical formulation of the proposed cooperative energy management

We propose a tri-objective optimization framework for optimal energy management of the sustainable MMG systems considering the total costs, emission of greenhouse gases, and ENS simultaneously. Given that we study the short-term scheduling of the MMG system, we only consider the ENS as the reliability index that its model is taken from [30] and [31]. The mathematical formulation of objectives are shown in (1)–(3): MinCost=MinCostPV+CostWT+CostDG+CostFC+CostMT+CostCL+CostGridMinEmissions=Minm=1M

Hybrid lexicography-compromise programming energy management

Fig. 1 shows the conceptual model of the proposed framework for the energy scheduling of multi-microgrid systems. We combine two effective multi-objective approaches to present a hybrid lexicography-compromise programming framework (HLCP). The proposed HLCP framework is formulated as a two-stage problem consists of three objective functions. At the first stage, the operating cost of the MMG system has been considered as the objective function to determine the best plan for the MMG system from

Case studies

In this section, the proposed cooperative model is tested on the IEEE 6-bus test system. Three MGs are located on the different nodes, according to Fig. 2. A scenario-generation and scenario-reduction method have been used to generate related scenarios for wind speed and solar radiation. It should be noted that the accuracy of the probabilistic approaches depends on the number of the selected scenarios and the CEMS is able to consider an acceptable accuracy for its problem. In this study, we

Fair cost allocation

One of the key issues in cooperative strategies is the fair allocation of costs or profits among the participants. The total cost of MGs in case I (Autonomous operation) is 5762.25 $. When the MGs form a coalition, the total cost of the MMG reaches 3818.93 $. In fact, with the formation of the coalition, the cost of the system will be reduced by 1943.32 $. This cost-saving should be divided fairly among MGs. It should be noted that fair allocation does not mean equal distribution of profits

Conclusion

In this paper, a multi-objective hierarchical strategy for the community microgrids energy management has been developed that considers total daily cost, ENS, and Co2 emissions simultaneously. In this model, microgrids cooperate with others to minimize their costs. Therefore, the energy transacts among the MGs and the main grid. A probability scenario generation and reduction method is utilized to handle the uncertainty of market prices and renewable generations. Compared to autonomous

CRediT authorship contribution statement

Hamid Karimi: Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Writing – original draft, Writing – review & editing. Shahram Jadid: Methodology, Project administration, Supervision, 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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