CN105743371A - Manufacturing method of MMC controller suitable for unbalanced voltage - Google Patents

Abstract

The invention provides a manufacturing method of an MMC controller suitable for an unbalanced voltage. The method comprises the following steps: (1) enabling an upper bridge arm voltage and a lower bridge arm voltage to tend to a target reference value through control of a current controller on the upper bridge arm voltage and the lower bridge arm voltage; and (2) uniformly controlling a positive-sequence component and a negative-sequence component of an AC component of an unbalanced current idiffj through an MMC circulation controller and independently controlling a zero-sequence component. The designed MMC controller is not complicated in principle and suitable for the conditions of balanced and unbalanced voltages, and the system stability is greatly improved.

Description

Method for manufacturing MMC controller suitable for unbalanced voltage

Technical Field

The invention relates to electrical engineering, in particular to a method for manufacturing a controller suitable for MMC under unbalanced voltage.

Background

The Modular Multilevel Converter (MMC) has a plurality of advantages in the field of high-voltage direct-current transmission and has an important role in transmitting new energy electric energy in the future. The bridge arm of the MMC topology does not adopt a large number of switching devices to be directly connected in series, but adopts a half-bridge submodule cascading mode, does not have the problems of dynamic voltage sharing and the like, and is particularly suitable for high-voltage direct-current power transmission occasions. Due to the fact that the direct current side of a three-phase bridge arm of the MMC is connected with the direct current bus in parallel, the fact that circulating current is inevitably generated between three phases when the MMC works is determined. The circulating current is superposed in the bridge arm current, so that the rated current capacity of the power device is improved, and the system cost is increased; meanwhile, the switching loss is increased, so that the power device generates heat seriously, the service life of the device is influenced, and the circulating current needs to be restrained. The traditional circulation controller adopts double-frequency negative sequence rotating coordinate transformation to decompose three-phase circulation inside the converter into two direct current components, so that circulation components in bridge arm currents are eliminated, but the circulation controller is only suitable for a three-phase balanced alternating current system.

Through the search of the existing literature, an article entitled "modular multilevel predictive control for back-to-back HVDC system" is published in IEEETransactionson Power delivery ", and the article provides a circulation controller based on a model prediction method through a discretization circulation mathematical model, but the method has large calculation amount, and when only N +1 level exists, the switching state has MMCThe control process is complicated.

Disclosure of Invention

In view of the drawbacks of the prior art, it is an object of the present invention to provide a method for manufacturing a controller suitable for an MMC under unbalanced voltage. The method aims at the MMC to carry out detailed mathematical model derivation, specifically analyzes the change conditions of alternating current active power and circulating instantaneous power under unbalanced voltage, designs an inner loop current controller based on positive and negative sequence control, and eliminates double frequency fluctuation of the active power; meanwhile, a circulation controller based on positive, negative and zero sequence circulation control is also designed.

The invention provides a method for manufacturing a controller suitable for MMC under unbalanced voltage, which comprises the following steps:

step 1: controlling the upper bridge arm voltage and the lower bridge arm voltage by a current controller to make the upper bridge arm voltage and the lower bridge arm voltage tend to target reference values;

step 2: unbalanced current i is transmitted through MMC circulating current controller_diffjThe positive sequence component and the negative sequence component of the alternating current component are controlled in a unified mode, and the zero sequence component is controlled independently.

Preferably, the step 1 comprises the steps of:

step 101: calculating the voltages of an upper bridge arm and a lower bridge arm in each phase of bridge arms as follows:

$\left\{\begin{array}{c}{U}_{pj}={\mathrm{\Σ}}_{i=1}^n{v}_{dci}{s}_i\\ U_{nj}={\mathrm{\Σ}}_{i=1}^n{v}_{dci}{s}_i\end{array}\right.$

wherein i ═ {1,2,3 … n }N is the number of submodules SM, j is { a, b, c }, a, b, c represent the three phases of the alternating current, U_pjRepresenting the upper arm voltage, U_njRepresenting lower arm voltage, v_dciFor the ith sub-module capacitor voltage, s_iThe on-off state of the ith sub-module; the upper bridge arm and the lower bridge arm are respectively formed by connecting N submodules SM in series to form an N +1 level converter;

step 102: supposing that SM voltage of a submodule in the MMC is constant, equivalent of each bridge arm voltage in the MMC is a controlled voltage source, and a single-phase equivalent circuit is obtained:

the three-phase continuous mathematical model of MMC is represented as:

$u_{vj}=e_j-\frac{R_0}{2}{i}_{vj}-\frac{L_0}{2}\·\frac{{\mathrm{di}}_{vj}}{dt}----j=a,b,c$

$u_{diffj}=L_0\·\frac{{\mathrm{di}}_{diffj}}{dt}+R_0{i}_{diffj}=\frac{U_{dc}}{2}-\frac{u_{pj}+u_{nj}}{2}$

wherein:

$e_j=\frac{u_{nj}-u_{pj}}{2}$

e_jdefined as the internal electromotive force, the value is half of the difference between the upper and lower bridge arm voltages;

$i_{diffj}=\frac{i_{pj}+i_{nj}}{2}=\frac{i_{dc}}{3}+i_{zj}$

i_diffjin order to achieve an internal unbalance of the current,representing the DC component of the internal unbalance current i_dcIs a direct current i_zjRepresenting the alternating current component of the internal unbalanced current, wherein the alternating current component is the bridge arm circulating current; l is₀Representing bridge arm inductance, R₀Representing bridge arm loss equivalent resistance; controlled voltage source U_pjRepresenting the equivalent upper arm voltage, U_njRepresenting the equivalent lower bridge arm voltage; i.e. i_pjRepresenting upper arm current, i_njRepresenting lower arm current, i_diffjIndicating an internal unbalanced current flowing through the upper and lower bridge arms; u. of_vj、i_vjRespectively j phase voltage, current, u at output point V of the level converter_diffjIs an unbalanced voltage; u shape_dcRepresents a direct voltage;

j-phase upper bridge arm current i_pjLower bridge arm current i_njComprises the following steps:

$\left\{\begin{array}{c}{i}_{pj}=i_{diffj}+\frac{i_{vj}}{2}\\ i_{nj}=i_{diffj}-\frac{i_{vj}}{2}\end{array}\right.$

obtaining j-phase upper bridge arm voltage U_pjLower bridge arm voltage U_nj：

$\left\{\begin{array}{c}{U}_{pj}=\frac{U_{dc}}{2}-u_{diffj}-e_j\\ U_{nj}=\frac{U_{dc}}{2}-u_{diffj}+e_j\end{array}\right.$

Step 103: the target reference value is obtained according to the following formula:

$\left\{\begin{array}{c}{U}_{pj\_ref}=\frac{U_{dc}}{2}-u_{diffj\_ref}-e_{j\_ref}\\ U_{nj\_ref}=\frac{U_{dc}}{2}-u_{diffj\_ref}+e_{j\_ref}\end{array}\right.$

U_{pj_ref}indicating the upper arm voltage by a reference value, U_{nj_ref}Indicating the lower arm voltage by reference value, u_{diffj_ref}For reference value of unbalanced voltage, e_{j_ref}The subscript _ ref is a reference value of the internal electromotive force;

step 104: when under unbalanced voltage, independently controlling the positive sequence component and the negative sequence component of the voltage, specifically, obtaining positive sequence component and negative sequence component expressions of the voltage, and recording the positive sequence component and negative sequence component expressions as an expression A:

$\left\{\begin{array}{c}{u}_{vj}^{+}=e_j^{+}-\frac{R_0}{2}{i}_j^{+}-\frac{L_0}{2}\·\frac{{\mathrm{di}}_j^{+}}{dt}\\ u_{vj}^{-}=e_j^{-}-\frac{R_0}{2}{i}_j^{-}-\frac{L_0}{2}\·\frac{{\mathrm{di}}_j^{-}}{dt}\end{array}\right.$

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

converting the expression A into d and q rotating coordinates, and respectively and independently controlling d-axis and q-axis components through decoupling, wherein an expression B under the rotating coordinates is as follows:

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

obtaining a corresponding current controller according to the expression B, and obtaining an internal electromotive force reference value e by adopting a PI (proportional integral) controller_{j_ref}Positive and negative sequence reference values of d and q axis components ofNamely:

wherein, ω is the power grid angular frequency, L is the line reactance value, R is the line resistance, PI (-) is the proportional-integral controller.

Preferably, the method further comprises the following steps:

when under unbalanced voltage, the active and reactive power on the grid side of the level converter will fluctuate by 2 times the fundamental frequency due to the presence of the negative sequence component of the voltage and current;

the active power and the reactive power of the grid side of the level converter generate positive sequence components and negative sequence components, and the method comprises the following steps:

$\left[\begin{array}{c}{P}_{g0}\\ Q_{g0}\\ P_{g\sin 2}\\ P_{g\cos 2}\end{array}\right]=\frac{3}{2}\left[\begin{array}{cccc}{V}_{gd}^{+}& V_{gq}^{+}& V_{gd}^{+}& V_{gq}^{-}\\ V_{gq}^{+}& -V_{gd}^{+}& V_{gq}^{-}& -V_{gd}^{-}\\ V_{gq}^{-}& -V_{gd}^{-}& -V_{gq}^{+}& V_{gd}^{+}\\ V_{gd}^{-}& V_{gq}^{-}& V_{gd}^{+}& V_{gq}^{+}\end{array}\right]\left[\begin{array}{c}{i}_d^{+}\\ i_q^{+}\\ i_d^{-}\\ i_q^{-}\end{array}\right]$

P_g＝P_g0+P_gsin2sin2ω_gt+P_gcos2cos2ω_gt

wherein, P_g0Representing active power, Q_g0It is meant that the reactive power is,a q-axis component representing the net-side current positive sequence component,a q-axis component representing the net-side current positive sequence component,a d-axis component representing the negative sequence component of the net-side current,a q-axis component representing the negative sequence component of the net-side current,a d-axis component representing the positive sequence component of the net-side voltage net-side component,a d-axis component representing the negative sequence component of the net-side voltage net-side component,is the q-axis component of the positive sequence component of the net-side voltage net-side component,the q-axis component of the negative sequence component of the network side voltage network side component, i represents the network side current, V represents the network side voltage, the superscripts "+", "-" respectively represent the positive sequence component and the negative sequence component, the subscripts d and q respectively represent the d-axis component and the q-axis component under the rotating coordinate, the subscript g represents the network side component, and the subscript 0 represents the fundamental frequency component; subscripts sin2 sine 2 times the fundamental frequency component and cos2 denotes cosine 2 times the fundamental frequency ripple component; p_gOmega is the angular frequency of the power grid for the total active power; p_g0Is the fundamental frequency component of the total active power; p_gsin2The total active power is sine 2 times of the fundamental frequency fluctuation component and P_gcos2The fundamental frequency fluctuation component is cosine 2 times of the total active power;

the fluctuation component of the active power 2 times the fundamental frequency is suppressed to be zero, namely P is controlled to be_gsin2＝0，P_gcos20; p represents active power, Q represents reactive power; specifically, the voltage V on the network side is taken to be vertical to the q axis as the initial condition analysis, thenAnd then the current negative sequence component expression:

$\left\{\begin{array}{c}{i}_d^{-}=\frac{V_{gd}^{-}{i}_q^{+}}{V_{gd}^{+}}-\frac{V_{gq}^{-}{i}_d^{+}}{V_{gd}^{+}}\\ i_q^{-}=-\frac{V_{gd}^{-}{i}_d^{+}}{V_{gd}^{+}}-\frac{V_{gq}^{-}{i}_q^{+}}{V_{gd}^{+}}\end{array}\right.$

in the formula,andcalculated from the power reference value and the network side voltage, specifically,

$\left\{\begin{array}{c}{i}_d^{+}=\frac{2P}{3V_{gd}^{+}}\\ i_q^{+}=\frac{2Q}{3V_{gd}^{+}}\end{array}\right..$

preferably, the step 2 comprises the steps of:

step 201: single phase transient of a-phase when under unbalanced voltagePower P_puaIn order to realize the purpose,

$\begin{array}{c}{P}_{pua}=\frac{U_{dc}{I}_{dc}}{6}\[k^{-}{m}^{+}\cos \left(2{\mathrm{\ω}}_{0}t+\mathrm{\α}\_+{\mathrm{\γ}}_{+}\right)+k^{+}{m}^{+}\cos \left(2{\mathrm{\ω}}_{0}t+{\mathrm{\α}}_{+}+{\mathrm{\γ}}_{+}\right)-\\ 2l^{-}\sin \left(2{\mathrm{\ω}}_{0}t+\mathrm{\β}\_\right)-k^{-}{m}^{+}\cos \left(\mathrm{\α}\_-{\mathrm{\γ}}_{+}\right)\]\end{array}$

in the formula, α₊、α_-Phase angles of positive sequence and negative sequence components of the internal electromotive force respectively; k is a radical of⁺、k^-The modulation ratios of the internal electromotive force positive sequence voltage and the negative sequence voltage are respectively; l^-Indicating a circulating currentCompensating voltageRatio to the dc voltage; m is⁺Is a positive sequence current modulation ratio, gamma₊Representing a current phase angle of a network side of the converter; u shape_dcRepresents a direct voltage; omega₀The initial angular frequency of the power grid; i is_dcβ being direct current_-Is 2 times of the initial phase angle of the fundamental frequency negative sequence component;

$k^{\±}=\frac{E_a^{\±}}{\frac{u_{dc}}{2}}$

$l^{-}=\frac{u_{diff}^{-}}{\frac{u_{dc}}{2}}$

wherein,magnitudes of positive and negative sequence components representing internal electromotive force;

step 202: unbalanced current i_diffjThe positive, negative and zero sequence expressions of the expression are shown as follows,

$i_{diffj}=\frac{I_{dc}}{3}+i_{zj}=\frac{I_{dc}}{3}+i_{zj}^{+}+i_{zj}^{-}+i_{zj}^0$

wherein,being the positive sequence component of the alternating component of the internal unbalance current,being the negative sequence component of the alternating component of the internal unbalance current,zero sequence component of the alternating component of the internal unbalance current, I_dcRepresenting a direct current.

Step 203: will unbalance the current i_diffjThe alternating current component of (a), namely the bridge arm circulating current is suppressed to zero; specifically, the unbalanced currenti_diffjThe positive sequence component and the negative sequence component of the alternating current component are controlled in a unified mode, and the zero sequence component is controlled independently, so that the MMC circulating current controller is as follows:

$u_{diff}^{{\±}^{*}}=PI\[\left(\frac{I_{dc}}{3}\right)-i_{diffj}\]$

$u_{diff}^{0^{*}}=PI\[i_{dc}^{*}-I_{dc}\]$

$i_{dc}^{*}=\frac{P_g}{V_{dc}}$

$u_{diff}^{*}=u_{diff}^{{\±}^{*}}+u_{diff}^{0^{*}}$

denotes the reference value of the direct current, I_dcRepresenting a direct current, PI (-) representing a PI controller,positive and negative sequence components of the unbalanced voltage reference,which is indicative of the reference value of the unbalanced voltage,indicating the reference value of unbalanced voltage, superscript +, -respectively indicating positive sequence component and negative sequence component, table 0 above indicating zero sequence component, P_g、V_dcRespectively representing the active power and the direct current voltage at the network side.

Compared with the prior art, the invention has the following beneficial effects:

1. aiming at the power change of the MMC under the unbalanced voltage, the invention designs the inner loop current controller based on positive and negative sequence control, and eliminates the double frequency fluctuation of active power.

2. The invention provides and designs a circulation controller based on direct control of three-sequence components of positive, negative and zero circulation based on instantaneous power theoretical analysis.

3. The MMC controller designed by the invention has a non-complex principle, is suitable for the conditions of balanced and unbalanced voltages, and greatly improves the stability of the system.

Drawings

Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:

FIG. 1 is a basic topology of an MMC in the present invention;

FIG. 2 is a single-phase equivalent circuit of a three-phase MMC in the present invention;

FIG. 3 is a block diagram of MMC current control in the present invention;

FIG. 4 is a block diagram of MMC loop control in the present invention;

FIG. 5 is a block diagram of the MMC complete control in the present invention;

FIG. 6 is a DC waveform of the balanced AC power grid of the present invention;

FIG. 7 is a circular current waveform of a lower bridge arm of a balanced AC power grid according to the present invention;

FIG. 8 is a graph of the active power waveform at unbalanced voltage in the present invention;

FIG. 9 is a DC waveform of the present invention with unbalanced voltage;

FIG. 10 is a graph showing the bridge arm circulating current waveform under unbalanced voltage in the present invention;

fig. 11 is a schematic structural diagram of a submodule SM in the basic MMC structure of the present invention.

Detailed Description

The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that variations and modifications can be made by persons skilled in the art without departing from the spirit of the invention. All falling within the scope of the present invention.

Step 1: establishing an MMC three-phase continuous mathematical model; the basic structure of the MMC consists of six three-phase bridge arms, each of which is formed by connecting N sub-modules SM (submodules, SMs) in series to form an N +1 level converter, as shown in fig. 1.

Step 101: calculating the voltages of an upper bridge arm and a lower bridge arm in each phase of bridge arm through the direct current capacitor voltage and the switching function as follows:

$\left\{\begin{array}{c}{U}_{pj}={\Σ}_{i=1}^n{v}_{dci}{s}_i\\ U_{nj}={\Σ}_{i=1}^n{v}_{dci}{s}_i\end{array}\right.---\left(1\right)$

where i is {1,2,3 … n }, n is the number of submodules SM, j is { a, b, c }, a, b, c represent three phases of alternating current, in fig. 1, SM represents a submodule, Ua, Ub, Uc represent three-phase alternating voltage, U represents three-phase alternating current voltage, and_pjrepresenting the upper arm voltage, U_njIndicating lower arm voltage, U_dcRepresenting a dc voltage and C a dc capacitance. v. of_dciFor the ith sub-module capacitor voltage, s_iIs the ith sub-module switch state.

Step 102: if the SM voltage is assumed to be constant, the voltage of each bridge arm in the MMC can be equivalent to a controlled voltage source, and then a single-phase equivalent circuit can be obtained;

as shown in FIG. 2, L₀Representing bridge arm inductance, R₀Representing bridge arm loss equivalent resistance; controlled voltage source U_pjRepresenting the equivalent upper arm voltage, U_njRepresenting the equivalent lower bridge arm voltage; i.e. i_pjRepresenting upper arm current, i_njRepresenting lower arm current, i_diffjIndicating an internal unbalanced current flowing through the upper and lower bridge arms;

the j phase voltage and the current at the output point V of the level converter are respectively u phase voltage and u current_vjAnd i_vj. According to kirchhoff's law, the three-phase continuous mathematical model of MMC can be expressed as:

$u_{vj}=e_j-\frac{R_0}{2}{i}_{vj}-\frac{L_0}{2}\·\frac{{\mathrm{di}}_{vj}}{dt},\left(j=a,b,c\right)---\left(2\right)$

$u_{diffj}=L_0\·\frac{{\mathrm{di}}_{diffj}}{dt}+R_0{i}_{diffj}=\frac{U_{dc}}{2}-\frac{u_{pj}+u_{nj}}{2}---\left(3\right)$

wherein:

$e_j=\frac{u_{nj}-u_{pj}}{2}---\left(4\right)$

e_jdefined as the internal electromotive force, having a value of,Half of the difference between the lower arm voltages;

$i_{diffj}=\frac{i_{pj}+i_{nj}}{2}=\frac{i_{dc}}{3}+i_{zj}---\left(5\right)$

i_diffjis an internal unbalanced current, which consists of two parts,representing a direct current component, i_zjRepresenting an alternating current component, i.e. the bridge arm circulating current, u_diffjIs an unbalanced voltage;

meanwhile, as can be seen from fig. 2, the j-phase upper arm current i_pjLower bridge arm current i_njCan be expressed as:

$\left\{\begin{array}{c}{i}_{pj}=i_{diffj}+\frac{i_{vj}}{2}\\ i_{nj}=i_{diffj}-\frac{i_{vj}}{2}\end{array}\right.---\left(6\right)$

similarly, j-phase upper bridge arm voltage U can be obtained_pjLower bridge arm voltage U_nj：

$\left\{\begin{array}{c}{U}_{pj}=\frac{U_{dc}}{2}-u_{diffj}-e_j\\ U_{nj}=\frac{U_{dc}}{2}-u_{diffj}+e_j\end{array}\right.---\left(7\right)$

Step 2: carrying out power analysis and current instruction calculation on the MMC;

under the condition of unbalanced voltage, due to the existence of a voltage and current negative sequence component, the active power and the reactive power of the grid side of the level converter are not constant, but can generate 2 times of fundamental frequency fluctuation;

the active power and the reactive power of the grid side of the level converter generate positive sequence components and negative sequence components, and the method comprises the following steps:

$\left[\begin{array}{c}{P}_{g0}\\ Q_{g0}\\ P_{g\sin 2}\\ P_{g\cos 2}\end{array}\right]=\frac{3}{2}\left[\begin{array}{cccc}{V}_{gd}^{+}& V_{gq}^{+}& V_{gd}^{+}& V_{gq}^{-}\\ V_{gq}^{+}& -V_{gd}^{+}& V_{gq}^{-}& -V_{gd}^{-}\\ V_{gq}^{-}& -V_{gd}^{-}& -V_{gq}^{+}& V_{gd}^{+}\\ V_{gd}^{-}& V_{gq}^{-}& V_{gd}^{+}& V_{gq}^{+}\end{array}\right]\left[\begin{array}{c}{i}_d^{+}\\ i_q^{+}\\ i_d^{-}\\ i_q^{-}\end{array}\right]---\left(8\right)$

P_g＝P_g0+P_gsin2sin2ω_gt+P_gcos2cos2ω_gt(9)

wherein, P_g0Representing active power, Q_g0It is meant that the reactive power is,a q-axis component representing the net-side current positive sequence component,a q-axis component representing the net-side current positive sequence component,a d-axis component representing the negative sequence component of the net-side current,a q-axis component representing the negative sequence component of the net-side current,q-axis component representing positive sequence component of network side voltage network side component, V represents network side voltage, superscripts "+", "" respectively represent positive sequence component and negative sequence component, subscripts d and q respectively represent rotation coordinateThe lower d-axis component and the q-axis component, the subscript g represents the net side component, and the subscript 0 represents the fundamental frequency component; the subscripts sin2 and cos2 represent the 2 times fundamental frequency ripple component; p_gOmega is the angular frequency of the power grid for the total active power; p_g0Is the fundamental frequency component of the total active power; p_gsin2And P_gcos2A fundamental frequency fluctuation component of 2 times of the total active power; it can be seen that the total active power is formed by overlapping an active power fundamental frequency component and an active power 2-fold fundamental frequency fluctuation component. The active power fluctuation can cause the corresponding 2-time fundamental frequency fluctuation of the direct current bus voltage, thereby influencing the electric energy quality.

Therefore, in order to ensure the active power to be constant, the fluctuation component of the fundamental frequency 2 times of the active power must be suppressed to zero, i.e. P is controlled to be constant_gsin2＝0，P_gcos20. The current command in this case is deduced backwards by using the mathematical back-stepping idea. Taking the vertical q-axis of the network side voltage as the initial condition analysis, thenThe current negative sequence component expression can be obtained from equation (8):

$\left\{\begin{array}{c}{i}_d^{-}=\frac{V_{gd}^{-}{i}_q^{+}}{V_{gd}^{+}}-\frac{V_{gq}^{-}{i}_d^{+}}{V_{gd}^{+}}\\ i_q^{-}=-\frac{V_{gd}^{-}{i}_d^{+}}{V_{gd}^{+}}-\frac{V_{gq}^{-}{i}_q^{+}}{V_{gd}^{+}}\end{array}\right.---\left(10\right)$

in the formula,andthe power reference value and the network side voltage are calculated to obtain:

$\left\{\begin{array}{c}{i}_d^{+}=\frac{2P}{3V_{gd}^{+}}\\ i_q^{+}=\frac{2Q}{3V_{gd}^{+}}\end{array}\right.---\left(11\right)$

and step 3: the design of the current controller for MMC control can be understood as that a proper gate driving signal is searched to control a system variable x (t) to enable the system variable x (t) to be as close as possible to a desired reference variable x (t), namely the control of the upper bridge arm voltage and the lower bridge arm voltage. Therefore, the control target reference value is derived from equation (7), specifically as follows:

$\left\{\begin{array}{c}{U}_{pj\_ref}=\frac{U_{dc}}{2}-u_{diffj\_ref}-e_{j\_ref}\\ U_{nj\_ref}=\frac{U_{dc}}{2}-u_{diffj\_ref}+e_{j\_ref}\end{array}\right.---\left(12\right)$

under unbalanced voltage, the positive sequence component and the negative sequence component must be controlled independently, and the positive sequence expression and the negative sequence expression can be obtained by the formula (2):

$\left\{\begin{array}{c}{u}_{vj}^{+}=e_j^{+}-\frac{R_0}{2}{i}_j^{+}-\frac{L_0}{2}\·\frac{{\mathrm{di}}_j^{+}}{dt}\\ u_{vj}^{-}=e_j^{-}-\frac{R_0}{2}{i}_j^{-}-\frac{L_0}{2}\·\frac{{\mathrm{di}}_j^{-}}{dt}\end{array}\right.---\left(13\right)$

converting the formula (13) into d and q rotating coordinates, and independently controlling the d-axis component and the q-axis component through decoupling respectively, wherein the expression under the rotating coordinates is as follows:

the corresponding current controller can be designed by the formula (14), and the PI controller is adopted to obtain the e of the internal electromotive force_{j_ref}D,Positive and negative sequence reference values for q-axis componentAndnamely:

FIG. 3 is a block diagram of a designed MMC current control.

In fig. 3, MMC is a modular multilevel converter, C denotes dc capacitance, R denotes line resistance, L denotes line reactance, P^*Representing the active power reference, Q^*Representing a reactive power reference value. The superscript denotes a reference value, θ denotes a grid voltage phase angle, ω denotes a grid angular frequency, and PI denotes a PI controller.

And 4, step 4: the MMC circulating current controller is designed, under the unbalanced voltage, the single-phase instantaneous power is shown in a formula (16), taking an A phase as an example:

$\begin{array}{c}{P}_{pua}=\frac{U_{dc}{I}_{dc}}{6}\[k^{-}{m}^{+}\cos \left(2{\mathrm{\ω}}_{0}t+\mathrm{\α}\_+{\mathrm{\γ}}_{+}\right)+k^{+}{m}^{+}\cos \left(2{\mathrm{\ω}}_{0}t+{\mathrm{\α}}_{+}+{\mathrm{\γ}}_{+}\right)-\\ 2l^{-}-sin(2{\mathrm{\ω}}_{0}t+\mathrm{\β}\_)-k^{-}{m}^{+}cos(\mathrm{\α}\_-{\mathrm{\γ}}_{+})\]\end{array}---\left(16\right)$

in the formula, α₊、α_-Phase angles representing positive and negative sequence components of the internal electromotive force; k is a radical of⁺、k^-The modulation ratio of the internal electromotive force positive sequence voltage and the negative sequence voltage is represented, and is specifically shown in a formula (17); l^-Indicating the circulating current compensation voltageThe ratio of the voltage to the DC voltage is specifically calculated as shown in formula (18); m is⁺Indicating the positive sequence current modulation ratio, gamma₊Representing the current phase angle of the grid side of the converter. It can be seen that under unbalanced voltage, the single-phase instantaneous power contains twice fundamental frequency zero sequence component (first term), twice fundamental frequency positive and negative sequence components (middle two terms) and direct current component (last term). The zero sequence component can cause the direct current voltage and the direct current to fluctuate, the double fundamental frequency positive and negative sequence components are directly related to the MMC circulating current, and the direct current components are mutually differed by 120 degrees in each phase, so that the direct current components are automatically eliminated.

$k^{\±}=\frac{E_a^{\±}}{\frac{u_{dc}}{2}}---\left(17\right)$

$l^{-}=\frac{u_{diff}^{-}}{\frac{u_{dc}}{2}}---\left(18\right)$

In the formula (17), the compound represented by the formula (I),representing the magnitude of the positive and negative sequence components of the internal electromotive force. By rewriting the equation (5), three-order expressions of positive, negative, and zero of the unbalanced current can be obtained as follows:

$i_{diffj}=\frac{i_{dc}}{3}+i_{zj}=\frac{i_{dc}}{3}+i_{zj}^{+}+i_{zj}^{-}+i_{zj}^0---\left(19\right)$

the alternating component of the unbalanced current, namely the bridge arm circulating current, needs to be suppressed to zero, and due to the existence of the three-sequence currents of positive, negative and zero, if each component independently adopts a PI controller, a notch filter is also needed. Considering that the sum of the positive sequence component and the negative sequence component of the circulating current is zero in the three-phase alternating current system, the positive sequence component and the negative sequence component can be uniformly controlled, namely the circulating current is directly controlled; the zero sequence component influences the fluctuation of the direct current and controls the direct current independently, and the designed controller comprises the following components:

$u_{diff}^{{\±}^{*}}=PI\[\left(\frac{i_{dc}}{3}\right)-i_{diffj}\]---\left(20\right)$

$u_{diff}^{0^{*}}=PI\[i_{dc}^{*}-i_{dc}\]---\left(21\right)$

$i_{dc}^{*}=\frac{P_g}{V_{dc}}---\left(22\right)$

$u_{diff}^{*}=u_{diff}^{{\±}^{*}}+u_{diff}^{0^{*}}---\left(23\right)$

a corresponding controller block diagram is shown in fig. 4. In the context of figure 4, it is shown,representing a DC current reference value, i_dcRepresenting direct current, PI representing PI controller, i_pjRepresenting upper arm current, i_njThe lower leg current is shown as being,and the reference value of the unbalanced voltage is represented, the superscript plus and minus respectively represent a positive sequence component and a negative sequence component, and 0 represents a zero sequence component. As can be seen from equation (13), the current controller controls e_{j_ref}Control u of circulation controller_{diffj_ref}And further controlling the voltage of the upper and lower bridge arms, wherein the whole MMC control block diagram is shown as 5.

In FIG. 5, i_pjRepresenting upper arm current, i_njThe lower leg current is shown as being,representing a DC current reference value, i_dcRepresenting direct current, P_g、V_dcRepresenting net side active power and DC voltage, P^*Representing the active power reference, Q^*Representing a reactive power reference value. Superscripts +, -represent the positive and negative sequence components, respectively, and subscripts d, q represent d in the rotation coordinate, respectivelyAxis component and q-axis component, subscript g denotes the web-side component, and superscript denotes the reference value.

In this embodiment, a 21-level MMC system is subjected to digital simulation study by using simulation software MATLAB/Simulink, and the validity and simulation parameters of the model and the control strategy are verified, as shown in table 1.

TABLE 1 simulation parameters

Fig. 6 and 7 show the response of the system under the equilibrium voltage. When the voltage is 0.3s, the proposed circulation controller is connected, and the control strategy shows that the current transformer has stable output current and voltage, obvious circulation restraining effect and obviously reduced direct current fluctuation. Simulation results show that the proposed control strategy is applicable at equilibrium voltages.

Fig. 8, 9, 10 show the response of the system at unbalanced voltages, compared to a conventional Circulating Current Suppressor (CCSC). At 0.3s, the system has a single-phase earth fault and is in an unbalanced voltage environment. Simulation results show that the traditional Circulating Current Suppressor (CCSC) is not suitable for control under the unbalanced voltage environment. The control method provided by the invention overcomes the defect, has a remarkable effect of inhibiting the circulation control, and effectively inhibits the fluctuation of the active power of the system.

The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes and modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention.

Claims (4)

1. A method of manufacturing a controller suitable for use in an MMC under unbalanced voltage, comprising the steps of:

step 1: controlling the upper bridge arm voltage and the lower bridge arm voltage by a current controller to make the upper bridge arm voltage and the lower bridge arm voltage tend to target reference values;

step 2: unbalanced current i is transmitted through MMC circulating current controller_diffjThe positive sequence component and the negative sequence component of the alternating current component are controlled in a unified mode, and the zero sequence component is controlled independently.

2. The method for manufacturing a controller for an MMC under unbalance voltage according to claim 1, wherein the step 1 comprises the steps of:

step 101: calculating the voltages of an upper bridge arm and a lower bridge arm in each phase of bridge arms as follows:

$\left\{\begin{array}{c}{U}_{pj}={\mathrm{\Σ}}_{i=1}^n{v}_{dci}{s}_i\\ U_{nj}={\mathrm{\Σ}}_{i=1}^n{v}_{dci}{s}_i\end{array}\right.$

wherein, i ═ 1,2,3 … n, n is the number of submodules SM, j ═ a, b, c, a, b, c represent the three phases of the alternating current, U_pjRepresenting the upper arm voltage, U_njRepresenting lower arm voltage, v_dciFor the ith sub-module capacitor voltage, s_iThe on-off state of the ith sub-module; the upper bridge arm and the lower bridge arm are respectively formed by connecting N submodules SM in series to form an N +1 level converter;

step 102: supposing that SM voltage of a submodule in the MMC is constant, equivalent of each bridge arm voltage in the MMC is a controlled voltage source, and a single-phase equivalent circuit is obtained:

the three-phase continuous mathematical model of MMC is represented as:

$u_{vj}=e_j-\frac{R_0}{2}{i}_{vj}-\frac{L_0}{2}\·\frac{{\mathrm{di}}_{vj}}{dt},j=a,b,c$

$u_{diffj}=L_0\·\frac{{\mathrm{di}}_{diffj}}{dt}+R_0{i}_{diffj}=\frac{U_{dc}}{2}-\frac{u_{pj}+u_{nj}}{2}$

wherein:

$e_j=\frac{u_{nj}-u_{pj}}{2}$

e_jdefined as the internal electromotive force, the value is half of the difference between the upper and lower bridge arm voltages;

$i_{diffj}=\frac{i_{pj}+i_{nj}}{2}=\frac{i_{dc}}{3}+i_{zj}$

i_diffjin order to achieve an internal unbalance of the current,representing the DC component of the internal unbalance current i_dcIs a direct current i_zjRepresenting the alternating current component of the internal unbalanced current, wherein the alternating current component is the bridge arm circulating current; l is₀Representing bridge arm inductance, R₀Representing bridge arm loss equivalent resistance; controlled voltage source U_pjRepresenting the equivalent upper arm voltage, U_njRepresenting the equivalent lower bridge arm voltage; i.e. i_pjRepresenting upper arm current, i_njRepresenting lower arm current, i_diffjIndicating an internal unbalanced current flowing through the upper and lower bridge arms; u. of_vj、i_vjRespectively j phase voltage, current, u at output point V of the level converter_diffjIs an unbalanced voltage; u shape_dcRepresents a direct voltage;

j-phase upper bridge arm current i_pjLower bridge arm current i_njComprises the following steps:

$\left\{\begin{array}{c}{i}_{pj}=i_{diffj}+\frac{i_{vj}}{2}\\ i_{nj}=i_{diffj}-\frac{i_{vj}}{2}\end{array}\right.$

obtaining j-phase upper bridge arm voltage U_pjLower bridge arm voltage U_nj：

$\left\{\begin{array}{c}{U}_{pj}=\frac{U_{dc}}{2}-u_{diffj}-e_j\\ U_{nj}=\frac{U_{dc}}{2}-u_{diffj}+e_j\end{array}\right.$

Step 103: the target reference value is obtained according to the following formula:

$\left\{\begin{array}{c}{U}_{pj\_ref}=\frac{U_{dc}}{2}-u_{diffj\_ref}-e_{j\_ref}\\ U_{nj\_ref}=\frac{U_{dc}}{2}-u_{diffj\_ref}+e_{j\_ref}\end{array}\right.$

U_{pj_ref}indicating the upper arm voltage by a reference value, U_{nj_ref}Indicating the lower arm voltage by reference value, u_{diffj_ref}For reference value of unbalanced voltage, e_{j_ref}The subscript _ ref is a reference value of the internal electromotive force;

step 104: when under unbalanced voltage, independently controlling the positive sequence component and the negative sequence component of the voltage, specifically, obtaining positive sequence component and negative sequence component expressions of the voltage, and recording the positive sequence component and negative sequence component expressions as an expression A:

$\left\{\begin{array}{c}{u}_{vj}^{+}=e_j^{+}-\frac{R_0}{2}{i}_j^{+}-\frac{L_0}{2}\·\frac{{\mathrm{di}}_j^{+}}{dt}\\ u_{vj}^{-}=e_j^{-}-\frac{R_0}{2}{i}_j^{-}-\frac{L_0}{2}\·\frac{{\mathrm{di}}_j^{-}}{dt}\end{array}\right.$

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

converting the expression A into d and q rotating coordinates, and respectively and independently controlling d-axis and q-axis components through decoupling, wherein an expression B under the rotating coordinates is as follows:

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

obtaining a corresponding current controller according to the expression B, and obtaining an internal electromotive force reference value e by adopting a PI (proportional integral) controller_{j_ref}Positive and negative sequence reference values of d and q axis components ofNamely:

wherein, ω is the power grid angular frequency, L is the line reactance value, R is the line resistance, PI (-) is the proportional-integral controller.

3. The method of manufacturing a controller for an MMC adapted for unbalanced voltage of claim 2, further comprising the steps of:

when under unbalanced voltage, the active and reactive power on the grid side of the level converter will fluctuate by 2 times the fundamental frequency due to the presence of the negative sequence component of the voltage and current;

the active power and the reactive power of the grid side of the level converter generate positive sequence components and negative sequence components, and the method comprises the following steps:

$\left[\begin{array}{c}{P}_{g0}\\ Q_{g0}\\ P_{g\sin 2}\\ P_{g\cos 2}\end{array}\right]=\frac{3}{2}\left[\begin{array}{cccc}{V}_{gd}^{+}& V_{gq}^{+}& V_{gd}^{-}& V_{gq}^{-}\\ V_{gq}^{+}& -V_{gd}^{+}& V_{gq}^{-}& -V_{gd}^{-}\\ V_{gq}^{-}& -V_{gd}^{-}& -V_{gq}^{+}& V_{gd}^{+}\\ V_{gd}^{-}& V_{gq}^{-}& V_{gd}^{+}& V_{gq}^{+}\end{array}\right]\left[\begin{array}{c}{i}_d^{+}\\ i_q^{+}\\ i_d^{-}\\ i_q^{-}\end{array}\right]$

P_g＝P_g0+P_gsin2sin2ω_gt+P_gcos2cos2ω_gt

wherein, P_g0Representing active power, Q_g0It is meant that the reactive power is,a q-axis component representing the net-side current positive sequence component,a q-axis component representing the net-side current positive sequence component,a d-axis component representing the negative sequence component of the net-side current,a q-axis component representing the negative sequence component of the net-side current,representing positive sequence components of net-side voltage net-side componentsThe component of the d-axis is,a d-axis component representing the negative sequence component of the net-side voltage net-side component,is the q-axis component of the positive sequence component of the net-side voltage net-side component,the q-axis component of the negative sequence component of the network side voltage network side component, i represents the network side current, V represents the network side voltage, the superscripts "+", "-" respectively represent the positive sequence component and the negative sequence component, the subscripts d and q respectively represent the d-axis component and the q-axis component under the rotating coordinate, the subscript g represents the network side component, and the subscript 0 represents the fundamental frequency component; subscripts sin2 sine 2 times the fundamental frequency component and cos2 denotes cosine 2 times the fundamental frequency ripple component; p_gOmega is the angular frequency of the power grid for the total active power; p_g0Is the fundamental frequency component of the total active power; p_gsin2The total active power is sine 2 times of the fundamental frequency fluctuation component and P_gcos2The fundamental frequency fluctuation component is cosine 2 times of the total active power;

the fluctuation component of the active power 2 times the fundamental frequency is suppressed to be zero, namely P is controlled to be_gsin2＝0，P_gcos20; p represents active power, Q represents reactive power; specifically, the voltage V on the network side is taken to be vertical to the q axis as the initial condition analysis, thenAnd then the current negative sequence component expression:

$\left\{\begin{array}{c}{i}_d^{-}=\frac{V_{gd}^{-}{i}_q^{+}}{V_{gd}^{+}}-\frac{V_{gq}^{-}{i}_d^{+}}{V_{gd}^{+}}\\ i_q^{-}=-\frac{V_{gd}^{-}{i}_d^{+}}{V_{gd}^{+}}-\frac{V_{gq}^{-}{i}_q^{+}}{V_{gd}^{+}}\end{array}\right.$

in the formula,andcalculated from the power reference value and the network side voltage, specifically,

$\left\{\begin{array}{c}{i}_d^{+}=\frac{2P}{3V_{gd}^{+}}\\ i_q^{+}=\frac{2Q}{3V_{gd}^{+}}\end{array}\right..$

4. the method for manufacturing a controller for an MMC under unbalance voltage according to claim 2, wherein the step 2 comprises the steps of:

step 201: when under unbalanced voltage, single-phase instantaneous power P of a phase_puaIn order to realize the purpose,

$\begin{array}{c}{P}_{pua}=\frac{U_{dc}{I}_{dc}}{6}\[k^{-}{m}^{+}\cos (2{\mathrm{\ω}}_{0}t+{\mathrm{\α}}_{-}+{\mathrm{\γ}}_{+})+k^{+}{m}^{+}\cos (2{\mathrm{\ω}}_{0}t+{\mathrm{\α}}_{+}+{\mathrm{\γ}}_{+})-\\ 2l^{-}\sin (2{\mathrm{\ω}}_{0}t+{\mathrm{\β}}_{-})-k^{-}{m}^{+}\cos ({\mathrm{\α}}_{-}-{\mathrm{\γ}}_{+})\]\end{array}$

in the formula, α₊、α_-Phase angles of positive sequence and negative sequence components of the internal electromotive force respectively; k is a radical of⁺、k^-The modulation ratios of the internal electromotive force positive sequence voltage and the negative sequence voltage are respectively; l^-Indicating the circulating current compensation voltageRatio to the dc voltage; m is⁺Is a positive sequence current modulation ratio, gamma₊Representing a current phase angle of a network side of the converter; u shape_dcRepresents a direct voltage; omega₀The initial angular frequency of the power grid; i is_dcβ being direct current_-Is 2 times of the initial phase angle of the fundamental frequency negative sequence component;

$k^{\±}=\frac{E_a^{\±}}{\frac{u_{dc}}{2}}$

$l^{-}=\frac{u_{diff}^{-}}{\frac{u_{dc}}{2}}$

wherein,magnitudes of positive and negative sequence components representing internal electromotive force;

step 202: unbalanced current i_diffjThe positive, negative and zero sequence expressions of the expression are shown as follows,

$i_{diffj}=\frac{I_{dc}}{3}+i_{zj}=\frac{I_{dc}}{3}+i_{zj}^{+}+i_{zj}^{-}+i_{zj}^0$

wherein,being the positive sequence component of the alternating component of the internal unbalance current,being the negative sequence component of the alternating component of the internal unbalance current,zero sequence component of the alternating component of the internal unbalance current, I_dcRepresenting a direct current.

Step 203: will unbalance the current i_diffjThe alternating current component of (a), namely the bridge arm circulating current is suppressed to zero; specifically, the unbalanced current i_diffjThe positive sequence component and the negative sequence component of the alternating current component are controlled in a unified mode, and the zero sequence component is controlled independently, so that the MMC circulating current controller is as follows:

$u_{diff}^{\±*}=PI\[\left(\frac{I_{dc}}{3}\right)-i_{diffj}\]$

$u_{diff}^{0*}=PI\[i_{dc}^{*}-I_{dc}\]$

$i_{dc}^{*}=\frac{P_g}{V_{dc}}$

$u_{diff}^{*}=u_{diff}^{\±*}+u_{diff}^{0*}$

denotes the reference value of the direct current, I_dcRepresenting a direct current, PI (-) representing a PI controller,positive and negative sequence components of the unbalanced voltage reference,which is indicative of the reference value of the unbalanced voltage,indicating the reference value of unbalanced voltage, superscript +, -respectively indicating positive sequence component and negative sequence component, table 0 above indicating zero sequence component, P_g、V_dcRespectively representing the active power and the direct current voltage at the network side.