CN115459335A - Inverter model prediction control method for improving stability of direct-current micro-grid - Google Patents

Inverter model prediction control method for improving stability of direct-current micro-grid Download PDF

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CN115459335A
CN115459335A CN202211396230.5A CN202211396230A CN115459335A CN 115459335 A CN115459335 A CN 115459335A CN 202211396230 A CN202211396230 A CN 202211396230A CN 115459335 A CN115459335 A CN 115459335A
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冷敏瑞
赵忠涛
周群
印月
刘雪山
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Sichuan University
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Abstract

The invention discloses an inverter model prediction control method for improving the stability of a direct-current micro-grid, and belongs to the technical field of power electronic converter model prediction control. An improved prediction model without a current sensor is provided, an objective function is separated, each part of the objective function is sequentially evaluated, a weighting factor is avoided, and the optimal switching tube state is finally obtained. The control method provided by the invention reduces the size and cost of the system, and the method can effectively stabilize the direct current micro-grid through a simple and economic mode and simultaneously meet the dynamic performance of small voltage overshoot, rapidness and stable response of an alternating current side; the problems that a traditional direct-current micro-grid stabilizing scheme is large in system size, high in hardware cost, low in system control precision and controllability and large in weight factor calculation amount are solved.

Description

Inverter model prediction control method for improving stability of direct-current micro-grid
Technical Field
The invention relates to the technical field of model predictive control of power electronic converters, in particular to an inverter model predictive control method for improving the stability of a direct-current micro-grid.
Background
In recent years, with the concept of 'energy transformation and green development', a micro-grid consisting of distributed power generation equipment and power consumption equipment is developed, has the advantages of simple structure, high efficiency, high reliability and the like, and is widely applied to modern grid-connected autonomous power distribution systems of electric vehicles, high-speed rails, green buildings, future carrier-based aircraft power systems, data centers and the like.
End users of the dc micro-grid mainly use electronic loads, and when these electronic loads are strictly regulated, a negative impedance effect may be generated, which is expressed as a Constant Power Load (CPL), and has a certain influence on the stability of the system. Meanwhile, the interaction between multiple converters in the microgrid can also cause power oscillation and even destabilize the system.
To overcome this instability, stabilization strategies have been discussed in recent years. The traditional method is a passive damping method, and the system damping is increased by connecting an additional RC or RL filter, so that the method has the advantages of simplicity, but the cost and the volume of the system are increased. Another approach is to incorporate various control techniques into the load or converter, called active damping, which is more complex but less costly. The active damping method is divided into linear and nonlinear methods. The linear method adopts a linear feedback closed-loop control transfer function, so small signals are more easily stabilized, while the nonlinear method has robustness and faster dynamic performance in a large range and is mainly suitable for large signal models. With the increasing popularity of nonlinear control converters, the method of adopting nonlinear stabilization micro-grid receives more and more attention.
In the nonlinear method, model Predictive Control (MPC) has an intuitive concept, and can realize fast tracking response, and thus is widely used. An important branch of MPC is finite control set model prediction control (FCS-MPC), and two problems exist in improving the stability of the direct-current microgrid by directly adopting an FCS-MPC algorithm: 1) In order to stabilize the dc micro-grid, a typical stabilization scheme requires sampling of dc side voltage, capacitive three-phase ac voltage (four voltage sensors), dc current, inductive current, and load three-phase ac current (seven current sensors), increasing the system size and hardware cost. In addition, the physical sensor has problems of noise, phase lag, limited lifetime, etc., which reduces the control accuracy and reliability of the system. 2) The design difficulty of multiple weight factors is caused by a multi-objective function containing an alternating current term and a direct current term, which is always an important challenge of a model prediction control strategy.
Disclosure of Invention
The invention aims to provide an inverter model prediction control method for improving the stability of a direct-current microgrid, so as to solve the problems of large system volume, high hardware cost, low system control precision and controllability and large weight factor calculation amount in the traditional direct-current microgrid stabilization scheme, and have better performance. In order to achieve the purpose, the invention adopts the technical scheme that:
an inverter model prediction control method for improving stability of a direct-current microgrid comprises the following steps:
step 1: sampling three-phase capacitor voltage on alternating current side of inverter at k momentv Ca ，v Cb ，v Cc And a DC voltagev dc To AC side three-phase capacitor voltagev Ca ，v Cb Andv Cc performing Clark coordinate transformation to obtainαβThree-phase capacitor voltage under coordinate system
Figure 139669DEST_PATH_IMAGE001
(ii) a Meanwhile, setting a direct current voltage reference value at the moment k
Figure 840908DEST_PATH_IMAGE002
Andαβthree-phase capacitance voltage reference value under coordinate system
Figure 81397DEST_PATH_IMAGE003
；
Step 2: estimating the capacitance current through an alternating-current side capacitance current observer to finish capacitance current prediction;
and step 3: the capacitor voltage is predicted through an alternating current side capacitor voltage prediction module;
and 4, step 4: the direct-current voltage is predicted through a direct-current voltage prediction module;
and 5: avoiding using a weight factor, separating the objective function, sequentially evaluating each part of the separated objective function, and evaluating to obtain an optimal voltage vector;
step 6: and converting the optimal voltage vector into a corresponding pulse signal through a pulse generation module to drive a switching tube.
Further, the specific steps of step 2 are as follows:
introduction of full-order observer to estimate capacitance current value
Figure 500877DEST_PATH_IMAGE004
The observer's discrete-time equation is:
Figure 852224DEST_PATH_IMAGE005
（1）
in the formula (I), the compound is shown in the specification,
Figure 906505DEST_PATH_IMAGE006
and
Figure 317895DEST_PATH_IMAGE007
estimated values of the capacitor voltage at the time k +1 and the time k respectively;
Figure 224671DEST_PATH_IMAGE008
and
Figure 114130DEST_PATH_IMAGE009
capacitance current estimated values at the k +1 moment and the k moment respectively;
Figure 55541DEST_PATH_IMAGE010
the output voltage at the moment k of the inverter;
Figure 637832DEST_PATH_IMAGE011
a three-phase capacitor voltage sampling value at the moment k;
Figure 766325DEST_PATH_IMAGE012
the three-phase capacitance current value at the k moment;
Figure 459475DEST_PATH_IMAGE013
，
Figure 488348DEST_PATH_IMAGE014
，
Figure 241541DEST_PATH_IMAGE015
wherein, the first and the second end of the pipe are connected with each other,Na gain matrix of the observer is used, and phi is a state transition matrix of a state space equation;T s in order to be the sampling period of time,Cis the capacitance value of the AC side;Lis an AC side inductance value; gamma is an intermediate quantity;
estimation value of capacitance current at k +1 moment
Figure 857330DEST_PATH_IMAGE016
Comprises the following steps:
Figure 354170DEST_PATH_IMAGE017
（2）
a two-step prediction strategy is adopted to compensate one-step control delay at the next sampling moment to obtain a capacitance current estimated value at the k +2 moment
Figure 4594DEST_PATH_IMAGE018
Comprises the following steps:
Figure 663109DEST_PATH_IMAGE019
（3）
wherein the content of the first and second substances,
Figure 31773DEST_PATH_IMAGE020
the output voltage of the inverter at time k +1,
Figure 299681DEST_PATH_IMAGE021
and the predicted value is the three-phase capacitor voltage at the moment k + 1.
Further, the specific steps of step 3 are as follows:
obtaining a discrete time model at an alternating current side by a zero-order hold discretization method:
Figure 70191DEST_PATH_IMAGE022
（4）
in the formula (I), the compound is shown in the specification,
Figure 899607DEST_PATH_IMAGE023
the predicted value of the inductance current at the alternating current side at the moment of k +1,
Figure 755567DEST_PATH_IMAGE024
the value of the inductance current at the alternating current side at the moment k;
Figure 594210DEST_PATH_IMAGE025
the alternating current side output current value at the time k;
Figure 688068DEST_PATH_IMAGE026
，
Figure 953965DEST_PATH_IMAGE027
，
Figure DEST_PATH_IMAGE028
，
Figure 264598DEST_PATH_IMAGE029
；
wherein the content of the first and second substances,A、B、A 1 、B 1 、a 11 、a 12 、a 21 、a 22 、b 11 、b 12 、b 21 、b 22 is an intermediate variable, without special meaning, willA 1 AndB 1 can be calculated by substituting into a formulaAAndB，AandBthe formula (b) is taken from the solution of the state space equation; τ is an integral variable representing time;
the predicted value of the capacitor voltage at the time k +1 is:
Figure 100002_DEST_PATH_IMAGE030
（5）
and (3) compensating one-step control delay at the next sampling moment by adopting a two-step prediction strategy to obtain a predicted value of the capacitor voltage at the k +2 moment as follows:
Figure 375773DEST_PATH_IMAGE031
（6）。
further, the specific steps of step 4 are as follows:
considering the differential equation of the inductor current, we derive:
Figure 100002_DEST_PATH_IMAGE032
（7）
in the formula (I), the compound is shown in the specification,C dc is a DC side capacitance value;v dc is a direct current voltage;S a 、S b andS c the switching states of the three bridge arms are respectively;v s outputting a voltage value for the rectifying module;L dc is a dc side inductance value;
Figure 100002_DEST_PATH_IMAGE033
is an alternating side inductive current;tis a differential variable representing time;
Figure 100002_DEST_PATH_IMAGE034
is an inverse matrix of a Clark transformation matrix;
according to the formula and the measurement result, the discrete method is adopted to obtain the predicted value of the direct current voltage at the k +2 moment as follows:
Figure 100002_DEST_PATH_IMAGE035
（8）
in the formula (I), the compound is shown in the specification,
Figure 100002_DEST_PATH_IMAGE036
and
Figure 432460DEST_PATH_IMAGE037
the predicted values of the direct-current voltage at the moment k +2 and the moment k +1 are respectively;
Figure 100002_DEST_PATH_IMAGE038
the value of the dc voltage at time k.
Further, the specific steps of step 5 are as follows:
obtaining direct current voltage, alternating current side capacitor voltage and capacitor current at the moment of k +2 according to prediction estimation;
knowing the expression for each objective function:
Figure 338099DEST_PATH_IMAGE039
（9）
in the formula (I), the compound is shown in the specification,G v 、G i andG dc respectively an alternating current side voltage objective function, an alternating current side current objective function and a direct current side voltage objective function;
Figure 100002_DEST_PATH_IMAGE040
and
Figure 371914DEST_PATH_IMAGE041
of the reference value of the capacitor voltage at the moment k +2αComponent sumβA component;
Figure 100002_DEST_PATH_IMAGE042
and
Figure 21201DEST_PATH_IMAGE043
predicted values of capacitor voltage at the time of k +2αComponent sumβA component;w ref is a reference angular frequency;
Figure DEST_PATH_IMAGE044
and
Figure 322607DEST_PATH_IMAGE045
respectively an alpha component and a beta component of the capacitance current estimation value at the moment of k + 2;
Figure DEST_PATH_IMAGE046
andv dc (k+ 2) are the direct-current voltage reference value and the predicted value at the moment of k +2 respectively;
evaluating each voltage vector by means of a first evaluation moduleG dc OrG v Selecting K objective functionsG dc OrG v A smaller voltage vector;
evaluating the K selected voltage vectors by means of a second evaluation moduleG v OrG dc Selecting M target functions from K voltage vectorsG v OrG dc A smaller voltage vector;
evaluating the M selected voltage vectors by a third evaluation moduleG i Selecting and obtaining an objective function from M voltage vectorsG i And the minimum voltage vector is the optimal voltage vector in the next control period.
Due to the adoption of the technical scheme, the invention has the following technical effects: the invention provides an inverter model prediction stabilization method without any current sensor, which can effectively eliminate the oscillation of direct current voltage and simultaneously keep good dynamic performance; complicated weight factor calculation is avoided, so that the problem of instability when the CPL is connected into the direct-current microgrid is solved; the current sensor is replaced by a full-order observer, so that the measurement of direct current, inductive current and load three-phase alternating current on the direct current side is omitted, and only direct current voltage and capacitance three-phase alternating current voltage on the direct current side need to be measured, so that the size and cost of the system are greatly reduced, and the isolation requirement is met; in addition, the multi-target function is divided into control objects of different parts, and evaluation is carried out in sequence, so that the use of weight factors is avoided.
Drawings
Fig. 1 is a structural diagram of an inverter model predictive control system for improving the stability of a direct-current microgrid according to the present invention.
FIG. 2 is a flow chart of an optimal objective function selection module according to the present invention.
FIG. 3 (a) is the average switching frequency at the time of K change of the comparison result when M is 2,K changed.
FIG. 3 (b) shows the DC voltage error when K is changed as a result of comparison when M is 2,K.
FIG. 3 (c) shows the amplitude error of the AC voltage when K is changed as a result of comparison when M is 2,K.
FIG. 4 (a) is the average switching frequency at which M varies as a result of comparison when K varies as 7,M.
FIG. 4 (b) shows the DC voltage error when M of the comparison result changes when K is 7,M.
FIG. 4 (c) shows the AC voltage amplitude error when M of the comparison result changes when K is 7,M.
FIG. 5 (a) is a drawingG v AndG dc when the evaluation sequence is different, the frequency domain characteristics corresponding to the input impedance of the inverter and the output impedance of the passive rectifier with the LC filter are adopted, namely, the traditional MPC is adopted.
FIG. 5 (b) isG v AndG dc is different, the frequency domain characteristics corresponding to the input impedance of the inverter and the output impedance of the passive rectifier with the LC filter are-K =4, M =2 (m)G cdc ）。
FIG. 5 (c) isG v AndG dc is different, the frequency domain characteristics corresponding to the input impedance of the inverter and the output impedance of the passive rectifier with the LC filter are-K =4, M =2 (m)G dcc ）。
FIG. 5 (d) isG v AndG dc is different, the frequency domain characteristics corresponding to the input impedance of the inverter and the output impedance of the passive rectifier with LC filter-K =6,m =3 (c) ((r))G dcc ）。
Fig. 6 (a) is a comparison of the steady state performance of the LC-VSI based microgrid-the steady state performance without stability control.
FIG. 6 (b) is the comparison result of the steady state performance of the micro-grid based on LC-VSI- -the stabilization method proposed by the present invention (G dcc ) Steady state performance of.
Fig. 6 (c) is a comparison of the steady state performance of the LC-VSI based microgrid-the steady state performance with a conventional MPC.
FIG. 6 (d) is the comparison result of the steady state performance of the micro-grid based on LC-VSI- -the stabilization method proposed by the present invention (G cdc ) Steady state performance of (a).
Fig. 7 (a) is a comparison result of transient performance of the LC-VSI based microgrid-transient performance without stability control.
FIG. 7 (b) is the transient performance comparison result of the micro-grid based on LC-VSI-the stabilization method proposed by the present invention (G dcc ) Transient performance of.
Fig. 7 (c) is a comparison result of transient performance of the LC-VSI based microgrid — transient performance using a conventional MPC.
Fig. 7 (d) is a comparison result of transient performance of the LC-VSI based microgrid — transient performance of the stabilization method () proposed by the present invention.
Detailed Description
The following further describes embodiments of the present invention with reference to the drawings.
As shown in fig. 1, an inverter model prediction system for improving the stability of a dc microgrid comprises a dc microgrid architecture and a control portion, wherein the dc microgrid architecture is composed of a rectification module, an inverter module, a sampling module and a load. The rectifier module converts alternating current into direct current, and the inverter module converts the direct current into required alternating current. The sampling module samples the three-phase voltage of the direct current side voltage and the three-phase voltage of the alternating current side capacitor and transmits sampling information to the control part. The control part consists of an estimation prediction module, a delay unit, an optimal target function selection module and a pulse generation module. The estimation and prediction module estimates an alternating current side three-phase current value and a direct current side current value according to the sampling value, predicts a voltage current value at the next moment, after passing through the delay unit, the estimated voltages at the direct current side and the alternating current side and the estimated capacitance current enter the optimal objective function selection module, the optimal objective function selection module carries out sequential evaluation on objective functions to obtain the optimal switching tube state, and finally, the pulse generation module outputs a pulse waveform according to the optimal switching tube state to drive the switching tube, so that the function of stable control is realized.
As shown in fig. 2, an inverter model predictive control method for improving the stability of a dc microgrid includes the following steps:
step 1: sampling a DC voltage at time k in a main circuit of an inverterv dc And three-phase capacitor voltage of AC sidev Ca 、v Cb Andv Cc and performing Clark coordinate transformation on the three-phase capacitor voltage at the alternating current side to obtainαβThree-phase capacitor voltage under coordinate system
Figure 133569DEST_PATH_IMAGE047
(ii) a Meanwhile, setting a direct current voltage reference value at the moment k
Figure DEST_PATH_IMAGE048
Andαβthree-phase capacitance voltage reference value under coordinate system
Figure 389101DEST_PATH_IMAGE049
；
Step 2: estimating the capacitance current through an alternating current side capacitance current observer to complete the capacitor current prediction, wherein the specific implementation process is as follows:
introduction of full-order observer to estimate capacitance current value
Figure DEST_PATH_IMAGE050
The observer's discrete-time equation is:
Figure 75035DEST_PATH_IMAGE051
（1）
in the formula (I), the compound is shown in the specification,
Figure 529150DEST_PATH_IMAGE006
and
Figure 307750DEST_PATH_IMAGE007
estimated values of the capacitor voltage at the time k +1 and the time k respectively;
Figure 847316DEST_PATH_IMAGE008
and
Figure 369564DEST_PATH_IMAGE009
capacitance current estimated values at the k +1 moment and the k moment respectively;
Figure DEST_PATH_IMAGE052
the output voltage at the moment k of the inverter;
Figure 147027DEST_PATH_IMAGE053
the sampling value of the voltage of the three-phase capacitor at the moment k is obtained;
Figure DEST_PATH_IMAGE054
the three-phase capacitance current value at the k moment;
Figure 63905DEST_PATH_IMAGE055
，
Figure 825188DEST_PATH_IMAGE014
whereinNA gain matrix of the observer is used, and phi is a state transition matrix of a state space equation;T s is a sampling period;Cis the capacitance value of the AC side;Lis an AC side inductance value; Γ is an intermediate quantity and the symbol ^ represents the estimated value.
Then, a characteristic equation of the characteristic equation can be deduced, in order to enable the error to be close to 0 and keep the observer to stably operate, the characteristic value of the characteristic equation is arranged in a unit circle of a z plane, when the characteristic value is closer to the origin, the transient performance of the observer is better, therefore, the characteristic value is selected to be 0, and then the gain matrix N can be obtained as follows:
Figure 151127DEST_PATH_IMAGE015
（2）
therefore, the estimated value of the capacitance current at the time k +1 is:
Figure DEST_PATH_IMAGE056
（3）
and step 3: the capacitor voltage prediction is completed through an alternating current side capacitor voltage prediction module, and the specific implementation process is as follows:
through a zero-order hold (ZOH) discretization method, an alternating-current-side discrete-time model can be obtained:
Figure 517517DEST_PATH_IMAGE057
（4）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE058
the predicted value of the inductance current on the alternating current side at the moment k +1,
Figure 106762DEST_PATH_IMAGE059
the AC side at time kAn inductance current value;
Figure DEST_PATH_IMAGE060
the alternating current side output current value at the time k;
Figure 588296DEST_PATH_IMAGE026
，
Figure 452347DEST_PATH_IMAGE027
，
Figure 469982DEST_PATH_IMAGE028
，
Figure 26865DEST_PATH_IMAGE029
；
wherein the content of the first and second substances,A、B、A 1 、B 1 、a 11 、a 12 、a 21 、a 22 、b 11 、b 12 、b 21 、b 22 is an intermediate variable, without special meaning, willA 1 AndB 1 can be calculated by substituting into a formulaAAndB，AandBis taken from the solution of the state space equation.
And can be derived from the relationship between inductor current, capacitance current and load current:
Figure 762740DEST_PATH_IMAGE061
（5）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE062
in order to output a voltage to the inverter,
Figure 899323DEST_PATH_IMAGE063
is a voltage of the capacitor current, and is,
Figure DEST_PATH_IMAGE064
for the purpose of outputting a current on the alternating-current side,
Figure 738841DEST_PATH_IMAGE065
is the capacitive current.
Since the load current changes slowly in one sampling period and can be assumed to be constant, the inductor current and the load current can be replaced by the capacitor current as a new state variable, and the corresponding model on the ac side can be expressed as:
Figure DEST_PATH_IMAGE066
（6）
for the capacitor voltage, it can be written as follows according to equations (4), (5), (6) and the measurement results:
Figure DEST_PATH_IMAGE067
（7）
in order to compensate the delay, a two-step prediction strategy is adopted, and a capacitance current estimation value and a capacitance voltage estimation value at the moment of k +2 can be obtained as follows:
Figure DEST_PATH_IMAGE068
（8）
Figure DEST_PATH_IMAGE069
（9）
and 4, step 4: the direct-current voltage prediction is completed through a direct-current voltage prediction module, and the specific implementation process is as follows:
for the dc side, from the second derivative of the capacitor voltage and the differential equation of the inductor current, one can deduce:
Figure DEST_PATH_IMAGE070
（10）
wherein, the first and the second end of the pipe are connected with each other,C dc is a DC side capacitance value;S a 、S b andS c respectively the on-off states of three bridge arms, toS a For example, when the upper pipe is communicated with the lower pipe and is closed,S a =1, when the upper pipe is communicated with the lower pipe and closed,S a =0；v s outputting a voltage value for the rectifying module;L dc is the inductance value of the direct current side,
Figure 810833DEST_PATH_IMAGE033
is an alternating side inductive current;tin order to represent a differential variable of time,
Figure 34004DEST_PATH_IMAGE034
is the inverse of the Clark transformation matrix.
According to the formula (6), the formula (10) and the measurement result, the direct current voltage predicted value at the k +2 moment can be obtained by a discretization method:
Figure DEST_PATH_IMAGE071
（11）
and 5: avoiding using a weight factor, separating the objective function, sequentially evaluating each part as shown in fig. 2, and evaluating to obtain an optimal voltage vector, wherein the specific implementation process is as follows:
predicting and estimating according to the step 2, the step 3 and the step 4 to obtain the direct current voltage, the alternating current side capacitor voltage and the capacitor current at the (k + 2) moment;
from (1), the expression of each objective function is:
Figure DEST_PATH_IMAGE072
（12）
in the formula (I), the compound is shown in the specification,G v 、G i andG dc respectively, an objective function of the voltage at the AC sideAn alternating current side current objective function and a direct current side voltage objective function;
Figure DEST_PATH_IMAGE073
and
Figure DEST_PATH_IMAGE074
of the reference value of the capacitor voltage at the moment k +2αComponent sumβA component;
Figure 348180DEST_PATH_IMAGE075
and
Figure 340406DEST_PATH_IMAGE076
predicted values of capacitor voltage at the time of k +2αComponent sumβA component;w ref is a reference angular frequency;
Figure 239092DEST_PATH_IMAGE077
and
Figure 182515DEST_PATH_IMAGE078
capacitance current estimation values at the time k +2αComponent sumβA component;
Figure 192060DEST_PATH_IMAGE079
and
Figure 304372DEST_PATH_IMAGE080
respectively, a direct current voltage reference value and a predicted value at the moment k + 2.
Since the control objective is to ensure stable operation of the system and to ensure good performance on the ac side, therefore,G dc andG v with a priority. In the context of figure 2 of the drawings,G dc orG v Firstly, evaluating and comparing all available switch states of the inverter to obtain K selected objective functionsG dc OrGSmaller voltage vectors, and then deliver to the next control step;
evaluating each voltage vector by a first evaluation moduleIs/are as followsG dc OrG v Selecting K objective functionsG dc OrG v A smaller voltage vector;
evaluating the K selected voltage vectors by means of a second evaluation moduleG v OrG dc Selecting M target functions from K voltage vectorsG v OrG dc A smaller voltage vector;
evaluating the M selected voltage vectors by means of a third evaluation moduleG i Selecting and obtaining an objective function from M voltage vectorsG i And the minimum voltage vector is the optimal voltage vector in the next control period.
The foregoing "G dc OrG v "and"G v OrG dc "means that the first evaluation module can be paired withG dc To evaluate, can alsoG v Performing evaluation if the first evaluation module is rightG dc The second evaluation module is used for evaluationG v The evaluation is carried out by naming the evaluation mode asG dcc (ii) a If the first evaluation module pairG v The second evaluation module is used for evaluationG dc The evaluation is carried out by naming the evaluation asG cdc 。
And 7: a simulation model is built by Matlab/Simulink, and the provided scheme is verified, wherein the specific implementation process is as follows:
different evaluation sequences (G v AndG dc ) And different values of K and M will affect the performance of the system, different evaluation sequences and different values of K and M are selected, and the average switching frequency is adjustedfThe dc voltage error and the ac side capacitor voltage amplitude error are compared as shown in fig. 3 (a) to 3 (c) and fig. 4 (a) to 4 (c), wherein,G dcc the dc portion is first evaluated for the first time,G cdc indicating side current of ACThe capacitance voltage is first evaluated.
FIGS. 3 (a) to 3 (c) are the results of comparison when M is 2,K and when K is 7,M, and when K is 3242, it can be seen from observation that, when the value of K is relatively large,G dc hardly plays a role, and thus oscillation occurs. When both the value of K and the value of M are relatively small,G dc andG v all play a great role. Observation ofG cdc Can find that firstly, the first pairG v When the value of K is smaller, the quality of the voltage on the alternating current side is higher, but the voltage on the direct current side is influenced to a certain extent. When the value of K is large, the smaller the value of M,G dc the larger the effect, the better the voltage performance on the dc side, but the voltage performance on the ac side is affected to some extent. Meanwhile, the larger the value of K, the larger the corresponding calculation amount. The voltage stability on the ac side is balanced against the voltage quality on the dc side, and it is recommended to choose a value of K that is half the total number of switch states.
In order to further investigate the influence of different evaluation sequences and the number of selected switching states on the proposed method for predicting the stability, the input impedance of the voltage-source inverter was measuredZ in And the method is used for researching the stability and transient performance of the system.
The stability of the dc microgrid may be evaluated by the Middlebrook criterion, i.e.
Figure 842801DEST_PATH_IMAGE081
. FIG. 5 (a) to FIG. 5 (d) areG v AndG dc when the evaluation sequence of the inverter is different, the frequency domain characteristic diagram corresponding to the input impedance of the inverter and the output impedance of the passive rectifier with the LC filter is firstly compared with the frequency domain characteristic diagram corresponding to the output impedance of the passive rectifier with the LC filterG v Is evaluated asG cdc Then go right againG dc To make an evaluationG dcc 。
As shown in fig. 5 (a), when the conventional MPC is used,
Figure 306143DEST_PATH_IMAGE082
and
Figure 588220DEST_PATH_IMAGE083
at a frequency of about 395Hz, the phase difference between the output impedance and the input impedance is greater than 180 deg., so that the system is unstable.
As shown in FIG. 5 (b), when the stabilization method proposed by the present invention is adopted, K is 4,M is 2 (C) ((B))G cdc ) At a frequency of 109Hz, the phase difference between the output impedance and the input impedance is 117 °, and the stability margin increases to 53 °.
As shown in FIG. 5 (c), K is 4,M is 2: (C)G dcc ) At a frequency of 83Hz, the phase difference between the output impedance and the input impedance is 109 °, and the stability margin is 53 °.
As shown in FIG. 5 (d), K is 6,M is 3: (A)G dcc ) When the temperature of the water is higher than the set temperature,
Figure 820618DEST_PATH_IMAGE082
and
Figure 795527DEST_PATH_IMAGE083
is approximately 366Hz and 436Hz. At 366Hz, the phase difference between the output impedance and the input impedance is about 181 °, indicating unstable operation of the dc microgrid.
By comparing the above, the control method provided by the invention selects K as 4,M as 2 (C)G dcc ) The stability margin is the largest, and the stability performance is better.
The time domain simulation is adopted to verify the steady-state performance and the transient performance of the stabilization method.
Comparing the steady-state performance of the microgrid based on the LC-VSI, fig. 6 (a) -6 (d) are comparison results of the steady-state performance of the microgrid based on the LC-VSI, and output voltage, output current and direct current voltage under different control methods are respectively compared.
As shown in FIG. 6 (a), when the stabilization control method is not employed, there is a large straight lineThe flow voltage oscillates. As shown in fig. 6 (c), when the conventional MPC control method is used, the dc microgrid can be stabilized compared to when the stability control method is not used. As shown in FIG. 6 (b) and FIG. 6 (d), the stabilizing method proposed by the present invention is adopted, K is 4,M is 2 (C)G dcc ) The steady state performance is better than that of the K of 4,M of 2: (G cdc ）。
Transient performance of the LC-VSI based microgrid is compared. Fig. 7 (a) to 7 (d) are transient performance comparison results of the microgrid based on the LC-VSI, and output voltage, output current, direct current voltage and direct current side current under different control methods are compared respectively. As can be seen from fig. 7 (a) to 7 (d), the overshoot of the stability control method provided by the present invention is 9.5V, the time required to reach the steady state is 0.058s, the overshoot of the conventional MPC is 8.9V, and the time required to reach the steady state is 0.062 s.
In summary, the stabilization method provided by the invention can effectively suppress the oscillation of the dc voltage while ensuring the quality of the ac side voltage, and has the advantages of simple method and low cost.

Claims (5)

1. An inverter model prediction control method for improving the stability of a direct-current microgrid is characterized by comprising the following steps:
step 1: sampling three-phase capacitor voltage on AC side of inverter at k momentv Ca ，v Cb ，v Cc And a DC voltagev dc For three-phase capacitor voltage on the AC sidev Ca ，v Cb Andv Cc performing Clark coordinate transformation to obtainαβThree-phase capacitor voltage under coordinate system
Figure DEST_PATH_IMAGE001
(ii) a Meanwhile, setting a direct current voltage reference value at the moment k
Figure 786434DEST_PATH_IMAGE002
Andαβthree-phase capacitance voltage reference value under coordinate system
Figure DEST_PATH_IMAGE003
；
Step 2: estimating the capacitance current through an alternating-current side capacitance current observer to finish capacitance current prediction;
and step 3: the capacitor voltage is predicted through an alternating current side capacitor voltage prediction module;
and 4, step 4: the direct-current voltage is predicted through a direct-current voltage prediction module;
and 5: avoiding using a weight factor, separating the objective function, sequentially evaluating each part of the separated objective function, and evaluating to obtain an optimal voltage vector;
step 6: and converting the optimal voltage vector into a corresponding pulse signal through a pulse generation module to drive a switching tube.
2. The inverter model prediction control method for improving the stability of the direct current microgrid according to claim 1, characterized in that the specific steps of the step 2 are as follows:
introduction of full-order observer to estimate capacitance current value
Figure 375679DEST_PATH_IMAGE004
The observer's discrete-time equation is:
Figure DEST_PATH_IMAGE005
（1）
in the formula (I), the compound is shown in the specification,
Figure 326055DEST_PATH_IMAGE006
and
Figure DEST_PATH_IMAGE007
are respectively ask+1 time andkan estimate of capacitor voltage at a time;
Figure 658947DEST_PATH_IMAGE008
and
Figure DEST_PATH_IMAGE009
are respectively ask+1 time andka capacitance current estimate at a time;
Figure 145423DEST_PATH_IMAGE010
for an inverterkAn output voltage at a time;
Figure DEST_PATH_IMAGE011
is composed ofkSampling values of three-phase capacitor voltage at a moment;
Figure 639990DEST_PATH_IMAGE012
is composed ofkThe current value of the three-phase capacitor at the moment;
Figure DEST_PATH_IMAGE013
，
Figure 812083DEST_PATH_IMAGE014
，
Figure DEST_PATH_IMAGE015
wherein the content of the first and second substances,Nis the gain matrix of the observer, phi is the state transition matrix of the state space equation;T s is a time period of the sampling, and,Cis the capacitance value of the AC side;Lis an AC side inductance value; gamma is an intermediate quantity;
kestimated value of capacitance current at +1 time
Figure 948666DEST_PATH_IMAGE016
Comprises the following steps:
Figure DEST_PATH_IMAGE017
（2）
a two-step prediction strategy is adopted to compensate the one-step control delay at the next sampling moment to obtainkEstimate of capacitance current at time +2
Figure 991446DEST_PATH_IMAGE018
Comprises the following steps:
Figure DEST_PATH_IMAGE019
（3）
wherein the content of the first and second substances,
Figure 922493DEST_PATH_IMAGE020
is composed ofkThe output voltage of the inverter at time +1,
Figure DEST_PATH_IMAGE021
is composed ofkAnd (4) predicting the three-phase capacitor voltage at the +1 moment.
3. The inverter model predictive control method for improving the stability of the direct-current microgrid according to claim 2, characterized in that the specific steps of the step 3 are as follows:
obtaining a discrete time model at an alternating current side by a zero-order hold discretization method:
Figure 348926DEST_PATH_IMAGE022
（4）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE023
is composed ofkThe predicted value of the inductance current on the alternating current side at the moment +1,
Figure 23621DEST_PATH_IMAGE024
is composed ofkThe current value of the alternating-current side inductor at the moment;
Figure DEST_PATH_IMAGE025
is composed ofkThe alternating current side at the moment outputs a current value;
Figure 717646DEST_PATH_IMAGE026
，
Figure DEST_PATH_IMAGE027
，
Figure 554015DEST_PATH_IMAGE028
，
Figure DEST_PATH_IMAGE029
；
wherein the content of the first and second substances,A、B、A 1 、B 1 、a 11 、a 12 、a 21 、a 22 、b 11 、b 12 、b 21 、b 22 is an intermediate variable, without special meaning, willA 1 AndB 1 can be calculated by substituting into a formulaAAndB，AandBthe formula (b) is taken from the solution of the state space equation; τ is an integral variable representing time;
kthe predicted value of the capacitor voltage at the time +1 is:
Figure DEST_PATH_IMAGE030
（5）
a two-step prediction strategy is adopted to compensate the one-step control delay at the next sampling moment to obtainkAt +2 hourThe predicted value of the capacitor voltage at the moment is as follows:
Figure DEST_PATH_IMAGE031
（6）。
4. the inverter model predictive control method for improving the stability of the direct-current microgrid according to claim 3, characterized in that the specific steps of the step 4 are as follows:
taking into account the differential equation of the inductor current, we derive:
Figure DEST_PATH_IMAGE032
（7）
in the formula (I), the compound is shown in the specification,C dc is the capacitance value of the direct current side;v dc is a direct current voltage;S a 、S b andS c the switching states of the three bridge arms are respectively;v s outputting a voltage value for the rectifying module;L dc is a dc side inductance value;
Figure DEST_PATH_IMAGE033
is an alternating side inductive current;tis a differential variable representing time;
Figure DEST_PATH_IMAGE034
is an inverse matrix of a Clark transformation matrix;
obtaining the result according to the formula and the measurement result by adopting a discretization methodkThe predicted value of the direct-current voltage at the +2 moment is as follows:
Figure DEST_PATH_IMAGE035
（8）
in the formula (I), the compound is shown in the specification,
Figure DEST_PATH_IMAGE036
and
Figure DEST_PATH_IMAGE037
the predicted values of the direct-current voltage at the moment k +2 and the moment k +1 are respectively;
Figure DEST_PATH_IMAGE038
the value of the dc voltage at time k.
5. The inverter model predictive control method for improving the stability of the direct-current microgrid according to claim 4, characterized in that the specific steps of the step 5 are as follows:
derived from predictive estimateskDc voltage, ac side capacitance voltage and capacitance current at +2 time;
knowing the expression for each objective function is:
Figure DEST_PATH_IMAGE039
（9）
in the formula (I), the compound is shown in the specification,G v 、G i andG dc respectively an alternating current side voltage objective function, an alternating current side current objective function and a direct current side voltage objective function;
Figure DEST_PATH_IMAGE040
and
Figure 90913DEST_PATH_IMAGE041
are respectively askOf the reference value of the capacitor voltage at time +2αComponent sumβA component;
Figure DEST_PATH_IMAGE042
and
Figure 38140DEST_PATH_IMAGE043
are respectively askPredicted value of capacitor voltage at +2 timeαComponent sumβA component;w ref is a reference angular frequency;
Figure 884874DEST_PATH_IMAGE044
and
Figure 921837DEST_PATH_IMAGE045
capacitance current estimation values at the time k +2αComponent sumβA component;
Figure 119601DEST_PATH_IMAGE046
andv dc (k+ 2) are eachkA direct-current voltage reference value and a predicted value at +2 moment;
evaluating each voltage vector by means of a first evaluation moduleG dc OrG v Selecting K objective functionsG dc OrG v A smaller voltage vector;
evaluating the K selected voltage vectors by means of a second evaluation moduleG v OrG dc Selecting M target functions from K voltage vectorsG v OrG dc A smaller voltage vector;
evaluating the M selected voltage vectors by means of a third evaluation moduleG i Selecting and obtaining an objective function from M voltage vectorsG i And the minimum voltage vector is the optimal voltage vector in the next control period.
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