Article
Economic Emission Dispatch Considering Renewable Energy
Resources—A Multi-Objective Cross Entropy
Optimization Approach
Qun Niu
1,
*, Ming You
1
, Zhile Yang
2
and Yang Zhang
1
Citation: Niu, Q.; You, M.; Yang, Z.;
Zhang, Y. Economic Emission
Dispatch Considering Renewable
Energy Resources—A
Multi-Objective Cross Entropy
Optimization Approach.
Sustainability 2021, 13, 5386.
https://doi.org/10.3390/su13105386
Academic Editor: João Carlos de
Oliveira Matias
Received: 15 April 2021
Accepted: 4 May 2021
Published: 12 May 2021
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4.0/).
1
School of Mechanical Engineering and Automation, Shanghai University, Shanghai 200444, China;
youming1227@shu.edu.cn (M.Y.); zy2016@shu.edu.cn (Y.Z.)
2
Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518055, China;
zyang07@qub.ac.uk
* Correspondence: nq@shu.edu.cn
Abstract:
The conventional electrical power system economic dispatch (ED) often only pursues
immediate economic benefits but neglects the harmful environment impacts of gas emissions from
thermal power plants. To address this shortfall, economic emission dispatch (EED) has drawn a lot of
attention in recent years. With the increasing penetration of renewable generation, the intermittence
and uncertainty of renewable energy such as solar power and wind power increase the difficulties
of power system scheduling. To enhance the dispatch performance with significant penetration of
renewable energy, a modified multi-objective cross entropy algorithm (MMOCE) is proposed in this
paper. To solve multi-objective optimization problems, a crowding–distance calculation technique
and a novel external archive mechanism are introduced into the conventional cross entropy method.
Additionally, the population updating process is simplified by introducing a self-adaptive parameter
operator that substitutes the smoothing parameters, while the solution diversity and the adaptability
in large scale systems are improved by introducing the crossover operator. Finally, a two-stage
evolutionary mechanism further enhances the diversity and the rate of convergence. To verify
the efficacy of the proposed MMOCE, eight benchmark functions and three different test systems
considering different mixes of renewable energy sources are employed. The dispatch results by the
proposed MMOCE are compared with other multi-objective cross entropy algorithms and published
heuristic methods, confirming the superiority of the proposed MMOCE over other methods in all
test systems.
Keywords:
economic emission dispatch; renewable energy sources; multi-objective cross entropy
algorithm; crossover operator
1. Introduction
The economic dispatch (ED) is a fundamental issue in electrical power system schedul-
ing that aims to maximize the economic profits by the optimal allocation of the output of
each generator unit [
1
]. It is shown that more than 10% of the total energy consumption can
be saved by means of economic dispatch [
2
]. However, in the last decades, environmental
issues have drawn substantial attention worldwide, and much effort has been made to
mitigate the negative effects of climate change and environment pollution [
3
]. As such,
managing pernicious gases emissions has become an important consideration when it
comes to the ED problem. The economic emission dispatch (EED) retains the original
characteristics while incorporating the emission factors, resulting in a multi-objective opti-
mization problem, which simultaneously minimizes the generating cost and the emission
level to the lowest possible values.
In China, about 70% of electricity supply comes from coal-fired power stations; ad-
dressing climate change while meeting future energy needs will inevitably impose greater
Sustainability 2021, 13, 5386. https://doi.org/10.3390/su13105386 https://www.mdpi.com/journal/sustainability
