Multi-objective optimization and decision making for power dispatch of a large-scale integrated energy system with distributed DHCs embedded☆
Introduction
The study of distributed renewable energy resources and their connections to a power grid has received much attention in recent years. Efficient utilization of various distributed renewable energy resources has also aroused intense interest in order to satisfy various types of energy demands [1]. As a significant type of renewable energy resources, wind power generation is integrated in power systems due to its clean and indigenous nature [2], [3]. On the other hand, apart from electricity loads, heating loads and cooling loads occupy a significant proportion of load demand needed to be served in the LSIES [4], [5], [6]. In the study of a traditional power system, heating loads and cooling loads are always served by the electricity-driven facilities, resulting in the increasing of electricity demands [7]. Accordingly, the rising of heating and cooling loads increases the valley-to-peak of daily variations in electricity demand and thereby also boosts the need for peak load power generation [8]. Therefore, it is necessary to handle the integrated utilization of a variety of distributed renewable energy resources and the increase of various energy demand.
Until now, a number of methods have been developed to investigate the coordinated scheduling of the distributed energy systems. Reference [9] reviewed the existing energy management system for microgrids and proposed microgrid control schemes which are based on central and distributed models. An energy management for both supply and demand of a grid-connected microgrid incorporating renewable energy resources was presented in [10]. The authors of reference [11] presented an energy management of microgrid in grid-connected and stand-alone modes based on a double-layer coordinated control approach, respectively, which consists of a schedule layer and a dispatch layer. Reference [12] formulated a dynamic optimal power flow for industrial microgrids, which includes both security and factories constraints considering plug-in electric time and energy related charging constraints.
In most of the previous studies, researchers have focused only on the power dispatch of the microgrids considering the uncertainties of renewable resources. As the types of renewable energy resources and energy demands increase, it is of great importance to integrate the distributed energy systems and the power grid in the LSIES in order to satisfy not only the electricity loads but also the heating loads and cooling loads.
In our previous research [13], [14], we presented a district heating and cooling (DHC) unit, which produces hot and cold fluids, and then distributes them throughout the residents with underground pipes. The DHC unit can ensure the reliability of heating and cooling supply with high efficiency and reduce fuel cost. However, the optimal power dispatch of the LSIES has not been investigated to optimize the multiple objectives and determine a final optimal solution for both the power grid and the DHCs.
This paper focuses on the problem of optimal power dispatch of the power grid and the distributed DHCs which are both included in the LSIES. On the other hand, the study of LSIES presented in this paper is also concerned with development of a novel methodology which could be efficiently used for optimization and decision making of the power dispatch. The concept of LSIES is extendable to cover various kinds of district, urban or even national energy networks in which distributed energy resources and loads are contained. In order to balance the conflicting interests of the power grid and the distributed DHCs, the optimal power dispatch of the LSIES is mathematically formulated as a multi-objective optimization problem considering the selected objectives representing the economy and reliability of the power grid and the DHCs. In addition, the multi-objective optimization problem also contains a variety of constraints to satisfy the optimal operation requirements of the LSIES.
Over the last decades, a number of multi-objective optimization algorithms have been developed to solve the multi-objective optimization problem. The techniques include non-dominated sorting genetic algorithm-II (NSGA-II) [15], [16], multi-objective particle swarm optimizer (MOPSO) [17], [18], multi-objective differential evolution algorithm (MODE) [19], etc. Inspired by a multi-objective evolutionary algorithm, group search optimizer with multiple producers (GSOMP) [20], this paper proposes a multi-objective group search optimizer with adaptive covariance and Lévy flights (MGSO-ACL) to solve the presented multi-objective optimization problem of the optimal power dispatch of a LSIES with distributed DHCs and wind power interconnected via a power grid.
The MGSO-ACL consists of three types of group members: producers, scroungers and rangers. In each generation, the members conferred with the best fitness value of each objective are chosen as the producers, and a number of members are randomly selected as the scroungers, then the rest of members are named the rangers. The producers are assigned to search for the best fitness value for their corresponding objectives, and perform the crappie search behavior which is characterized by maximum pursuit angle, maximum pursuit distance, and maximum pursuit height [21]. The scroungers employ the concepts based on covariance matrix adaptation evolution strategy [22], [23] to design optimum searching strategy. Moreover, Lévy flights, which are found to be more efficient than random walks for searching resource [24], [25], are employed by the rangers to increase the diversity of group in this paper. Applying the MGSO-ACL, a Pareto-optimal set can be obtained. The Pareto-optimal set contains all the feasible and optimal solutions, called Pareto-optimal solutions. In addition, the quality of the Pareto-optimal solutions can be measured by the metrics utilizing the index of inverted generational distance (IGD), hypervolume (HV) [26], the mean Euclidian distance (MED), the spacing index and the number of Pareto-optimal solutions (NPS) [27], [28].
When the Pareto-optimal set is obtained by the MGSO-ACL, it is necessary for system operators to determine a final optimal solution from the Pareto-optimal solutions. In this paper, an evidential reasoning (ER) approach [29], [30] is applied to conduct decision making for a final optimal solution, with the preference of the operators. Compared with other decision making methods [17], [18], [31], the ER makes decision with adequate evidence fully considering both the multiple objectives and the multiple criteria in order to make full use of the operators’ knowledge. Instead of using certain relative weights to multiple objectives in [20], the ER takes into account the uncertainties of the operators’ cognition. Accordingly, the ER is able to make a convincing decision, determining a final optimal solution which is more preferable for the operators. Furthermore, it is potential to conduct the ER on the different variable spaces to diminish the region of interest, which can help lessen the computation burden during the decision making process.
The rest of the paper is organized as follows: Section 2 formulates a large-scale integrated energy system containing distributed DHCs and wind power interconnected via a power grid. In this section, the models of the power grid, the DHC unit and wind power generation are discussed in detailed. Section 3 investigates the proposed multi-objective optimization methodology. The decision making method for determining a final optimal solution is presented in Section 4. The multi-objective group search optimizer with adaptive covariance and Lévy flights and the evidential reasoning approach are evaluated in Section 5. Finally, the last section draws the conclusion of this paper.
Section snippets
System description
A framework of a large-scale integrated energy system is shown in Fig. 1. The figure describes the interactions between different modules integrated in the LSIES. The electricity loads, distributed generators, wind power and DHCs are interconnected via the power grid. The electricity loads are satisfied by the power supply from the power grid, and it is treated as an operation constraint. The distributed generators is dispatched in the power grid in order to provide adequate power source from
Multi-objective optimization
The optimal power dispatch of an integrated energy system consisting of distributed DHCs and wind power interconnected via a power grid is formulated as a multi-objective optimization problem mathematically. The objectives can be addressed for the economy and reliability viewpoint of both the power grid and the DHCs. Moreover, the optimization problem must satisfy various of constraints aforementioned to maintain the stable operation of the LSIES. Consequently, the problem is a complex
Decision making for a final optimal solution
The evidential reasoning approach is utilized to determine a final optimal solution in this paper. Consisting of multi-attribute analysis, multi-evidence reasoning and utility evaluation, the ER combines multiple evidence and provides a suitable mechanism to map the assessment grades to utility evaluation. The multi-attribute analysis, multi-evidence reasoning and utility evaluation are related to the Pareto-optimal solutions of the power dispatch problem. The calculation of the ER is based on
Simulation studies
In this section, simulation studies are conducted to verify the performance of the proposed multi-objective optimization algorithm and the decision making approach for the optimal power dispatch of the power grid and distributed DHCs. Simulation studies are carried out on the modified IEEE 30-bus system with distributed DHCs and wind power generation integrated. The distributed energy units are interconnected via the 30-bus power grid, hence the test system can be treated as a LSIES. The
Conclusion
This paper has presented the study of a large-scale integrated energy system considering distributed district heating and cooling units and wind power generation interconnected via a power grid. The multi-objective group search optimizer with adaptive covariance and Lévy flights addresses the adaptive covariance and Lévy flights to increase its exploration and exploitation abilities. The objectives of economy and reliability for the power grid and distributed DHCs are taken into consideration.
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The project is funded by the State Key Program of National Natural Science of China (Grant No. 51437006) and Guangdong Innovative Research Team Program (No. 201001N0104744201).