CN111355388B - MMC bridge arm current control method and system based on two-step model predictive control - Google Patents

MMC bridge arm current control method and system based on two-step model predictive control Download PDF

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CN111355388B
CN111355388B CN202010053134.5A CN202010053134A CN111355388B CN 111355388 B CN111355388 B CN 111355388B CN 202010053134 A CN202010053134 A CN 202010053134A CN 111355388 B CN111355388 B CN 111355388B
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bridge arm
predicted
lower bridge
current
voltage
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CN111355388A (en
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尹项根
王祯
陈卫
赖锦木
许贤昶
尹昕
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Guangzhou Zhiguang Electric Co ltd
Huazhong University of Science and Technology
Changsha University of Science and Technology
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Guangzhou Zhiguang Electric Co ltd
Huazhong University of Science and Technology
Changsha University of Science and Technology
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/483—Converters with outputs that each can have more than two voltages levels
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M7/00—Conversion of ac power input into dc power output; Conversion of dc power input into ac power output
    • H02M7/42—Conversion of dc power input into ac power output without possibility of reversal
    • H02M7/44—Conversion of dc power input into ac power output without possibility of reversal by static converters
    • H02M7/48—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode
    • H02M7/53—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal
    • H02M7/537—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters
    • H02M7/5387—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration
    • H02M7/53871—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration with automatic control of output voltage or current
    • H02M7/53873—Conversion of dc power input into ac power output without possibility of reversal by static converters using discharge tubes with control electrode or semiconductor devices with control electrode using devices of a triode or transistor type requiring continuous application of a control signal using semiconductor devices only, e.g. single switched pulse inverters in a bridge configuration with automatic control of output voltage or current with digital control
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H02M1/0067—Converter structures employing plural converter units, other than for parallel operation of the units on a single load
    • H02M1/0074—Plural converter units whose inputs are connected in series

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Abstract

The invention discloses an MMC bridge arm current control method and system based on two-step model predictive control, which comprises a first step of prediction and a second step of prediction, wherein the first step of prediction comprises calculating a first predicted current, designing a cost function of the first step of prediction, and solving an optimal voltage increment to obtain a bridge arm voltage instruction value of the first step of prediction; and the second step of prediction comprises the steps of calculating a third predicted current based on the first predicted current and the bridge arm voltage command value predicted in the first step, designing a cost function predicted in the second step, solving the optimal voltage increment to obtain the bridge arm voltage command value predicted in the second step, and taking the bridge arm voltage command value predicted in the second step as the output of the bridge arm current controller. The MMC bridge arm current control method based on two-step model predictive control eliminates the inherent one-beat time delay influence of a digital signal processor, does not need to design control parameters, reduces the design complexity of a controller, does not need to design the controller by frequency division when tracking the current instruction value of the bridge arm, and has simple control structure.

Description

MMC bridge arm current control method and system based on two-step model predictive control
Technical Field
The invention belongs to the field of power transmission and distribution of a power system, and particularly relates to an MMC bridge arm current control method and system based on two-step model predictive control.
Background
An MMC (Modular Multilevel Converter) is widely applied to medium and high voltage scenes due to its advantages of modularization, easy expansion, low switching frequency, good harmonic characteristics, and the like. Commonly used MMC controllers include linear controllers based on a classical Control theory and MPC (Model Predictive Control) controllers based on an optimal Control theory.
The control structure of an MMC generally comprises two parts: and the alternating current side controller and the circulating current suppressor are used for respectively realizing alternating current side current control and circulating current suppression. And designing a PI controller and a PR controller based on a classical control theory to realize AC side and circulation control. In fact, all current information, such as ac side current, dc current, and circulating current, is included in the MMC bridge arm current, and ac side current control and circulating current suppression can be simultaneously achieved by controlling the bridge arm current. At present, a method for controlling bridge arm current is provided based on a classical control theory, but a plurality of controllers such as a PI controller and a PR controller are required to be connected in parallel to complete tracking of current instruction values with different frequencies in bridge arm current, the control structure is complex, the number of the controllers is large, and control parameters required to be designed are large.
The model predictive control is used as a time domain control method, and the modeling is convenient; by adopting a rolling optimization strategy instead of global one-time optimization, the method can effectively compensate prediction errors caused by factors such as model mismatch and external disturbance, has certain disturbance resistance, has good dynamic performance, and can accurately track the multi-band composite signal. In the existing MMC control method based on MPC, the calculated amount of a controller is related to the number of cascaded sub-modules, and the calculated amount exponentially increases along with the increase of the number of the cascaded sub-modules.
At present, a digital signal processor is generally adopted in engineering to realize a control algorithm. However, due to the processes of sampling, calculating, and PWM duty cycle updating, there is usually a control period delay in the digital signal processor. The control quantity calculated in the current control period is actually applied to the system in the next control period, which affects the performance of the controller.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide an MMC bridge arm current control method and system based on two-step model predictive control, aiming at solving the problems of large quantity of controllers, complex parameter setting and slow dynamic response of the existing MMC bridge arm current control strategy while eliminating the inherent one-beat delay of a digital signal processor.
In order to achieve the purpose, the invention provides an MMC bridge arm current control method based on two-step model prediction control, which comprises two-step prediction based on an MMC bridge arm model:
the first step of prediction: carrying out differential discretization on mathematical models of an upper bridge arm and a lower bridge arm of the MMC to obtain first predicted currents of the upper bridge arm and the lower bridge arm:
Figure BDA0002371908070000021
wherein p and n represent an upper arm and a lower arm, respectively, and j is a, b, c; i.e. ipj_pre1(k+1|k)、inj_pre1(k +1| k) represents the upper and lower leg first predicted currents,
Figure BDA0002371908070000022
Rfis equivalent resistance L of bridge armfFor bridge arm inductance, TsTo control the period, urefpj(k-1)、urefnj(k-1) is the upper and lower bridge arm voltage instruction value output by the k-1 control period, ipj(k)、inj(k) Representing the current sampling values of the upper and lower bridge arms of the k control period, uoj(k) Representative k control period grid-connected point voltage sampling value Udc(k) Representing a sampling value of the direct-current side bus voltage of the k control period;
designing upper and lower bridge arm cost function J predicted in the first stepp1(k)、Jn1(k) Solving the optimal voltage increment delta u of the upper bridge arm and the lower bridge arm predicted in the first steprefpj(k)、Δurefnj(k)：
Figure BDA0002371908070000023
Figure BDA0002371908070000031
Wherein ipj_pre2(k+1|k)、inj_pre2(k +1| k) represents the second predicted current for the upper and lower arms, irefpj(k+1)、irefnjAnd (k +1) is a command value of the upper and lower bridge arm currents in the k +1 control period.
Adding the predicted optimal voltage increment of the upper and lower bridge arms in the first step with the command values of the voltage of the upper and lower bridge arms output in the last control period to obtain the predicted command values u of the voltage of the upper and lower bridge arms in the first steprefpj(k)、urefnj(k)：
Figure BDA0002371908070000032
And a second step of prediction: first prediction current i based on upper and lower bridge armspj_pre1(k+1|k)、inj_pre1(k +1| k) and the upper and lower arm voltage command values u predicted in the first steprefpj(k)、urefnj(k) And calculating the third predicted current of the upper bridge arm and the lower bridge arm:
Figure BDA0002371908070000033
designing cost function J of upper and lower bridge arms predicted in the second stepp2(k)、Jn2(k) Solving the predicted optimal voltage increment delta u of the upper bridge arm and the lower bridge arm in the second steprefpj(k+1)、Δurefnj(k+1)：
Figure BDA0002371908070000034
Figure BDA0002371908070000035
Wherein ipj_pre2(k+2|k+1)、inj_pre2(k +2| k +1) represents the fourth predicted current for the upper and lower arms, irefpj(k+2)、irefnjAnd (k +2) is the current instruction value of the upper bridge arm and the lower bridge arm in the control period of k + 2.
The predicted optimal voltage increment delta u of the upper bridge arm and the lower bridge arm in the second steprefpj(k+1)、Δurefnj(k +1) and the upper and lower bridge arm voltage command values u predicted in the first steprefpj(k)、urefnj(k) Adding to obtain the upper and lower bridge arm voltage command values u predicted in the second steprefpj(k+1)、urefnj(k+1)：
Figure BDA0002371908070000041
The predicted upper and lower bridge arm voltage instruction values u of the second steprefpj(k+1)、urefnjAnd (k +1) as the upper and lower bridge arm voltage instruction values output by the k control period, inputting the upper and lower bridge arm voltage instruction values into the modulation unit to obtain the output voltage of the MMC bridge arm controlled by the driving signal, thereby realizing bridge arm current control.
Specifically, the second predicted currents of the upper and lower bridge arms are as follows:
Figure BDA0002371908070000042
specifically, the fourth predicted currents of the upper and lower bridge arms are as follows:
Figure BDA0002371908070000043
specifically, the optimal voltage increment delta u of the upper bridge arm and the lower bridge arm predicted in the first steprefpj(k)、Δurefnj(k) The derivative derived from deriving the cost function is 0, as follows:
Figure BDA0002371908070000044
specifically, the second step of predicting the optimal voltage increment delta u of the upper bridge arm and the lower bridge armrefpj(k+1)、Δurefnj(k +1), derived by taking the derivative of the cost function as 0, as follows:
Figure BDA0002371908070000045
specifically, the command value i of the bridge arm current in the k +1 control cyclerefpjInstruction values i of bridge arm currents in control periods of (k +1) and k +2refpj(k +2) all the upper bridge arm current instruction values input in the k control period are taken; instruction value i of bridge arm current in k +1 control periodrefnjInstruction values i of bridge arm currents in (k +1) and k +2 control periodsrefnjAnd (k +2) all take the lower bridge arm current instruction value input in the k control period.
According to another aspect of the present invention, there is provided an MMC bridge arm current control system based on two-step model predictive control, comprising:
the first-step prediction module is used for carrying out differential discretization on mathematical models of an upper bridge arm and a lower bridge arm of the MMC to obtain first predicted currents of the upper bridge arm and the lower bridge arm, solving the predicted optimal voltage increment of the upper bridge arm and the lower bridge arm in the first step based on the predicted cost function of the upper bridge arm and the predicted cost function of the lower bridge arm in the first step, and adding the predicted optimal voltage increment of the upper bridge arm and the predicted optimal voltage increment of the lower bridge arm in the first step with the voltage instruction values of the upper bridge arm and the lower bridge arm output in the last control period to obtain predicted voltage instruction values of the upper bridge arm and the lower bridge arm in the first step;
the second-step prediction module is used for calculating third predicted currents of the upper bridge arm and the lower bridge arm based on the first predicted currents of the upper bridge arm and the lower bridge arm and the voltage command values of the upper bridge arm and the lower bridge arm predicted in the first step, solving the optimal voltage increment of the upper bridge arm and the lower bridge arm predicted in the second step based on the cost function of the upper bridge arm and the lower bridge arm predicted in the second step, and adding the optimal voltage increment of the upper bridge arm and the lower bridge arm predicted in the second step and the voltage command values of the upper bridge arm and the lower bridge arm predicted in the first step to obtain the voltage command values of the upper bridge arm and the lower bridge arm predicted in the second step;
and the control module is used for inputting the upper and lower bridge arm voltage instruction values predicted in the second step into the modulation unit as the upper and lower bridge arm voltage instruction values output in the k control period to obtain the bridge arm voltage of the MMC controlled by the driving signal, so that the control of the bridge arm current is realized.
Through the technical scheme, compared with the prior art, the invention has the following beneficial effects:
1. according to the MMC bridge arm current control method based on two-step model predictive control, the control quantity of the next control period is calculated and output in the current control period, so that the influence of inherent one-beat time delay of a digital signal processor can be eliminated;
2. the MMC bridge arm current control method based on the two-step model predictive control does not need parameter setting, and reduces the complexity of a controller;
3. the MMC bridge arm current control method based on the two-step model prediction control can realize accurate tracking of multi-band composite signals, can realize accurate tracking of MMC bridge arm current instruction values by only designing a two-step model prediction controller, and has the advantages of simple control structure and quick dynamic response;
4. the MMC bridge arm current control method based on the two-step model predictive control does not need to design a controller by frequency division when tracking the bridge arm current instruction value, does not adopt a control structure with a plurality of frequency domain controllers connected in parallel, and reduces the number of the controllers.
Drawings
FIG. 1 is a schematic diagram of a topological structure of an MMC provided by an embodiment of the present invention;
FIG. 2 is a flowchart of an MMC bridge arm current control method based on two-step model prediction according to an embodiment of the present invention;
fig. 3 is a simulated waveform diagram of the network-side voltage and current of the MMC rectifier in a steady state according to the embodiment of the present invention;
fig. 4 is a simulation waveform diagram of the instruction value and the actual value of the bridge arm current on the a phase of the MMC rectifier provided in the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The invention discloses an MMC bridge arm current control method and system based on two-step model predictive control. The first-step prediction module calculates a first prediction current, designs a cost function of the first-step prediction, and solves the optimal voltage control increment of the first-step prediction of the upper bridge arm and the lower bridge arm to obtain the voltage instruction values of the first-step prediction of the upper bridge arm and the lower bridge arm. And the second-step prediction module calculates a third predicted current based on the first predicted current predicted in the first step and the voltage command values predicted in the first step of the upper bridge arm and the lower bridge arm, designs a cost function predicted in the second step, and solves the optimal voltage control increment predicted in the second step of the upper bridge arm and the lower bridge arm to obtain the voltage command values predicted in the second step of the upper bridge arm and the lower bridge arm. And taking the voltage command values predicted in the second step of the upper bridge arm and the lower bridge arm as the output of the bridge arm current controller. The MMC bridge arm current control method based on the two-step model predictive control has the advantages of three aspects: 1) the influence of inherent one-beat time delay of the digital signal processor is eliminated; 2) control parameter design is not needed, and the complexity of controller design is reduced; 3) when the bridge arm current instruction value is tracked, a frequency division design controller is not needed, the number of the controllers is reduced, and the control structure is simple.
In order to illustrate the correctness and the control effect of the MMC bridge arm current control method based on the two-step model predictive control, a simulation model is established, the model is as shown in figure 1, the MMC is a topological structure of the MMC provided by the embodiment of the invention, the MMC is composed of three parallel phase units, each phase unit is divided into an upper bridge arm and a lower bridge arm, and each bridge arm is provided with 2 cascading sub-modules. Rated voltage line voltage effective value U of system power supplys190V; sub-module capacitance Cdc6000 μ F, sub-module capacitor voltage command value 175V; bridge arm inductance parameters: l isarm＝10mH,Rarm＝0.5Ω。
As shown in fig. 2, the control method proposed by the present invention specifically includes two-step prediction. The first step of prediction: carrying out differential discretization on mathematical models of an upper bridge arm and a lower bridge arm of the MMC to obtain first predicted currents of the upper bridge arm and the lower bridge arm:
Figure BDA0002371908070000071
wherein p and n represent an upper arm and a lower arm, respectively, and j is a, b, c; i.e. ipj_pre1(k+1|k)、inj_pre1(k +1| k) represents the upper and lower leg first predicted currents,
Figure BDA0002371908070000072
Rfis equivalent resistance L of bridge armfFor bridge arm inductance, TsTo control the period, urefpj(k-1)、urefnj(k-1) is the upper and lower bridge arm voltage instruction value output by the k-1 control period, ipj(k)、inj(k) Representing the current sampling values of the upper and lower bridge arms of the k control period, uoj(k) Representative k control period grid-connected point voltage sampling value Udc(k) Representing a sampling value of the direct-current side bus voltage of the k control period;
designing upper and lower bridge arm cost function J predicted in the first stepp1(k)、Jn1(k) Solving the optimal voltage increment delta u of the upper bridge arm and the lower bridge arm predicted in the first steprefpj(k)、Δurefnj(k)：
Figure BDA0002371908070000073
Figure BDA0002371908070000081
Wherein ipj_pre2(k+1|k)、inj_pre2(k +1| k) represents the second predicted current for the upper and lower arms, irefpj(k+1)、irefnjAnd (k +1) is a command value of the upper and lower bridge arm currents in the k +1 control period.
Adding the predicted optimal voltage increment of the upper and lower bridge arms in the first step with the command values of the voltage of the upper and lower bridge arms output in the last control period to obtain the predicted command values u of the voltage of the upper and lower bridge arms in the first steprefpj(k)、urefnj(k)：
Figure BDA0002371908070000082
And a second step of prediction: first prediction current i based on upper and lower bridge armspj_pre1(k+1|k)、inj_pre1(k +1| k) and the upper and lower arm voltage command values u predicted in the first steprefpj(k)、urefnj(k) And calculating the third predicted current of the upper bridge arm and the lower bridge arm:
Figure BDA0002371908070000083
designing cost function J of upper and lower bridge arms predicted in the second stepp2(k)、Jn2(k) Solving the predicted optimal voltage increment delta u of the upper bridge arm and the lower bridge arm in the second steprefpj(k+1)、Δurefnj(k+1)：
Figure BDA0002371908070000084
Figure BDA0002371908070000085
Wherein ipj_pre2(k+2|k+1)、inj_pre2(k +2| k +1) represents the fourth predicted current for the upper and lower arms, irefpj(k+2)、irefnjAnd (k +2) is the current instruction value of the upper bridge arm and the lower bridge arm in the control period of k + 2.
The predicted optimal voltage increment delta u of the upper bridge arm and the lower bridge arm in the second steprefpj(k+1)、Δurefnj(k +1) and the upper and lower bridge arm voltage command values u predicted in the first steprefpj(k)、urefnj(k) Adding to obtain the predicted upper and lower bridge arm circuitsPressure command value urefpj(k+1)、urefnj(k+1)：
Figure BDA0002371908070000091
The predicted upper and lower bridge arm voltage instruction values u of the second steprefpj(k+1)、urefnj(k +1) upper and lower arm voltage command values output as a k control period.
Specifically, the second predicted currents of the upper and lower bridge arms are as follows:
Figure BDA0002371908070000092
specifically, the fourth predicted currents of the upper and lower bridge arms are as follows:
Figure BDA0002371908070000093
specifically, the optimal voltage increment delta u of the upper bridge arm and the lower bridge arm predicted in the first steprefpj(k)、Δurefnj(k) The derivative derived from deriving the cost function is 0, as follows:
Figure BDA0002371908070000094
specifically, the second step of predicting the optimal voltage increment delta u of the upper bridge arm and the lower bridge armrefpj(k+1)、Δurefnj(k +1), derived by taking the derivative of the cost function as 0, as follows:
Figure BDA0002371908070000095
specifically, the command value i of the bridge arm current in the k +1 control cyclerefpjInstruction values i of bridge arm currents in control periods of (k +1) and k +2refpj(k +2) upper bridge arm current finger with k control period inputA starting value; instruction value i of bridge arm current in k +1 control periodrefnjInstruction values i of bridge arm currents in (k +1) and k +2 control periodsrefnjAnd (k +2) all take the lower bridge arm current instruction value input in the k control period.
Fig. 3 shows a simulated waveform of the voltage and current on the network side of the MMC rectifier under the steady state condition, the harmonic content of the output current is low, and the THD is only 0.93%.
Fig. 4 is a waveform diagram showing the command value and the actual value of the bridge arm current on the a phase of the MMC rectifier. In the figure, the black solid line is an instruction value, the gray dotted line is an actual value, and the two curves are superposed, so that the provided control method is accurate in tracking and high in control precision. The load is increased in 2.5s, the actual value and the instruction value are changed basically and simultaneously, and the two curves are overlapped, so that the control method provided by the invention has the advantages of quick dynamic response and good dynamic performance.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (3)

1. A MMC bridge arm current control method based on two-step model predictive control is characterized by comprising two-step prediction:
the first step of prediction: carrying out differential discretization on mathematical models of an MMC upper bridge arm and a MMC lower bridge arm to obtain first predicted currents of the upper bridge arm and the lower bridge arm; the first predicted current i of the upper bridge arm and the lower bridge armpj_pre1(k+1|k)、inj_pre1(k +1| k) as follows:
Figure FDA0003074943780000011
wherein p and n represent an upper arm and a lower arm, respectively, and j is a, b, c; i.e. ipj_pre1(k+1|k)、inj_pre1(k +1| k) represents the upper and lower leg first predicted currents,
Figure FDA0003074943780000012
Rfis equivalent resistance L of bridge armfFor bridge arm inductance, TsTo control the period, urefpj(k-1)、urefnj(k-1) is the upper and lower bridge arm voltage instruction value output by the k-1 control period, ipj(k)、inj(k) Representing the current sampling values of the upper and lower bridge arms of the k control period, uoj(k) Representative k control period grid-connected point voltage sampling value Udc(k) Representing a sampling value of the direct-current side bus voltage of the k control period;
based on the upper bridge arm cost function and the lower bridge arm cost function predicted in the first step, solving the optimal voltage increment of the upper bridge arm and the lower bridge arm predicted in the first step; the cost function J of the upper and lower bridge arms predicted in the first stepp1(k)、Jn1(k) The following formula:
Figure FDA0003074943780000013
the first step of predicting the optimal voltage increment delta u of the upper bridge arm and the lower bridge armrefpj(k)、Δurefnj(k) The following formula:
Figure FDA0003074943780000014
wherein ipj_pre2(k+1|k)、inj_pre2(k +1| k) represents the second predicted current for the upper and lower arms, irefpj(k+1)、irefnj(k +1) is a command value of upper and lower bridge arm currents in a k +1 control period;
the second predicted current i of the upper bridge arm and the lower bridge armpj_pre2(k+1|k)、inj_pre2(k +1| k) as follows:
Figure FDA0003074943780000021
wherein ipj_pre1(k+1|k)、inj_pre1(k +1| k) is the first predicted current for the upper and lower arms, Δ urefpj(k)、Δurefnj(k) For the predicted optimal voltage increment of the upper and lower bridge arms in the first step,
Figure FDA0003074943780000022
Lfis bridge arm inductance, TsIs a control period;
adding the predicted optimal voltage increment of the upper and lower bridge arms in the first step with the voltage command values of the upper and lower bridge arms output in the last control period to obtain the predicted voltage command values of the upper and lower bridge arms in the first step;
and a second step of prediction: calculating third predicted currents of the upper bridge arm and the lower bridge arm based on the first predicted currents of the upper bridge arm and the lower bridge arm and the voltage command values of the upper bridge arm and the lower bridge arm predicted in the first step; the third predicted current i of the upper bridge arm and the lower bridge armpj_pre1(k+2|k+1)、inj_pre1(k +2| k +1) as follows:
Figure FDA0003074943780000023
wherein p and n represent an upper arm and a lower arm, respectively, and j is a, b, c; i.e. ipj_pre1(k+2|k+1)、inj_pre1(k +2| k +1) represents the third predicted currents of the upper and lower bridge arms,
Figure FDA0003074943780000024
Rfis equivalent resistance L of bridge armfFor bridge arm inductance, TsTo control the period, urefpj(k)、urefnj(k) Upper and lower bridge arm voltage command value i output for k control periodpj_pre1(k+1|k)、inj_pre1(k +1| k) is the first predicted current for the upper and lower arms, uoj(k) Representative k control period grid-connected point voltage sampling value Udc(k) Representing a sampling value of the direct-current side bus voltage of the k control period;
based on the cost functions of the upper bridge arm and the lower bridge arm predicted in the second step, solving the optimal voltage increment of the upper bridge arm and the lower bridge arm predicted in the second step; the cost function J of the upper bridge arm and the lower bridge arm predicted in the second stepp2(k)、Jn2(k) The following formula:
Figure FDA0003074943780000031
the second step of predicting the optimal voltage increment delta u of the upper bridge arm and the lower bridge armrefpj(k+1)、Δurefnj(k +1) is represented by the following formula:
Figure FDA0003074943780000032
wherein ipj_pre2(k+2|k+1)、inj_pre2(k +2| k +1) represents the fourth predicted current for the upper and lower arms, irefpj(k+2)、irefnj(k +2) is the current instruction value of the upper bridge arm and the lower bridge arm in the k +2 control period;
the fourth predicted current i of the upper and lower bridge armspj_pre2(k+2|k+1)、inj_pre2(k +2| k +1) as follows:
Figure FDA0003074943780000033
wherein ipj_pre1(k+2|k+1)、inj_pre1(k +2| k +1) is the third predicted current of the upper and lower bridge arms, Δ urefpj(k+1)、Δurefnj(k +1) is the predicted optimal voltage increment of the upper bridge arm and the lower bridge arm in the second step,
Figure FDA0003074943780000034
Lfis bridge arm inductance, TsIs a control period;
adding the predicted optimal voltage increment of the upper and lower bridge arms in the second step with the predicted voltage command values of the upper and lower bridge arms in the first step to obtain the predicted voltage command values of the upper and lower bridge arms in the second step;
and inputting the upper and lower bridge arm voltage instruction values predicted in the second step into the modulation unit as the upper and lower bridge arm voltage instruction values output in the current control period to obtain the bridge arm voltage of the MMC controlled by the driving signal, thereby realizing the control of the bridge arm current.
2. The method according to claim 1, wherein the k +1 control period upper arm current command value irefpjBridge arm current instruction values i in (k +1) and k +2 control periodsrefpj(k +2) all the upper bridge arm current instruction values input in the k control period are taken; instruction value i of bridge arm current in k +1 control periodrefnjInstruction values i of bridge arm currents in (k +1) and k +2 control periodsrefnjAnd (k +2) all take the lower bridge arm current instruction value input in the k control period.
3. The MMC bridge arm current control system based on two-step model predictive control is characterized by comprising the following steps of:
the first-step prediction module is used for carrying out differential discretization on mathematical models of an upper bridge arm and a lower bridge arm of the MMC to obtain first predicted currents of the upper bridge arm and the lower bridge arm, solving the predicted optimal voltage increment of the upper bridge arm and the lower bridge arm in the first step based on the predicted cost function of the upper bridge arm and the predicted cost function of the lower bridge arm in the first step, and adding the predicted optimal voltage increment of the upper bridge arm and the predicted optimal voltage increment of the lower bridge arm in the first step with the voltage instruction values of the upper bridge arm and the lower bridge arm output in the last control period to obtain predicted voltage instruction values of the upper bridge arm and the lower bridge arm in the first step; the first step prediction module comprises:
the first prediction current obtaining unit is used for carrying out differential discretization on mathematical models of the upper bridge arm and the lower bridge arm of the MMC to obtain first prediction currents i of the upper bridge arm and the lower bridge armpj_pre1(k+1|k)、inj_pre1(k+1|k)：
Figure FDA0003074943780000041
Wherein p and n represent an upper arm and a lower arm, respectively, and j is a, b, c; i.e. ipj_pre1(k+1|k)、inj_pre1(k +1| k) represents the first predicted current predicted by the first step of the upper and lower legs,
Figure FDA0003074943780000042
Rffor bridge armEquivalent resistance, LfFor bridge arm inductance, TsTo control the period, urefpj(k-1)、urefnj(k-1) is the upper and lower bridge arm voltage instruction value output by the k-1 control period, ipj(k)、inj(k) Representing the current sampling values of the upper and lower bridge arms of the k control period, uoj(k) Representative k control period grid-connected point voltage sampling value Udc(k) Representing a sampling value of the direct-current side bus voltage of the k control period;
a first optimal voltage increment obtaining unit based on the upper and lower bridge arm cost function J predicted in the first stepp1(k)、Jn1(k) Solving the optimal voltage increment delta u of the upper bridge arm and the lower bridge arm predicted in the first steprefpj(k)、Δurefnj(k)：
Figure FDA0003074943780000043
Figure FDA0003074943780000051
Wherein ipj_pre2(k+1|k)、inj_pre2(k +1| k) represents the second predicted current for the upper and lower arms, irefpj(k+1)、irefnj(k +1) is the current instruction value of the upper bridge arm and the lower bridge arm in the control period of k + 1;
a first voltage instruction value obtaining unit, which adds the predicted optimal voltage increment of the upper and lower bridge arms in the first step with the instruction value of the upper and lower bridge arm voltage output in the last control period to obtain the predicted upper and lower bridge arm voltage instruction value u in the first steprefpj(k)、urefnj(k)：
Figure FDA0003074943780000052
The second-step prediction module is used for calculating third predicted currents of the upper bridge arm and the lower bridge arm based on the first predicted currents of the upper bridge arm and the lower bridge arm and the voltage command values of the upper bridge arm and the lower bridge arm predicted in the first step, solving the optimal voltage increment of the upper bridge arm and the lower bridge arm predicted in the second step based on the cost function of the upper bridge arm and the lower bridge arm predicted in the second step, and adding the optimal voltage increment of the upper bridge arm and the lower bridge arm predicted in the second step and the voltage command values of the upper bridge arm and the lower bridge arm predicted in the first step to obtain the voltage command values of the upper bridge arm and the lower bridge arm predicted in the second step; the second-step prediction module comprises:
a third predicted current obtaining unit for obtaining the first predicted current i based on the upper and lower bridge armspj_pre1(k+1|k)、inj_pre1(k +1| k) and the upper and lower arm voltage command values u predicted in the first steprefpj(k)、urefnj(k) Calculating the third predicted current i of the upper and lower bridge armspj_pre1(k+2|k+1)、inj_pre1(k+2|k+1)：
Figure FDA0003074943780000053
Wherein p and n represent an upper arm and a lower arm, respectively, and j is a, b, c; i.e. ipj_pre1(k+2|k+1)、inj_pre1(k +2| k +1) represents the third predicted currents of the upper and lower bridge arms,
Figure FDA0003074943780000054
Rfis equivalent resistance L of bridge armfFor bridge arm inductance, TsTo control the period, urefpj(k)、urefnj(k) Command values of upper and lower bridge arm voltages, i, output for k control periodspj_pre1(k+1|k)、inj_pre1(k +1| k) is the first predicted current for the upper and lower arms, uoj(k) Representative k control period grid-connected point voltage sampling value Udc(k) Representing a sampling value of the direct-current side bus voltage of the k control period;
a second optimal voltage increment obtaining unit based on the upper and lower bridge arm cost function J predicted in the second stepp2(k)、Jn2(k) Solving the predicted optimal voltage increment delta u of the upper bridge arm and the lower bridge arm in the second steprefpj(k+1)、Δurefnj(k+1)：
Figure FDA0003074943780000061
Figure FDA0003074943780000062
Wherein ipj_pre2(k+2|k+1)、inj_pre2(k +2| k +1) represents the fourth predicted current for the upper and lower arms, irefpj(k+2)、irefnj(k +2) is the current instruction value of the upper bridge arm and the lower bridge arm in the k +2 control period;
a second voltage instruction value obtaining unit for obtaining the predicted optimal voltage increment delta u of the upper and lower bridge arms in the second steprefpj(k+1)、Δurefnj(k +1) and the upper and lower bridge arm voltage command values u predicted in the first steprefpj(k)、urefnj(k) Adding to obtain the upper and lower bridge arm voltage command values u predicted in the second steprefpj(k+1)、urefnj(k+1)：
Figure FDA0003074943780000063
And the control module is used for inputting the upper and lower bridge arm voltage instruction values predicted in the second step as the upper and lower bridge arm voltage instruction values output in the current control period into the modulation unit to obtain the bridge arm voltage of the MMC controlled by the driving signal, so that the control of the bridge arm current is realized.
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