基于NLP建模的ICPT系统参数优化
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摘要
感应耦合电能传输（Inductively Coupled Power Transfer，ICPT）技术是一种集现代电力变换技术、控制技术、磁耦合技术等于一体的新型电源接入传输技术，具有安全、可靠、灵活、高效、易维护等优点，克服了传统有线电能传输的诸多问题，开创了电能接入的新方式。尽管ICPT技术具有广阔的应用前景，仍存在许多关键问题未得到很好地解决，如频率稳定性、参数全局优化、软开关控制等问题，特别是在参数优化方面一直缺乏一种有效的能综合考虑多方面因素的全局优化方法。
在ICPT系统参数优化方面，传统的“三要素”法、图示估计法、迭代逐个优化法等存在的主要缺点有：
1、是一类局部优化方法，考虑的因素较少；
2、主要采用“求导”的方法得到连续函数的极点来作为最优值，不能用于离散函数优化问题，适应面窄；
3、优化方法效率低，参数设计周期长；
4、最优参数的最优性不强，参数难以达到同时最优。
针对传统方法的不足，本文引入了非线性规划（Nonlinear Programming，NLP）的思想，并采用智能优化算法来得到系统的全局最优参数。新的全局优化方法具有如下特点：
1、是一种能综合考虑多种因素的全局优化方法；
2、是目前在软开关条件下考虑系统频率稳定性问题解决复杂拓扑参数优化的一种有效方法；
3、是一种能扩展到各种拓扑的通用型优化方法；
4、具有开放性，能加入更多的要素；
5、优化方法效率高，一次优化能得到所有参数的最优解或得到多种最优参数组合方案；
6、最优解质量高，能使各参数同时达到最优。
总体结构以“全局优化”为目标，以“NLP建模”及“约束优化”为2个关键点，将参数优化过程分为NLP建模及模型优化处理两部分。首先，为了更好地建立系统的规划模型，以电压型ICPT系统为例，分别对4种典型拓扑的输入输出关系及频率稳定性等进行了研究，得到了一些不同于传统观点的新特性。其次，针对ICPT系统的特点提出了将具体的电路模型抽象为一般的规划模型的基本规则，即需要考虑的各种因素；并结合系统特性基于优化思想提出了4种NLP建模方法，为引入优化方法来处理多参数多约束问题打好基础。接着，在对NLP模型进行优化处理过程中，发现了一类难点问题即约束优化问题，以该问题为出发点对约束处理方法进行了系统研究，在一些经典算法的基础上，结合其他优化策略，分别提出了一种改进型自适应罚函数法及一种改进型多目标优化法。最后，通过一个ICPT系统参数优化实例，对2种改进算法、交流阻抗NLP建模方法及大范围频率稳定等特性进行仿真及实验验证。
文章主要贡献及创新点有：
1、为了提高参数设计的合理性及可靠性，对ICPT系统输入输出等特性进行了研究，得到了一些有利于参数优化建模的新观点：ICPT原边输入采用恒流或恒压设计方式应该根据负载输出恒流或恒压特性进行选择，负载输出特性为恒流源或恒压源应该根据系统的整体结构来判断。
2、在传统频率稳定性问题研究基础上，进一步研究了电压型ICPT系统在分叉域内的频率稳定性问题，分析了4种典型拓扑在分叉域内的不同规律，得到了系统在频率分叉域内不一定不稳定的结论，即频率分叉域内系统的谐振频率有可能保持为最佳谐振频率点不变，降低了NLP模型中频率稳定性条件的约束强度。
3、为了合理、全面、规律地建立规划模型，提出了ICPT系统NLP规划的建模规则，即需要考虑频率稳定性条件、参数的额定值约束、系统品质因数约束、器件的实际限制条件、参数间相互关系约束等主要因素。
4、为了实现ICPT系统由具体电路模型向数学规划模型转换，基于ICPT电路分析的常用方法及优化算法的基本思想，提出了交流阻抗NLP模型、广义状态空间平均NLP模型、时域微分NLP模型、基于仿真的综合NLP模型4种规划模型，以更好地利用优化领域的研究成果得到系统全局最优参数。
5、针对自适应罚函数法在处理约束优化问题中存在全局搜索能力、收敛性、鲁棒性等方面的不足，采用了排序归一化策略、自适应权重罚系数策略、动态精英保留策略3点改进，提出了一种改进的自适应罚函数法。
6、为了提高多目标优化法的约束处理能力、全局收敛性能、最优解的稳定性、算法的鲁棒性等，采用4种策略即猫映射混沌初始化、自适应拉普拉斯交叉算子、按需分层机制、隔代交替的约束处理策略对其进行了改进，提出了一种改进的多目标优化法。
Inductively coupled power transfer (ICPT) technology is a new wireless powertransfer technology by combination of modern power conversion, control and magneticcoupling techniques, and has the advantage of security, reliability, flexibility, highefficiency, and easy maintenance, it overcomes many shortcomings brought by thetraditional power transmission with cable and a new method has been opened up.Although the ICPT technology has broad application prospects, there are still many keyissues have not been a good solution, in particular, there has always been a lack of aneffective comprehensive consideration of various factors in ICPT parameteroptimization aspect.
In ICPT parameter optimization design aspect, the traditional ‘three-factor’ method,icon estimation method, iteration individually optimization method etc. have thefollowing disadvantages:
1. They are local optimization ways considering little factors.
2. Using ‘derivation’ as the main method to find the pole of a continuous functionas the optimal value, the application adaptation is so narrow that they are not capable ofdiscrete function.
3. Operation efficiency is low and the design cycle is long.
4. Quality of the optimal solution is low, parameters are difficult to achieve optimalsimultaneously.
For shortcomings of traditional methods, this paper introduces the NLP thoughtand using intelligent optimization algorithm to get global optimal system parameters.New global optimization method has the following characteristics:
1. It is a comprehensive consideration of various factors open global optimizationmethod.
2. It is an effective way to solve parameter optimization problems of complextopologies considering the frequency stability in soft-switching conditions nowadays.
3. It is a general optimization method can be extended to a variety of topologies.
4. It is an open method that can add more factors.
5. The optimization method is high efficiency that can get the optimal solution forall parameters or get many combination programs of optimal parameters in one time.
6. The optimal solution with high quality can achieve various parameters optimal at the same time.
Overall structure of this article is taking ‘optimization’ as the only goal, taking‘NLP model’ and ‘constrained optimization’ as two key problems, separating theoptimization process into NLP modeling and model optimization handing two parts.First, in order to establish the programming model in a better way, taking voltage-fedICPT system as examples, we studied the input-output relationship and frequencystability issues of four typical topologies, some new features different from traditionalview were brought up. Second, based on the characteristics of ICPT system, weproposed a general principle that transfer specific circuit model into general NLP model,i.e. the various factors needed to consider. Combining system features and based onoptimization idea, four different NLP modeling method was proposed in order to lay agood foundation to deal with the multi-parameter multi-constraint problems. Third,there is a class of difficult problems in the process of sloving model optimizationproblems, i.e. constrained optimization problem, then, taking this problem as a startingpoint we made a systematic research to constraint handing methods, based on someclassical algorithm, combining with other optimization strategies, an inproved adaptivepenalty function method and an modified multi-objective optimization method wereproposed. Finally, the two improved methods and an AC impedance NLP modelingmethod and characteristics such as a wide range of frequency stability etc. were provedby simulation and experiments of an ICPT system parameter optimizaton instance.
Major contribution and innovation of this paper are as follows:
1. In order to improve the rationality and reliability of parameter design, ICPTsystem input-output characteristics etc. were studied, some new perspectives can helpparameter optimization modeling were summarized. ICPT primary input constantcurrent or constant voltage design should be selected according to the load outputconstant current or constant voltage characteristics. The output characteristics of theconstant current source or constant voltage source should be based on the overallstructure of the system to determine.
2. Based on the traditonal research of frequency stability problem, a further studyof frequency stability problem in bifurcation region of the voltage-fed ICPT systemswas taken, the different laws of four typical topologies were analysed, it is concludedthat system frequency is not necessarily unstable in bifurcation domain especially forcomplex topologies, i.e. system resonant frequency in bifurcation frequency domainmay remain as the best resonant frequency unchanged, made the constraint strength of frequency stability condition in NLP model less strict.
3. To be reasonable, comprehensive, regularly to establish programming model, aNLP modeling rule of ICPT system was proposed, i.e. some main factors such asfrequency stability, parameter rating, system quality factor, practical limitations ofdevices and relationship between parameters etc. need to be considered.
4. In order to achieve the conversion from specific circuit model to mathematicalprogramming model for ICPT systems, based on the common method of ICPT systemanalysis and the basic idea of optimization algorithms, the four programming modelsthat is the AC impedance NLP model, the generalized state space averaging NLP model,the time domain differential NLP model, the integrated NLP model based on simulationwas proposed, so that it can make better use of the research achievement in optimizationfield.
5. For a more advanced adaptive penalty function method still has shortcomings todeal with constrained optimization problems in global search capability, convergenceand robustness etc. aspects, based on it a improved adaptive penalty function wasproposed in three aspects i.e. the sort normalization strategy, the adaptive weightpenalty coefficient strategy, and dynamic elitist strategy.
6. In order to improve constraint handing capacity, global convergenceperformance, stability of the optimal solution and robustness of the algorithm of amulti-objective optimization method, a modified multi-objective optimization problemwas proposed and it has four improvement aspects i.e. the cat mapping chaosinitialization strategy, the adaptive Laplace crossover operator, the demand tieredmechanism and the generational alternating constraint handling strategy.
在ICPT系统参数优化方面，传统的“三要素”法、图示估计法、迭代逐个优化法等存在的主要缺点有：
1、是一类局部优化方法，考虑的因素较少；
2、主要采用“求导”的方法得到连续函数的极点来作为最优值，不能用于离散函数优化问题，适应面窄；
3、优化方法效率低，参数设计周期长；
4、最优参数的最优性不强，参数难以达到同时最优。
针对传统方法的不足，本文引入了非线性规划（Nonlinear Programming，NLP）的思想，并采用智能优化算法来得到系统的全局最优参数。新的全局优化方法具有如下特点：
1、是一种能综合考虑多种因素的全局优化方法；
2、是目前在软开关条件下考虑系统频率稳定性问题解决复杂拓扑参数优化的一种有效方法；
3、是一种能扩展到各种拓扑的通用型优化方法；
4、具有开放性，能加入更多的要素；
5、优化方法效率高，一次优化能得到所有参数的最优解或得到多种最优参数组合方案；
6、最优解质量高，能使各参数同时达到最优。
总体结构以“全局优化”为目标，以“NLP建模”及“约束优化”为2个关键点，将参数优化过程分为NLP建模及模型优化处理两部分。首先，为了更好地建立系统的规划模型，以电压型ICPT系统为例，分别对4种典型拓扑的输入输出关系及频率稳定性等进行了研究，得到了一些不同于传统观点的新特性。其次，针对ICPT系统的特点提出了将具体的电路模型抽象为一般的规划模型的基本规则，即需要考虑的各种因素；并结合系统特性基于优化思想提出了4种NLP建模方法，为引入优化方法来处理多参数多约束问题打好基础。接着，在对NLP模型进行优化处理过程中，发现了一类难点问题即约束优化问题，以该问题为出发点对约束处理方法进行了系统研究，在一些经典算法的基础上，结合其他优化策略，分别提出了一种改进型自适应罚函数法及一种改进型多目标优化法。最后，通过一个ICPT系统参数优化实例，对2种改进算法、交流阻抗NLP建模方法及大范围频率稳定等特性进行仿真及实验验证。
文章主要贡献及创新点有：
1、为了提高参数设计的合理性及可靠性，对ICPT系统输入输出等特性进行了研究，得到了一些有利于参数优化建模的新观点：ICPT原边输入采用恒流或恒压设计方式应该根据负载输出恒流或恒压特性进行选择，负载输出特性为恒流源或恒压源应该根据系统的整体结构来判断。
2、在传统频率稳定性问题研究基础上，进一步研究了电压型ICPT系统在分叉域内的频率稳定性问题，分析了4种典型拓扑在分叉域内的不同规律，得到了系统在频率分叉域内不一定不稳定的结论，即频率分叉域内系统的谐振频率有可能保持为最佳谐振频率点不变，降低了NLP模型中频率稳定性条件的约束强度。
3、为了合理、全面、规律地建立规划模型，提出了ICPT系统NLP规划的建模规则，即需要考虑频率稳定性条件、参数的额定值约束、系统品质因数约束、器件的实际限制条件、参数间相互关系约束等主要因素。
4、为了实现ICPT系统由具体电路模型向数学规划模型转换，基于ICPT电路分析的常用方法及优化算法的基本思想，提出了交流阻抗NLP模型、广义状态空间平均NLP模型、时域微分NLP模型、基于仿真的综合NLP模型4种规划模型，以更好地利用优化领域的研究成果得到系统全局最优参数。
5、针对自适应罚函数法在处理约束优化问题中存在全局搜索能力、收敛性、鲁棒性等方面的不足，采用了排序归一化策略、自适应权重罚系数策略、动态精英保留策略3点改进，提出了一种改进的自适应罚函数法。
6、为了提高多目标优化法的约束处理能力、全局收敛性能、最优解的稳定性、算法的鲁棒性等，采用4种策略即猫映射混沌初始化、自适应拉普拉斯交叉算子、按需分层机制、隔代交替的约束处理策略对其进行了改进，提出了一种改进的多目标优化法。
Inductively coupled power transfer (ICPT) technology is a new wireless powertransfer technology by combination of modern power conversion, control and magneticcoupling techniques, and has the advantage of security, reliability, flexibility, highefficiency, and easy maintenance, it overcomes many shortcomings brought by thetraditional power transmission with cable and a new method has been opened up.Although the ICPT technology has broad application prospects, there are still many keyissues have not been a good solution, in particular, there has always been a lack of aneffective comprehensive consideration of various factors in ICPT parameteroptimization aspect.
In ICPT parameter optimization design aspect, the traditional ‘three-factor’ method,icon estimation method, iteration individually optimization method etc. have thefollowing disadvantages:
1. They are local optimization ways considering little factors.
2. Using ‘derivation’ as the main method to find the pole of a continuous functionas the optimal value, the application adaptation is so narrow that they are not capable ofdiscrete function.
3. Operation efficiency is low and the design cycle is long.
4. Quality of the optimal solution is low, parameters are difficult to achieve optimalsimultaneously.
For shortcomings of traditional methods, this paper introduces the NLP thoughtand using intelligent optimization algorithm to get global optimal system parameters.New global optimization method has the following characteristics:
1. It is a comprehensive consideration of various factors open global optimizationmethod.
2. It is an effective way to solve parameter optimization problems of complextopologies considering the frequency stability in soft-switching conditions nowadays.
3. It is a general optimization method can be extended to a variety of topologies.
4. It is an open method that can add more factors.
5. The optimization method is high efficiency that can get the optimal solution forall parameters or get many combination programs of optimal parameters in one time.
6. The optimal solution with high quality can achieve various parameters optimal at the same time.
Overall structure of this article is taking ‘optimization’ as the only goal, taking‘NLP model’ and ‘constrained optimization’ as two key problems, separating theoptimization process into NLP modeling and model optimization handing two parts.First, in order to establish the programming model in a better way, taking voltage-fedICPT system as examples, we studied the input-output relationship and frequencystability issues of four typical topologies, some new features different from traditionalview were brought up. Second, based on the characteristics of ICPT system, weproposed a general principle that transfer specific circuit model into general NLP model,i.e. the various factors needed to consider. Combining system features and based onoptimization idea, four different NLP modeling method was proposed in order to lay agood foundation to deal with the multi-parameter multi-constraint problems. Third,there is a class of difficult problems in the process of sloving model optimizationproblems, i.e. constrained optimization problem, then, taking this problem as a startingpoint we made a systematic research to constraint handing methods, based on someclassical algorithm, combining with other optimization strategies, an inproved adaptivepenalty function method and an modified multi-objective optimization method wereproposed. Finally, the two improved methods and an AC impedance NLP modelingmethod and characteristics such as a wide range of frequency stability etc. were provedby simulation and experiments of an ICPT system parameter optimizaton instance.
Major contribution and innovation of this paper are as follows:
1. In order to improve the rationality and reliability of parameter design, ICPTsystem input-output characteristics etc. were studied, some new perspectives can helpparameter optimization modeling were summarized. ICPT primary input constantcurrent or constant voltage design should be selected according to the load outputconstant current or constant voltage characteristics. The output characteristics of theconstant current source or constant voltage source should be based on the overallstructure of the system to determine.
2. Based on the traditonal research of frequency stability problem, a further studyof frequency stability problem in bifurcation region of the voltage-fed ICPT systemswas taken, the different laws of four typical topologies were analysed, it is concludedthat system frequency is not necessarily unstable in bifurcation domain especially forcomplex topologies, i.e. system resonant frequency in bifurcation frequency domainmay remain as the best resonant frequency unchanged, made the constraint strength of frequency stability condition in NLP model less strict.
3. To be reasonable, comprehensive, regularly to establish programming model, aNLP modeling rule of ICPT system was proposed, i.e. some main factors such asfrequency stability, parameter rating, system quality factor, practical limitations ofdevices and relationship between parameters etc. need to be considered.
4. In order to achieve the conversion from specific circuit model to mathematicalprogramming model for ICPT systems, based on the common method of ICPT systemanalysis and the basic idea of optimization algorithms, the four programming modelsthat is the AC impedance NLP model, the generalized state space averaging NLP model,the time domain differential NLP model, the integrated NLP model based on simulationwas proposed, so that it can make better use of the research achievement in optimizationfield.
5. For a more advanced adaptive penalty function method still has shortcomings todeal with constrained optimization problems in global search capability, convergenceand robustness etc. aspects, based on it a improved adaptive penalty function wasproposed in three aspects i.e. the sort normalization strategy, the adaptive weightpenalty coefficient strategy, and dynamic elitist strategy.
6. In order to improve constraint handing capacity, global convergenceperformance, stability of the optimal solution and robustness of the algorithm of amulti-objective optimization method, a modified multi-objective optimization problemwas proposed and it has four improvement aspects i.e. the cat mapping chaosinitialization strategy, the adaptive Laplace crossover operator, the demand tieredmechanism and the generational alternating constraint handling strategy.
引文
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