光伏并网逆变器的电流谐波抑制策略

来源：九壹网

ocusing on ways and means of improving and upgrading work, further development of \"three to split\". (A) fully grasp \"no unauthorised\" created. The township \"no unauthorised\" created the existing building \"one household, one document\" survey and file storage work must be unconditional and full coverage. Main corridor leading to the town (road, river) village, the Central built-up area of the town on both sides must be to create a \"no unauthorised village\". According to \"five hundred villages\" created and shanty towns, villages, old houses, reconstruction of old plant, expand create, upgrading creates files, the real \"no unauthorised village\" created into the benefit of the people of very good thing. (B) to strictly manage count as unauthorised controls. Promoting the \"new\" control work to move the center of gravity, management measures to the front, and earnestly pipes effectively. A strict new unauthorised network responsibility. Sectors such as land, housing and basic stations (stations) and the Township of grid accountability mechanisms must be strictly in accordance with the new regulatory requirements, effective implementation of the area of responsibility of the new inspections, suppression, demolition work to ensure that the new \"zero tolerance\". Second, public security, water, electricity, water, oceans and fisheries, tourism collaboration, market supervision departments should strictly enforce the illegal construction of disposal of relevant provisions of the regulations, effective fulfilment of responsibilities, particularly in electricity and water supply, and other units may not be new illegal buildings to supply water and electcity supply. While more regulation to prevent personal privacy violations. Illicit trading in illegal construction in the Ministry of public security sector to strictly from the blow. Three is to create additional offence reporting system of incentives. According to building law and covers an area of nature, to report timely degree divided report grade, effective after the removal of certain incentives. (C) integrated implementation \ding demolition, modification, use\" combination. Demolition is the means and purpose built is. To adhere to the building demolished, combination of construction and demolition waste, demolished with combined efforts to improve the scientific level of three to split; second, we must pay attention to \"three to split\" and \"five hundred\" and \"five water treatment\des\shackDistrict transformation, and dangerous old room transformation and \"two road sides\s work organic combined up, active do River, and along demolition work, and manpower advance village in the, and old residential demolition work, to improved masses housing conditions and live environment; three to put \"three modified a split\" as traditional low, and small, and bulk industry structure transformation upgrade of important initiatives to caught, speed up advance industry Park, effective optimization park environment光伏并网逆变器的电流谐波抑制策略

1 引言

并网逆变器作为光伏电池与电网的接口装置，将光伏电池的直流电能转换成交流电能并传输到电网上，在光伏并网发电系统中起着至关重要的作用。随着投入应用的并网逆变器日益增多，其输出的并网电流谐波对电网电压的污染也不容忽视。按照GB/ T 19939-2005所要求，光伏并网逆变器的总输出谐波电流应小于逆变器额定输出的5%，各次谐波也应在表1所列的百分比之内：奇次谐波 3次至 9次 11次至 15次 17次至 21次 23次至 33次畸变限值 <4.0% <2.0% <1.5% 0.6% 偶次谐波 2次至8次 10次至32次表1 谐波电流畸变限值

谐波限值 <1.0% <0.5% nd improve idle land of utilization, real achieved environment improved and productivity development mutual promoting total win. Five, firmly implement, promoting work ahead, to create highlights. Third deployment, implementation of seven, then it is imperative to strengthen responsibility and improve the mechanisms nd implementation. All localities and departments must be convinced that goals, going all out, mustering spirit, work together to ensure that this year's objectives carry out tasks, at the forefront. First, we must strengthen the leadership to implemnt. Departments at all levels should always work and rural \"five water treatment\portant position, and carry the main responsibility, main leader personally, leaders arrested and layers of responsibility rank transmission pressure established hierarchical accountability, and work together to promote the work of the mechanism, a concerted effort pay attention to implementation. County nongban, flood, three to one down to further play a leading catch total, integrated and coordinated role of all kinds is \"long\or\" to effectively fulfill their responsibilities, formed the alignment on the fire line and management a lively situation. Second, we must strengthen the test implementation of the Governor. Role play the Governor got the baton, for agricultural and rural focus and \"five water treatment\split\" work, refine improve assessment methods and evaluation system, accurate assessment. Combined with \"dare play, tree benchmark\" style building five major operations, carry on and gain firsthand experience of supervision, in particular, to strengthen the focus on the \"long\" signs \"go left\s supervision, urged all levels longer on duty in place. Through the supervisory assessment, to promote habits, stimulating power. Third, we must strengthen implementation style. Departments at all levels to work in rural areas and \"five water treatment\split\" as training cadres for major platforms, compete against large examination room, inspection cadres work performance of the ring, water control and the Japanese pulled a workout, training, discovery and selection of cadres. Than good catch up, first to excellence-oriented. Party members and cadres at all levels must adhere to the rural, water control and the Japanese pulled a grass-roots, \"put down the shelf, leaned\" pragmatic style, the spirit of play, become a benchmark model. Four, we must strengthen propaganda implementation. Comprehensive utilization of micro-credit, micro-blogging, new media, mining, summarizing, good publicity work in the countryside and \"five water treatment\odels, point to gather positive energy for the community to see the results of our work in time, increase public awareness, participation rates, satisfaction and support. Play gongqingfu, a mass organization and grass-roots such as schools, communityThe role ofocusing on ways and means of improving and upgrading work, further development of \"three to split\". (A) fully grasp \"no unauthorised\" created. The township \"no unauthorised\" created the existing building \"one household, one document\" survey and file storage work must be unconditional and full coverage. Main corridor leading to the town (road, river) village, the Central built-up area of the town on both sides must be to create a \"no unauthorised village\". According to \"five hundred villages\" created and shanty towns, villages, old houses, reconstruction of old plant, expand create, upgrading creates files, the real \"no unauthorised village\" created into the benefit of the people of very good thing. (B) to strictly manage count as unauthorised controls. Promoting the \"new\" control work to move the center of gravity, management measures to the front, and earnestly pipes effectively. A strict new unauthorised network responsibility. Sectors such as land, housing and basic stations (stations) and the Township of grid accountability mechanisms must be strictly in accordance with the new regulatory requirements, effective implementation of the area of responsibility of the new inspections, suppression, demolition work to ensure that the new \"zero tolerance\". Second, public security, water, electricity, watr, oceans and fisheries, tourism collaboration, market supervision departments should strictly enforce the illegal construction of disposal of relevant provisions of the regulations, effective fulfilment of responsibilities, particularly in electricity and water supply, and other units may not be new illegal buildings to supply water and electricity supply. While more regulation to prevent personal privacy violations. Illicit trading in illegal construction in the Ministry of public security sector to strictly from the blow. Three is to create additional offence reporting system of incentives. According to building law and covers an area of nature, to report timely degree divided report grade, effective after the removal of certain incentives. (C) integrated implementation \ding demolition, modification, use\" combination. Demolition is the means and purpose built is. To adhere to the building demolished, combination of construction and demolition waste, demolished with combined efforts to improve he scientific level of three to split; second, we must pay attention to \"three to split\" and \"five hundred\" and \"five water treatment\des\shackDistrict transformation, and dangerous old room transformation and \"two road sides\", series work organic combined up, active do River, and along demolition work, and manpower advance village in the, and old residential demolition work, to improved masses housing conditions and live environment; three to put \"three modified a split\" as traditional low, and small, and bulk industry structure transformation upgrade of important initiatives to caught, speed up advance industry Park, effective optimization park environment2 基于d-q坐标系的控制策略

T1D1D6T6T3T5D3D4D5L1D2B1iLC1L2ABCT4T2

图1 光伏逆变器电路结构

如图1所示，在三相静止对称坐标系中，其交流侧的物理量均为时变交流量，

不利于控制系统的设计。为此考虑通过坐标变换将三相静止对称坐标系转换成以电网基波频率同步旋转的d-q坐标系。这样经过坐标变换后，三相静止对称坐标系中的基波正弦变量将转化为d-q坐标系中的直流分量。

在d-q坐标系下，其数学模型可描述为：

edLpRLidvdeiv LpRqqqL

3(vdidvqiq)vdcidc 2 （2-1）

（2-2）

式中 ed、eq——电网电动势矢量Edq的d、q分量

vd、vq——三相VSR交流侧电压矢量Vdq的d、q分量 id、iq——三相VSR交流侧电流矢量Idq的d、q分量

p——微分算子

由式2-1可以看出，由于VSR的d、q轴变量相互耦合，因而给控制器设计造成一定困难。为此，可采用前馈解耦控制策略，当电流调节器采用PI调节器时，则

nd improve idle land of utilization, real achieved environment improved and productivity development mutual promoting total win. Five, firmly implement, promoting work ahead, to create highlights. Third deployment, implementation of seven, then it is imperative to strengthen responsibility and improve the mechanisms and implementation. All localities and departments must be convinced that goals, going all out, mustering spirit, work together to ensure that this year's objectives carry out tasks, at the forefront. First, we must strengthen the leadership to implement. Departments at all levels should always work and rural \"five water treatment\portant position, and carry the main responsibility, main leader personally, leaders arrested and layers of responsibility rank transmission pressure established hierarchical accountability, and work together to promote the work of the mechanism, a concerted effort pay attention to implementation. County nongban, flood, three to one down to further play a leading catch total, integrated and coordinated role of all kinds is \"long\or\" to effectively fulfill their responsibilities, formed the alignment on the fire line and management a lively situation. Second, we must strengthen the test implementation of the Governor. Role play the Governor got the baton, for agricultural and rural focus and \"five water treatment\split\" work, refine improve assessment methods and evaluation system, accurate assessment. Combined with \"dare play, tree benchmark\" style building five major operations, carry on and gain firsthand experience of supervision, in particular, to strengthen the focus on the \"long\" signs \"go left\s supervision, urged all levels longer on duty in place. Through the supervisory assessment, to promote habits, stimulating power. Third, we must strengthen implementation style. Departments at all levels to work in rural areas and \"five water treatment\split\" as training cadres for major platforms, compete against large examination room, inspection cadres work performance of the ring, water control and the Japanese pulled a workout, training, discovery and selection of cadres. Than good catch up, first to excellence-oriented. Party members and cadres at all levels must adhere to the rural, water control and the Japanese pulled a grass-roots, \"put down the shelf, leaned\" pragmatic style, the spirit of play, become a benchmark model. Four, we must strengthen propaganda implementation. Comprehensive utilization of micro-credit, micro-blogging, new media, mining, summarizing, good publicity work in the countryside and \"five water treatment\odels, point to gather positive energy for the community to see the results of our work in time, increase public awareness, participation rates, satisfaction and support. Play gongqingfu, a mass organization and grass-roots such as schools, communityThe role ofocusing on ways and means of improving and upgrading work, further development of \"three to split\". (A) fully grasp \"no unauthorised\" created. The township \"no unauthorised\" created the existing building \"one household, one document\" survey and file storage work must be unconditional and full coverage. Main corridor leading to the town (road, river) village, the Central built-up area of the town on both sides must be to create a \"no unauthorised village\". According to \"five hundred villages\" created and shanty towns, villages, old houses, reconstruction of old plant, expand create, upgrading creates files, the real \"no unauthorised village\" created into the benefit of the people of very good thing. (B) to strictly manage count as unauthorised controls. Promoting the \"new\" control work to move the center of gravity, management measures to the front, and earnestly pipes effectively. A strict new unauthorised network responsibility. Sectors such as land, housing and basic stations (stations) and the Township of grid accountability mechanisms must be strictly in accordance with the new regulatory requirements, effective implementation of the area of responsibility of the new inspections, suppression, demolition work to ensure that the new \"zero tolerance\". Second, public security, water, electricity, water, oceans and fisheries, tourism collaboration, market supervision departments should strictly enforce the illegal construction of disposal of relevant provisions of the regulations, effective fulfilment of responsibilities, particularly in electricity and water supply, and other units may not be new illegal buildings to supply water and electricity supply. While more regulation to prevent personal privacy violations. Illicit trading in illegal construction in the Ministry of public security sector to strictly from the blow. Three is to create additional offence reporting system of incentives. According to building law and covers an area of nature, to report timely degree divided report grade, effective after the removal of certain incentives. (C) integrated implementation \ding demolition, modification, use\" combination. Demolition is the means and purpose built is. To adhere to the building demolished, combination of construction and demolition waste, demolished with combined efforts to improve the scientific level of three to split; second, we must pay attention to \"three to split\" and \"five hundred\" and \"five water treatment\des\shackDistrict transformation, and dangerous old room transformation and \"two road sides\s work organic combined up, active do River, and along demolition work, and manpower advance village in the, and old residential demolition work, to improved masses housing conditions and live environment; three to put \"three modified a split\" as traditional low, and small, and bulk industry structure transformation upgrade of important initiatives to caught, speed up advance industry Park, effective optimization park environmentvd、vq的控制方程如下：

vq(KiPKil*)(iqiq)Lideq s

（2-3）（2-4）

vd(KiPKil*)(idid)Liqed s式中 KiP、Kil ——电流内环比例调节增益和积分调节增益

**、id iq——id、iq电流指令值

将式2-3、式2-4代入式2-1，并化简得：

*KilidKilidpid(RKiP)(KiP)

sLsL同样，求得：

*KiliqKiliqpiq(RKiP)(KiP)

sLsL显然，上式表明，基于前馈的控制算法2-3、2-4使得三相VSR电流内环(id,iq)实现了解耦控制，如下图所示：

*iq+_iq_PI+_vqiaLPWMibid_i*dL_PI+icvd++ed

图2 三相VSR电流内环解耦控制结构

由于两电流内环的对称性，因而下面以iq控制为例讨论电流调节器的设计。考虑电流内环信号采样的延迟和PWM控制的小惯性特性，已解耦的iq电流内环结构如图3所示

nd improve idle land of utilization, real achieved environment improved and productivity development mutual promoting total win. Five, firmly implement, promoting work ahead, to create highlights. Third deployment, implementation of seven, then it is imperative to strengthen responsibility and improve the mechanisms and implementation. All localities and departments must be convinced that goals, going all out, mustering spirit, work together to ensure that this year's objectives carry out tasks, at the forefront. First, we must strengthen the leadership to implement. Departments at all levels should always work and rural \"five water treatment\portant position, and carry the main responsibility, main leader personally, leaders arrested and layers of responsibility rank transmission pressure established hierarchical accountability, and work together to promote the work of the mechanism, a concerted effort pay attention to implementation. County nongban, flood, three to one down to further play a leading catch total, integrated and coordinated role of all kinds is \"long\or\" to effectively fulfill their responsibilities, formed the alignment on the fire line and management a lively situation. Second, we must strengthen the test implementation of the Governor. Role play the Governor got the baton, for agricultural and rural focus and \"five water treatment\split\" work, refine improve assessment methods and evaluation system, accurate assessment. Combined with \"dare play, tree benchmark\" style building five major operations, carry on and gain firsthand experience of supervision, in particular, to strengthen the focus on the \"long\" signs \"go left\s supervision, urged all levels longer on duty in place. Through the supervisory assessment, to promote habits, stimulating power. Third, we must strengthen implementation style. Departments at all levels to work in rural areas and \"five water treatment\split\" as training cadres for major platforms, compete against large examination room, inspection cadres work performance of the ring, water control and the Japanese pulled a workout, training, discovery and selection of cadres. Than good catch up, first to excellence-oriented. Party members and cadres at all levels must adhere to the rural, water control and the Japanese pulled a grass-roots, \"put down the shelf, leaned\" pragmatic style, the spirit of play, become a benchmark model. Four, we must strengthen propaganda implementation. Comprehensive utilization of micro-credit, micro-blogging, new media, mining, summarizing, good publicity work in the countryside and \"five water treatment\odels, point to gather positive energy for the community to see the results of our work in time, increase public awareness, participation rates, satisfaction and support. Play gongqingfu, a mass organization and grass-roots such as schools, communityThe role ofocusing on ways and means of improving and upgrading work, further development of \"three to split\". (A) fully grasp \"no unauthorised\" created. The township \"no unauthorised\" created the existing building \"one household, one document\" survey and file storage work must be unconditional and full coverage. Main corridor leading to the town (road, river) village, the Central built-up area of the town on both sides must be to create a \"no unauthorised village\". According to \"five hundred villages\" created and shanty towns, villages, old houses, reconstruction of old plant, expand create, upgrading creates files, the real \"no unauthorised village\" created into the benefit of the people of very good thing. (B) to strictly manage count as unauthorised controls. Promoting the \"new\" control work to move the center of gravity, management measures to the front, and earnestly pipes effectively. A strict new unauthorised network responsibility. Sectors such as land, housing and basic stations (stations) and the Township of grid accountability mechanisms must be strictly in accordance with the new regulatory requirements, effective implementation of the area of responsibility of the new inspections, suppression, demolition work to ensure that the new \"zero tolerance\". Second, public security, water, electricity, watr, oceans and fisheries, tourism collaboration, market supervision departments should strictly enforce the illegal construction of disposal of relevant provisions of the regulations, effective fulfilment of responsibilities, particularly in electricity and water supply, and other units may not be new illegal buildings to supply water and electricity supply. While more regulation to prevent personal privacy violations. Illicit trading in illegal construction in the Ministry of public security sector to strictly from the blow. Three is to create additional offence reporting system of incentives. According to building law and covers an area of nature, to report timely degree divided report grade, effective after the removal of certain incentives. (C) integrated implementation \ding demolition, modification, use\" combination. Demolition is the means and purpose built is. To adhere to the building demolished, combination of construction and demolition waste, demolished with combined efforts to improve he scientific level of three to split; second, we must pay attention to \"three to split\" and \"five hundred\" and \"five water treatment\des\shackDistrict transformation, and dangerous old room transformation and \"two road sides\", series work organic combined up, active do River, and along demolition work, and manpower advance village in the, and old residential demolition work, to improved masses housing conditions and live environment; three to put \"three modified a split\" as traditional low, and small, and bulk industry structure transformation upgrade of important initiatives to caught, speed up advance industry Park, effective optimization park environmenteqi*q+_1Tss1KKipilsKPWM0.5Tss1_+1/R1(L/R)siq

图3 iq电流环结构

3 波形畸变的原因

3.1 死区对波形的影响

在逆变器的工作过程中，为了防止逆变器桥臂上、下开关管直通，一般都要在

两管的开关信号中插入死区时间，在此时间内上、下两管都处于关断状态，此时的输出电压由电感上的电流方向决定。设电感电流iL和输出电压U的参考方向如图1所示，则在死区期间，若电感电流iL0，则续流二极管D6导通，输出电压为负；若电感电流iL0，则续流二极管D1导通，输出电压为正。

由图2可以看出，死区使实际逆变器输出PWM波形与理想PWM波形之间存在差异，两者之差是一组包络线为正负对称方波、极性与电流方向相反、幅值为

Ed/2，宽度为死区时间Td的电压脉冲序列。由于方波里不仅含有基波分量，而且还含有大量的谐波分量，因此死区的存在一方面会影响输出基波电压的幅值和相位，令一方面又会使输出电压波形发生畸变。

图4 死区对波形的影响

3.2 并网点电压畸变

内模原理意味着只有将系统外部信号的动力学模型植入控制器以构成反馈控制

系统，才能实现无静差地跟随输入信号。对于一个交流信号而言，由于PI控制策略并不具备所需的动力学模型，也就无法实现无静差的跟踪。

在基于d-q坐标系的控制策略中，若只考虑交流基波分量，则在稳态时d-q坐标

系中，其id、iq均为直流分量。毫无疑问，在这种情况下PI控制策略能实现无静差的控制。然而，如果并网点电压ea、eb、ec存在波形畸变或不平衡等情况，则在d-q坐标系中，ed、eq存在一定的交流量。而PI控制策略将无法对这些非直流信号实现有效的无静差控制。

3.3 SVPWM高频谐波

对于PWM控制的电压型逆变器，其输出电压波形为矩形波，含有大量的谐波。

与SPWM相比，SVPWM通过选择适当的开关状态，来控制电压空间矢量的运动轨

nd improve idle land of utilization, real achieved environment improved and productivity development mutual promoting total win. Five, firmly implement, promoting work ahead, to create highlights. Third deployment, implementation of seven, then it is imperative to strengthen responsibility and improve the mechanisms and implementation. All localities and departments must be convinced that goals, going all out, mustering spirit, work together to ensure that this year's objectives carry out tasks, at the forefront. First, we must strengthen the leadership to implement. Departments at all levels should always work and rural \"five water treatment\portant position, and carry the main responsibility, main leader personally, leaders arrested and layers of responsibility rank transmission pressure established hierarchical accountability, and work together to promote the work of the mechanism, a concerted effort pay attention to implementation. County nongban, flood, three to one down to further play a leading catch total, integrated and coordinated role of all kinds is \"long\or\" to effectively fulfill their responsibilities, formed the alignment on the fire line and management a lively situation. Second, we must strengthen the test implementation of the Governor. Role play the Governor got the baton, for agricultural and rural focus and \"five water treatment\split\" work, refine improve assessment methods and evaluation system, accurate assessment. Combined with \"dare play, tree benchmark\" style building five major operations, carry on and gain firsthand experience of supervision, in particular, to strengthen the focus on the \"long\" signs \"go left\s supervision, urged all levels longer on duty in place. Through the supervisory assessment, to promote habits, stimulating power. Third, we must strengthen implementation style. Departments at all levels to work in rural areas and \"five water treatment\split\" as training cadres for major platforms, compete against large examination room, inspection cadres work performance of the ring, water control and the Japanese pulled a workout, training, discovery and selection of cadres. Than good catch up, first to excellence-oriented. Party members and cadres at all levels must adhere to the rural, water control and the Japanese pulled a grass-roots, \"put down the shelf, leaned\" pragmatic style, the spirit of play, become a benchmark model. Four, we must strengthen propaganda implementation. Comprehensive utilization of micro-credit, micro-blogging, new media, mining, summarizing, good publicity work in the countryside and \"five water treatment\odels, point to gather positive energy for the community to see the results of our work in time, increase public awareness, participation rates, satisfaction and support. Play gongqingfu, a mass organization and grass-roots such as schools, communityThe role ofocusing on ways and means of improving and upgrading work, further development of \"three to split\". (A) fully grasp \"no unauthorised\" created. The township \"no unauthorised\" created the existing building \"one household, one document\" survey and file storage work must be unconditional and full coverage. Main corridor leading to the town (road, river) village, the Central built-up area of the town on both sides must be to create a \"no unauthorised village\". According to \"five hundred villages\" created and shanty towns, villages, old houses, reconstruction of old plant, expand create, upgrading creates files, the real \"no unauthorised village\" created into the benefit of the people of very good thing. (B) to strictly manage count as unauthorised controls. Promoting the \"new\" control work to move the center of gravity, management measures to the front, and earnestly pipes effectively. A strict new unauthorised network responsibility. Sectors such as land, housing and basic stations (stations) and the Township of grid accountability mechanisms must be strictly in accordance with the new regulatory requirements, effective implementation of the area of responsibility of the new inspections, suppression, demolition work to ensure that the new \"zero tolerance\". Second, public security, water, electricity, watr, oceans and fisheries, tourism collaboration, market supervision departments should strictly enforce the illegal construction of disposal of relevant provisions of the regulations, effective fulfilment of responsibilities, particularly in electricity and water supply, and other units may not be new illegal buildings to supply water and electricity supply. While more regulation to prevent personal privacy violations. Illicit trading in illegal construction in the Ministry of public security sector to strictly from the blow. Three is to create additional offence reporting system of incentives. According to building law and covers an area of nature, to report timely degree divided report grade, effective after the removal of certain incentives. (C) integrated implementation \ding demolition, modification, use\" combination. Demolition is the means and purpose built is. To adhere to the building demolished, combination of construction and demolition waste, demolished with combined efforts to improve he scientific level of three to split; second, we must pay attention to \"three to split\" and \"five hundred\" and \"five water treatment\des\shackDistrict transformation, and dangerous old room transformation and \"two road sides\", series work organic combined up, active do River, and along demolition work, and manpower advance village in the, and old residential demolition work, to improved masses housing conditions and live environment; three to put \"three modified a split\" as traditional low, and small, and bulk industry structure transformation upgrade of important initiatives to caught, speed up advance industry Park, effective optimization park environment迹，具有谐波总畸变率小、直流电压利用率高的优点。

根据参考文献1所述，写出A相调制函数：

cos()6uAm3cos()cos()63245, 333325,2330,43 （3-1）

式中，m——SVPWM的线电压调制度。

由于三相调制波相互对称，仅在相位上相差120°，因此可得其线电压的调制函

数为：

uABuAuB2mcos(6) （3-2）

由于SVPWM的波形较为复杂，采样得到的相电压包含两种角频率，故采用二

维傅立叶分析的方法。

令：

x(t)ct，y(t)rt

式中： c——载波角频率；

r——调制波角频率；

对于由x(t)、y(t)共同作用的uAB(x,y)，写出其傅立叶展开式：

uAB(x,y)Kknnej(kxny)

k0n0 （3-3）

式中： Kkn1(2)j202uAB(x,y)ej(kxny)dxdy

n1e2n3

参考SVPWM规则采样示意，令载波幅值为1，考虑式3-1的调制波分段函数，

得到SVPWM脉冲在6个区间内的开关时间：

图5 SVPWM调制波规则采样示意

1. 调制波在(0,/3)区间

1mcosy1126 1mcosy21262. 调制波在(/3,2/3)区间

（3-4）

13mcosy122 13mcosy222 （3-5）

3. 调制波在(2/3,)区间

1mcosy1326 1mcosy2326

（3-6）

对于调制波在其(,4/3)，(4/3,5/3)，(5/3,2)内，开关区间的选择对应

重复式3-4~式3-6。

对于由图3规则采样得到的SVPWM波形，其相电压ua中含有vdc/2两种电平，

计算其傅立叶系数时，内积分需要分成3段讨论，计算复杂。为简化计算量，在ua波形上注入一个直流量，得到的效果是将ua波形整体上移vdc/2。此时ua波形中只

nd improve idle land of utilization, real achieved environment improved and productivity development mutual promoting total win. Five, firmly implement, promoting work ahead, to create highlights. Third deployment, implementation of seven, then it is imperative to strengthen responsibility and improve the mechanisms and implementation. All localities and departments must be convinced that goals, going all out, mustering spirit, work together to ensure that this year's objectives carry out tasks, at the forefront. First, we must strengthen the leadership to implement. Departments at all levels should always work and rural \"five water treatment\portant position, and carry the main responsibility, main leader personally, leaders arrested and layers of responsibility rank transmission pressure established hierarchical accountability, and work together to promote the work of the mechanism, a concerted effort pay attention to implementation. County nongban, flood, three to one down to further play a leading catch total, integrated and coordinated role of all kinds is \"long\or\" to effectively fulfill their responsibilities, formed the alignment on the fire line and management a lively situation. Second, we must strengthen the test implementation of the Governor. Role play the Governor got the baton, for agricultural and rural focus and \"five water treatment\split\" work, refine improve assessment methods and evaluation system, accurate assessment. Combined with \"dare play, tree benchmark\" style building five major operations, carry on and gain firsthand experience of supervision, in particular, to strengthen the focus on the \"long\" signs \"go left\s supervision, urged all levels longer on duty in place. Through the supervisory assessment, to promote habits, stimulating power. Third, we must strengthen implementation style. Departments at all levels to work in rural areas and \"five water treatment\split\" as training cadres for major platforms, compete against large examination room, inspection cadres work performance of the ring, water control and the Japanese pulled a workout, training, discovery and selection of cadres. Than good catch up, first to excellence-oriented. Party members and cadres at all levels must adhere to the rural, water control and the Japanese pulled a grass-roots, \"put down the shelf, leaned\" pragmatic style, the spirit of play, become a benchmark model. Four, we must strengthen propaganda implementation. Comprehensive utilization of micro-credit, micro-blogging, new media, mining, summarizing, good publicity work in the countryside and \"five water treatment\odels, point to gather positive energy for the community to see the results of our work in time, increase public awareness, participation rates, satisfaction and support. Play gongqingfu, a mass organization and grass-roots such as schools, communityThe role ofocusing on ways and means of improving and upgrading work, further development of \"three to split\". (A) fully grasp \"no unauthorised\" created. The township \"no unauthorised\" created the existing building \"one household, one document\" survey and file storage work must be unconditional and full coverage. Main corridor leading to the town (road, river) village, the Central built-up area of the town on both sides must be to create a \"no unauthorised village\". According to \"five hundred villages\" created and shanty towns, villages, old houses, reconstruction of old plant, expand create, upgrading creates files, the real \"no unauthorised village\" created into the benefit of the people of very good thing. (B) to strictly manage count as unauthorised controls. Promoting the \"new\" control work to move the center of gravity, management measures to the front, and earnestly pipes effectively. A strict new unauthorised network responsibility. Sectors such as land, housing and basic stations (stations) and the Township of grid accountability mechanisms must be strictly in accordance with the new regulatory requirements, effective implementation of the area of responsibility of the new inspections, suppression, demolition work to ensure that the new \"zero tolerance\". Second, public security, water, electricity, watr, oceans and fisheries, tourism collaboration, market supervision departments should strictly enforce the illegal construction of disposal of relevant provisions of the regulations, effective fulfilment of responsibilities, particularly in electricity and water supply, and other units may not be new illegal buildings to supply water and electricity supply. While more regulation to prevent personal privacy violations. Illicit trading in illegal construction in the Ministry of public security sector to strictly from the blow. Three is to create additional offence reporting system of incentives. According to building law and covers an area of nature, to report timely degree divided report grade, effective after the removal of certain incentives. (C) integrated implementation \ding demolition, modification, use\" combination. Demolition is the means and purpose built is. To adhere to the building demolished, combination of construction and demolition waste, demolished with combined efforts to improve he scientific level of three to split; second, we must pay attention to \"three to split\" and \"five hundred\" and \"five water treatment\des\shackDistrict transformation, and dangerous old room transformation and \"two road sides\", series work organic combined up, active do River, and along demolition work, and manpower advance village in the, and old residential demolition work, to improved masses housing conditions and live environment; three to put \"three modified a split\" as traditional low, and small, and bulk industry structure transformation upgrade of important initiatives to caught, speed up advance industry Park, effective optimization park environment含有vdc、0两种电平，在计算傅立叶系数时，可将双重积分内限由、变为1x、。只需在最终的结果中，减去注入的直流分量即可。 2x（x1,2,3）

由此：Kkn/321ej(kxny)dxdy2/322ej(kxny)dxdy/3120114/321vdc23j(kxny)j(kxny)edxdyedxdy 22/3131145/322223j(kxny)j(kxny)edxdyedxdy5/3134/312 （3-7）

根据以上各部分的计算，考虑到cr，可得到SVPWM线电压波形谐波分

析的结论：

1、谐波主要集中在采样频率fs以及fs的整数倍附近

2、在线性调制阶段，载波频率fs增加，低次谐波分量总量会减少，总的谐波畸

变率会有相应的降低

3、随着调制系数m的降低，低次谐波分量会增加，总的谐波畸变率会增大，这

是由于零矢量相对增强。

4、在过调制阶段，低次谐波分量按不同次数有不同程度的增加，这是因为调制

波本身就发生了畸变，矢量轨迹并非圆形，而是在圆形和正六边形之间相互切换。

4 死区补偿

以逆变器中一个桥臂的A相为例进行死区效应分析，其负载为感性。在理想状况下，功率管VT1和VT2的开关状态是互补的。但是置入死区时间Td后，功率管要延迟Td才能导通。因此在死区时间内，VT1和VT2都处于关断状态，输出电流经过二极管续流。由图4可见，假设电流流入感性负载的方向为正，流出为负。在死区时间内，i0时，VD2导通，相当于下桥臂开关管导通，a点连接到光伏电池

图6 VT1、VT2开通和关断时的电流流向 Fig 6 Current directions when VT1、VT2 is on an off）

一个载波周期内，开关管的理想和实际开关状态如图5所示。图中，Sa和Sa分

别为上下管的触发导通信号，a和b为上下桥臂的理想触发信号；c和d为实际开关信号，阴影部分时，上下管均处于关断状态。i>0时，下桥臂二极管导通，就上管而言，输出正电压的脉冲宽度减少了Td，即实际导通时间比理想导通时间缩短了Td，而下管的实际导通时间则比理想导通时间延长了Td。需要做的补偿是将上管的理想导通时间延长Td，由于信号的互补性，下管的理想导通时间相应缩短了Td，达到了实际导通时间与理想的相一致的目的，从而保证了实际脉冲信号与给定脉冲信号的一样性。同理可知，i<0时，补偿方法是将上管的理想导通时间缩短Td

nd improve idle land of utilization, real achieved environment improved and productivity development mutual promoting total win. Five, firmly implement, promoting work ahead, to create highlights. Third deployment, implementation of seven, then it is imperative to strengthen responsibility and improve the mechanisms and implementation. All localities and departments must be convinced that goals, going all out, mustering spirit, work together to ensure that this year's objectives carry out tasks, at the forefront. First, we must strengthen the leadership to implement. Departments at all levels should always work and rural \"five water treatment\portant position, and carry the main responsibility, main leader personally, leaders arrested and layers of responsibility rank transmission pressure established hierarchical accountability, and work together to promote the work of the mechanism, a concerted effort pay attention to implementation. County nongban, flood, three to one down to further play a leading catch total, integrated and coordinated role of all kinds is \"long\or\" to effectively fulfill their responsibilities, formed the alignment on the fire line and management a lively situation. Second, we must strengthen the test implementation of the Governor. Role play the Governor got the baton, for agricultural and rural focus and \"five water treatment\split\" work, refine improve assessment methods and evaluation system, accurate assessment. Combined with \"dare play, tree benchmark\" style building five major operations, carry on and gain firsthand experience of supervision, in particular, to strengthen the focus on the \"long\" signs \"go left\s supervision, urged all levels longer on duty in place. Through the supervisory assessment, to promote habits, stimulating power. Third, we must strengthen implementation style. Departments at all levels to work in rural areas and \"five water treatment\split\" as training cadres for major platforms, compete against large examination room, inspection cadres work performance of the ring, water control and the Japanese pulled a workout, training, discovery and selection of cadres. Than good catch up, first to excellence-oriented. Party members and cadres at all levels must adhere to the rural, water control and the Japanese pulled a grass-roots, \"put down the shelf, leaned\" pragmatic style, the spirit of play, become a benchmark model. Four, we must strengthen propaganda implementation. Comprehensive utilization of micro-credit, micro-blogging, new media, mining, summarizing, good publicity work in the countryside and \"five water treatment\odels, point to gather positive energy for the community to see the results of our work in time, increase public awareness, participation rates, satisfaction and support. Play gongqingfu, a mass organization and grass-roots such as schools, communityThe role ofocusing on ways and means of improving and upgrading work, further development of \"three to split\". (A) fully grasp \"no unauthorised\" created. The township \"no unauthorised\" created the existing building \"one household, one document\" survey and file storage work must be unconditional and full coverage. Main corridor leading to the town (road, river) village, the Central built-up area of the town on both sides must be to create a \"no unauthorised village\". According to \"five hundred villages\" created and shanty towns, villages, old houses, reconstruction of old plant, expand create, upgrading creates files, the real \"no unauthorised village\" created into the benefit of the people of very good thing. (B) to strictly manage count as unauthorised controls. Promoting the \"new\" control work to move the center of gravity, management measures to the front, and earnestly pipes effectively. A strict new unauthorised network responsibility. Sectors such as land, housing and basic stations (stations) and the Township of grid accountability mechanisms must be strictly in accordance with the new regulatory requirements, effective implementation of the area of responsibility of the new inspections, suppression, demolition work to ensure that the new \"zero tolerance\". Second, public security, water, electricity, watr, oceans and fisheries, tourism collaboration, market supervision departments should strictly enforce the illegal construction of disposal of relevant provisions of the regulations, effective fulfilment of responsibilities, particularly in electricity and water supply, and other units may not be new illegal buildings to supply water and electricity supply. While more regulation to prevent personal privacy violations. Illicit trading in illegal construction in the Ministry of public security sector to strictly from the blow. Three is to create additional offence reporting system of incentives. According to building law and covers an area of nature, to report timely degree divided report grade, effective after the removal of certain incentives. (C) integrated implementation \ding demolition, modification, use\" combination. Demolition is the means and purpose built is. To adhere to the building demolished, combination of construction and demolition waste, demolished with combined efforts to improve he scientific level of three to split; second, we must pay attention to \"three to split\" and \"five hundred\" and \"five water treatment\des\shackDistrict transformation, and dangerous old room transformation and \"two road sides\", series work organic combined up, active do River, and along demolition work, and manpower advance village in the, and old residential demolition work, to improved masses housing conditions and live environment; three to put \"three modified a split\" as traditional low, and small, and bulk industry structure transformation upgrade of important initiatives to caught, speed up advance industry Park, effective optimization park environmentnd improve idle land of utilization, real achieved environment improved and productivity development mutual promoting total win. Five, firmly implement, promoting work ahead, to create down to further play a leading catch total, integrated and coordinated role of all kinds is \"long\or\" to effectively fulfill their responsibilities, formed the alignment on the fire line and managemecompete against large examination room, inspection cadres work performance of the ring, water control and the Japanese pulled a workout, training, discovery and selection of cadres. Than good

图7 理想触发信号和实际开关信号 Fig.7 Ideal trigger signals and real switch signals）

nt, implementation of seven, then it is imperative to strengthen responsibility and improve the mechanisms and implementation. All localities and departments must be convinced that goals, going all out, mustering spirit, work together to ensure that this year's objectives carry out tasks, at the forefront. First, we must strengthen the leadership to implement. Departments at all levels should always work and rural \"five water treatment\portant position, and carry the main responsibility, main leader personally, leaders arrested and layers of responsibility rank transmission pressure established hierarchical accountability, and work together to promote the work of the mechanism, a concerted effort pay attention to implementation. County nongban, flood, three to one ust strengthen the test implementation of the Governor. Role play the Governor got the baton, for agricultural and rural focus and \"five water treatment\split\" work, refine improve assessment methods and evaluation system, accurate assessment. Combined with \"dare play, tree benchmark\" style building five major operations, carry on and gain firsthand experience of supervision, in particular, to strengthen the focus on the \"long\" signs \"go left\s supervision, urged all levels longer on duty in place. Through the supervisory assessment, to promote habits, stimulating power. Third, we must strengthen implementation style. Departments at all levels to work in rural areas and \"five water treatment\split\" as training cadres for major platforms, d. Party members and cadres at all levels must adhere to the rural, water control and the Japanese pulled a grass-roots, \"put down the shelf, leaned\" pragmatic style, the spirit of play, become a benchmark model. Four, we must strengthen propaganda implementation. Comprehensive utilization of micro-credit, micro-blogging, new media, mining, summarizing, good publicity work in the countryside and \"five water treatment\odels, point to gather positive energy for the community to see the results of our work in time, increase public awareness, participation rates, satisfaction and support. Play gongqingfu, a mass organization and grass-roots such as schools, communityThe role of（highlights. Third deployment a lively situation. Second, we mcatch up, first to excellence-orienteocusing on ways and means of improving and upgrading work, further development of \"three to split\". (A) fully grasp \"no unauthorised\" created. The township \"no unauthorised\" created the existing building \"one household, one document\" survey and file storage work must be unconditional and full coverage. Main corridor leading to the town (road, river) village, the Central built-up area of the town on both sides must be to create a \"no unauthorised village\". According to \"five hundred villages\" created and shanty towns, villages, old houses, reconstruction of old plant, expand create, upgrading creates files, the real \"no unauthorised village\" created into the benefit of the people of very good thing. (B) to strictly manage count as unauthorised controls. Promoting the \"new\" control work to move the center of gravity, management measures to the front, and earnestly pipes effectively. A strict new unauthorised network responsibility. Sectors such as land, housing and basic stations (stations) and the Township of grid accountability mechanisms must be strictly in accordance with the new regulatory requirements, effective implementation of the area of responsibility of the new inspections, suppression, demolition work to ensure that the new \"zero tolerance\". Second, public security, water, electricity, water, oceans and fisheries, tourism collaboration, market supervision departments should strictly enforce the illegal construction of disposal of relevant provisions of the regulations, effective fulfilment of responsibilities, particularly in electricity and water supply, and other units may not be new illegal buildings to supply water and electricity supply. While more regulation to prevent personal privacy violations. Illicit trading in illegal construction in the Ministry of public security sector to strictly from the blow. Three is to create additional offence reporting system of incentives. According to building law and covers an area of nature, to report timely degree divided report grade, effective after the removal of certain incentives. (C) integrated implementation \ding demolition, modification, use\" combination. Demolition is the means and purpose built is. To adhere to the building demolished, combination of construction and demolition waste, demolished with combined efforts to improve the scientific level of three to split; second, we must pay attention to \"three to split\" and \"five hundred\" and \"five water treatment\des\shackDistrict transformation, and dangerous old room transformation and \"two road sides\s work organic combined up, active do River, and along demolition work, and manpower advance village in the, and old residential demolition work, to improved masses housing conditions and live environment; three to put \"three modified a split\" as traditional low, and small, and bulk industry structure transformation upgrade of important initiatives to caught, speed up advance industry Park, effective optimization park environment5 基于广义积分的控制策略

在两相静止坐标系下，被控对象为交流量。传统的PI控制器，只能无差跟踪直流给定信号，如要使得被控对象在控制器的作用下，其输出能无差地跟踪交流量，则必须采用新的控制器。

根据内模原理，如果系统的给定信号或扰动为单一频率的正弦信号，那么只要在控制器中植入与指令同频的正弦信号模型 G(s)静差跟踪。

如果外部信号包含其它频率成分，这种情况下，若要实现无静差，只需针对每

，就可以实现系统的无

s22一种频率的信号设置一个内模即可。

e*i+_1Tss1KKipils22KPWM0.5Tss1_+1/R1(L/R)si

图8 基于广义积分的控制信号流图

与基于d-q坐标系的控制策略相比，该方案无交叉耦合项，无需前馈解耦，运

算更为简单，而且由于比例环节已能对输出电流波形进行一定控制，如能通过广义积分环节对少数几个谐波畸变率较大的频率成分进行改善，该控制策略不失为一个简单有效的方案。

6 基于重复控制的控制策略

当然，如果频率成分复杂，则基于广义积分的控制策略将会导致内模数量大，

nd improve idle land of utilization, real achieved environment improved and productivity development mutual promoting total win. Five, firmly implement, promoting work ahead, to create highlights. Third deployment, implementation of seven, then it is imperative to strengthen responsibility and improve the mechanisms and implementation. All localities and departments must be convinced that goals, going all out, mustering spirit, work together to ensure that this year's objectives carry out tasks, at the forefront. First, we must strengthen the leadership to implement. Departments at all levels should always work and rural \"five water treatment\portant position, and carry the main responsibility, main leader personally, leaders arrested and layers of responsibility rank transmission pressure established hierarchical accountability, and work together to promote the work of the mechanism, a concerted effort pay attention to implementation. County nongban, flood, three to one down to further play a leading catch total, integrated and coordinated role of all kinds is \"long\or\" to effectively fulfill their responsibilities, formed the alignment on the fire line and management a lively situation. Second, we must strengthen the test implementation of the Governor. Role play the Governor got the baton, for agricultural and rural focus and \"five water treatment\split\" work, refine improve assessment methods and evaluation system, accurate assessment. Combined with \"dare play, tree benchmark\" style building five major operations, carry on and gain firsthand experience of supervision, in particular, to strengthen the focus on the \"long\" signs \"go left\s supervision, urged all levels longer on duty in place. Through the supervisory assessment, to promote habits, stimulating power. Third, we must strengthen implementation style. Departments at all levels to work in rural areas and \"five water treatment\split\" as training cadres for major platforms, compete against large examination room, inspection cadres work performance of the ring, water control and the Japanese pulled a workout, training, discovery and selection of cadres. Than good catch up, first to excellence-oriented. Party members and cadres at all levels must adhere to the rural, water control and the Japanese pulled a grass-roots, \"put down the shelf, leaned\" pragmatic style, the spirit of play, become a benchmark model. Four, we must strengthen propaganda implementation. Comprehensive utilization of micro-credit, micro-blogging, new media, mining, summarizing, good publicity work in the countryside and \"five water treatment\odels, point to gather positive energy for the community to see the results of our work in time, increase public awareness, participation rates, satisfaction and support. Play gongqingfu, a mass organization and grass-roots such as schools, communityThe role ofocusing on ways and means of improving and upgrading work, further development of \"three to split\". (A) fully grasp \"no unauthorised\" created. The township \"no unauthorised\" created the existing building \"one household, one document\" survey and file storage work must be unconditional and full coverage. Main corridor leading to the town (road, river) village, the Central built-up area of the town on both sides must be to create a \"no unauthorised village\". According to \"five hundred villages\" created and shanty towns, villages, old houses, reconstruction of old plant, expand create, upgrading creates files, the real \"no unauthorised village\" created into the benefit of the people of very good thing. (B) to strictly manage count as unauthorised controls. Promoting the \"new\" control work to move the center of gravity, management measures to the front, and earnestly pipes effectively. A strict new unauthorised network responsibility. Sectors such as land, housing and basic stations (stations) and the Township of grid accountability mechanisms must be strictly in accordance with the new regulatory requirements, effective implementation of the area of responsibility of the new inspections, suppression, demolition work to ensure that the new \"zero tolerance\". Second, public security, water, electricity, watr, oceans and fisheries, tourism collaboration, market supervision departments should strictly enforce the illegal construction of disposal of relevant provisions of the regulations, effective fulfilment of responsibilities, particularly in electricity and water supply, and other units may not be new illegal buildings to supply water and electricity supply. While more regulation to prevent personal privacy violations. Illicit trading in illegal construction in the Ministry of public security sector to strictly from the blow. Three is to create additional offence reporting system of incentives. According to building law and covers an area of nature, to report timely degree divided report grade, effective after the removal of certain incentives. (C) integrated implementation \ding demolition, modification, use\" combination. Demolition is the means and purpose built is. To adhere to the building demolished, combination of construction and demolition waste, demolished with combined efforts to improve he scientific level of three to split; second, we must pay attention to \"three to split\" and \"five hundred\" and \"five water treatment\des\shackDistrict transformation, and dangerous old room transformation and \"two road sides\", series work organic combined up, active do River, and along demolition work, and manpower advance village in the, and old residential demolition work, to improved masses housing conditions and live environment; three to put \"three modified a split\" as traditional low, and small, and bulk industry structure transformation upgrade of important initiatives to caught, speed up advance industry Park, effective optimization park environment控制器结构复杂，从应用角度而言不太合理，工程上也不易实现。因此需要寻找一种新的内模形式来描述此种类型的外部信号。

分析可知，上面所述两种情况的干扰信号具有两个特点：首先是可重复性，即

周期性。其次是指令信号的谐波形式。因此扰动信号在每个基波周期都以完全相同

eLs的波形出现。对于这样的信号，可采用如下形式的内模：G(s)，L为给定Ls1e信号的周期。这是一个周期延时正反馈环节，不管什么形式的信号，只要重复出现，而且频率是基波的倍数，那么该内模的输出就是对输入信号的逐周期累加。当输入信号衰减为0，该内模依然会不断的逐周期输出与上周期相同的信号，相当于任意信号发生器。它的作用类似于积分环节，区别仅在于它是逐周期的累加，因此这样的内模能够满足要求。采用这种特殊形式内模的闭环控制系统称之为重复控制系统。由于上式中的存延时环节eLs难以用模拟器件实现，因而在应用中重复控制都是以

ZN离散的数字形式实现。重复控制器内模的离散形式为G，N为一个周期的N1Z采样次数。见图9。

图9 理想内模重复控制系统结构图

对于重复控制控制而言，内模是系统的核心，它提供了稳定持续的控制信号，

当内模为理想情况时，输入信号为0的情况下输出可以无衰减的反复重现上一周期的信号。但是理想内模的极点分布在虚轴上，处于临界振荡状态，系统稳定性较差。当受控对象的参数稍有变化，整个闭环系统很可能不稳定。图9所示的重复控制器

ZNERY；YP*U； U*E N1Z整理后得： ER(1ZN)E(1P)ZN，此式表明，系统稳定的条件是等式右

面第二项是稳定收敛的。由此可见，系统稳定存在约束条件1P1。这表明在理想内模条件下，只有满足此约束条件误差才会收敛。但在一般情况下，被控对象难以在整个频段满足此条件，此时可对内模加以改造，即采用QZN代替ZN，保证系统稳定收敛。Q可为小于1的常数，也可以为具有低通性质的函数。使得回路满足Q(1P)1。改进型内模结构见图10。

图10 改进型内模原理图

引入Q之后，内模的“纯积分”特性也被破坏，当输入信号为0时，改进内模的输出不能完全复现上个周期的信号，而是逐周期的衰减。如果Q为常数，那么仅为幅值衰减，如果Q为低通函数，对于非单一频谱的信号而言，信号的形式就会发生变化

ZN位于重复控制系统的前向通道上，使控制信号延时为１个周期。由于指令

信号和扰动信号均为周期性，这样可使控制信号对下一周期而言具有一定的超前性。而且对于超前相位补偿，此环节也是必须的。但在引入周期延迟环节后，系统的快速性受到影响，有较大的控制滞后。因此在使用重复控制器时多采用嵌入式结构，保留指令信号的快速通路，见图11

nd improve idle land of utilization, real achieved environment improved and productivity development mutual promoting total win. Five, firmly implement, promoting work ahead, to create highlights. Third deployment, implementation of seven, then it is imperative to strengthen responsibility and improve the mechanisms and implementation. All localities and departments must be convinced that goals, going all out, mustering spirit, work together to ensure that this year's objectives carry out tasks, at the forefront. First, we must strengthen the leadership to implement. Departments at all levels should always work and rural \"five water treatment\portant position, and carry the main responsibility, main leader personally, leaders arrested and layers of responsibility rank transmission pressure established hierarchical accountability, and work together to promote the work of the mechanism, a concerted effort pay attention to implementation. County nongban, flood, three to one down to further play a leading catch total, integrated and coordinated role of all kinds is \"long\or\" to effectively fulfill their responsibilities, formed the alignment on the fire line and management a lively situation. Second, we must strengthen the test implementation of the Governor. Role play the Governor got the baton, for agricultural and rural focus and \"five water treatment\split\" work, refine improve assessment methods and evaluation system, accurate assessment. Combined with \"dare play, tree benchmark\" style building five major operations, carry on and gain firsthand experience of supervision, in particular, to strengthen the focus on the \"long\" signs \"go left\s supervision, urged all levels longer on duty in place. Through the supervisory assessment, to promote habits, stimulating power. Third, we must strengthen implementation style. Departments at all levels to work in rural areas and \"five water treatment\split\" as training cadres for major platforms, compete against large examination room, inspection cadres work performance of the ring, water control and the Japanese pulled a workout, training, discovery and selection of cadres. Than good catch up, first to excellence-oriented. Party members and cadres at all levels must adhere to the rural, water control and the Japanese pulled a grass-roots, \"put down the shelf, leaned\" pragmatic style, the spirit of play, become a benchmark model. Four, we must strengthen propaganda implementation. Comprehensive utilization of micro-credit, micro-blogging, new media, mining, summarizing, good publicity work in the countryside and \"five water treatment\odels, point to gather positive energy for the community to see the results of our work in time, increase public awareness, participation rates, satisfaction and support. Play gongqingfu, a mass organization and grass-roots such as schools, communityThe role ofocusing on ways and means of improving and upgrading work, further development of \"three to split\". (A) fully grasp \"no unauthorised\" created. The township \"no unauthorised\" created the existing building \"one household, one document\" survey and file storage work must be unconditional and full coverage. Main corridor leading to the town (road, river) village, the Central built-up area of the town on both sides must be to create a \"no unauthorised village\". According to \"five hundred villages\" created and shanty towns, villages, old houses, reconstruction of old plant, expand create, upgrading creates files, the real \"no unauthorised village\" created into the benefit of the people of very good thing. (B) to strictly manage count as unauthorised controls. Promoting the \"new\" control work to move the center of gravity, management measures to the front, and earnestly pipes effectively. A strict new unauthorised network responsibility. Sectors such as land, housing and basic stations (stations) and the Township of grid accountability mechanisms must be strictly in accordance with the new regulatory requirements, effective implementation of the area of responsibility of the new inspections, suppression, demolition work to ensure that the new \"zero tolerance\". Second, public security, water, electricity, watr, oceans and fisheries, tourism collaboration, market supervision departments should strictly enforce the illegal construction of disposal of relevant provisions of the regulations, effective fulfilment of responsibilities, particularly in electricity and water supply, and other units may not be new illegal buildings to supply water and electricity supply. While more regulation to prevent personal privacy violations. Illicit trading in illegal construction in the Ministry of public security sector to strictly from the blow. Three is to create additional offence reporting system of incentives. According to building law and covers an area of nature, to report timely degree divided report grade, effective after the removal of certain incentives. (C) integrated implementation \ding demolition, modification, use\" combination. Demolition is the means and purpose built is. To adhere to the building demolished, combination of construction and demolition waste, demolished with combined efforts to improve he scientific level of three to split; second, we must pay attention to \"three to split\" and \"five hundred\" and \"five water treatment\des\shackDistrict transformation, and dangerous old room transformation and \"two road sides\", series work organic combined up, active do River, and along demolition work, and manpower advance village in the, and old residential demolition work, to improved masses housing conditions and live environment; three to put \"three modified a split\" as traditional low, and small, and bulk industry structure transformation upgrade of important initiatives to caught, speed up advance industry Park, effective optimization park environment 图11 重复控制系统框图

6.1 补偿器

补偿器S(z)是针对对象P(z)特性而设置的，它决定了重复控制系统的性能。当

重复控制器的内模输出了包含指令和扰动信息的信号后，如何使控制对象的输出完美地跟踪指令信号，这是补偿器要解决的问题。对于控制系统而言，极点的位置和系统的性能有着密切的关系，因此本文从极点分布的角度对补偿器的特性进行研究。

由图11给出r到e的传递函数：

e(1P)(1QZN) Nr1Z(QSP)

由传递函数可知，系统的极点：ZNQSP，当所有的极点都位于圆心上，即

z=0时，系统具有最好的动静态特性，此时QSP，在理想内模情况下Q1，即

SP1。所以当取SP1形式时，系统既有最好的稳定性，又具有最快的误差收敛

速度和最小的稳态误差。但是有两个因素制约着Ｓ无法取P1的形式。首先，如果Ｐ包含单元圆外的零点，这样按照SP1会存在单位圆外的极点，补偿器会不稳定，导致整个系统无法稳定。其次，要想在整个频段保证SP1，前提是获得一个完美精确的逆变电源模型Ｐ，这在一定程度上是很难实现的，尤其是针对其高频的特性。

zdB(z1)假定受控对象P，ｄ为受控对象的响应延时，根据前面的结论设计1Az

zdA(z1)控制器S(z)，可以实现完美的跟踪特性。但由于上述原因（补偿器的极1B(z)点为受控对象的零点，当受控对象的零点在单位圆外时，可能会导致补偿器不稳定）不能对受控对象直接求逆的方法设计S(z)。传统的方法是通过零相移误差跟踪理论设计相应的S(z)控制器。

u首先对B(z1)进行分解，得到B(z1)Bca(z1)Bc(z1)，其中Bca(z1)包含所有单

位圆内的零点，Bcu(z1)包含单位圆外以及单位圆上的零点。新设计的补偿器形式为

A(z1)S(z)a1uzd，其中Bcu(1)的作用是调整S(z)的增益。根据零相移误差跟踪

Bc(z)Bc(1)理论，S(z)P(z)应满足零相移、零增益的条件，因此有如下推导：

Bcu(z1)zdB(z1)A(z1)d SP*a1uz1uA(z)Bc(z)Bc(1)Bc(1)定义：

Bcu(Bcu(ejT))Bcu(ejT)， MuuBc(1)Bc(1)uusBc(z1)bcu0bcu1z1bcu2z2......bcsz

Bcu(ejT)SP的频率形式为：Re()jIm()

Bcu(1)ubcu0bcu1cos(t)bcu2cos(2t)......bcscos(st)其中： Re() uuuubc0bc1bc2......bcsubcu0bcu1sin(t)bcu2sin(2t)......bcssin(st) Im()uuuubc0bc1bc2......bcs

得出：MRe2()Im2()，tan1(Im()/Re())

nd improve idle land of utilization, real achieved environment improved and productivity development mutual promoting total win. Five, firmly implement, promoting work ahead, to create highlights. Third deployment, implementation of seven, then it is imperative to strengthen responsibility and improve the mechanisms and implementation. All localities and departments must be convinced that goals, going all out, mustering spirit, work together to ensure that this year's objectives carry out tasks, at the forefront. First, we must strengthen the leadership to implement. Departments at all levels should always work and rural \"five water treatment\portant position, and carry the main responsibility, main leader personally, leaders arrested and layers of responsibility rank transmission pressure established hierarchical accountability, and work together to promote the work of the mechanism, a concerted effort pay attention to implementation. County nongban, flood, three to one down to further play a leading catch total, integrated and coordinated role of all kinds is \"long\or\" to effectively fulfill their responsibilities, formed the alignment on the fire line and management a lively situation. Second, we must strengthen the test implementation of the Governor. Role play the Governor got the baton, for agricultural and rural focus and \"five water treatment\split\" work, refine improve assessment methods and evaluation system, accurate assessment. Combined with \"dare play, tree benchmark\" style building five major operations, carry on and gain firsthand experience of supervision, in particular, to strengthen the focus on the \"long\" signs \"go left\s supervision, urged all levels longer on duty in place. Through the supervisory assessment, to promote habits, stimulating power. Third, we must strengthen implementation style. Departments at all levels to work in rural areas and \"five water treatment\split\" as training cadres for major platforms, compete against large examination room, inspection cadres work performance of the ring, water control and the Japanese pulled a workout, training, discovery and selection of cadres. Than good catch up, first to excellence-oriented. Party members and cadres at all levels must adhere to the rural, water control and the Japanese pulled a grass-roots, \"put down the shelf, leaned\" pragmatic style, the spirit of play, become a benchmark model. Four, we must strengthen propaganda implementation. Comprehensive utilization of micro-credit, micro-blogging, new media, mining, summarizing, good publicity work in the countryside and \"five water treatment\odels, point to gather positive energy for the community to see the results of our work in time, increase public awareness, participation rates, satisfaction and support. Play gongqingfu, a mass organization and grass-roots such as schools, communityThe role ofocusing on ways and means of improving and upgrading work, further development of \"three to split\". (A) fully grasp \"no unauthorised\" created. The township \"no unauthorised\" created the existing building \"one household, one document\" survey and file storage work must be unconditional and full coverage. Main corridor leading to the town (road, river) village, the Central built-up area of the town on both sides must be to create a \"no unauthorised village\". According to \"five hundred villages\" created and shanty towns, villages, old houses, reconstruction of old plant, expand create, upgrading creates files, the real \"no unauthorised village\" created into the benefit of the people of very good thing. (B) to strictly manage count as unauthorised controls. Promoting the \"new\" control work to move the center of gravity, management measures to the front, and earnestly pipes effectively. A strict new unauthorised network responsibility. Sectors such as land, housing and basic stations (stations) and the Township of grid accountability mechanisms must be strictly in accordance with the new regulatory requirements, effective implementation of the area of responsibility of the new inspections, suppression, demolition work to ensure that the new \"zero tolerance\". Second, public security, water, electricity, watr, oceans and fisheries, tourism collaboration, market supervision departments should strictly enforce the illegal construction of disposal of relevant provisions of the regulations, effective fulfilment of responsibilities, particularly in electricity and water supply, and other units may not be new illegal buildings to supply water and electricity supply. While more regulation to prevent personal privacy violations. Illicit trading in illegal construction in the Ministry of public security sector to strictly from the blow. Three is to create additional offence reporting system of incentives. According to building law and covers an area of nature, to report timely degree divided report grade, effective after the removal of certain incentives. (C) integrated implementation \ding demolition, modification, use\" combination. Demolition is the means and purpose built is. To adhere to the building demolished, combination of construction and demolition waste, demolished with combined efforts to improve he scientific level of three to split; second, we must pay attention to \"three to split\" and \"five hundred\" and \"five water treatment\des\shackDistrict transformation, and dangerous old room transformation and \"two road sides\", series work organic combined up, active do River, and along demolition work, and manpower advance village in the, and old residential demolition work, to improved masses housing conditions and live environment; three to put \"three modified a split\" as traditional low, and small, and bulk industry structure transformation upgrade of important initiatives to caught, speed up advance industry Park, effective optimization park environment分析可知，幅值和频率随频率的变化有明显变化。尽管在实际系统中需跟踪的信号频率都很低，M和变化都很小，但是/较大，所以会引起较大的延时，明显影响对信号的跟踪特性。此时可采用下面的数学特性达到零相移跟踪，即：

Bcu(z1)Bcu(z1)uus，其中Bc*u(z)bcu0bcu1zbcu2z2......bcsz，计算得: uBc(1)Bc(1)Bcu(ejT)Bcu(ejT)*(Re()jIm())*(Re()jIm())uuBc(1)Bc(1) Re2()Im2()

上式计算结果为一实数，这表明任何频率下的相移均为0，在低频段增益接近1。当受控对象含有单元圆外零点时，补偿器的形式为下面形式：

S(z)A(z1)Bcu*(z1)Bca(z1)Bcu(1)2zds，

us2u其中Bcu*(z1)bcu0zsbcu1zs1bc ......bcs2z7 基于谐波补偿

本节从谐波补偿的角度出发，采用改进型FFT算法对输出电流误差信号进行实

时频谱分析，把由软件产生的经过预畸变的谐波信号注入逆变器，由此达到抑制非线性扰动从而达到校正输出电流波形的目的。

图12为基于谐波补偿的控制系统的系统结构框图。G1(s)表示控制对象，在这

里就是输出LC滤波器的传递函数，其离散化形式由G1(z)表示。G2(z)表示内部模型，它与G1(z)相等。

考虑扰动信号d(z)在输出点的相应。由图12可以很容易得到扰动信号的传递函

数：

Hd(z)1Gc(z)G1(z)

1G1(z)G2(z)Gc(z) （7-1）

由于G1(z)G2(z)，故Hd(z)可简化为：

Hd(z)1Gc(z)G1(z)

1 （7-2）

显然，只要Gc(z)G1(z)，则Hd(z)0，即扰动可以得到完全的抑制。不幸的是，实际逆变器的z域传递函数含有一个纯延时环节，这就意味着谐波

补偿器Gc(z)必须含有一个超前环节，这在物理上是无法实现的。但在实际应用中，我们只需抑制低次谐波即可获得较好的输出电流波形，所以，只需要使得谐波补偿低频段频率特性是控制对象G1(z)低频段频率特性的逆就可以了。

7.2 谐波补偿器

谐波补偿器是由FFT和谐波发生器组成。FFT算法对输出电流误差进行实时频

nd improve idle land of utilization, real achieved environment improved and productivity development mutual promoting total win. Five, firmly implement, promoting work ahead, to create highlights. Third deployment, implementation of seven, then it is imperative to strengthen responsibility and improve the mechanisms and implementation. All localities and departments must be convinced that goals, going all out, mustering spirit, work together to ensure that this year's objectives carry out tasks, at the forefront. First, we must strengthen the leadership to implement. Departments at all levels should always work and rural \"five water treatment\portant position, and carry the main responsibility, main leader personally, leaders arrested and layers of responsibility rank transmission pressure established hierarchical accountability, and work together to promote the work of the mechanism, a concerted effort pay attention to implementation. County nongban, flood, three to one down to further play a leading catch total, integrated and coordinated role of all kinds is \"long\or\" to effectively fulfill their responsibilities, formed the alignment on the fire line and management a lively situation. Second, we must strengthen the test implementation of the Governor. Role play the Governor got the baton, for agricultural and rural focus and \"five water treatment\split\" work, refine improve assessment methods and evaluation system, accurate assessment. Combined with \"dare play, tree benchmark\" style building five major operations, carry on and gain firsthand experience of supervision, in particular, to strengthen the focus on the \"long\" signs \"go left\s supervision, urged all levels longer on duty in place. Through the supervisory assessment, to promote habits, stimulating power. Third, we must strengthen implementation style. Departments at all levels to work in rural areas and \"five water treatment\split\" as training cadres for major platforms, compete against large examination room, inspection cadres work performance of the ring, water control and the Japanese pulled a workout, training, discovery and selection of cadres. Than good catch up, first to excellence-oriented. Party members and cadres at all levels must adhere to the rural, water control and the Japanese pulled a grass-roots, \"put down the shelf, leaned\" pragmatic style, the spirit of play, become a benchmark model. Four, we must strengthen propaganda implementation. Comprehensive utilization of micro-credit, micro-blogging, new media, mining, summarizing, good publicity work in the countryside and \"five water treatment\odels, point to gather positive energy for the community to see the results of our work in time, increase public awareness, participation rates, satisfaction and support. Play gongqingfu, a mass organization and grass-roots such as schools, communityThe role ofocusing on ways and means of improving and upgrading work, further development of \"three to split\". (A) fully grasp \"no unauthorised\" created. The township \"no unauthorised\" created the existing building \"one household, one document\" survey and file storage work must be unconditional and full coverage. Main corridor leading to the town (road, river) village, the Central built-up area of the town on both sides must be to create a \"no unauthorised village\". According to \"five hundred villages\" created and shanty towns, villages, old houses, reconstruction of old plant, expand create, upgrading creates files, the real \"no unauthorised village\" created into the benefit of the people of very good thing. (B) to strictly manage count as unauthorised controls. Promoting the \"new\" control work to move the center of gravity, management measures to the front, and earnestly pipes effectively. A strict new unauthorised network responsibility. Sectors such as land, housing and basic stations (stations) and the Township of grid accountability mechanisms must be strictly in accordance with the new regulatory requirements, effective implementation of the area of responsibility of the new inspections, suppression, demolition work to ensure that the new \"zero tolerance\". Second, public security, water, electricity, watr, oceans and fisheries, tourism collaboration, market supervision departments should strictly enforce the illegal construction of disposal of relevant provisions of the regulations, effective fulfilment of responsibilities, particularly in electricity and water supply, and other units may not be new illegal buildings to supply water and electricity supply. While more regulation to prevent personal privacy violations. Illicit trading in illegal construction in the Ministry of public security sector to strictly from the blow. Three is to create additional offence reporting system of incentives. According to building law and covers an area of nature, to report timely degree divided report grade, effective after the removal of certain incentives. (C) integrated implementation \ding demolition, modification, use\" combination. Demolition is the means and purpose built is. To adhere to the building demolished, combination of construction and demolition waste, demolished with combined efforts to improve he scientific level of three to split; second, we must pay attention to \"three to split\" and \"five hundred\" and \"five water treatment\des\shackDistrict transformation, and dangerous old room transformation and \"two road sides\", series work organic combined up, active do River, and along demolition work, and manpower advance village in the, and old residential demolition work, to improved masses housing conditions and live environment; three to put \"three modified a split\" as traditional low, and small, and bulk industry structure transformation upgrade of important initiatives to caught, speed up advance industry Park, effective optimization park environment谱分析。由于系统电压谐波畸变主要在于次数较低的奇次谐波，所以，只需分析出1、3、5、7、9次谐波的幅值和初相角就可以满足要求了。

设x(n)为N点有限长序列，其FFT为：

X(k)x(n)WNn0N1nk （7-3）

式中：

k0,1,...,N1；

WNnkej2nkN

显然，常规的FFT算法，其输出点数和输入点数是相等的，但在本系统中只需

求出X(1)、X(3)、X(5)、X(7)、X(9)等几个输出点即可。根据基于FFT的蝶形计算流程图可以知道，在只需计算指定的若干输出点的情况下，可以大大减少计算量，节省大量的DSP时钟，这就使得基于FFT的实时频谱分析成为可能。

谐波发生器的作用是将FFT分析出的谐波进行预畸变，然后把预畸变的谐波信

号作为补偿指令送给控制对象。

8 总结

本文首先介绍了光伏并网逆变器所广泛采用的基于d-q坐标系的电流波形控制

策略，其后介绍了该策略将会导致电流波形产生畸变的原因，最后介绍了三种改善的控制策略。重复控制是近年来研究较多的一种控制方法，但其Q值的存在以及补偿器S的设计都是一个难点，而且设计不好将会导致系统的不稳定。个人觉得基于广义积分和谐波补偿的控制策略，其针对性强，实现简单，是工程上较为实用的控制策略。

[1]. 王建宽，崔巍，江建中．SVPWM 技术的理论分析及仿真

微特电机， 2006 (6)： 15-20.

[2]. 仇志凌．邹丽霞，熊蕊，基于谐波补偿的逆变器波形控制技术研究 .

电源技术应用， 2004（3）： 1-167.

[3]. 陈宏．基于重复控制理论的逆变电源控制技术研究 .南京航空航天大学，

博士学位论文， 2003

[4]. 朱荣伍，戴鹏，刘剑．基于两相静止坐标系三相电压型PWM整流器控制策略的研究 .

变频器世界， 2009 （4）： 42-44.

[5]. 魏凯，尚敬，廖长鑫．SVPWM逆变器死区补偿的研究与实现.

大功率变流技术， 2009（ 6 ）： 18-23. [6]. 张崇巍，张兴．PWM整流器及其控制

[7]. 张超，于岩，张义君，SVPWM逆变器输出电压谐波分析

煤矿机械，2011(6)：115-117

因篇幅问题不能全部显示，请点此查看更多更全内容

查看全文