CN115241912A - Model mismatch compensation method for model predictive control three-phase grid-connected inverter - Google Patents
Model mismatch compensation method for model predictive control three-phase grid-connected inverter Download PDFInfo
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- H—ELECTRICITY
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- 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
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Abstract
The invention provides a model mismatch compensation method for a model predictive control three-phase grid-connected inverter. It is then observed by the model mismatch module. And finally, compensating the observed disturbance to a predicted inverter output voltage initial value, and realizing the control of the inverter through a model prediction controller. The method solves the problem that the performance of the three-phase grid-connected inverter based on model predictive control is reduced due to inaccurate control of the mathematical model of the controlled object on the premise of not improving the complexity of a predictive model. The control efficiency and quality of the MPC are effectively improved, and the reliability of the three-phase grid-connected inverter is improved.
Description
Technical Field
The invention relates to the field of predictive control of distributed power generation systems, in particular to a model mismatch compensation method for a three-phase grid-connected inverter based on model predictive control.
Background
With the increasing computing power of microprocessors, model Predictive Control (MPC) is widely researched in the field of power electronic transformation, so that distributed power generation systems, alternating current motor control, uninterruptible power supplies and the like have good static and dynamic performances. The MPC can decouple the control loops which are mutually dependent, so that the dynamic response of the system is improved, and the response speed of the three-phase grid-connected inverter based on the MPC algorithm is much higher than that of the three-phase grid-connected inverter based on the MPC algorithm by adopting a classical controller.
Three-phase grid-connected inverters generally employ LCL filtering. Compared with the L filter, the LCL filter has the characteristic of a third-order low-pass filter, and the total inductance value of the LCL filter is smaller than the single inductance value of the L filter under the same harmonic standard and lower switching frequency.
However, the three-phase grid-connected inverter based on the MPC algorithm has some problems if the LCL filter is selected for filtering. In terms of control algorithm, a mathematical model of the three-phase grid-connected inverter becomes more complex, and the design difficulty of the MPC controller is improved. In terms of hardware design, a sampling circuit needs to be additionally configured for acquiring a current value flowing into a capacitor, so that the equipment cost is increased. Therefore, in most application processes of the three-phase grid-connected inverter based on the MPC algorithm, the inflow capacitance current is ignored, and an inverter dynamic model is established on the basis of the traditional inductance L filtering, so that an unmodeled part exists in a mathematical model of a controlled object, and a control error is generated; in addition, the ferromagnetic material of the filter inductor changes according to the magnetization curve, so that the actual value of the inductor is time-varying under different working conditions. Meanwhile, the resistance in the model is not only the stray resistance of the inductor, but also other unknown resistances such as the line resistance which cannot be effectively measured in the inverter system. Therefore, the inductance and resistance parameters in the model often deviate from the actual object, reducing the control performance of the MPC algorithm. How to compensate for the above model errors is very important to improve MPC performance.
In order to improve the control performance of MPC, some parameter identification methods are used in some projects to improve the accuracy of mathematical models. However, this control strategy has the following disadvantages: 1) the unmodeled part of the model cannot be compensated 2) the resistance parameters are not observed 3) the calculated amount of the controller is increased, thereby increasing the requirement of the inverter system on the control chip.
Disclosure of Invention
In view of this, the invention aims to provide a model mismatch compensation method for a three-phase grid-connected inverter based on model predictive control, which solves the problem that a model of the three-phase grid-connected inverter based on the model predictive control is not accurate due to model unmolding and parameter time variation, effectively improves the control efficiency and quality of an MPC (dynamic host computer controller) and improves the reliability of the three-phase grid-connected inverter.
In order to achieve the purpose, the invention adopts the following technical scheme:
a model mismatch compensation method for a model predictive control three-phase grid-connected inverter comprises the following steps:
s1, establishing a three-phase grid-connected inverter discrete mathematical model based on an L filter, substituting a sampling signal and a given current value into the three-phase grid-connected inverter discrete mathematical model based on the L filter, and calculating an initial value u of output voltage of a prediction inverter anref0 、u bnref0 、u cnref0 ；
S2, establishing an actual mathematical model of the three-phase grid-connected inverter based on the LCL filter, defining the voltage generated by the current flowing into the capacitor as model disturbance, and defining the sum of the voltage generated by the resistance inductance deviation value and the model disturbance as system unknown disturbance; defining the collected power grid voltage as known disturbance;
s3, defining the known inductance as a control gain and outputting a voltage u by the inverter an 、u bn 、u cn As input for model mismatch compensation, the inverter side current i a 、i b 、i c As the output of the model mismatch compensation, a model mismatch compensation module is established, and beta is set based on the model mismatch compensation module a1 、β a2 、β b1 、β b2 、β c1 、β c2 Posterior observationUnknown disturbance z of the output system a2 、z b2 、z c2 ；
S4, compensating the unknown disturbance of the system to the initial value u of the output voltage of the prediction inverter anref0 、u bnref0 、u cnref0 Obtain three-phase predicted inverter output voltage u anref 、u bnref 、u cnref ；
Step S5: according to u anref 、u bnref 、u cnref And designing a cost function, and sending the output voltage of the three-phase prediction inverter into a model prediction controller for traversal, and then selecting a voltage vector for the control of the inverter at the next moment.
Further, the step S1 specifically includes:
the mathematical model under the static abc coordinate system of the grid-connected inverter based on the LCL filter is
Wherein u is rx ＝-L x2 di cx /dt-R x2 i cx Is a model perturbation term; l is a radical of an alcohol x And R x Respectively, the sum of the inductances on both sides of the capacitor and their parasitic resistances, i.e. L x ＝L x1 +L x2 ，R x ＝R x1 +R x2 ；
Neglecting a model disturbance term, establishing an L filter simplified inverter dynamic model:
because of the sampling period T s Short enough, the forward euler method can be used to discretize equation (2) to obtain the discrete mathematical model of the inverter:
when the sampling time is less than the preset time, obtaining:
for a given current i under a two-phase rotating coordinate system dref 、i qref The following transformations are performed:
and (3) substituting the formula (5) for the formula (3) to obtain the initial value of the output voltage of the inverter under the abc static coordinate system at the k time:
further, the step S2 specifically includes:
if the actual system and the prediction model have inductance resistance deviation Delta L between phases x And Δ R x Then, the actual mathematical model of the three-phase grid-connected inverter based on the LCL filter specifically includes:
let the voltage error generated by parameter mismatch be internal unknown disturbance respectively
f a (i a )＝(u ra +ΔL a di a /dt+ΔR a i a )
f b (i b )＝(u rb +ΔL b di b /dt+ΔR b i b )
f c (i c )＝(u rc +ΔL c di c /dt+ΔR c i c )，
The external known disturbance is the three-phase network-side phase voltage w a (t)＝-e a 、w b (t)＝-e b And w c (t)＝-e c The control gains are respectively b a ＝1/L a 、b b ＝1/L b And b c ＝1/L c
Then:
let u an 、u bn 、u cn For system input u as 、u bs 、u cs ，i a 、i b 、i c Output y for the system a1 、y b1 、y c1 ；i a 、i b 、i c Is a state variable x a1 、x b1 、x c1 The first order system was constructed as follows:
let state variable x a2 ＝f a (i a )、x b2 ＝f b (i b )、x c2 ＝f c (i c ) The new system is constructed as follows:
further, the step S3 specifically includes:
will inverter output voltage u an 、u bn 、u cn Phase current i of three phases on the inversion side a 、i b 、i c And predicting an initial value u of the inverter output voltage anref0 、u bnref0 、u cnref0 Substituting the model mismatch compensation module to calculate as follows:
compensation of a-phase model mismatch: e.g. of the type a1 ＝z a1 -i a ,
And b-phase model mismatch compensation: e.g. of the type b1 ＝z b1 -i b ,
c-phase model mismatch compensation: e.g. of a cylinder c1 ＝z c1 -i c ,
Wherein z is a1 、z b1 、z c1 Is an estimate of the three-phase current,
are each z a1 、z b1 、z c1 The derivative of (a) is determined,
are each z a2 、z b2 、z c2 Derivative of e a1 、e b1 、e c1 And the error value of the three-phase current estimated value and the three-phase current sampling value on the inversion side.
Further, the step S4 specifically includes:
compensating unknown disturbance of the system to the initial value u of the output voltage of the prediction inverter anref0 、u bnref0 、u cnref0 To obtain IIIPhase predicting the output voltage of the inverter to obtain the compensated network side reference voltage at the moment k:
further, the cost function g (k) is specifically:
g(k)＝(u anref (k)-u a (k)) 2 +(u bnref (k)-u b (k)) 2 +(u cnref (k)-u c (k)) 2
wherein u is a (k)、u b (k)、u c (k) Is the estimated inverter output voltage of each voltage vector.
Compared with the prior art, the invention has the following beneficial effects:
the method solves the problem that the mathematical model of the controlled object of the three-phase grid-connected inverter based on model prediction control is not accurate, effectively improves the control efficiency and quality of the MPC, and improves the reliability of the three-phase grid-connected inverter.
Drawings
FIG. 1 is a block diagram of the method architecture of the present invention;
FIG. 2 is a block diagram of a structure for predicting an initial value of an output voltage of an inverter according to an embodiment of the invention;
FIG. 3 is a block diagram of a model mismatch compensation architecture in an embodiment of the present invention;
FIG. 4 is a hardware structure of a three-phase grid-connected inverter system according to an embodiment of the present invention;
FIG. 5 illustrates coordinate system definitions in accordance with an embodiment of the present invention.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
Referring to fig. 1, the system of the present embodiment is composed of a dc power supply V dc And supplying power, wherein any inverter topology is connected into the LCL filter and then is merged into the power grid. Wherein L is a1 、L b1 、L c1 And R a1 、R b1 、R c1 Parasitic resistances of the inverter side inductance and the inverter side inductance, respectively;L a2 、L b2 、L c2 and R a2 、R b2 、R c2 Parasitic resistances of the network side inductor and the network side inductor respectively; c a 、C b 、C c Is a filter capacitor; r a 、R b 、R c Is a passive damping resistor; filter capacitor i a 、i b 、i c Is the inverter output current; i.e. i ca 、i cb 、i cc Is the current flowing into the filter capacitor; i.e. i ga 、i gb 、i gc Is the three-phase current at the network side; u. of an 、u bn 、u cn Is the inverter side output phase voltage; e.g. of the type a 、e b 、e c Is the grid side phase voltage.
Fig. 2 is a block diagram illustrating a structure for predicting an initial value of an output voltage of an inverter. Establishing a three-phase grid-connected inverter discrete mathematical model based on an L filter, an inversion side three-phase current, a grid side phase voltage and a three-phase given current i aref 、i bref 、i cref As the input of the predicted inverter output voltage initial value, the three-phase predicted inverter output voltage initial value u in the static coordinate system is output anref0 、u bnref0 、u cnref0 。
Fig. 3 is a block diagram of a model mismatch compensation structure. Wherein z is a1 、z b1 、z c1 Are respectively a state variable i a 、i b 、i c An estimated value of (d); z is a radical of a2 、z b2 、z c2 Is an estimate of the model mismatch error. Beta is a beta a1 、β a2 、β b1 、β b2 、β c1 、β c2 Is an adjustable correction factor. Inversion side three-phase current i a 、i b 、i c Three-phase output voltage initial value prediction u anref0 、u bnref0 、u cnref0 And the inverter output voltage u an 、u bn 、u cn Outputting a three-phase predicted inverter output voltage u as an input to a model mismatch anref 、u bnref 、u cnref 。
Referring to fig. 4, the entire control system in the present embodiment includes: the system comprises a direct-current power supply, a three-phase grid-connected inverter, a filter circuit, a relay switch, a direct-current bus sampling circuit, a three-phase grid voltage acquisition circuit, an inverter side three-phase current acquisition circuit, a controller, an isolation drive, a human-computer interaction part and the like.
Wherein the three-phase inverter is provided by a suitable dc power supply. The power tube in the inverter adopts IGBT or MOSFET with parallel diode, and the controller adopts DSP or single chip microcomputer. The inverter side three-phase current acquisition circuit is formed by combining a Hall current sensor and an operational amplifier, or can be formed by combining a winding series power resistor and a differential operational amplifier. The Hall sensor scheme can effectively realize the electrical isolation of the control loop and the main loop, and the winding series power resistance scheme can reduce the system cost. The power grid voltage acquisition circuit is formed by combining a precise voltage sensor and an operational amplifier, and can also be formed by combining a voltage follower formed by connecting an operational amplifier after voltage division of a parallel resistor. The current detection circuit, the voltage sampling circuit and the output weak current signal are sent to an A/D conversion module of the controller. When the grid-connected mode or the island mode is entered, the GPIO module of the controller outputs a relay action signal, and the relay is actuated by the isolation drive after passing through the level conversion chip.
The coordinate system is defined as shown in fig. 5, where the abc axis is a stationary three-phase coordinate system, the α β axis is a stationary two-phase coordinate system, and the dq axis is a rotating two-phase coordinate system.
The grid-side phase voltage e is defined according to the coordinate system in fig. 5 a 、e b 、e c Performing Clark transformation:
according to e gα 、e gβ The phase angle theta can be calculated g ：
According to the coordinate system definition in FIG. 5, for a given current i in a two-phase rotating coordinate system dref 、i qref The following transformations are performed:
in this embodiment, a model mismatch compensation method for a three-phase grid-connected inverter based on model predictive control is provided, which includes the following steps:
a model mismatch compensation method for a model predictive control three-phase grid-connected inverter is characterized by comprising the following steps:
s1, establishing a three-phase grid-connected inverter discrete mathematical model based on an L filter, substituting a sampling signal and a given current value into the three-phase grid-connected inverter discrete mathematical model based on the L filter, and calculating an initial value u of output voltage of a prediction inverter anref0 、u bnref0 、u cnref0 ；
S2, establishing an actual mathematical model of the three-phase grid-connected inverter based on the LCL filter, defining the voltage generated by the current flowing into the capacitor as model disturbance, and defining the sum of the voltage generated by the resistance inductance deviation value and the model disturbance as system unknown disturbance; defining the collected power grid voltage as known disturbance;
s3, defining the known inductance as a control gain and outputting a voltage u by the inverter an 、u bn 、u cn As input for model mismatch compensation, the inverter side current i a 、i b 、i c As the output of the model mismatch compensation, a model mismatch compensation module is established, and beta is set based on the model mismatch compensation module a1 、β a2 、β b1 、β b2 、β c1 、β c2 Post-observation of unknown disturbance z of the system a2 、z b2 、z c2 ；
S4, compensating unknown disturbance of the system to a predicted initial value u of the output voltage of the inverter anref0 、u bnref0 、u cnref0 Obtain three-phase predicted inverter output voltage u anref 、u bnref 、u cnref ；
Step S5: according to u anref 、u bnref 、u cnref And designing a cost function, and sending the output voltage of the three-phase prediction inverter into a model prediction controller for traversal, and then selecting a voltage vector for the control of the inverter at the next moment.
In the embodiment, the direct current voltage passes through an inverter system, and is merged into a power grid after current higher harmonics are eliminated through an LCL filter; collecting the voltage e of the network side phase a 、e b 、e c Transforming the two-phase stationary coordinate system to obtain e gα 、e gβ Wherein the calculation formula is as follows:
calculating the phase angle theta of the phase voltage at the network side g Wherein the calculation formula is as follows:
a given current i in a two-phase rotating coordinate system dref 、i qref Converting the three-phase static coordinate system to obtain i aref 、i bref 、i cref Wherein the calculation formula is as follows:
will give a current i aref 、i bref 、i cref Phase current i of three phases on the inversion side a 、i b 、i c And the grid side phase voltage e a 、e b 、e c Substituting the discrete mathematical model of the three-phase grid-connected inverter based on the L filter to obtain the initial value u of the output voltage of the predicted inverter anref0 、u bnref0 、u cnref0 ,
In this embodiment, step S2 specifically includes:
setting that the inductance resistance deviation Delta L exists between each phase of the actual system and the prediction model x And Δ R x Then, the actual mathematical model of the three-phase grid-connected inverter based on the LCL filter specifically includes:
let the voltage error generated by parameter mismatch be internal unknown disturbance respectively
f a (i a )＝(u ra +ΔL a di a /dt+ΔR a i a )
f b (i b )＝(u rb +ΔL b di b /dt+ΔR b i b )
f c (i c )＝(u rc +ΔL c di c /dt+ΔR c i c )，
The external known disturbances are the three-phase network-side phase voltages w a (t)＝-e a 、w b (t)＝-e b And w c (t)＝-e c The control gains are respectively b a ＝1/L a 、b b ＝1/L b And b c ＝1/Lc
Then:
let u an 、u bn 、u cn For system input u as 、u bs 、u cs ，i a 、i b Ic is the system output y a1 、y b1 、y c1 ；i a 、i b Ic is a state variable x a1 、x b1 、x c1 The first order system was constructed as follows:
let state variable x a2 ＝f a (i a )、x b2 ＝f b (i b )、x c2 ＝f c (i c ) The new system is constructed as follows:
the model mismatch compensation module can be based on the system input u an 、u bn 、u cn And an output quantity i a 、i b 、i b For the state variable x a1 、x b1 、x c1 And x a2 、x b2 、x c2 Estimating to further realize dynamic disturbance feedforward compensation, and establishing the following equation aiming at the formula system:
taking phase a as an example, as can be seen from the above formula, z a2 Is x a2 Value, z, filtered by a second order low pass filter a1 Is x a1 Filtered and then phase compensated. Beta is a beta a2 The value of (b) directly affects the estimation capability of the parameter mismatch compensation, along with beta a2 The anti-interference of the system is enhanced, namely the time for the system to recover to a steady state after disturbance is short. But beta. Is a2 Further increases will cause the system to oscillate and be sensitive to noise, while increasing β a1 To suppress this problem, but beta a1 Too large will cause the system to diverge. In conclusion, in the actual parameter setting process, the observer pole needs to be properly selected according to specific situations.
The same analysis method can be used to illustrate the b-phase and c-phase current loops, and the analysis is not repeated here.
And finally, adding an observation result to obtain the compensated network side reference voltage at the moment k:
preferably, in the present embodiment, the cost function is designed only with the current tracking as a unique target. In the current control of the grid-connected inverter, current, voltage or power is generally selected as a main constraint variable, and a cost function g (k) is established by taking the voltage constraint variable as an example:
g(k)＝(u anref (k)-u a (k)) 2 +(u bnref (k)-u b (k)) 2 +(u cnref (k)-u c (k)) 2
wherein u is a (k)、u b (k)、u c (k) Is the predicted inverter output voltage of each voltage vector because the three-phase current is tracked as the sameA dimension is such that the coefficients of each square phase are 1. And traversing all vectors by the cost function to obtain a voltage vector which enables g (k) to be minimum, wherein the voltage vector is used for controlling the three-phase grid-connected inverter at the next moment.
The above description is only a preferred embodiment of the present invention, and all the equivalent changes and modifications made according to the claims of the present invention should be covered by the present invention.
Claims (6)
1. A model mismatch compensation method for a three-phase grid-connected inverter based on model predictive control is characterized by comprising the following steps:
s1, establishing a three-phase grid-connected inverter discrete mathematical model based on an L filter, substituting a sampling signal and a given current value into the three-phase grid-connected inverter discrete mathematical model based on the L filter, and calculating an initial value u of output voltage of a prediction inverter anref0 、u bnref0 、u cnref0 ；
S2, establishing an actual mathematical model of the three-phase grid-connected inverter based on the LCL filter, defining the voltage generated by the current flowing into the capacitor as model disturbance, and defining the sum of the voltage generated by the resistance inductance deviation value and the model disturbance as system unknown disturbance; defining the collected power grid voltage as known disturbance;
s3, defining the known inductance as a control gain and outputting a voltage u by the inverter an 、u bn 、u cn As input for model mismatch compensation, the inverter side current i a 、i b 、i c As the output of the model mismatch compensation, a model mismatch compensation module is established, and beta is set based on the model mismatch compensation module a1 、β a2 、β b1 、β b2 、β c1 、β c2 The unknown disturbance z of the system is observed after the observation a2 、z b2 、z c2 ；
S4, compensating unknown disturbance of the system to a predicted initial value u of the output voltage of the inverter anref0 、u bnref0 、u cnref0 To obtain the output voltage u of the three-phase prediction inverter anref 、u bnref 、u cnref ；
Step S5: according to u anref 、u bnref 、u cnref And designing a cost function, and sending the output voltage of the three-phase prediction inverter into a model prediction controller for traversal, and then selecting a voltage vector for the control of the inverter at the next moment.
2. The model mismatch compensation method for the model predictive controlled three-phase grid-connected inverter according to claim 1, wherein the step S1 specifically comprises:
the mathematical model under the static abc coordinate system of the grid-connected inverter based on the LCL filter is
Wherein u is rx ＝-L x2 di cx /dt-R x2 i cx Is a model disturbance term; l is a radical of an alcohol x And R x Respectively, the sum of the inductances on both sides of the capacitor and their parasitic resistances, i.e. L x ＝L x1 +L x2 ，R x ＝R x1 +R x2 ；
Neglecting a model disturbance term, establishing an L filter simplified inverter dynamic model:
because of the sampling period T s The method is short enough, a forward Euler method can be used, and the discrete mathematical model of the inverter is obtained after discretizing the formula (2):
when the sampling time is less than the preset time, obtaining:
for a given current i in a two-phase rotating coordinate system dref 、i qref The following transformations are performed:
substituting equation (5) for equation (3) to obtain an initial value of the predicted inverter output voltage at time k abc in a stationary coordinate system:
3. the model mismatch compensation method for the model predictive controlled three-phase grid-connected inverter according to claim 1, wherein the step S2 specifically comprises:
setting that the inductance resistance deviation Delta L exists between each phase of the actual system and the prediction model x And Δ R x Then, the actual mathematical model of the three-phase grid-connected inverter based on the LCL filter specifically includes:
let the voltage error generated by parameter mismatch be an internal unknown disturbance respectively
f a (i a )＝(u ra +ΔL a di a /dt+ΔR a i a )
f b (i b )＝(u rb +ΔL b di b /dt+ΔR b i b )
f c (i c )＝(u rc +ΔL c di c /dt+ΔR c i c )，
The external known disturbances are the three-phase network-side phase voltages w a (t)＝-e a 、w b (t)＝-e b And w c (t)＝-e c The control gains are respectively b a ＝1/L a 、b b ＝1/L b And b c ＝1/L c
Then:
let u an 、u bn 、u cn Input u for the system as 、u bs 、u cs ，i a 、i b 、i c Output y for the system a1 、y b1 、y c1 ；i a 、i b 、i c Is a state variable x a1 、x b1 、x c1 The first order system was constructed as follows:
let the state variable x a2 ＝f a (i a )、x b2 ＝f b (i b )、x c2 ＝f c (i c ) The new system is constructed as follows:
4. the model mismatch compensation method for the model predictive controlled three-phase grid-connected inverter according to claim 3, wherein the step S3 specifically comprises:
will output the inverter voltage u an 、u bn 、u cn Phase current i of three phases on the inversion side a 、i b 、i c And predicting an initial value u of the inverter output voltage anref0 、u bnref0 、u cnref0 Substituting the model mismatch compensation module to calculate as follows:
compensation of a-phase model mismatch:
and b-phase model mismatch compensation:
c-phase model mismatch compensation:
wherein z is a1 、z b1 、z c1 Is an estimate of the three-phase current,
are each z a1 、z b1 、z c1 The derivative of (a) of (b),
are each z a2 、z b2 、z c2 Derivative of e a1 、e b1 、e c1 Inversion side three-phase currentAn error value of the estimated value and the three-phase current sample value.
5. The model mismatch compensation method for the model predictive controlled three-phase grid-connected inverter according to claim 4, wherein the step S4 specifically comprises:
compensating unknown disturbance of the system to the initial value u of the output voltage of the prediction inverter anref0 、u bnref0 、u cnref0 Obtaining the output voltage of the three-phase prediction inverter, and obtaining the compensated network side reference voltage at the moment k:
6. the model mismatch compensation method for the model predictive controlled three-phase grid-connected inverter according to claim 1, wherein the cost function g (k) is specifically:
g(k)＝(u anref (k)-u a (k)) 2 +(u bnref (k)-u b (k)) 2 +(u cnref (k)-u c (k)) 2
wherein u is a (k)、u b (k)、u c (k) Is the predicted inverter output voltage of each voltage vector.
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