CN105743371A

CN105743371A - Manufacturing method of MMC controller suitable for unbalanced voltage

Info

Publication number: CN105743371A
Application number: CN201610228393.0A
Authority: CN
Inventors: 江斌开; 王志新
Original assignee: Shanghai Jiao Tong University
Current assignee: Shanghai Jiao Tong University
Priority date: 2016-04-13
Filing date: 2016-04-13
Publication date: 2016-07-06

Abstract

The invention provides a method for manufacturing a controller suitable for MMC under unbalanced voltage, comprising the following steps: Step 1: Control the voltage of the upper bridge arm and the voltage of the lower bridge arm through the current controller to make the voltage of the upper bridge arm, the voltage of the lower bridge arm The bridge arm voltage tends to the target reference value; Step 2: The positive sequence component and the negative sequence component of the AC component of the unbalanced current i _diffj are uniformly controlled by the MMC circulating current controller, and the zero sequence component is controlled separately. The principle of the MMC controller designed by the invention is not complicated, it is suitable for the situation of balanced and unbalanced voltage, and the stability of the system is greatly improved.

Description

Controller manufacturing method suitable for MMC under unbalanced voltage

技术领域technical field

本发明涉及电气工程，具体地，涉及一种适用于不平衡电压下的MMC的控制器制造方法。The invention relates to electrical engineering, in particular to a method for manufacturing a controller suitable for MMC under unbalanced voltage.

背景技术Background technique

模块化多电平变流器(Modularmultilevelconverter，MMC)在高压直流输电领域有着众多优势，在未来传输新能源电能中有着重要作用。MMC拓扑的桥臂并非采用大量开关器件直接串联,而是采用半桥子模块级联形式，不存在动态均压等问题，特别适用于高压直流输电场合。由于MMC的三相桥臂直流侧与直流母线并联的结构，决定了MMC在工作时三相之间必然产生环流。环流叠加在桥臂电流中，不仅提高了功率器件的额定电流容量，增加了系统成本；同时增加了开关损耗，使功率器件发热严重，影响装置使用寿命，因而有必要对环流进行抑制。传统环流控制器采用二倍频负序旋转坐标变换将换流器内部的三相环流分解为两个直流分量，从而消除了桥臂电流中的环流分量，但该环流控制器只适用于三相平衡交流系统。Modular multilevel converter (MMC) has many advantages in the field of high-voltage direct current transmission, and will play an important role in the transmission of new energy in the future. The bridge arm of the MMC topology does not use a large number of switching devices to be directly connected in series, but adopts the cascading form of half-bridge sub-modules, which does not have problems such as dynamic voltage equalization, and is especially suitable for high-voltage direct current transmission occasions. Due to the parallel structure of the DC side of the three-phase bridge arm of the MMC and the DC bus, it is determined that a circulating current must be generated between the three phases of the MMC during operation. The circulating current is superimposed on the bridge arm current, which not only increases the rated current capacity of the power device and increases the system cost; at the same time, it increases the switching loss, causes the power device to heat up seriously, and affects the service life of the device. Therefore, it is necessary to suppress the circulating current. The traditional circulating current controller uses double frequency negative sequence rotation coordinate transformation to decompose the three-phase circulating current inside the converter into two DC components, thereby eliminating the circulating current component in the bridge arm current, but the circulating current controller is only suitable for three-phase Balanced AC system.

经对现有文献检索发现，《IEEETransactionsonPowerDelivery》上发表了题为“Predictivecontrolofamodularmultilevelconverterforaback-to-backHVDCsystem(针对背靠背HVDC系统的模块化多电平预测控制)”的文章，该文通过离散化环流数学模型，提出一种基于模型预测方法的环流控制器，但该方法计算量大，当MMC只有N+1电平时，开关状态有种，控制过程繁琐。After searching the existing literature, it was found that "IEEE Transactions on Power Delivery" published an article entitled "Predictive control of a modular multilevel converter for a back-to-back HVDC system (for back-to-back HVDC system modular multi-level predictive control)". A circulating current controller based on the model prediction method, but this method has a large amount of calculation. When the MMC has only N+1 level, the switch state has species, the control process is cumbersome.

发明内容Contents of the invention

针对现有技术中的缺陷，本发明的目的是提供一种适用于不平衡电压下的MMC的控制器制造方法。本发明针对MMC进行详细的数学模型推导，具体分析了不平衡电压下的交流有功功率和环流瞬时功率的变化情况，设计了基于正、负序控制的内环电流控制器，消除有功功率二倍频波动；同时，还设计了一种基于正、负、零序环流控制的环流控制器。Aiming at the defects in the prior art, the object of the present invention is to provide a controller manufacturing method suitable for MMC under unbalanced voltage. The present invention conducts detailed mathematical model derivation for MMC, specifically analyzes the change of AC active power and circulating instantaneous power under unbalanced voltage, designs an inner loop current controller based on positive and negative sequence control, and eliminates the doubling of active power frequency fluctuation; at the same time, a circulation controller based on positive, negative and zero-sequence circulation control is also designed.

根据本发明提供的适用于不平衡电压下的MMC的控制器制造方法，包括如下步骤：The manufacturing method of the controller applicable to the MMC under the unbalanced voltage provided by the present invention comprises the following steps:

步骤1：通过电流控制器对上桥臂电压、下桥臂电压的控制使上桥臂电压、下桥臂电压趋向于目标参考值；Step 1: Control the voltage of the upper bridge arm and the lower bridge arm through the current controller to make the voltage of the upper bridge arm and the lower bridge arm tend to the target reference value;

步骤2：通过MMC环流控制器将不平衡电流i_diffj的交流分量的正序分量和负序分量统一控制，零序分量单独控制。Step 2: The positive sequence component and the negative sequence component of the AC component of the unbalanced current i _diffj are uniformly controlled by the MMC circulating current controller, and the zero sequence component is controlled separately.

优选地，所述步骤1包括如下步骤：Preferably, said step 1 includes the following steps:

步骤101：计算每相桥臂中上桥臂、下桥臂电压如下：Step 101: Calculate the voltage of the upper bridge arm and the lower bridge arm of each phase bridge arm as follows:

$\{\begin{matrix} {U u}_{p p j j} = = {Σ Σ}_{i i = = 11}^{n no} {v v}_{d d c c i i} {s the s}_{i i} \\ {U u}_{n no j j} = = {Σ Σ}_{i i = = 11}^{n no} {v v}_{d d c c i i} {s the s}_{i i} \end{matrix}$

其中，i＝{1,2,3…n}，n为子模块SM的数量，j＝{a，b，c}，a、b、c表示交流电的三相，U_pj表示上桥臂电压，U_nj表示下桥臂电压，v_dci为第i个子模块电容电压，s_i为第i个子模块的开关状态；上桥臂、下桥臂均由N个子模块SM串联而成，构成N+1电平变流器；Among them, i={1,2,3...n}, n is the number of sub-modules SM, j={a, b, c}, a, b, c represent the three phases of alternating current, U _pj represents the voltage of the upper bridge arm , U _nj represents the voltage of the lower bridge arm, v _dci is the capacitor voltage of the i-th sub-module, s _i is the switch state of the i-th sub-module; both the upper bridge arm and the lower bridge arm are composed of N sub-modules SM in series, forming an N+ 1 level converter;

步骤102：假定MMC中的子模块SM电压恒定，MMC中各桥臂电压等效为受控电压源，得到单相等效电路：Step 102: Assuming that the voltage of the sub-module SM in the MMC is constant, the voltage of each bridge arm in the MMC is equivalent to a controlled voltage source, and a single-phase equivalent circuit is obtained:

MMC的三相连续数学模型表示为：The three-phase continuous mathematical model of MMC is expressed as:

${u u}_{v v j j} = = {e e}_{j j} - - \frac{{R R}_{00}}{22} {i i}_{v v j j} - - \frac{{L L}_{00}}{22} \cdot &Center Dot; \frac{{di di}_{v v j j}}{d d t t} - - - - - - - - j j = = a a,, b b,, c c$

${u u}_{d d i i f f f f j j} = = {L L}_{00} \cdot &Center Dot; \frac{{di di}_{d d i i f f f f j j}}{d d t t} + + {R R}_{00} {i i}_{d d i i f f f f j j} = = \frac{{U u}_{d d c c}}{22} - - \frac{{u u}_{p p j j} + + {u u}_{n no j j}}{22}$

其中：in:

${e e}_{j j} = = \frac{{u u}_{n no j j} - - {u u}_{p p j j}}{22}$

e_j定义为内部电动势，值为上、下桥臂电压之差的一半；e _j is defined as the internal electromotive force, which is half of the difference between the upper and lower arm voltages;

${i i}_{d d i i f f f f j j} = = \frac{{i i}_{p p j j} + + {i i}_{n no j j}}{22} = = \frac{{i i}_{d d c c}}{33} + + {i i}_{z z j j}$

i_diffj为内部不平衡电流，表示内部不平衡电流的直流分量，i_dc为直流电流，i_zj表示内部不平衡电流的交流分量，该交流分量即为桥臂环流；L₀表示桥臂电感，R₀表示桥臂损耗等效电阻；受控电压源U_pj表示等效上桥臂电压，U_nj表示等效下桥臂电压；i_pj表示上桥臂电流，i_nj表示下桥臂电流，i_diffj表示流经上、下桥臂的内部不平衡电流；u_vj、i_vj分别为电平变流器输出点V处的j相电压、电流，u_diffj为不平衡电压；U_dc表示直流电压；i _diffj is the internal unbalanced current, Indicates the DC component of the internal unbalanced current, i _dc is the DC current, and i _zj indicates the AC component of the internal unbalanced current, which is the bridge arm circulation current; L ₀ indicates the bridge arm inductance, R ₀ indicates the bridge arm loss equivalent resistance; the controlled voltage source U _pj represents the equivalent upper bridge arm voltage, U _nj represents the equivalent lower bridge arm voltage; i _pj represents the upper bridge arm current, i _nj represents the lower bridge arm current, and i _diffj represents the current flowing through the upper and lower bridge arms The internal unbalanced current of the bridge arm; u _vj and i _vj are the j-phase voltage and current at the output point V of the level converter respectively, and u _diffj is the unbalanced voltage; U _dc represents the DC voltage;

j相上桥臂电流i_pj、下桥臂电流i_nj为：The current i _pj of the upper bridge arm and the current i _nj of the lower bridge arm of phase j are:

$\{\begin{matrix} {i i}_{p p j j} = = {i i}_{d d i i f f f f j j} + + \frac{{i i}_{v v j j}}{22} \\ {i i}_{n no j j} = = {i i}_{d d i i f f f f j j} - - \frac{{i i}_{v v j j}}{22} \end{matrix}$

得到j相上桥臂电压U_pj、下桥臂电压U_nj：Obtain the j-phase upper bridge arm voltage U _pj and lower bridge arm voltage U _nj :

$\{\begin{matrix} {U u}_{p p j j} = = \frac{{U u}_{d d c c}}{22} - - {u u}_{d d i i f f f f j j} - - {e e}_{j j} \\ {U u}_{n no j j} = = \frac{{U u}_{d d c c}}{22} - - {u u}_{d d i i f f f f j j} + + {e e}_{j j} \end{matrix}$

步骤103：根据下式得到目标参考值，具体如下：Step 103: Obtain the target reference value according to the following formula, specifically as follows:

$\{\begin{matrix} {U u}_{p p j j__r r e e f f} = = \frac{{U u}_{d d c c}}{22} - - {u u}_{d d i i f f f f j j__r r e e f f} - - {e e}_{j j__r r e e f f} \\ {U u}_{n no j j__r r e e f f} = = \frac{{U u}_{d d c c}}{22} - - {u u}_{d d i i f f f f j j__r r e e f f} + + {e e}_{j j__r r e e f f} \end{matrix}$

U_{pj_ref}表示上桥臂电压示参考值，U_{nj_ref}表示下桥臂电压示参考值，u_{diffj_ref}为不平衡电压参考值，e_{j_ref}为内部电动势的参考值，下标_ref表示参考值；U _{pj_ref} indicates the reference value of the upper arm voltage, U _{nj_ref} indicates the reference value of the lower arm voltage, u _{diffj_ref} is the reference value of the unbalanced voltage, e _{j_ref} is the reference value of the internal electromotive force, and the subscript _ref indicates the reference value;

步骤104：当在不平衡电压下时，对电压的正序分量和负序分量独立控制，具体为，得到电压的正序分量和负序分量表达式，记为表达式A：Step 104: When under unbalanced voltage, independently control the positive sequence component and negative sequence component of the voltage, specifically, obtain the expression of the positive sequence component and negative sequence component of the voltage, which is recorded as expression A:

$\{\begin{matrix} {u u}_{v v j j}^{+ +} = = {e e}_{j j}^{+ +} - - \frac{{R R}_{00}}{22} {i i}_{j j}^{+ +} - - \frac{{L L}_{00}}{22} \cdot \cdot \frac{{di di}_{j j}^{+ +}}{d d t t} \\ {u u}_{v v j j}^{- -} = = {e e}_{j j}^{- -} - - \frac{{R R}_{00}}{22} {i i}_{j j}^{- -} - - \frac{{L L}_{00}}{22} \cdot \cdot \frac{{di di}_{j j}^{- -}}{d d t t} \end{matrix}$

其中，为电平变流器输出点V处的j相电压的正序分量，为内部电动势的正序分量，为j相电流的正序分量，为电平变流器输出点V处的j相电压的负序分量，为内部电动势的负序分量，为j相电流的负序分量；t为时间；in, is the positive sequence component of the j-phase voltage at the output point V of the level converter, is the positive sequence component of the internal electromotive force, is the positive sequence component of phase j current, is the negative sequence component of the j-phase voltage at the output point V of the level converter, is the negative sequence component of the internal electromotive force, is the negative sequence component of phase j current; t is time;

将表达式A变换至d、q旋转坐标，通过解耦，分别独立控制d轴和q轴分量，旋转坐标下的表达式B如下：Transform the expression A to the d and q rotation coordinates, and independently control the d-axis and q-axis components through decoupling. The expression B under the rotation coordinates is as follows:

其中，为电流的d、q轴正序分量，为电平变流器输出的电压的d、q轴正序分量，为内部电动势的d、q轴正序分量，为电流的d、q轴负序分量，为电平变流器输出的电压的d、q轴负序分量，为内部电动势的d、q轴负序分量；in, are the positive sequence components of the d and q axes of the current, d and q axis positive sequence components of the voltage output by the level converter, are the positive sequence components of the d and q axes of the internal electromotive force, is the negative sequence component of the d and q axes of the current, d, q-axis negative sequence components of the voltage output by the level converter, is the negative sequence component of the d and q axes of the internal electromotive force;

根据表达式B得到对应的电流控制器，采用PI控制器，得到内部电动势参考值e_{j_ref}的d、q轴分量的正、负序参考值即：According to the expression B, the corresponding current controller is obtained, and the positive and negative sequence reference values of the d and q axis components of the internal electromotive force reference value e _{j_ref} are obtained by using the PI controller which is:

其中，ω为电网角频率，L为线路电抗值，R为线路电阻，PI(·)为比例积分控制器。Among them, ω is the angular frequency of the power grid, L is the line reactance value, R is the line resistance, and PI(·) is the proportional-integral controller.

优选地，还包括如下步骤：Preferably, the following steps are also included:

-当在不平衡电压下时，由于电压电流负序分量的存在，电平变流器网侧的有功功率和无功功率将会产生2倍基频波动；- When under unbalanced voltage, due to the existence of voltage and current negative sequence components, the active power and reactive power on the grid side of the level converter will produce 2 times the fundamental frequency fluctuation;

电平变流器网侧有功功率与无功功率均产生了正序与负序分量，具体如下：The active power and reactive power on the grid side of the level converter both produce positive and negative sequence components, as follows:

$[\begin{matrix} {P P}_{g g 00} \\ {Q Q}_{g g 00} \\ {P P}_{g g sin sin 22} \\ {P P}_{g g cos cos 22} \end{matrix}] = = \frac{33}{22} [\begin{matrix} {V V}_{g g d d}^{+ +} & {V V}_{g g q q}^{+ +} & {V V}_{g g d d}^{+ +} & {V V}_{g g q q}^{- -} \\ {V V}_{g g q q}^{+ +} & - - {V V}_{g g d d}^{+ +} & {V V}_{g g q q}^{- -} & - - {V V}_{g g d d}^{- -} \\ {V V}_{g g q q}^{- -} & - - {V V}_{g g d d}^{- -} & - - {V V}_{g g q q}^{+ +} & {V V}_{g g d d}^{+ +} \\ {V V}_{g g d d}^{- -} & {V V}_{g g q q}^{- -} & {V V}_{g g d d}^{+ +} & {V V}_{g g q q}^{+ +} \end{matrix}] [\begin{matrix} {i i}_{d d}^{+ +} \\ {i i}_{q q}^{+ +} \\ {i i}_{d d}^{- -} \\ {i i}_{q q}^{- -} \end{matrix}]$

P_g＝P_g0+P_gsin2sin2ω_gt+P_gcos2cos2ω_gtP _g ＝P _g0 +P _gsin2 sin2ω _g t+P _gcos2 cos2ω _g t

其中，P_g0表示有功功率，Q_g0表示无功功率，表示网侧电流正序分量的q轴分量，表示网侧电流正序分量的q轴分量，表示网侧电流负序分量的d轴分量，表示网侧电流负序分量的q轴分量，表示网侧电压网侧分量正序分量的d轴分量，表示网侧电压网侧分量负序分量的d轴分量，为网侧电压网侧分量正序分量的q轴分量，为网侧电压网侧分量负序分量的q轴分量，i表示网侧电流，V表示网侧电压，上标“+”、“-”分别表示正序分量、负序分量，下标d、q分别表示旋转坐标下的d轴分量、q轴分量，下标g表示网侧分量，下标0表示基频分量；下标sin2正弦2倍基频分量和cos2表示余弦2倍基频波动分量；P_g为总的有功功率，ω为电网角频率；P_g0为总的有功功率的基频分量；P_gsin2为总的有功功率正弦2倍基频波动分量和P_gcos2为总的有功功率的余弦2倍基频波动分量；Among them, P _g0 represents active power, Q _g0 represents reactive power, Indicates the q-axis component of the positive sequence component of the grid side current, Indicates the q-axis component of the positive sequence component of the grid side current, Indicates the d-axis component of the negative sequence component of the grid side current, Indicates the q-axis component of the negative sequence component of the grid side current, Indicates the d-axis component of the positive sequence component of the grid-side voltage grid-side component, Indicates the d-axis component of the negative sequence component of the grid-side voltage grid-side component, is the q-axis component of the positive sequence component of the grid-side voltage grid-side component, is the q-axis component of the negative-sequence component of the grid-side voltage grid-side component, i represents the grid-side current, V represents the grid-side voltage, the superscripts "+" and "-" represent the positive-sequence component and negative-sequence component respectively, and the subscripts d, q represents the d-axis component and q-axis component under the rotating coordinates, the subscript g represents the grid side component, and the subscript 0 represents the fundamental frequency component; the subscript sin2 sine 2 times the fundamental frequency component and cos2 represents the cosine 2 times the fundamental frequency fluctuation component ; P _g is the total active power, ω is the grid angular frequency; P _g0 is the fundamental frequency component of the total active power; P _gsin2 is the sinusoidal 2 times fundamental frequency fluctuation component of the total active power and P _gcos2 is the total active power Cosine 2 times fundamental frequency fluctuation component;

将有功功率2倍基频波动分量抑制为零，即通过控制使得P_gsin2＝0，P_gcos2＝0；P表示有功功率，Q表示无功功率；具体为，取网侧电压V垂直q轴时为初始条件分析，则进而电流负序分量表达式：Suppress the active power 2 times the fundamental frequency fluctuation component to zero, that is, make P _gsin2 = 0, P _gcos2 = 0 through control; P represents active power, and Q represents reactive power; specifically, when the grid side voltage V is vertical to the q-axis For initial condition analysis, then Then the expression of negative sequence component of current:

$\{\begin{matrix} {i i}_{d d}^{- -} = = \frac{{V V}_{g g d d}^{- -} {i i}_{q q}^{+ +}}{{V V}_{g g d d}^{+ +}} - - \frac{{V V}_{g g q q}^{- -} {i i}_{d d}^{+ +}}{{V V}_{g g d d}^{+ +}} \\ {i i}_{q q}^{- -} = = - - \frac{{V V}_{g g d d}^{- -} {i i}_{d d}^{+ +}}{{V V}_{g g d d}^{+ +}} - - \frac{{V V}_{g g q q}^{- -} {i i}_{q q}^{+ +}}{{V V}_{g g d d}^{+ +}} \end{matrix}$

式中，与由功率参考值及网侧电压计算得到，具体为，In the formula, and Calculated from the power reference value and grid-side voltage, specifically,

$\{\begin{matrix} {i i}_{d d}^{+ +} = = \frac{22 P P}{33 {V V}_{g g d d}^{+ +}} \\ {i i}_{q q}^{+ +} = = \frac{22 Q Q}{33 {V V}_{g g d d}^{+ +}} \end{matrix} . .$

优选地，所述步骤2包括如下步骤：Preferably, said step 2 includes the following steps:

步骤201：当在不平衡电压下，a相的单相瞬时功率P_pua为，Step 201: When under unbalanced voltage, the single-phase instantaneous power P _pua of phase a is,

$\begin{matrix} {P P}_{p p u u a a} = = \frac{{U u}_{d d c c} {I I}_{d d c c}}{66} [[{k k}^{- -} {m m}^{+ +} cos cos ((22 {ω ω}_{00} t t + + α α__+ + {γ γ}_{+ +})) + + {k k}^{+ +} {m m}^{+ +} cos cos ((22 {ω ω}_{00} t t + + {α α}_{+ +} + + {γ γ}_{+ +})) - - \\ 22 {l l}^{- -} sin sin ((22 {ω ω}_{00} t t + + β β__)) - - {k k}^{- -} {m m}^{+ +} cos cos ((α α__- - {γ γ}_{+ +}))]] \end{matrix}$

式中，α₊、α_-分别为内部电动势的正序、负序分量的相角；k⁺、k^-分别为内部电动势正序电压、负序电压调制比；l^-表示环流补偿电压与直流电压之比；m⁺为正序电流调制比，γ₊表示变流器网侧电流相角；U_dc表示直流电压；ω₀为电网初始角频率；I_dc为直流电流；β_-为2倍基频负序分量初始相角；In the formula, α ₊ , α _- are the phase angles of the positive sequence and negative sequence components of the internal electromotive force respectively; k ⁺ , k ^- are the modulation ratios of positive sequence voltage and negative sequence voltage of the internal electromotive force respectively; l ^- represents the circulating current compensation voltage Ratio to DC voltage; m ⁺ is positive sequence current modulation ratio, γ ₊ is grid side current phase angle of converter; U _dc is DC voltage; ω ₀ is grid initial angular frequency; I _dc is DC current; β _- is 2 times the initial phase angle of the negative sequence component of the fundamental frequency;

${k k}^{&PlusMinus; &PlusMinus;} = = \frac{{E E.}_{a a}^{&PlusMinus; &PlusMinus;}}{\frac{{u u}_{d d c c}}{22}}$

${l l}^{- -} = = \frac{{u u}_{d d i i f f f f}^{- -}}{\frac{{u u}_{d d c c}}{22}}$

其中，表示内部电动势的正序分量和负序分量的幅值；in, Indicates the magnitude of the positive and negative sequence components of the internal electromotive force;

步骤202：不平衡电流i_diffj的正、负、零三序表达式，如下所示，Step 202: The positive, negative and zero three-sequence expressions of the unbalanced current i _diffj are as follows,

${i i}_{d d i i f f f f j j} = = \frac{{I I}_{d d c c}}{33} + + {i i}_{z z j j} = = \frac{{I I}_{d d c c}}{33} + + {i i}_{z z j j}^{+ +} + + {i i}_{z z j j}^{- -} + + {i i}_{z z j j}^{00}$

其中，为内部不平衡电流的交流分量的正序分量，为内部不平衡电流的交流分量的负序分量，为内部不平衡电流的交流分量的零序分量,I_dc表示直流电流。in, is the positive sequence component of the AC component of the internal unbalanced current, is the negative sequence component of the AC component of the internal unbalanced current, Idc is the zero-sequence component of the AC component of the internal unbalanced current, and I _dc represents the DC current.

步骤203：将不平衡电流i_diffj的交流分量，即桥臂环流抑制为零；具体为，不平衡电流i_diffj的交流分量的正序分量和负序分量统一控制，零序分量单独控制，从而MMC环流控制器为：Step 203: Suppress the AC component of the unbalanced current i _diffj , that is, the bridge arm circulating current to zero; specifically, the positive sequence component and the negative sequence component of the AC component of the unbalanced current i _diffj are controlled uniformly, and the zero sequence component is controlled separately, so that The MMC circulation controller is:

${u u}_{d d i i f f f f}^{{&PlusMinus; &PlusMinus;}^{* *}} = = P P I I [[((\frac{{I I}_{d d c c}}{33})) - - {i i}_{d d i i f f f f j j}]]$

${u u}_{d d i i f f f f}^{00^{* *}} = = P P I I [[{i i}_{d d c c}^{* *} - - {I I}_{d d c c}]]$

${i i}_{d d c c}^{* *} = = \frac{{P P}_{g g}}{{V V}_{d d c c}}$

${u u}_{d d i i f f f f}^{* *} = = {u u}_{d d i i f f f f}^{{&PlusMinus; &PlusMinus;}^{* *}} + + {u u}_{d d i i f f f f}^{00^{* *}}$

表示直流电流参考值，I_dc表示直流电流，PI(·)表示PI控制器，为不平衡电压参考值的正序分量、负序分量，表示不平衡电压参考值，表示不平衡电压参考值，上标+、-分别表示正序分量、负序分量，上表0表示零序分量，P_g、V_dc分别表示网侧有功功率、直流电压。 Indicates the DC current reference value, I _dc indicates the DC current, PI(·) indicates the PI controller, are the positive sequence component and negative sequence component of the unbalanced voltage reference value, Indicates the unbalanced voltage reference value, Indicates the unbalanced voltage reference value, superscripts + and - indicate positive sequence component and negative sequence component respectively, 0 in the above table indicates zero sequence component, P _g and V _dc respectively indicate grid-side active power and DC voltage.

与现有技术相比，本发明具有如下的有益效果：Compared with the prior art, the present invention has the following beneficial effects:

1、本发明针对MMC在不平衡电压下的功率变化，设计了基于正、负序控制的内环电流控制器，消除有功功率二倍频波动。1. Aiming at the power change of MMC under unbalanced voltage, the present invention designs an inner loop current controller based on positive and negative sequence control to eliminate double frequency fluctuation of active power.

2、本发明基于瞬时功率理论分析，提出并设计了一种基于直接控制环流正、负、零三序分量的环流控制器。2. Based on the theoretical analysis of instantaneous power, the present invention proposes and designs a circulating current controller based on direct control of the positive, negative and zero three-sequence components of the circulating current.

3、本发明所设计的MMC控制器原理并不复杂，适用于平衡和不平衡电压下的情况，极大提高了系统稳定性。3. The principle of the MMC controller designed by the present invention is not complicated, and it is suitable for the situation of balanced and unbalanced voltage, which greatly improves the stability of the system.

附图说明Description of drawings

通过阅读参照以下附图对非限制性实施例所作的详细描述，本发明的其它特征、目的和优点将会变得更明显：Other characteristics, objects and advantages of the present invention will become more apparent by reading the detailed description of non-limiting embodiments made with reference to the following drawings:

图1为本发明中MMC基本拓扑结构；Fig. 1 is MMC basic topological structure among the present invention;

图2为本发明中三相MMC的单相等效电路；Fig. 2 is the single-phase equivalent circuit of three-phase MMC among the present invention;

图3为本发明中MMC电流控制框图；Fig. 3 is MMC current control block diagram among the present invention;

图4为本发明中MMC环流控制框图；Fig. 4 is MMC circulation control block diagram among the present invention;

图5为本发明中MMC完整控制框图；Fig. 5 is the complete control block diagram of MMC among the present invention;

图6为本发明中平衡交流电网下直流电流波形；Fig. 6 is the DC current waveform under the balanced AC grid in the present invention;

图7为本发明中平衡交流电网下桥臂环流波形；Fig. 7 is the circular current waveform of the lower bridge arm of the balanced AC grid in the present invention;

图8为本发明中不平衡电压下的有功功率波形；Fig. 8 is the active power waveform under unbalanced voltage among the present invention;

图9为本发明中不平衡电压下的直流电流波形；Fig. 9 is the DC current waveform under unbalanced voltage among the present invention;

图10为本发明中不平衡电压下的桥臂环流波形；Fig. 10 is the bridge arm circulation waveform under unbalanced voltage in the present invention;

图11为本发明中MMC基本结构中子模块SM的结构示意图。Fig. 11 is a schematic structural diagram of the sub-module SM in the basic structure of the MMC in the present invention.

具体实施方式detailed description

下面结合具体实施例对本发明进行详细说明。以下实施例将有助于本领域的技术人员进一步理解本发明，但不以任何形式限制本发明。应当指出的是，对本领域的普通技术人员来说，在不脱离本发明构思的前提下，还可以做出若干变形和改进。这些都属于本发明的保护范围。The present invention will be described in detail below in conjunction with specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that those skilled in the art can make several modifications and improvements without departing from the concept of the present invention. These all belong to the protection scope of the present invention.

步骤1：建立MMC三相连续数学模型；其中MMC基本结构由三相六桥臂组成，每个桥臂由N个子模块SM(SubModule,SM)串联而成，构成N+1电平变流器，如图1所示。Step 1: Establish a three-phase continuous mathematical model of MMC; the basic structure of MMC is composed of three-phase six bridge arms, and each bridge arm is composed of N submodules SM (SubModule, SM) connected in series to form an N+1 level converter ,As shown in Figure 1.

步骤101：通过直流电容电压、开关函数计算每相桥臂中上桥臂、下桥臂电压如下：Step 101: Calculate the voltage of the upper bridge arm and the lower bridge arm of each phase bridge arm through the DC capacitor voltage and the switching function as follows:

$\{\begin{matrix} {U u}_{p p j j} = = {Σ Σ}_{i i = = 11}^{n no} {v v}_{d d c c i i} {s the s}_{i i} \\ {U u}_{n no j j} = = {Σ Σ}_{i i = = 11}^{n no} {v v}_{d d c c i i} {s the s}_{i i} \end{matrix} - - - - - - ((11))$

其中，i＝{1,2,3…n}，n为子模块SM的数量，j＝{a，b，c}，a、b、c表示交流电的三相，图1中，SM表示子模块，Ua，Ub，Uc表示三相交流电压，U_pj表示上桥臂电压，U_nj表示下桥臂电压，U_dc表示直流电压，C表示直流电容。v_dci为第i个子模块电容电压，s_i为第i个子模块开关状态。Among them, i={1,2,3...n}, n is the number of sub-module SM, j={a, b, c}, a, b, c represent the three phases of alternating current, in Figure 1, SM represents the sub-module Module, Ua, Ub, Uc represent the three-phase AC voltage, U _pj represents the voltage of the upper bridge arm, U _nj represents the voltage of the lower bridge arm, U _dc represents the DC voltage, and C represents the DC capacitance. v _dci is the capacitance voltage of the i-th sub-module, and s _i is the switching state of the i-th sub-module.

步骤102：若假定SM电压恒定，MMC中各桥臂电压可等效为受控电压源，则能够得到单相等效电路；Step 102: If it is assumed that the SM voltage is constant, the voltage of each bridge arm in the MMC can be equivalent to a controlled voltage source, then a single-phase equivalent circuit can be obtained;

如图2所示，L₀表示桥臂电感，R₀表示桥臂损耗等效电阻；受控电压源U_pj表示等效上桥臂电压，U_nj表示等效下桥臂电压；i_pj表示上桥臂电流，i_nj表示下桥臂电流，i_diffj表示流经上、下桥臂的内部不平衡电流；As shown in Figure 2, L ₀ represents the inductance of the bridge arm, R ₀ represents the equivalent resistance of the bridge arm loss; the controlled voltage source U _pj represents the equivalent upper bridge arm voltage, U _nj represents the equivalent lower bridge arm voltage; i _pj represents The current of the upper bridge arm, i _nj represents the current of the lower bridge arm, and i _diffj represents the internal unbalanced current flowing through the upper and lower bridge arms;

电平变流器输出点V处的j相电压与电流分别为u_vj和i_vj。根据基尔霍夫定律，MMC的三相连续数学模型可以表示为：The j-phase voltage and current at the output point V of the level converter are u _vj and i _vj respectively. According to Kirchhoff's law, the three-phase continuous mathematical model of MMC can be expressed as:

${u u}_{v v j j} = = {e e}_{j j} - - \frac{{R R}_{00}}{22} {i i}_{v v j j} - - \frac{{L L}_{00}}{22} \cdot &Center Dot; \frac{{di di}_{v v j j}}{d d t t},, ((j j = = a a,, b b,, c c)) - - - - - - ((22))$

${u u}_{d d i i f f f f j j} = = {L L}_{00} \cdot \cdot \frac{{di di}_{d d i i f f f f j j}}{d d t t} + + {R R}_{00} {i i}_{d d i i f f f f j j} = = \frac{{U u}_{d d c c}}{22} - - \frac{{u u}_{p p j j} + + {u u}_{n no j j}}{22} - - - - - - ((33))$

其中：in:

${e e}_{j j} = = \frac{{u u}_{n no j j} - - {u u}_{p p j j}}{22} - - - - - - ((44))$

e_j定义为内部电动势，其值为上、下桥臂电压之差的一半；e _j is defined as the internal electromotive force, and its value is half of the difference between the upper and lower arm voltages;

${i i}_{d d i i f f f f j j} = = \frac{{i i}_{p p j j} + + {i i}_{n no j j}}{22} = = \frac{{i i}_{d d c c}}{33} + + {i i}_{z z j j} - - - - - - ((55))$

i_diffj为内部不平衡电流，其由两部分组成，表示直流分量，i_zj表示交流分量，该交流分量即为桥臂环流，u_diffj为不平衡电压；i _diffj is the internal unbalanced current, which consists of two parts, Indicates the DC component, i _zj indicates the AC component, the AC component is the bridge arm circulating current, and u _diffj is the unbalanced voltage;

同时，由图2可知，j相上桥臂电流i_pj、下桥臂电流i_nj可表示为：At the same time, it can be known from Fig. 2 that the j-phase upper bridge arm current _ipj and lower bridge arm current i _nj can be expressed as:

$\{\begin{matrix} {i i}_{p p j j} = = {i i}_{d d i i f f f f j j} + + \frac{{i i}_{v v j j}}{22} \\ {i i}_{n no j j} = = {i i}_{d d i i f f f f j j} - - \frac{{i i}_{v v j j}}{22} \end{matrix} - - - - - - ((66))$

同理，可以得到j相上桥臂电压U_pj、下桥臂电压U_nj：Similarly, the voltage U _pj of the upper bridge arm and the voltage U _nj of the lower bridge arm of phase j can be obtained:

$\{\begin{matrix} {U u}_{p p j j} = = \frac{{U u}_{d d c c}}{22} - - {u u}_{d d i i f f f f j j} - - {e e}_{j j} \\ {U u}_{n no j j} = = \frac{{U u}_{d d c c}}{22} - - {u u}_{d d i i f f f f j j} + + {e e}_{j j} \end{matrix} - - - - - - ((77))$

步骤2：对MMC进行功率分析、电流指令计算；Step 2: Perform power analysis and current command calculation on MMC;

在不平衡电压情况下，由于电压电流负序分量的存在，电平变流器网侧的有功功率和无功功率并非恒定，而是会产生2倍基频波动；In the case of unbalanced voltage, due to the existence of voltage and current negative sequence components, the active power and reactive power on the grid side of the level converter are not constant, but will produce 2 times the fundamental frequency fluctuation;

$[\begin{matrix} {P P}_{g g 00} \\ {Q Q}_{g g 00} \\ {P P}_{g g sin sin 22} \\ {P P}_{g g cos cos 22} \end{matrix}] = = \frac{33}{22} [\begin{matrix} {V V}_{g g d d}^{+ +} & {V V}_{g g q q}^{+ +} & {V V}_{g g d d}^{+ +} & {V V}_{g g q q}^{- -} \\ {V V}_{g g q q}^{+ +} & - - {V V}_{g g d d}^{+ +} & {V V}_{g g q q}^{- -} & - - {V V}_{g g d d}^{- -} \\ {V V}_{g g q q}^{- -} & - - {V V}_{g g d d}^{- -} & - - {V V}_{g g q q}^{+ +} & {V V}_{g g d d}^{+ +} \\ {V V}_{g g d d}^{- -} & {V V}_{g g q q}^{- -} & {V V}_{g g d d}^{+ +} & {V V}_{g g q q}^{+ +} \end{matrix}] [\begin{matrix} {i i}_{d d}^{+ +} \\ {i i}_{q q}^{+ +} \\ {i i}_{d d}^{- -} \\ {i i}_{q q}^{- -} \end{matrix}] - - - - - - ((88))$

P_g＝P_g0+P_gsin2sin2ω_gt+P_gcos2cos2ω_gt(9)P _g ＝P _g0 +P _gsin2 sin2ω _g t+P _gcos2 cos2ω _g t(9)

其中，P_g0表示有功功率，Q_g0表示无功功率，表示网侧电流正序分量的q轴分量，表示网侧电流正序分量的q轴分量，表示网侧电流负序分量的d轴分量，表示网侧电流负序分量的q轴分量，表示网侧电压网侧分量正序分量的q轴分量，V表示网侧电压，上标“+”、“-”分别表示正序分量、负序分量，下标d、q分别表示旋转坐标下的d轴分量、q轴分量，下标g表示网侧分量，下标0表示基频分量；下标sin2和cos2表示2倍基频波动分量；P_g为总的有功功率，ω为电网角频率；P_g0为总的有功功率的基频分量；P_gsin2和P_gcos2总的有功功率的2倍基频波动分量；，能够看出总的有功功率由有功功率基频分量和有功功率2倍基频波动分量叠加而成。由于有功功率波动会造成直流母线电压出现相应的2倍基频波动，从而影响电能质量。Among them, P _g0 represents active power, Q _g0 represents reactive power, Indicates the q-axis component of the positive sequence component of the grid side current, Indicates the q-axis component of the positive sequence component of the grid side current, Indicates the d-axis component of the negative sequence component of the grid side current, Indicates the q-axis component of the negative sequence component of the grid side current, Indicates the q-axis component of the positive sequence component of the grid-side voltage grid-side component, V indicates the grid-side voltage, the superscripts "+" and "-" respectively indicate the positive-sequence component and negative-sequence component, and the subscripts d and q respectively indicate the rotation coordinates The d-axis component and q-axis component of the grid, the subscript g represents the grid side component, the subscript 0 represents the fundamental frequency component; the subscripts sin2 and cos2 represent 2 times the fundamental frequency fluctuation component; P _g is the total active power, and ω is the grid angle Frequency; P _g0 is the fundamental frequency component of the total active power; P _gsin2 and P _gcos2 are 2 times the fundamental frequency fluctuation component of the total active power; it can be seen that the total active power is doubled by the fundamental frequency component of the active power and the active power The fundamental frequency fluctuation components are superimposed. Since active power fluctuations will cause corresponding 2 times fundamental frequency fluctuations in the DC bus voltage, thereby affecting power quality.

因此，为保证有功功率恒定，必须将有功功率2倍基频波动分量抑制为零，即通过控制使得P_gsin2＝0，P_gcos2＝0。利用数学反步法思想，倒推该情况下的电流指令。取网侧电压垂直q轴时为初始条件分析，则由式(8)可以得到电流负序分量表达式：Therefore, in order to keep the active power constant, it is necessary to suppress the active power twice the fundamental frequency fluctuation component to zero, that is, make P _gsin2 =0 and P _gcos2 =0 through control. Using the idea of mathematical backstepping, reverse the current command in this case. The initial condition analysis is taken when the grid-side voltage is vertical to the q-axis, then From formula (8), the expression of negative sequence component of current can be obtained:

$\{\begin{matrix} {i i}_{d d}^{- -} = = \frac{{V V}_{g g d d}^{- -} {i i}_{q q}^{+ +}}{{V V}_{g g d d}^{+ +}} - - \frac{{V V}_{g g q q}^{- -} {i i}_{d d}^{+ +}}{{V V}_{g g d d}^{+ +}} \\ {i i}_{q q}^{- -} = = - - \frac{{V V}_{g g d d}^{- -} {i i}_{d d}^{+ +}}{{V V}_{g g d d}^{+ +}} - - \frac{{V V}_{g g q q}^{- -} {i i}_{q q}^{+ +}}{{V V}_{g g d d}^{+ +}} \end{matrix} - - - - - - ((1010))$

式中，与由功率参考值及网侧电压计算得到：In the formula, and Calculated from the power reference value and grid-side voltage:

$\{\begin{matrix} {i i}_{d d}^{+ +} = = \frac{22 P P}{33 {V V}_{g g d d}^{+ +}} \\ {i i}_{q q}^{+ +} = = \frac{22 Q Q}{33 {V V}_{g g d d}^{+ +}} \end{matrix} - - - - - - ((1111))$

步骤3：电流控制器设计，对MMC控制，可以理解为寻找合适的门极驱动信号去控制系统变量x(t)，使其尽量接近所希望的参考变量x*(t)，即对上桥臂电压、下桥臂电压的控制。因此，控制目标参考值由式(7)推导而出，具体如下：Step 3: Current controller design. For MMC control, it can be understood as finding a suitable gate drive signal to control the system variable x(t), making it as close as possible to the desired reference variable x*(t), that is, for the upper bridge arm voltage, lower arm voltage control. Therefore, the control target reference value is derived from formula (7), as follows:

$\{\begin{matrix} {U u}_{p p j j__r r e e f f} = = \frac{{U u}_{d d c c}}{22} - - {u u}_{d d i i f f f f j j__r r e e f f} - - {e e}_{j j__r r e e f f} \\ {U u}_{n no j j__r r e e f f} = = \frac{{U u}_{d d c c}}{22} - - {u u}_{d d i i f f f f j j__r r e e f f} + + {e e}_{j j__r r e e f f} \end{matrix} - - - - - - ((1212))$

在不平衡电压下，正序分量和负序分量必须独立控制，由式(2)可以得到其正序和负序表达式：Under unbalanced voltage, the positive sequence component and the negative sequence component must be controlled independently, and the positive sequence and negative sequence expressions can be obtained from formula (2):

$\{\begin{matrix} {u u}_{v v j j}^{+ +} = = {e e}_{j j}^{+ +} - - \frac{{R R}_{00}}{22} {i i}_{j j}^{+ +} - - \frac{{L L}_{00}}{22} \cdot &Center Dot; \frac{{di di}_{j j}^{+ +}}{d d t t} \\ {u u}_{v v j j}^{- -} = = {e e}_{j j}^{- -} - - \frac{{R R}_{00}}{22} {i i}_{j j}^{- -} - - \frac{{L L}_{00}}{22} \cdot \cdot \frac{{di di}_{j j}^{- -}}{d d t t} \end{matrix} - - - - - - ((1313))$

将式(13)变换至d、q旋转坐标，通过解耦，分别独立控制d轴和q轴分量，旋转坐标下的表达式如下：Transform Equation (13) to the d and q rotation coordinates, and through decoupling, the d-axis and q-axis components are independently controlled respectively. The expressions under the rotation coordinates are as follows:

由式(14)可以设计出对应的电流控制器，采用PI控制器，得到内部电动势的e_{j_ref}的d、q轴分量的正负序参考值和即：The corresponding current controller can be designed according to the formula (14), and the positive and negative sequence reference values of the d and q axis components of the e _{j_ref} of the internal electromotive force can be obtained by using the PI controller and which is:

图3为所设计的MMC电流控制框图。Figure 3 is a block diagram of the designed MMC current control.

图3中，MMC为模块化多电平变流器，C表示直流电容，R表示线路电阻，L表示线路电抗，P^*表示有功功率参考值，Q^*表示无功功率参考值。上标*表示参考值，θ表示电网电压相角，ω表示电网角频率，PI表示PI控制器。In Fig. 3, MMC is a modular multilevel converter, C represents a DC capacitor, R represents a line resistance, L represents a line reactance, P ^* represents a reference value of active power, and Q ^* represents a reference value of reactive power. The superscript * indicates the reference value, θ indicates the grid voltage phase angle, ω indicates the grid angular frequency, and PI indicates the PI controller.

步骤4：MMC环流控制器设计，在不平衡电压下，单相瞬时功率如式(16)所示，以A相为例：Step 4: MMC circulating current controller design, under unbalanced voltage, single-phase instantaneous power is shown in formula (16), taking phase A as an example:

$\begin{matrix} {P P}_{p p u u a a} = = \frac{{U u}_{d d c c} {I I}_{d d c c}}{66} [[{k k}^{- -} {m m}^{+ +} cos cos ((22 {ω ω}_{00} t t + + α α__+ + {γ γ}_{+ +})) + + {k k}^{+ +} {m m}^{+ +} cos cos ((22 {ω ω}_{00} t t + + {α α}_{+ +} + + {γ γ}_{+ +})) - - \\ 22 {l l}^{- -} - - s the s i i n no ((22 {ω ω}_{00} t t + + β β__)) - - {k k}^{- -} {m m}^{+ +} c c o o s the s ((α α__- - {γ γ}_{+ +}))]] \end{matrix} - - - - - - ((1616))$

式中，α₊、α_-表示内部电动势的正序、负序分量的相角；k⁺、k^-表示内部电动势正序电压、负序电压调制比，具体如式(17)所示；l^-表示环流补偿电压与直流电压之比，具体计算如式(18)所示；m⁺表示正序电流调制比，γ₊表示变流器网侧电流相角。可以看出，在不平衡电压下，单相瞬时功率含有两倍基频零序分量(第一项)，两倍基频正、负序分量(中间两项)和直流分量(最后一项)。零序分量会导致直流电压与直流电流产生波动，两倍基频正、负序分量与MMC环流直接相关，直流分量由于在各相中互差120°，因而自动消除。In the formula, α ₊ , α _- represent the phase angle of the positive sequence and negative sequence components of the internal electromotive force; k ⁺ , k ^- represent the modulation ratio of the positive sequence voltage and negative sequence voltage of the internal electromotive force, specifically as shown in formula (17); l ^- Indicates the circulating current compensation voltage The specific calculation of the ratio to the DC voltage is shown in formula (18); m ⁺ represents the positive sequence current modulation ratio, and γ ₊ represents the current phase angle of the converter grid side. It can be seen that under unbalanced voltage, the single-phase instantaneous power contains twice the fundamental frequency zero-sequence component (the first item), twice the fundamental frequency positive and negative sequence components (the middle two items) and the DC component (the last item) . The zero-sequence component will cause fluctuations in DC voltage and DC current. The positive and negative sequence components of twice the fundamental frequency are directly related to the MMC circulation. The DC component is automatically eliminated due to the 120° difference between each phase.

${k k}^{&PlusMinus; &PlusMinus;} = = \frac{{E E.}_{a a}^{&PlusMinus; &PlusMinus;}}{\frac{{u u}_{d d c c}}{22}} - - - - - - ((1717))$

${l l}^{- -} = = \frac{{u u}_{d d i i f f f f}^{- -}}{\frac{{u u}_{d d c c}}{22}} - - - - - - ((1818))$

式(17)中，表示内部电动势的正序分量和负序分量的幅值。改写式(5)，可以得到不平衡电流的正、负、零三序表达式，如下所示：In formula (17), Indicates the magnitude of the positive and negative sequence components of the internal electromotive force. Rewriting equation (5), the positive, negative and zero sequence expressions of the unbalanced current can be obtained, as follows:

${i i}_{d d i i f f f f j j} = = \frac{{i i}_{d d c c}}{33} + + {i i}_{z z j j} = = \frac{{i i}_{d d c c}}{33} + + {i i}_{z z j j}^{+ +} + + {i i}_{z z j j}^{- -} + + {i i}_{z z j j}^{00} - - - - - - ((1919))$

不平衡电流的交流分量，即桥臂环流，需要被抑制为零，由于正、负、零三序电流的存在，若每项分量单独采用PI控制器，则还需要陷波滤波器。考虑到在三相交流系统中，环流的正序分量和负序分量之和为零，因此，对于正序和负序分量可进行统一控制，即对环流直接控制；零序分量影响直流电流波动，对其进行单独控制，所设计的控制器如下：The AC component of the unbalanced current, that is, the bridge arm circulation, needs to be suppressed to zero. Due to the existence of positive, negative, and zero three-sequence currents, if each component uses a separate PI controller, a notch filter is also required. Considering that in the three-phase AC system, the sum of the positive sequence component and the negative sequence component of the circulating current is zero, therefore, the positive sequence and negative sequence components can be uniformly controlled, that is, the circulating current is directly controlled; the zero sequence component affects the DC current fluctuation , to control it separately, the designed controller is as follows:

${u u}_{d d i i f f f f}^{{&PlusMinus; &PlusMinus;}^{* *}} = = P P I I [[((\frac{{i i}_{d d c c}}{33})) - - {i i}_{d d i i f f f f j j}]] - - - - - - ((2020))$

${u u}_{d d i i f f f f}^{00^{* *}} = = P P I I [[{i i}_{d d c c}^{* *} - - {i i}_{d d c c}]] - - - - - - ((21 twenty one))$

${i i}_{d d c c}^{* *} = = \frac{{P P}_{g g}}{{V V}_{d d c c}} - - - - - - ((22 twenty two))$

${u u}_{d d i i f f f f}^{* *} = = {u u}_{d d i i f f f f}^{{&PlusMinus; &PlusMinus;}^{* *}} + + {u u}_{d d i i f f f f}^{00^{* *}} - - - - - - ((23 twenty three))$

相应的控制器框图如图4所示。图4中，表示直流电流参考值，i_dc表示直流电流，PI表示PI控制器，i_pj表示上桥臂电流，i_nj表示下桥臂电流，表示不平衡电压参考值，上标+、-分别表示正序分量和负序分量，0表示零序分量。由式(13)可以看出，电流控制器控制e_{j_ref}，环流控制器控制u_{diffj_ref}，进而控制上、下桥臂电压，整个MMC控制框图如5所示。The block diagram of the corresponding controller is shown in Figure 4. Figure 4, Indicates the DC current reference value, i _dc indicates the DC current, PI indicates the PI controller, i _pj indicates the upper bridge arm current, i _nj indicates the lower bridge arm current, Indicates the unbalanced voltage reference value, the superscripts + and - indicate the positive sequence component and negative sequence component respectively, and 0 indicates the zero sequence component. It can be seen from formula (13) that the current controller controls e _{j_ref} , the circulating current controller controls u _{diffj_ref} , and then controls the upper and lower bridge arm voltages. The entire MMC control block diagram is shown in Figure 5 .

图5中，i_pj表示上桥臂电流，i_nj表示下桥臂电流，表示直流电流参考值，i_dc表示直流电流，P_g、V_dc表示网侧有功功率和直流电压，P^*表示有功功率参考值，Q^*表示无功功率参考值。上标+、-分别表示正序分量和负序分量，下标d、q分别表示旋转坐标下的d轴分量和q轴分量，下标g表示网侧分量，上标*表示参考值。In Figure 5, i _pj represents the current of the upper bridge arm, and i _nj represents the current of the lower bridge arm, Indicates the reference value of DC current, i _dc indicates the DC current, P _g and V _dc indicate the grid-side active power and DC voltage, P ^* indicates the reference value of active power, and Q ^* indicates the reference value of reactive power. The superscripts + and - represent the positive and negative sequence components respectively, the subscripts d and q represent the d-axis component and the q-axis component under the rotating coordinates respectively, the subscript g represents the grid side component, and the superscript * represents the reference value.

在本实施例中，利用用仿真软件MATLAB/Simulink对21电平MMC系统进行数字仿真研究，验证模型和控制策略的有效性,仿真参数，见表1。In this embodiment, the simulation software MATLAB/Simulink is used to carry out digital simulation research on the 21-level MMC system to verify the effectiveness of the model and control strategy. See Table 1 for the simulation parameters.

表1仿真参数Table 1 Simulation parameters

图6、图7给出了系统在平衡电压下的响应。在0.3s时，接入所提出的环流控制器，可以看出，在该控制策略下，变流器输出电流、电压稳定，环流抑制作用明显，直流电流波动明显变小。仿真结果表明所提出的控制策略在平衡电压下适用。Figure 6 and Figure 7 show the response of the system at a balanced voltage. At 0.3s, the proposed circulating current controller is connected. It can be seen that under this control strategy, the output current and voltage of the converter are stable, the circulating current suppression effect is obvious, and the DC current fluctuation is significantly reduced. Simulation results show that the proposed control strategy is applicable under balanced voltage.

图8、图9、图10给出了系统在不平衡电压下的响应，并与传统环流抑制器(CCSC)进行对比。在0.3s时，系统发生单相接地故障，处于不平衡电压环境。仿真结果表明，传统环流抑制器(CCSC)不适用不平衡电压环境下的控制。本文提出的控制方法克服了该缺点，环流控制抑制效果显著，同时有效地抑制了系统有功功率的波动。Figure 8, Figure 9, and Figure 10 show the response of the system under unbalanced voltage, and compare it with the traditional circulating current suppressor (CCSC). At 0.3s, the system has a single-phase ground fault and is in an unbalanced voltage environment. The simulation results show that the traditional circulating current suppressor (CCSC) is not suitable for the control in unbalanced voltage environment. The control method proposed in this paper overcomes this shortcoming, and the circulation control has a significant suppression effect, and at the same time effectively suppresses the fluctuation of the active power of the system.

以上对本发明的具体实施例进行了描述。需要理解的是，本发明并不局限于上述特定实施方式，本领域技术人员可以在权利要求的范围内做出各种变形或修改，这并不影响本发明的实质内容。Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention.

Claims

1. A controller manufacturing method applicable to MMC under unbalanced voltage, is characterized in that, comprises the steps:

Step 1: Control the voltage of the upper bridge arm and the lower bridge arm through the current controller to make the voltage of the upper bridge arm and the lower bridge arm tend to the target reference value;

Step 2: The positive sequence component and the negative sequence component of the AC component of the unbalanced current i _diffj are uniformly controlled by the MMC circulating current controller, and the zero sequence component is controlled separately.

2. the controller manufacturing method applicable to the MMC under unbalanced voltage according to claim 1, is characterized in that, described step 1 comprises the steps:

Step 101: Calculate the voltage of the upper bridge arm and the lower bridge arm of each phase bridge arm as follows:

\{\begin{matrix} {U u}_{p p j j} = = {Σ Σ}_{i i = = 11}^{n no} {v v}_{d d c c i i} {s the s}_{i i} \\ {U u}_{n no j j} = = {Σ Σ}_{i i = = 11}^{n no} {v v}_{d d c c i i} {s the s}_{i i} \end{matrix}

Among them, i={1,2,3...n}, n is the number of sub-modules SM, j={a, b, c}, a, b, c represent the three phases of alternating current, U _pj represents the voltage of the upper bridge arm , U _nj represents the voltage of the lower bridge arm, v _dci is the capacitor voltage of the i-th sub-module, s _i is the switch state of the i-th sub-module; both the upper bridge arm and the lower bridge arm are composed of N sub-modules SM in series, forming an N+ 1 level converter;

Step 102: Assuming that the voltage of the sub-module SM in the MMC is constant, the voltage of each bridge arm in the MMC is equivalent to a controlled voltage source, and a single-phase equivalent circuit is obtained:

The three-phase continuous mathematical model of MMC is expressed as:

{u u}_{v v j j} = = {e e}_{j j} - - \frac{{R R}_{00}}{22} {i i}_{v v j j} - - \frac{{L L}_{00}}{22} \cdot \cdot \frac{{di di}_{v v j j}}{d d t t},, j j = = a a,, b b,, c c

{u u}_{d d i i f f f f j j} = = {L L}_{00} \cdot \cdot \frac{{di di}_{d d i i f f f f j j}}{d d t t} + + {R R}_{00} {i i}_{d d i i f f f f j j} = = \frac{{U u}_{d d c c}}{22} - - \frac{{u u}_{p p j j} + + {u u}_{n no j j}}{22}

in:

{e e}_{j j} = = \frac{{u u}_{n no j j} - - {u u}_{p p j j}}{22}

e _j is defined as the internal electromotive force, which is half of the difference between the upper and lower arm voltages;

{i i}_{d d i i f f f f j j} = = \frac{{i i}_{p p j j} + + {i i}_{n no j j}}{22} = = \frac{{i i}_{d d c c}}{33} + + {i i}_{z z j j}

i _diffj is the internal unbalanced current, Indicates the DC component of the internal unbalanced current, i _dc is the DC current, and i _zj indicates the AC component of the internal unbalanced current, which is the bridge arm circulation current; L ₀ indicates the bridge arm inductance, R ₀ indicates the bridge arm loss equivalent resistance; the controlled voltage source U _pj represents the equivalent upper bridge arm voltage, U _nj represents the equivalent lower bridge arm voltage; i _pj represents the upper bridge arm current, i _nj represents the lower bridge arm current, and i _diffj represents the current flowing through the upper and lower bridge arms The internal unbalanced current of the bridge arm; u _vj and i _vj are the j-phase voltage and current at the output point V of the level converter respectively, and u _diffj is the unbalanced voltage; U _dc represents the DC voltage;

The current i _pj of the upper bridge arm and the current i _nj of the lower bridge arm of phase j are:

\{\begin{matrix} {i i}_{p p j j} = = {i i}_{d d i i f f f f j j} + + \frac{{i i}_{v v j j}}{22} \\ {i i}_{n no j j} = = {i i}_{d d i i f f f f j j} - - \frac{{i i}_{v v j j}}{22} \end{matrix}

Obtain the j-phase upper bridge arm voltage U _pj and lower bridge arm voltage U _nj :

\{\begin{matrix} {U u}_{p p j j} = = \frac{{U u}_{d d c c}}{22} - - {u u}_{d d i i f f f f j j} - - {e e}_{j j} \\ {U u}_{n no j j} = = \frac{{U u}_{d d c c}}{22} - - {u u}_{d d i i f f f f j j} + + {e e}_{j j} \end{matrix}

Step 103: Obtain the target reference value according to the following formula, specifically as follows:

\{\begin{matrix} {U u}_{p p j j__r r e e f f} = = \frac{{U u}_{d d c c}}{22} - - {u u}_{d d i i f f f f j j__r r e e f f} - - {e e}_{j j__r r e e f f} \\ {U u}_{n no j j__r r e e f f} = = \frac{{U u}_{d d c c}}{22} - - {u u}_{d d i i f f f f j j__r r e e f f} + + {e e}_{j j__r r e e f f} \end{matrix}

U _{pj_ref} indicates the reference value of the upper arm voltage, U _{nj_ref} indicates the reference value of the lower arm voltage, u _{diffj_ref} is the reference value of the unbalanced voltage, e _{j_ref} is the reference value of the internal electromotive force, and the subscript _ref indicates the reference value;

Step 104: When under unbalanced voltage, independently control the positive sequence component and negative sequence component of the voltage, specifically, obtain the expression of the positive sequence component and negative sequence component of the voltage, which is recorded as expression A:

\{\begin{matrix} {u u}_{v v j j}^{+ +} = = {e e}_{j j}^{+ +} - - \frac{{R R}_{00}}{22} {i i}_{j j}^{+ +} - - \frac{{L L}_{00}}{22} \cdot \cdot \frac{{di di}_{j j}^{+ +}}{d d t t} \\ {u u}_{v v j j}^{- -} = = {e e}_{j j}^{- -} - - \frac{{R R}_{00}}{22} {i i}_{j j}^{- -} - - \frac{{L L}_{00}}{22} \cdot \cdot \frac{{di di}_{j j}^{- -}}{d d t t} \end{matrix}

in, is the positive sequence component of the j-phase voltage at the output point V of the level converter, is the positive sequence component of the internal electromotive force, is the positive sequence component of phase j current, is the negative sequence component of the j-phase voltage at the output point V of the level converter, is the negative sequence component of the internal electromotive force, is the negative sequence component of phase j current; t is time;

Transform the expression A to the d and q rotation coordinates, and independently control the d-axis and q-axis components through decoupling. The expression B under the rotation coordinates is as follows:

in, are the positive sequence components of the d and q axes of the current, d and q axis positive sequence components of the voltage output by the level converter, are the positive sequence components of the d and q axes of the internal electromotive force, is the negative sequence component of the d and q axes of the current, d, q-axis negative sequence components of the voltage output by the level converter, is the negative sequence component of the d and q axes of the internal electromotive force;

According to the expression B, the corresponding current controller is obtained, and the positive and negative sequence reference values of the d and q axis components of the internal electromotive force reference value e _{j_ref} are obtained by using the PI controller which is:

Among them, ω is the angular frequency of the power grid, L is the line reactance value, R is the line resistance, and PI(·) is the proportional-integral controller.

3. the controller manufacturing method applicable to the MMC under unbalanced voltage according to claim 2, is characterized in that, also comprises the steps:

- When under unbalanced voltage, due to the existence of voltage and current negative sequence components, the active power and reactive power on the grid side of the level converter will produce 2 times the fundamental frequency fluctuation;

Both the active power and reactive power on the grid side of the level converter produce positive and negative sequence components, as follows:

[\begin{matrix} {P P}_{g g 00} \\ {Q Q}_{g g 00} \\ {P P}_{g g sin sin 22} \\ {P P}_{g g cos cos 22} \end{matrix}] = = \frac{33}{22} [\begin{matrix} {V V}_{g g d d}^{+ +} & {V V}_{g g q q}^{+ +} & {V V}_{g g d d}^{- -} & {V V}_{g g q q}^{- -} \\ {V V}_{g g q q}^{+ +} & - - {V V}_{g g d d}^{+ +} & {V V}_{g g q q}^{- -} & - - {V V}_{g g d d}^{- -} \\ {V V}_{g g q q}^{- -} & - - {V V}_{g g d d}^{- -} & - - {V V}_{g g q q}^{+ +} & {V V}_{g g d d}^{+ +} \\ {V V}_{g g d d}^{- -} & {V V}_{g g q q}^{- -} & {V V}_{g g d d}^{+ +} & {V V}_{g g q q}^{+ +} \end{matrix}] [\begin{matrix} {i i}_{d d}^{+ +} \\ {i i}_{q q}^{+ +} \\ {i i}_{d d}^{- -} \\ {i i}_{q q}^{- -} \end{matrix}]

P _g ＝P _g0 +P _gsin2 sin2ω _g t+P _gcos2 cos2ω _g t

Among them, P _g0 represents active power, Q _g0 represents reactive power, Indicates the q-axis component of the positive sequence component of the grid side current, Indicates the q-axis component of the positive sequence component of the grid side current, Indicates the d-axis component of the negative sequence component of the grid side current, Indicates the q-axis component of the negative sequence component of the grid side current, Indicates the d-axis component of the positive sequence component of the grid-side voltage grid-side component, Indicates the d-axis component of the negative sequence component of the grid-side voltage grid-side component, is the q-axis component of the positive sequence component of the grid-side voltage grid-side component, is the q-axis component of the negative-sequence component of the grid-side voltage grid-side component, i represents the grid-side current, V represents the grid-side voltage, the superscripts "+" and "-" represent the positive-sequence component and negative-sequence component respectively, and the subscripts d, q represents the d-axis component and q-axis component under the rotating coordinates, the subscript g represents the grid side component, and the subscript 0 represents the fundamental frequency component; the subscript sin2 sine 2 times the fundamental frequency component and cos2 represents the cosine 2 times the fundamental frequency fluctuation component ; P _g is the total active power, ω is the grid angular frequency; P _g0 is the fundamental frequency component of the total active power; P _gsin2 is the sinusoidal 2 times fundamental frequency fluctuation component of the total active power and P _gcos2 is the total active power Cosine 2 times fundamental frequency fluctuation component;

Suppress the active power 2 times the fundamental frequency fluctuation component to zero, that is, make P _gsin2 = 0, P _gcos2 = 0 through control; P represents active power, and Q represents reactive power; specifically, when the grid side voltage V is vertical to the q-axis For initial condition analysis, then Then the expression of negative sequence component of current:

\{\begin{matrix} {i i}_{d d}^{- -} = = \frac{{V V}_{g g d d}^{- -} {i i}_{q q}^{+ +}}{{V V}_{g g d d}^{+ +}} - - \frac{{V V}_{g g q q}^{- -} {i i}_{d d}^{+ +}}{{V V}_{g g d d}^{+ +}} \\ {i i}_{q q}^{- -} = = - - \frac{{V V}_{g g d d}^{- -} {i i}_{d d}^{+ +}}{{V V}_{g g d d}^{+ +}} - - \frac{{V V}_{g g q q}^{- -} {i i}_{q q}^{+ +}}{{V V}_{g g d d}^{+ +}} \end{matrix}

In the formula, and Calculated from the power reference value and grid-side voltage, specifically,

\{\begin{matrix} {i i}_{d d}^{+ +} = = \frac{22 P P}{33 {V V}_{g g d d}^{+ +}} \\ {i i}_{q q}^{+ +} = = \frac{22 Q Q}{33 {V V}_{g g d d}^{+ +}} \end{matrix} . .

4. the controller manufacturing method applicable to the MMC under unbalanced voltage according to claim 2, is characterized in that, described step 2 comprises the steps:

Step 201: When under unbalanced voltage, the single-phase instantaneous power P _pua of phase a is,

\begin{matrix} {P P}_{p p u u a a} = = \frac{{U u}_{d d c c} {I I}_{d d c c}}{66} [[{k k}^{- -} {m m}^{+ +} cos cos ((22 {ω ω}_{00} t t + + {α α}_{- -} + + {γ γ}_{+ +})) + + {k k}^{+ +} {m m}^{+ +} cos cos ((22 {ω ω}_{00} t t + + {α α}_{+ +} + + {γ γ}_{+ +})) - - \\ 22 {l l}^{- -} sin sin ((22 {ω ω}_{00} t t + + {β β}_{- -})) - - {k k}^{- -} {m m}^{+ +} cos cos (({α α}_{- -} - - {γ γ}_{+ +}))]] \end{matrix}

In the formula, α ₊ , α _- are the phase angles of the positive sequence and negative sequence components of the internal electromotive force respectively; k ⁺ , k ^- are the modulation ratios of positive sequence voltage and negative sequence voltage of the internal electromotive force respectively; l ^- represents the circulating current compensation voltage Ratio to DC voltage; m ⁺ is positive sequence current modulation ratio, γ ₊ is grid side current phase angle of converter; U _dc is DC voltage; ω ₀ is grid initial angular frequency; I _dc is DC current; β _- is 2 times the initial phase angle of the negative sequence component of the fundamental frequency;

{k k}^{&PlusMinus; &PlusMinus;} = = \frac{{E E.}_{a a}^{&PlusMinus; &PlusMinus;}}{\frac{{u u}_{d d c c}}{22}}

{l l}^{- -} = = \frac{{u u}_{d d i i f f f f}^{- -}}{\frac{{u u}_{d d c c}}{22}}

in, Indicates the magnitude of the positive and negative sequence components of the internal electromotive force;

Step 202: The positive, negative and zero three-sequence expressions of the unbalanced current i _diffj are as follows,

{i i}_{d d i i f f f f j j} = = \frac{{I I}_{d d c c}}{33} + + {i i}_{z z j j} = = \frac{{I I}_{d d c c}}{33} + + {i i}_{z z j j}^{+ +} + + {i i}_{z z j j}^{- -} + + {i i}_{z z j j}^{00}

in, is the positive sequence component of the AC component of the internal unbalanced current, is the negative sequence component of the AC component of the internal unbalanced current, Idc is the zero-sequence component of the AC component of the internal unbalanced current, and I _dc represents the DC current.

Step 203: Suppress the AC component of the unbalanced current i _diffj , that is, the bridge arm circulating current to zero; specifically, the positive sequence component and the negative sequence component of the AC component of the unbalanced current i _diffj are controlled uniformly, and the zero sequence component is controlled separately, so that The MMC circulation controller is:

{u u}_{d d i i f f f f}^{&PlusMinus; &PlusMinus; * *} = = P P I I [[((\frac{{I I}_{d d c c}}{33})) - - {i i}_{d d i i f f f f j j}]]

{u u}_{d d i i f f f f}^{00 * *} = = P P I I [[{i i}_{d d c c}^{* *} - - {I I}_{d d c c}]]

{i i}_{d d c c}^{* *} = = \frac{{P P}_{g g}}{{V V}_{d d c c}}

{u u}_{d d i i f f f f}^{* *} = = {u u}_{d d i i f f f f}^{&PlusMinus; &PlusMinus; * *} + + {u u}_{d d i i f f f f}^{00 * *}

Indicates the DC current reference value, I _dc indicates the DC current, PI(·) indicates the PI controller, are the positive sequence component and negative sequence component of the unbalanced voltage reference value, Indicates the unbalanced voltage reference value, Indicates the unbalanced voltage reference value, superscripts + and - indicate positive sequence component and negative sequence component respectively, 0 in the above table indicates zero sequence component, P _g and V _dc respectively indicate grid-side active power and DC voltage.