WO2022165861A1 - 一种非线性自抗扰飞机电网相位角度跟踪器 - Google Patents

一种非线性自抗扰飞机电网相位角度跟踪器 Download PDF

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WO2022165861A1
WO2022165861A1 PCT/CN2021/077161 CN2021077161W WO2022165861A1 WO 2022165861 A1 WO2022165861 A1 WO 2022165861A1 CN 2021077161 W CN2021077161 W CN 2021077161W WO 2022165861 A1 WO2022165861 A1 WO 2022165861A1
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grid
phase angle
voltage
aircraft
power grid
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PCT/CN2021/077161
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French (fr)
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孙希明
林平
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大连理工大学
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Priority to US17/625,307 priority Critical patent/US11802895B2/en
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R29/00—Arrangements for measuring or indicating electric quantities not covered by groups G01R19/00 - G01R27/00
    • G01R29/16—Measuring asymmetry of polyphase networks
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R25/00—Arrangements for measuring phase angle between a voltage and a current or between voltages or currents
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R25/00—Arrangements for measuring phase angle between a voltage and a current or between voltages or currents
    • G01R25/005—Circuits for comparing several input signals and for indicating the result of this comparison, e.g. equal, different, greater, smaller, or for passing one of the input signals as output signal
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/005—Testing of electric installations on transport means
    • G01R31/008—Testing of electric installations on transport means on air- or spacecraft, railway rolling stock or sea-going vessels

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  • the invention belongs to the technical field of aviation electrical and electric power, and in particular relates to an aircraft power grid phase angle tracker.
  • the multi-electric aircraft can reduce the consumption rate of aviation kerosene, improve the working efficiency of the aero-engine, and reduce the emission of nitrogen oxides.
  • the power grid is an important part of the multi-electric aircraft.
  • the aircraft power grid provides power for the flight control system and environmental control system, and on the other hand, it provides power for the aircraft starter/generator. Its performance directly affects the working status of the aircraft system, and even affects the safety and reliability of the aircraft. sex.
  • the tracking of the power grid phase angle is one of the important tasks of the aircraft power grid system.
  • the literatures published at home and abroad are all based on the proportional-integral method or the proportional-integral-derivative method to design the grid phase angle tracker.
  • the existing methods cannot well suppress the interference of harmonics to the angle of the aircraft power grid.
  • most of the current grid phase angle trackers are based on a single grid operating frequency, and for the grid of multi-electric aircraft, the frequency changes in the range of 360-800Hz, and the change of grid frequency will also affect the tracking accuracy of the grid phase angle tracker.
  • the existing methods cannot meet the requirements of high-precision tracking of the phase angle of the aircraft power grid.
  • the current design method has gradually been unable to meet the actual needs of the project. Therefore, it has become an urgent problem to explore an effective design method of high-precision grid phase angle tracker suitable for engineering practice. Therefore, the high-precision tracking of the phase angle of the aircraft power grid has broad research and application prospects.
  • the present invention proposes a nonlinear power grid phase angle tracking method with high accuracy.
  • a nonlinear active disturbance rejection aircraft grid phase angle tracker comprising the following steps:
  • the first step is the modeling of the aircraft power grid
  • the second step is to design the grid phase angle tracker according to the aircraft grid model
  • the third step is the error analysis of grid phase angle tracking.
  • the first step is the modeling of the aircraft power grid
  • Step 1 In order to facilitate the analysis, first define the coordinate system
  • Step 2 According to the nominal power grid parameters of the general multi-electric aircraft, the nominal power grid model of the multi-electric aircraft is obtained;
  • Step 3 On the basis of Step 1, in the case of considering the unbalance of the grid voltage amplitude, the higher harmonics of the grid and the DC offset, the non-standard grid model of the multi-electric aircraft is obtained;
  • the second step is to design the grid phase angle tracker according to the aircraft grid model
  • Step 4 Considering the condition of grid voltage amplitude imbalance, obtain a mathematical expression between grid voltage amplitude imbalance and grid phase angle;
  • Step 5 Considering the high-order harmonics of the power grid, obtain the mathematical expression between the high-order harmonics of the power grid and the phase angle of the power grid;
  • Step 6 Consider the DC offset of the grid, and obtain the mathematical expression between the DC offset of the grid and the phase angle of the grid;
  • Step 7 In order to sort out the model information derived in Step 4, Step 5 and Step 6, the nominal model required for the design of the nonlinear active disturbance rejection controller is obtained;
  • Step 8 Design a nonlinear active disturbance rejection grid phase angle tracker based on Step 7;
  • the third step is the error analysis of grid phase angle tracking.
  • Step 9 In the MATLAB/Simulink environment, use the modular modeling technology to build the aircraft power grid model and build the nonlinear ADRC aircraft grid phase tracker to verify the performance of the nonlinear ADRR aircraft grid phase angle tracker.
  • the estimation error of the nonlinear ADRC aircraft grid phase angle tracker is compared with the estimation error of the linear ADRC aircraft grid phase angle tracker.
  • the nonlinear ADRC aircraft grid phase angle In the face of fast-changing grid disturbances, the nonlinear ADRC aircraft grid phase angle The accuracy of the tracker is higher, and the convergence speed of the tracking error of the grid phase angle is faster, indicating that the method proposed in the present invention can accurately estimate the grid phase angle.
  • the existing aircraft power grid phase angle tracker is difficult to achieve high-precision tracking of the power grid phase angle.
  • the method of proportional integral, proportional integral derivative or linear active disturbance rejection method is commonly used to design the power grid phase angle tracker.
  • the tracking accuracy of the linear active disturbance rejection power grid phase angle tracker is higher than Proportional-integral and proportional-integral-derivative grid phase angle trackers are high.
  • the invention provides a high-precision nonlinear grid phase angle tracking method based on model information, which makes up for the deficiency of the existing linear active disturbance rejection grid phase tracker technology.
  • the invention applies the nonlinear active disturbance rejection technology to the phase angle tracking of the multi-electric aircraft power grid, has simple operation, high accuracy, and can realize the high-precision tracking of the power grid phase angle. This method has certain expansibility and can be extended to other fields.
  • Figure 1 is a block diagram of the local structure of the aircraft power grid.
  • Figure 2 is an overall block diagram of an aircraft grid phase angle tracker.
  • Figure 3 is a schematic diagram of a nonlinear active disturbance rejection aircraft grid phase angle tracker.
  • Figure 4 is a schematic diagram of the nonlinear active disturbance rejection generalized integral nonlinear extended state observer (GI-ESO).
  • Fig. 5(a) is an overall schematic diagram of the comparison of grid phase angle errors of two grid phase trackers.
  • Figure 5(b) is a partial schematic diagram of the grid phase angle error comparison between two grid phase trackers.
  • Figure 5(c) is a partial schematic diagram of the comparison of grid phase angle errors of two grid phase trackers.
  • Figure 5(d) is a partial schematic diagram of the comparison of grid phase angle errors of two grid phase trackers.
  • Figure 5(e) is a partial schematic diagram of the comparison of grid phase angle errors of two grid phase trackers.
  • FIG. 6 is a comparison diagram of the calculated value of the grid phase angle error under the time multiplied absolute error integration criterion.
  • An aircraft grid phase angle tracker with a nonlinear active disturbance rejection framework which can also be called a grid synchronization (phase-locked loop) module, namely the grid synchronization (phase-locked loop) module in Figure 1, is used to estimate the AC side of the aircraft grid. Since the coaxial generator in the aircraft power grid is built in the compressor of the aviation gas turbine engine, and the coaxial generator is directly coupled with the aviation gas turbine engine, the AC frequency of the coaxial generator varies with the aviation gas turbine.
  • V a V m cos( ⁇ t)
  • V m the amplitude of the three-phase alternating current
  • V a , V b and V c respectively represent the three-phase alternating current
  • the core work of this patent is to design a nonlinear reactive reactance under complex conditions such as three-phase AC amplitude changes, frequency changes, unbalanced grid voltage amplitudes, high-order harmonics in the grid, and DC offsets.
  • the grid phase angle is estimated by the disturbance aircraft grid phase tracker, which includes the following steps:
  • Step 1 In order to facilitate the analysis, first define the coordinate system.
  • the conversion relationship between each coordinate system can be described by formula (1);
  • Step 2 The coaxial generator is regarded as an AC voltage source, and the nominal AC voltage source model of the multi-electric aircraft is obtained according to the nominal power grid parameters of the general multi-electric aircraft, and its mathematical expression satisfies the formula (2).
  • Convert the alternating current V abc in the three-phase stationary rotating coordinate system of formula (2) to the two-phase rotating coordinate system ⁇ qd , and by controlling ⁇ d 0, it can ensure that the estimated value of the grid phase angle finally converges to the value of the grid phase angle. actual value.
  • Step 3 Due to the unbalanced voltage amplitude, high-order harmonics and DC offset in the power grid, the AC power in the multi-electric aircraft power grid no longer meets the condition shown in formula (2).
  • the power grid has voltage amplitude imbalance, power grid high-order harmonics and DC bias, the corresponding mathematical expressions satisfy formula (3), formula (4) and formula (5) respectively;
  • ⁇ and ⁇ are the voltage amplitude unbalance coefficients of the three-phase power grid of the aircraft, respectively.
  • v 5 is the amplitude of the 5th order voltage harmonic component of the three-phase power grid of the aircraft
  • v 2n-1 is the amplitude of the 2n-1th order voltage harmonic component of the three-phase power grid of the aircraft
  • V ao , V bo , and V co are the Voltage DC bias of the three-phase grid.
  • the second step is to design the grid phase angle tracker
  • v 5 is the 5th voltage harmonic amplitude
  • v 7 is the 7th voltage harmonic amplitude
  • v 11 is the 11th voltage harmonic amplitude
  • v 13 is the 13th voltage harmonic amplitude
  • v 6n-1 is the 6n-1 order voltage harmonic amplitude
  • v 6n+1 is the 6n+1 order voltage harmonic amplitude
  • E 6h is the voltage amplitude synthesized by the 5th harmonic and the 7th harmonic component amplitude
  • E 12h is The voltage amplitude synthesized by the 11th harmonic and the 13th harmonic component
  • E 6nh is the voltage amplitude synthesized by the 6n-1 harmonic and the 6n+1 harmonic component
  • n is a positive integer
  • V ao , V bo , and V co are the voltage DC offsets of the three-phase power grid of the aircraft, respectively, E do is the amplitude gain coefficient caused by the grid DC offset, and ⁇ do is the initial phase angle caused by the grid DC offset.
  • Step 7 Through the introduction of step 4, step 5 and step 6, it is shown that the grid has voltage amplitude imbalance, grid high-order harmonics and DC offset, which will cause static error in the estimation of grid phase angle.
  • the grid synchronization (phase-locked loop) module shown in Figure 1 The traditional proportional-integral grid phase angle tracker/proportional
  • the integral and differential grid phase angle trackers cannot integrate the model information into the grid synchronization (phase-locked loop) module, and their anti-interference ability is not strong, so it is necessary to design a nonlinear active disturbance rejection grid phase angle tracker based on model information. .
  • step 4 Before designing the grid phase tracker, according to the principle of linear superposition, superimpose the information of step 4, step 5 and step 6 into formula (9), and sort out the nominal mathematics required for designing the nonlinear active disturbance rejection grid phase angle tracker model, as shown in formula (9);
  • VH V m E 6h sin 6 ⁇ +V m E 12h sin 6 ⁇ +...+V m E 6nh sin 6n ⁇ ,
  • b is the control input gain coefficient
  • u is the control input
  • b 0 is the estimated value of the control input gain coefficient
  • ⁇ is the grid frequency
  • d total is the total disturbance
  • d PU is the disturbance caused by voltage unbalance
  • d VO is the disturbance caused by the voltage DC bias
  • d VH is the disturbance caused by the higher harmonics of the voltage
  • d LIN is the linearity the disturbance caused by the change.
  • Step 8 Design a nonlinear active disturbance rejection grid phase angle tracker based on formula (9), as shown in Figure 3, which is composed of formulas (10) and (11), formula (10) is the linear state error feedback law, formula ( 11) is the generalized integral nonlinear extended state observer (GI-ESO), formula (11) corresponds to Fig. 4, and u calculated in formula (10) is the difference between the estimated grid frequency and the real grid frequency , the real grid frequency ⁇ is equal to the sum of u and the speed of the aviation gas turbine engine. Since the speed of the aviation gas turbine engine can be measured by sensors, this information can be used as known information. Pay special attention to the unit of the speed of the aviation gas turbine engine here.
  • ⁇ 1 , ⁇ 2 are real numbers between 0 and 1.
  • Step 9 In the MATLAB/Simulink environment, use the modular modeling technology to build the aircraft power grid model and build the nonlinear ADRC aircraft grid phase tracker to verify the performance of the nonlinear ADRR aircraft grid phase angle tracker.
  • the estimation error of the nonlinear ADRC aircraft grid phase angle tracker is compared with the estimated error of the linear ADRC aircraft grid phase angle tracker.
  • the nonlinear ADRC aircraft grid phase angle In the face of the fast-changing sinusoidal disturbance of the grid, the nonlinear ADRC aircraft grid phase angle
  • the accuracy of the angle tracker is higher, the convergence speed of the tracking error of the grid phase angle is faster, and the ability to suppress sinusoidal disturbance is strong.
  • Figure 5 and Figure 6 The calculated value under the time multiplication absolute error integration criterion in Figure 6 is higher. The small shows that the performance of the power grid phase angle tracker is better, so it shows that the method proposed by the present invention can accurately estimate the power grid phase angle.

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  • General Physics & Mathematics (AREA)
  • Control Of Eletrric Generators (AREA)
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Abstract

一种非线性自抗扰飞机电网相位角度跟踪器，用于估计飞机电网交流电侧的电网相位角度，由于飞机电网中同轴发电机内置于航空燃气涡轮发动机压气机内部，由于同轴发电机直接和航空燃气涡轮发动机进行耦合，故同轴发电机的交流电频率随着航空燃气涡轮发动机的转速变化而变化。该相位角度跟踪器将非线性自抗扰技术应用到多电飞机电网的相位角度跟踪，操作简单，准确率高，并可实现电网相位角度的高精度跟踪。

Description

一种非线性自抗扰飞机电网相位角度跟踪器 技术领域
本发明属于与航空电气与电力技术领域，具体涉及一种飞机电网相位角度跟踪器。
背景技术
随着飞机电气程度的不断提高，多电飞机应运而生，多电飞机能降低航空煤油消耗率，提高航空发动机的工作效率，降低氮氧化物排放量，电网是多电飞机的重要组成部分。飞机电网一方面为飞控系统、环境控制系统等提供电源，另一方面为飞机起动/发电一体机提供电源，其性能好坏直接影响飞机系统的工作状态，甚至会影响飞机的安全性和可靠性。电网相位角度的跟踪是飞机电网系统的重要工作之一，一旦电网相位角度跟踪不准确，就会影响飞机电网的工作安全，造成电网质量下降，轻则损坏飞机电气设备，重则影响到飞机的飞行安全。因此，尤其是在电网存在谐波干扰的情况下，对飞机电网角度的准确跟踪是非常有价值的，能提高飞机电网的稳定裕度。
在飞机电网相位角度跟踪器方面，国内外公开发表的文献都是基于比例积分方法或者比例积分微分方法设计电网相位角度跟踪器。特别是在电网存在快变正弦谐波干扰的情况下，目前已有的方法不能很好地抑制谐波对飞机电网角度的干扰。同时，目前的电网相位角度跟踪器大多基于单一电网工作频率，而对于多电飞机的电网，其频率在360-800Hz范围内变化，电网频率的变化也会影响到电网相位角度跟踪器的跟踪精度，目前已有的方法不能满足飞机电网相位角度高精度跟踪的要求。
对于飞机电网相位角度跟踪器而言，当前的设计方法已经渐渐满足不了工 程的实际需要。因此，探索出一种有效且适用于工程实践的高精度电网相位角度跟踪器设计方法成为一个亟需解决的问题。飞机电网相位角度的高精度跟踪也因此具备了广阔的研究和应用前景。
发明内容
本发明是为了解决现有技术存在的操作繁复，效率低下，电网相位角度跟踪精度不高的问题，而提出的一种非线性的电网相位角度高精度跟踪的方法。
一种非线性自抗扰飞机电网相位角度跟踪器，包括以下步骤：
第一步，飞机电网的建模；
第二步，根据飞机电网模型设计电网相位角度跟踪器；
第三步，电网相位角度跟踪的误差分析。
现具体阐述如下：
第一步，飞机电网的建模；
步骤1：为了便于分析，首先定义坐标系；
步骤2：根据通用多电飞机标称电网参数，得到多电飞机标称电网模型；
步骤3：在步骤1的基础上，在考虑电网电压幅值不平衡、电网高次谐波和直流偏置的情况下，得到多电飞机非标准电网模型；
第二步，根据飞机电网模型设计电网相位角度跟踪器；
步骤4：考虑电网电压幅值不平衡的条件，得到电网电压幅值不平衡与电网相位角度之间的数学表达式；
步骤5：考虑电网高次谐波，得到电网高次谐波与电网相位角度之间的数学表达式；
步骤6：考虑电网直流偏置，得到电网直流偏置与电网相位角度之间的数学 表达式；
步骤7：为了将步骤4、步骤5和步骤6推导的模型信息进行整理，得到非线性自抗扰控制器设计所需的标称模型；
步骤8：基于步骤7设计非线性自抗扰电网相位角度跟踪器；
第三步，电网相位角度跟踪的误差分析。
步骤9：在MATLAB/Simulink环境下，采用模块化建模技术，搭建飞机电网模型和搭建非线性自抗扰飞机电网相位跟踪器，验证非线性自抗扰飞机电网相位角度跟踪器的性能，将非线性自抗扰飞机电网相位角度跟踪器的估计误差与线性自抗扰飞机电网相位角度跟踪器的估计误差进行比较，在面对电网的快变干扰时，非线性自抗扰飞机电网相位角度跟踪器的精度更高，电网相位角度的跟踪误差收敛速度更快，说明本发明提出的方法是能准确估计出电网相位角度。
本发明的有益效果：
现有飞机电网相位角度跟踪器，难以实现电网相位角度高精度的跟踪。在工程实践中，目前普遍采用是基于比例积分、比例积分微分的方法或者线性自抗扰方法设计电网相位角度跟踪器，根据已有文献表明，线性自抗扰电网相位角度跟踪器的跟踪精度较比例积分和比例积分微分电网相位角度跟踪器高。本发明提供了一种基于模型信息的高精度的非线性电网相位角度跟踪方法，弥补了现有线性自抗扰电网相位跟踪器技术的不足。本发明将非线性自抗扰技术应用到多电飞机电网的相位角度跟踪，操作简单，准确率高，并可实现电网相位角度的高精度跟踪。该方法具有一定的拓展性，可推广到其它领域。
附图说明
图1为飞机电网局部结构框图。
图2为飞机电网相位角度跟踪器的整体框图。
图3为非线性自抗扰飞机电网相位角度跟踪器的原理图。
图4为非线性自抗扰广义积分非线性扩张状态观测器(GI-ESO)的原理图。
图5(a)为两种电网相位跟踪器的电网相位角度误差比较整体示意图。
图5(b)为两种电网相位跟踪器的电网相位角度误差比较局部示意图。
图5(c)为两种电网相位跟踪器的电网相位角度误差比较局部示意图。
图5(d)为两种电网相位跟踪器的电网相位角度误差比较局部示意图。
图5(e)为两种电网相位跟踪器的电网相位角度误差比较局部示意图。
图6为电网相位角度误差在时间乘绝对误差积分准则下的计算值比较图。
具体实施方式
为了使本发明的目的、技术及优点更加清楚明白，以下结合附图及实例，对本发明进行进一步详细说明。
一种非线性自抗扰框架的飞机电网相位角度跟踪器，也可以称作电网同步(锁相环)模块，即图1中的电网同步(锁相环)模块，用于估计飞机电网交流电侧的电网相位角度，由于飞机电网中同轴发电机内置于航空燃气涡轮发动机压气机内部，由于同轴发电机直接和航空燃气涡轮发动机进行耦合，故同轴发电机的交流电频率随着航空燃气涡轮发动机的转速变化而变化，交流发电机发出的三相交流电具体可以描述为V a＝V m cos(ωt)，
Figure PCTCN2021077161-appb-000001
其中，V m为三相交流电的幅值，V a，V b和V c分别表示三相交流电，ω三相交流电频率，θ＝ωt为电网 相位角度。本专利的核心工作就是在三相交流电幅值变化、频率变化、电网电压幅值不平衡、电网存在高次谐波和存在直流偏置的情况下等复杂情况下，设计一款非线性自抗扰飞机电网相位跟踪器估计出电网相位角度，包括以下步骤：
步骤1：为了便于分析，首先定义坐标系，定义坐标系的目的是为了将三相静止旋转坐标系下的交流电V abc转换到两相静止坐标系υ αβ，最终转换到两相旋转坐标系υ qd，转换到两相旋转坐标系的最终目的是为了通过控制υ d＝0，从而为间接地估计出电网相位角度奠定了基础，各个坐标系之间的转换关系可用公式(1)描述；
Figure PCTCN2021077161-appb-000002
其中，
Figure PCTCN2021077161-appb-000003
Figure PCTCN2021077161-appb-000004
为电网相位角度的估计值。
步骤2：将同轴发电机当做一个交流电压源，根据通用多电飞机标称电网参数，得到多电飞机标称交流电压源模型，其数学表达式满足公式(2)。
Figure PCTCN2021077161-appb-000005
式中，V a，V b，V c分别为飞机三相交流电的电压，θ＝ωt为电网相位角度，ω三相交流电频率，V m三相电压幅值。将公式(2)三相静止旋转坐标系下的交流电V abc 转换到两相旋转坐标系υ qd，通过控制υ d＝0，从而就能保证电网相位角度的估计值最终收敛到电网相位角度的真实值。
步骤3：由于电网存在电压幅值不平衡、电网高次谐波和直流偏置的情况下，使得多电飞机电网中交流电不再满足公式(2)所示的情况。电网存在电压幅值不平衡、电网高次谐波和直流偏置情况下分别对应于数学表达式分别满足公式(3)、公式(4)和公式(5)；
Figure PCTCN2021077161-appb-000006
Figure PCTCN2021077161-appb-000007
Figure PCTCN2021077161-appb-000008
式中，β，γ分别为飞机三相电网的电压幅值不平衡系数。v 5为飞机三相电网的5次电压谐波分量幅值，v 2n-1分别为飞机三相电网的2n-1次电压谐波分量幅值；V ao，V bo，V co分别为飞机三相电网的电压直流偏置。
第二步，设计电网相位角度跟踪器；
步骤4：考虑电网电压幅值不平衡的条件，当υ d＝0时，通过数学推导可以得到电网相位角度的估计值与电网相位角度的真实值之间存在一个静态误差，如公式(6)所示；
Figure PCTCN2021077161-appb-000009
其中，
Figure PCTCN2021077161-appb-000010
为飞机电网相位角度的估计值，E pu为电压不平衡引起的幅值增益系数，φ pu为电压不平衡引起的初始相位角度。
步骤5：考虑电网存在高次谐波的情况下，当υ d＝0时，通过数学推导可以得到电网相位角度的估计值与电网相位角度的真实值之间存在一个静态误差，如公式(7)所示；
Figure PCTCN2021077161-appb-000011
其中，v 5为5次电压谐波幅值，v 7为7次电压谐波幅值，v 11为11次电压谐波幅值，v 13为13次电压谐波幅值，v 6n-1为6n-1次电压谐波幅值，v 6n+1为6n+1次电压谐波幅值，E 6h为5次谐波和7次谐波分量幅值合成的电压幅值，E 12h为11次谐波和13次谐波分量幅值合成的电压幅值，E 6nh为6n-1次谐波和6n+1次谐波分量幅值合成的电压幅值，n为正整数；
步骤6：考虑电网直流偏置的情况下，当υ d＝0时，通过数学推导可以得到电网相位角度的估计值与电网相位角度的真实值之间存在一个静态误差，如公式(8)所示；
Figure PCTCN2021077161-appb-000012
其中，V ao，V bo，V co分别为飞机三相电网的电压直流偏置，E do为电网直流偏置引起的幅值增益系数，φ do为电网直流偏置引起的初始相位角度。
步骤7：通过步骤4、步骤5和步骤6的简介，表明电网存在电压幅值不平衡、电网高次谐波和直流偏置的情况会对电网相位角度估计造成静态误差，为了消除此静态误差，需要将电网存在电压幅值不平衡、电网高次谐波和直流偏置的信息集成到图1所示的电网同步(锁相环)模块中，传统的比例积分电网相位角度跟踪器/比例积分微分电网相位角度跟踪器均无法将模型信息集成到电网同步(锁相环)模块中，同时其抗干扰能力不强，故此处需要设计基于模型信息的非线性自抗扰电网相位角度跟踪器。设计电网相位跟踪器之前，根据线性叠加原理，将步骤4、步骤5和步骤6的信息叠加到公式(9)中，整理得到设计非线性自抗扰电网相位角度跟踪器所需的标称数学模型，公式(9)所示；
Figure PCTCN2021077161-appb-000013
其中，
Figure PCTCN2021077161-appb-000014
Figure PCTCN2021077161-appb-000015
Figure PCTCN2021077161-appb-000016
d VO＝E do cos(θ+φ do),
d VH＝V mE 6h sin 6θ+V mE 12h sin 6θ+...+V mE 6nh sin 6nθ,
Figure PCTCN2021077161-appb-000017
b为控制输入增益系数，u为控制输入，b 0为控制输入增益系数的估计值，ω为电网频率，
Figure PCTCN2021077161-appb-000018
为电网频率的估计值，d total为总扰动，d PU为电压不平衡引起的 扰动，d VO为电压直流偏置引起的扰动，d VH为电压高次谐波引起的扰动，d LIN为线性化引起的扰动。
步骤8：基于公式(9)设计非线性自抗扰电网相位角度跟踪器，如图3所示，由公式(10)和(11)组成，公式(10)为线性状态误差反馈律，公式(11)为广义积分非线性扩张状态观测器(GI-ESO)，公式(11)对应于图4，公式(10)中所计算得到的u为估计的电网频率与真实电网频率之间的差值，真实的电网频率ω等于u与航空燃气涡轮发动机转速之和，由于航空燃气涡轮发动机转速可以通过传感器测得，该信息可以作为已知信息，特别注意，此处的航空燃气涡轮发动机转速的单位应以幅度每秒(rad/s)的形式存在，最后对ω进行积分运算，即得到了飞机电网的相位角度。特别说明：其中引入了非线性切换函数fal(e 1,α i)，对观测误差e 1进行非线性变换，相比于广义积分线性扩张状态观测器，引入非线性函数，从而能提高广义积分非线性扩张状态观测器的观测效率；
Figure PCTCN2021077161-appb-000019
Figure PCTCN2021077161-appb-000020
其中，
Figure PCTCN2021077161-appb-000021
其中，
Figure PCTCN2021077161-appb-000022
为υ d的参考值，k p为比例系数，z 1为x 1的估计值，z 2为x 2的估计值，L 1和L 2为广义积分非线性扩张状态观测器的增益系数，
Figure PCTCN2021077161-appb-000023
Figure PCTCN2021077161-appb-000024
z 2(0)为未建模动态估计值，
Figure PCTCN2021077161-appb-000025
Figure PCTCN2021077161-appb-000026
Figure PCTCN2021077161-appb-000027
为d 1对时间的导数，
Figure PCTCN2021077161-appb-000028
为d 2对时间的导数，
Figure PCTCN2021077161-appb-000029
为d 3对时间的导数，ω r1＝ω为电网电压存在直流偏置情况下的频率补偿，K r1为其频率补偿增益系数，ω r2＝2ω为电网电压不平衡情况下的频率补偿，K r2为其频率补偿增益系数，ω r3＝6ω为电网电压存在高次谐波情况下的频率补偿，K r3为其频率补偿增益系数，
Figure PCTCN2021077161-appb-000030
为u 1对时间的导数。α 1，α 2均为0到1之间的实数。
步骤9：在MATLAB/Simulink环境下，采用模块化建模技术，搭建飞机电网模型和搭建非线性自抗扰飞机电网相位跟踪器，验证非线性自抗扰飞机电网相位角度跟踪器的性能，将非线性自抗扰飞机电网相位角度跟踪器的估计误差与线性自抗扰飞机电网相位角度跟踪器的估计误差进行比较，在面对电网的快 变正弦干扰时，非线性自抗扰飞机电网相位角度跟踪器的精度更高，电网相位角度的跟踪误差收敛速度更快，对正弦扰动抑制能力强，具体详见图5和图6，图6中的时间乘绝对误差积分准则下的计算值越小说明电网相位角度跟踪器的性能越好，故说明本发明提出的方法是能准确估计出电网相位角度。

Claims (1)

  1. 一种非线性自抗扰飞机电网相位角度跟踪器，为电网同步模块，用于估计飞机电网交流电侧的电网相位角度；飞机电网中同轴发电机内置于航空燃气涡轮发动机压气机中，同轴发电机直接和航空燃气涡轮发动机进行耦合，故同轴发电机的交流电频率随着航空燃气涡轮发动机的转速变化而变化；因此，设计一种非线性自抗扰飞机电网相位角度跟踪器用于估计出电网相位角度的方法，其特征在于，包括以下步骤：
    步骤1：首先定义坐标系，将三相静止旋转坐标系下的交流电V abc转换到两相静止坐标系υ αβ，最终转换到两相旋转坐标系υ qd；进而通过控制υ d＝0，估计出电网相位角度，各个坐标系之间的转换关系用公式(1)描述；
    Figure PCTCN2021077161-appb-100001
    其中，
    Figure PCTCN2021077161-appb-100002
    Figure PCTCN2021077161-appb-100003
    为电网相位角度的估计值；
    步骤2：将同轴发电机作为交流电压源，根据多电飞机标称电网参数，得到多电飞机标称交流电压源模型，其数学表达式满足公式(2)：
    Figure PCTCN2021077161-appb-100004
    其中，V a，V b，V c为飞机三相交流电的电压，θ＝ωt为电网相位角度，ω三 相交流电频率，V m三相电压幅值；将公式(2)三相静止旋转坐标系下的交流电V abc转换到两相旋转坐标系υ qd，通过控制υ d＝0，就能保证电网相位角度的估计值最终收敛到电网相位角度的真实值；
    步骤3：由于电网存在电压幅值不平衡、电网高次谐波和直流偏置的情况下，使得多电飞机电网中交流电不再满足公式(2)所示的情况；电网存在电压幅值不平衡、高次谐波和直流偏置情况下分别对应于数学表达式分别满足公式(3)、公式(4)和公式(5)；
    Figure PCTCN2021077161-appb-100005
    Figure PCTCN2021077161-appb-100006
    Figure PCTCN2021077161-appb-100007
    其中，β，γ分别为飞机三相电网的电压幅值不平衡系数；v 5为飞机三相电网的5次电压谐波分量幅值，v 2n-1分别为飞机三相电网的2n-1次电压谐波分量幅值；V ao，V bo，V co分别为飞机三相电网的电压直流偏置；
    步骤4：考虑电网电压幅值不平衡的条件，当υ d＝0时，到电网相位角度的估计值与电网相位角度的真实值之间存在一个静态误差，如公式(6)所示；
    Figure PCTCN2021077161-appb-100008
    其中，
    Figure PCTCN2021077161-appb-100009
    为飞机电网相位角度的估计值；
    步骤5：考虑电网存在高次谐波的情况下，当υ d＝0时，得到电网相位角度的估计值与电网相位角度的真实值之间存在一个静态误差，如公式(7)所示；
    Figure PCTCN2021077161-appb-100010
    其中，v 5为5次电压谐波幅值，v 7为7次电压谐波幅值，v 11为11次电压谐波幅值，v 13为13次电压谐波幅值，v 6n-1为6n-1次电压谐波幅值，v 6n+1为6n+1次电压谐波幅值，E 6h为5次谐波和7次谐波分量幅值合成的电压幅值，E 12h为11次谐波和13次谐波分量幅值合成的电压幅值，E 6nh为6n-1次谐波和6n+1次谐波分量幅值合成的电压幅值，n为正整数；
    步骤6：考虑电网直流偏置的情况下，当υ d＝0时，得到电网相位角度的估计值与电网相位角度的真实值之间存在一个静态误差，如公式(8)所示；
    Figure PCTCN2021077161-appb-100011
    其中，V ao，V bo，V co分别为飞机三相电网的电压直流偏置，E do为电网直流偏置 引起的幅值增益系数，φ do为电网直流偏置引起的初始相位角度；
    步骤7：步骤4、步骤5和步骤6表明电网存在电压幅值不平衡、高次谐波和直流偏置的情况对电网相位角度估计造成静态误差，为了消除此静态误差，需要将电网存在电压幅值不平衡、高次谐波和直流偏置的信息集成到电网同步模块中；根据线性叠加原理，将步骤4、步骤5和步骤6的信息叠加到公式(9)中，整理得到非线性自抗扰飞机电网相位角度跟踪器所需的标称数学模型，公式(9)所示；
    Figure PCTCN2021077161-appb-100012
    其中，
    Figure PCTCN2021077161-appb-100013
    Figure PCTCN2021077161-appb-100014
    Figure PCTCN2021077161-appb-100015
    d VO＝E docos(θ+φ do),
    d VH＝V mE 6hsin 6θ+V mE 12hsin 6θ+...+V mE 6nhsin 6nθ,
    Figure PCTCN2021077161-appb-100016
    其中，b为控制输入增益系数，u为控制输入，b 0为控制输入增益系数的估计值，ω为电网频率，
    Figure PCTCN2021077161-appb-100017
    为电网频率的估计值，d total为总扰动，d PU为电压不平衡引起的扰动，d VO为电压直流偏置引起的扰动，d VH为电压高次谐波引起的扰动，d LIN为线性化引起的扰动；
    步骤8：基于公式(9)设计非线性自抗扰飞机电网相位角度跟踪器，由公 式(10)和(11)组成，公式(10)为线性状态误差反馈律，公式(11)为广义积分非线性扩张状态观测器，公式(10)中所计算得到的u为估计的电网频率与真实电网频率之间的差值，真实的电网频率ω等于u与航空燃气涡轮发动机转速之和，由于航空燃气涡轮发动机转速可以通过传感器测得，该信息作为已知信息，特别注意，此处的航空燃气涡轮发动机转速的单位应以幅度每秒的形式存在，最后对ω进行积分运算，即得到了飞机电网的相位角度；
    Figure PCTCN2021077161-appb-100018
    Figure PCTCN2021077161-appb-100019
    其中，
    Figure PCTCN2021077161-appb-100020
    其中，
    Figure PCTCN2021077161-appb-100021
    为υ d的参考值，k p为比例系数，z 1为x 1的估计值，z 2为x 2的估计值，L 1和L 2为广义积分非线性扩张状态观测器的增益系数，
    Figure PCTCN2021077161-appb-100022
    Figure PCTCN2021077161-appb-100023
    z 2(0)为未建模动态估计值，
    Figure PCTCN2021077161-appb-100024
    Figure PCTCN2021077161-appb-100025
    为d 1对时间的导数，
    Figure PCTCN2021077161-appb-100026
    为d 2对时间的导数，
    Figure PCTCN2021077161-appb-100027
    为d 3对时间的导数，ω r1＝ω为电网电压存在直流偏置情况下的频率补偿，K r1为其频率补偿增益系数，ω r2＝2ω为电网电压不平衡情况下的频率补偿，K r2为其频率补偿增益系数，ω r3＝6ω为电网电压存在高次谐波情况下的频率补偿，K r3为其频率补偿增益系数，
    Figure PCTCN2021077161-appb-100028
    为u 1对时间的导数；α 1，α 2均为0到1之间的实数。
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