October  2018, 14(4): 1565-1577. doi: 10.3934/jimo.2018021

Frequency $H_{2}/H_{∞}$ optimizing control for isolated microgrid based on IPSO algorithm

Key Lab of Industrial Computer Control Engineering of Hebei Province, College of Electric Engineering, Yanshan University, Qinhuangdao 066004, China

* Corresponding author: Zhong-Qiang Wu

Received  February 2017 Revised  August 2017 Published  October 2018 Early access  January 2018

Fund Project: The first author is supported by the Hebei Natural Science(F2016203006).

Affected by the fluctuation of wind and load, large frequency change will occur in independently islanded wind-diesel complementary microgrid. In order to suppress disturbance and ensure the normal operation of microgrid, a $H_{2}/H_{∞}$ controller optimized by improved particle swarm algorithm is designed to control the frequency of microgrid. $H_{2}/H_{∞}$ hybrid control can well balance the robustness and the performance of system. Particle swarm algorithm is improved. Adaptive method is used to adjust the inertia weight, and cloud fuzzy deduction is used to determine the learning factor. Improved particle swarm algorithm can solve the problem of local extremum, so the global optimal goal can be achieved. It is used to optimize $H_{2}/H_{∞}$ controller, so as to overcome the conservative property of solution by linear matrix inequality and improve the adaptive ability of controller. Simulation results show that with a $H_{2}/H_{∞}$ controller optimized by improved particle swarm algorithm, the frequency fluctuations caused by the wind and load is decreased, and the safety and stable operation of microgrid is guaranteed.

Citation: Zhong-Qiang Wu, Xi-Bo Zhao. Frequency $H_{2}/H_{∞}$ optimizing control for isolated microgrid based on IPSO algorithm. Journal of Industrial and Management Optimization, 2018, 14 (4) : 1565-1577. doi: 10.3934/jimo.2018021
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C. W. AhnJ. An and J. C. Yoo, Estimation of particle swarm distribution algorithms: Combining the benefits of PSO and EDAs, Information Sciences, 192 (2012), 109-119. 

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H. BaekJ. Ryu and J. Oh, Optimal design of multi-storage network for combined sewer overflow management using a diversity-guided, cyclic-networking particle swarm optimizer-A case study in the Gunja subcatchment area, Korea, Expert Systems with Applications, 42 (2015), 6966-6975. 

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B. XuD. Chen and H. Zhang, Hamiltonian model and dynamic analyses for a hydro-turbine governing system with fractional item and time-lag, Commun Nonlinear Sci Numer Simulat, 47 (2017), 35-47. 

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W. DuQ. Jiang and J. Chen, Frequency Control Strategy of Distributed Generations Based on Virtual Inertia in a Microgrid, Automation of Electric Power Systems, 35 (2012), 26-31. 

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H. DuanQ. Luo and Y. Shi, Hybrid particle swarm optimization and genetic algorithm for multi-UAV Formation Reconfiguration, IEEE Computational Intelligence Magazine, 8 (2013), 16-27. 

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M. Iqbal and M. A. M. De Oca, An estimation of distribution particle swarm optimization algorithm, Springer Berlin Heidelberg, German, 4150 (2006), 72-83. 

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H. J. JiaY. Qi and Y. F. Mu, Frequency response of autonomous microgrid based on family-friendly controllable loads, Science China Technological Sciences, 56 (2013), 693-702. 

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H. LiB. FuC. YangB. Zhao and X. Tang, Research on microgrid and its application in China, Proceedings of the CSEE, 32 (2012), 24-31. 

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Y. Mi and C. Wang, Frequency optimization control for isolated photovoltaic-diesel hybrid microgrid based on load estimation, Proceedings of the CSEE, 33 (2013), 115-121. 

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H. LiD. ChenH. ZhanC. Wu and X. Wang, Hamiltonian analysis of a hydro-energy generation system in the transient of sudden load increasing, Applied Energy, 185 (2017), 244-253. 

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J. J. LiangA. K. Qin and P. N. Suganthan, Comprehensive learning particle swarm optimizer for global optimization of multimodal functions, IEEE Transactions on Evolutionary Computation, 10 (2006), 281-295. 

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H. LiuL. Gao and Q. Pan, A hybrid particle swarm optimization with estimation of distribution algorithm for solving permutation flowshop scheduling problem, Expert Systems with Applications, 38 (2011), 4348-4360. 

[14]

M. LiuL. Guo and C. Wang, A coordinated operating control strategy for hybrid isolated microgrid including wind power, photovoltaic system, diesel generator, and battery storage, Dianli Xitong Zidonghua(Automation of Electric Power Systems), 36 (2012), 19-24. 

[15]

X. MaY. WuH. Fang and Y. Sun, Optimal sizing of hybrid solar-wind distributed generation in an islanded microgrid using improved bacterial foraging algorithm, Proceedings of the CSEE, 31 (2012), 17-25. 

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Y. MaP. Yang and J. Wu, Hybrid control strategy of islanded microgrid with numerous distributed generators, Automation of Electric Power Systems, 39 (2015), 104-109. 

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A. Nandar and C. Supriyadi, Robust PI control of smart controllable load for frequency stabilization of microgrid power system, Renewable Energy, 56 (2013), 16-23. 

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M. J. Sanjari and G. B. Gharehpetian, Game-theoretic approach to cooperative control of distributed energy resources in islanded microgrid considering voltage and frequency stability, Neural Computing and Applications, 25 (2014), 343-351. 

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C. ShenW. Gu and Z. Wu, An Underfrequency Load Shedding Strategy for Islanded Microgrid, Automation of Electric Power Systems, 35 (2011), 47-52. 

[20]

L. SuJ. Zhang and L. Wang, Study on some key problems and technique related to microgrid, Power System Protection and Control, 19 (2010), 235-239. 

[21]

F. Van den Bergh and A. P. Engelbrecht, A cooperative approach to particle swarm optimization, IEEE Transactions on Evolutionary Computation, 8 (2004), 225-239. 

[22]

J. Wang, Genetic particle swarm optimization based on estimation of distribution, Springer Berlin Heidelberg, German, 4688 (2007), 287-296. 

[23]

H. Wang and G. Li, Control strategy of microgrid with differend DG types, Electric Power Automation Equipment, 32 (2012), 19-23. 

[24] D. Wang, The optimal control theory ofand, Harbin Institute of Technology Press, Harbin, 2001. 
[25]

B. WuD.-Y. Chen and H. Zhang, Modeling and stability analysis of a fractional-order francis hydro-turbine governing system, Chaos, Solitons and Fractals, 75 (2015), 50-61.  doi: 10.1016/j.chaos.2015.01.025.

[26]

X. WuX. YinX. Song and J. Wang, Reactive current allocation and control strategies improvement of low voltage ride though for doubly fed induction wind turbine generation system, High Voltage Apparatus, 49 (2013), 142-149. 

[27]

B. XuF. WangD. Chen and H. Zhang, Hamiltonian modeling of multi-hydro-turbine governing systems with sharing common penstock and dynamic analyses under shock load, Energy Conversion and Management, 108 (2016), 478-487. 

[28]

B. XuD. ChenH. Zhang and R. Zhou, Dynamic analysis and modeling of a novel fractional-order hydro-turbine-generator unit, Nonlinear Dynamics, 81 (2015), 1263-1274. 

[29]

B. XueM. Zhang and W. N. Browne, Particle swarm optimization for feature selection in classification: A multi-objective approach, IEEE Trans Cybern, 43 (2013), 1656-1671. 

[30] L. Yu, Robust Control: The Processing of the Linear Matrix Inequality Approach, Tsinghua University Press, Beijing, 2002. 
[31]

Q. ZhangC. Peng and Y. Chen, A Control Strategy for Parallel Operation of Multi-inverters in Microgrid, Proceedings of the CSEE, 32 (2012), 126-132. 

show all references

References:
[1]

C. W. AhnJ. An and J. C. Yoo, Estimation of particle swarm distribution algorithms: Combining the benefits of PSO and EDAs, Information Sciences, 192 (2012), 109-119. 

[2]

H. BaekJ. Ryu and J. Oh, Optimal design of multi-storage network for combined sewer overflow management using a diversity-guided, cyclic-networking particle swarm optimizer-A case study in the Gunja subcatchment area, Korea, Expert Systems with Applications, 42 (2015), 6966-6975. 

[3]

B. XuD. Chen and H. Zhang, Hamiltonian model and dynamic analyses for a hydro-turbine governing system with fractional item and time-lag, Commun Nonlinear Sci Numer Simulat, 47 (2017), 35-47. 

[4]

W. DuQ. Jiang and J. Chen, Frequency Control Strategy of Distributed Generations Based on Virtual Inertia in a Microgrid, Automation of Electric Power Systems, 35 (2012), 26-31. 

[5]

H. DuanQ. Luo and Y. Shi, Hybrid particle swarm optimization and genetic algorithm for multi-UAV Formation Reconfiguration, IEEE Computational Intelligence Magazine, 8 (2013), 16-27. 

[6]

M. El-Abd, Preventing premature convergence in a PSO and EDA hybrid, IEEE Congress on Evolutionary Computation, (2009), 3060-3066. 

[7]

M. Iqbal and M. A. M. De Oca, An estimation of distribution particle swarm optimization algorithm, Springer Berlin Heidelberg, German, 4150 (2006), 72-83. 

[8]

H. J. JiaY. Qi and Y. F. Mu, Frequency response of autonomous microgrid based on family-friendly controllable loads, Science China Technological Sciences, 56 (2013), 693-702. 

[9]

H. LiB. FuC. YangB. Zhao and X. Tang, Research on microgrid and its application in China, Proceedings of the CSEE, 32 (2012), 24-31. 

[10]

Y. Mi and C. Wang, Frequency optimization control for isolated photovoltaic-diesel hybrid microgrid based on load estimation, Proceedings of the CSEE, 33 (2013), 115-121. 

[11]

H. LiD. ChenH. ZhanC. Wu and X. Wang, Hamiltonian analysis of a hydro-energy generation system in the transient of sudden load increasing, Applied Energy, 185 (2017), 244-253. 

[12]

J. J. LiangA. K. Qin and P. N. Suganthan, Comprehensive learning particle swarm optimizer for global optimization of multimodal functions, IEEE Transactions on Evolutionary Computation, 10 (2006), 281-295. 

[13]

H. LiuL. Gao and Q. Pan, A hybrid particle swarm optimization with estimation of distribution algorithm for solving permutation flowshop scheduling problem, Expert Systems with Applications, 38 (2011), 4348-4360. 

[14]

M. LiuL. Guo and C. Wang, A coordinated operating control strategy for hybrid isolated microgrid including wind power, photovoltaic system, diesel generator, and battery storage, Dianli Xitong Zidonghua(Automation of Electric Power Systems), 36 (2012), 19-24. 

[15]

X. MaY. WuH. Fang and Y. Sun, Optimal sizing of hybrid solar-wind distributed generation in an islanded microgrid using improved bacterial foraging algorithm, Proceedings of the CSEE, 31 (2012), 17-25. 

[16]

Y. MaP. Yang and J. Wu, Hybrid control strategy of islanded microgrid with numerous distributed generators, Automation of Electric Power Systems, 39 (2015), 104-109. 

[17]

A. Nandar and C. Supriyadi, Robust PI control of smart controllable load for frequency stabilization of microgrid power system, Renewable Energy, 56 (2013), 16-23. 

[18]

M. J. Sanjari and G. B. Gharehpetian, Game-theoretic approach to cooperative control of distributed energy resources in islanded microgrid considering voltage and frequency stability, Neural Computing and Applications, 25 (2014), 343-351. 

[19]

C. ShenW. Gu and Z. Wu, An Underfrequency Load Shedding Strategy for Islanded Microgrid, Automation of Electric Power Systems, 35 (2011), 47-52. 

[20]

L. SuJ. Zhang and L. Wang, Study on some key problems and technique related to microgrid, Power System Protection and Control, 19 (2010), 235-239. 

[21]

F. Van den Bergh and A. P. Engelbrecht, A cooperative approach to particle swarm optimization, IEEE Transactions on Evolutionary Computation, 8 (2004), 225-239. 

[22]

J. Wang, Genetic particle swarm optimization based on estimation of distribution, Springer Berlin Heidelberg, German, 4688 (2007), 287-296. 

[23]

H. Wang and G. Li, Control strategy of microgrid with differend DG types, Electric Power Automation Equipment, 32 (2012), 19-23. 

[24] D. Wang, The optimal control theory ofand, Harbin Institute of Technology Press, Harbin, 2001. 
[25]

B. WuD.-Y. Chen and H. Zhang, Modeling and stability analysis of a fractional-order francis hydro-turbine governing system, Chaos, Solitons and Fractals, 75 (2015), 50-61.  doi: 10.1016/j.chaos.2015.01.025.

[26]

X. WuX. YinX. Song and J. Wang, Reactive current allocation and control strategies improvement of low voltage ride though for doubly fed induction wind turbine generation system, High Voltage Apparatus, 49 (2013), 142-149. 

[27]

B. XuF. WangD. Chen and H. Zhang, Hamiltonian modeling of multi-hydro-turbine governing systems with sharing common penstock and dynamic analyses under shock load, Energy Conversion and Management, 108 (2016), 478-487. 

[28]

B. XuD. ChenH. Zhang and R. Zhou, Dynamic analysis and modeling of a novel fractional-order hydro-turbine-generator unit, Nonlinear Dynamics, 81 (2015), 1263-1274. 

[29]

B. XueM. Zhang and W. N. Browne, Particle swarm optimization for feature selection in classification: A multi-objective approach, IEEE Trans Cybern, 43 (2013), 1656-1671. 

[30] L. Yu, Robust Control: The Processing of the Linear Matrix Inequality Approach, Tsinghua University Press, Beijing, 2002. 
[31]

Q. ZhangC. Peng and Y. Chen, A Control Strategy for Parallel Operation of Multi-inverters in Microgrid, Proceedings of the CSEE, 32 (2012), 126-132. 

Figure 1.  Independent wind-diesel microgrid
Figure 2.  The dynamic model of microgrid
Figure 3.  Flow chart of PSO algorithm
Figure 4.  Cloud membership function of $D(i, {g}_{best})$
Figure 5.  Cloud membership functions of $c_{1}$, $c_{2}$
Figure 6.  Load and maximum power output of wind in microgrid
Figure 7.  Output power of diesel generator
Figure 8.  Frequency deviation of microgrid (with $H_{2}/H_{\infty}$ control based on LMI)
Figure 9.  Frequency deviation of microgrid (with $H_{2}/H_{\infty}$ control based on PSO algorithm)
Figure 10.  Frequency deviation of microgrid (with $H_{2}/H_{\infty}$ control based on IPSO algorithm)
Table 1.  The fuzzy rules of $c_{1}$ and $c_{2}$
Rules $D(i, {g}_{best})$ $c_{1}$ $c_{2}$
1 Near Small Big
2 Middle Middle Middle
3 Far Big Small
Rules $D(i, {g}_{best})$ $c_{1}$ $c_{2}$
1 Near Small Big
2 Middle Middle Middle
3 Far Big Small
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