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The purpose of this paper is to execute the efficiency analysis of the selected metaheuristic algorithms (MAs) based on the investigation of analytical functions and investigation optimization processes for permanent magnet motor.

A comparative performance analysis was conducted for selected MAs. Optimization calculations were performed for as follows: genetic algorithm (GA), particle swarm optimization algorithm (PSO), bat algorithm, cuckoo search algorithm (CS) and only best individual algorithm (OBI). All of the optimization algorithms were developed as computer scripts. Next, all optimization procedures were applied to search the optimal of the line-start permanent magnet synchronous by the use of the multi-objective objective function.

The research results show, that the best statistical efficiency (mean objective function and standard deviation [SD]) is obtained for PSO and CS algorithms. While the best results for several runs are obtained for PSO and GA. The type of the optimization algorithm should be selected taking into account the duration of the single optimization process. In the case of time-consuming processes, algorithms with low SD should be used.

The new proposed simple nondeterministic algorithm can be also applied for simple optimization calculations. On the basis of the presented simulation results, it is possible to determine the quality of the compared MAs.

The decarbonization of power generation is key to achieving carbon neutrality in China by the end of 2060. This paper aims to examine how green finance influences China’s low-carbon transition of power generation. Using a provincial panel data set as an empirical study example, green finance is assessed first, then empirically analyses the influences of green finance on the low-carbon transition of power generation, as well as intermediary mechanisms at play. Finally, this paper makes relevant recommendations for peak carbon and carbon neutrality in China.

To begin with, an evaluation index system with five indicators is constructed with entropy weighting method. Second, this paper uses the share of coal-fired power generation that takes in total power generation as an inverse indicator to measure the low-carbon transition in power generation. Finally, the authors perform generalized method of moments (GMM) econometric model to examine how green finance influences China’s low-carbon transition of power generation by taking advantage of 30 provincial panel data sets, spanning the period of 2007–2019. Meanwhile, the implementation of the 2016 Guidance on Green Finance is used as a turning point to address endogeneity using difference-in-difference method (DID).

The prosperity of green finance can markedly reduce the share of thermal power generation in total electricity generation, which implies a trend toward China’s low-carbon transformation in the power generation industry. Urbanization and R&D investment are driving forces influencing low-carbon transition, while economic development hinders the low-carbon transition. The conclusions remain robust after a series of tests such as the DID method, instrumental variable method and replacement indicators. Notably, the results of the mechanism analysis suggest that green finance contributes to low-carbon transformation in power generation by reducing secondary sectoral share, reducing the production of export products, promoting the advancement of green technologies and expanding the proportion of new installed capacity of renewable energy.

This paper puts forward relevant suggestions for promoting the green finance development with countermeasures such as allowing low interest rate for renewable energy power generation, facilitating market function and using carbon trade market. Additional policy implication is to promote high quality urbanization and increase R&D investment while pursuing high quality economic development. The last implication is to develop mechanism to strengthen the transformation of industrial structure, to promote high quality trade from high carbon manufactured products to low-carbon products, to stimulate more investment in green technology innovation and to accelerate the greening of installed structure in power generation industry.

This paper first attempts to examine the low-carbon transition in power generation from a new perspective of green finance. Second, this paper analyses the mechanism through several aspects: the share of secondary industry, the output of exported products, advances in green technology and the share of renewable energy in new installed capacity, which has not yet been done. Finally, this study constructs a system of indicators to evaluate green finance, including five indicators with entropy weighting method. In conclusion, this paper provides scientific references for sustainable development in China, and meanwhile for other developing countries with similar characteristics.