CN112018783A - Model reduced order feedback control method for direct-drive fan subsynchronous oscillation suppression - Google Patents

Model reduced order feedback control method for direct-drive fan subsynchronous oscillation suppression Download PDF

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CN112018783A
CN112018783A CN202010729417.7A CN202010729417A CN112018783A CN 112018783 A CN112018783 A CN 112018783A CN 202010729417 A CN202010729417 A CN 202010729417A CN 112018783 A CN112018783 A CN 112018783A
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CN112018783B (en
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李星原
张鹏
韩晨阳
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North China Electric Power University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/24—Arrangements for preventing or reducing oscillations of power in networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/38—Arrangements for parallely feeding a single network by two or more generators, converters or transformers
    • H02J3/381—Dispersed generators
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2300/00—Systems for supplying or distributing electric power characterised by decentralized, dispersed, or local generation
    • H02J2300/20—The dispersed energy generation being of renewable origin
    • H02J2300/28—The renewable source being wind energy

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Abstract

The invention relates to a model reduced order feedback control method for subsynchronous oscillation suppression of a direct-drive fan, which comprises the following steps of 1, linearizing a mathematical model of the direct-drive fan and a controller thereof, and establishing a small signal model of the direct-drive fan containing all state variables. 2. And reducing the order of the small signal model according to the characteristic value of the complete small signal model, observability of the state variable and the influence degree on the oscillation, and establishing a reduced order model of the direct-drive fan. 3. And designing a feedback controller by utilizing the reduced-order direct-drive fan small-signal model. According to the method, through the linearization of mathematical models of the direct-drive fan and the controller thereof, a direct-drive fan small-signal model containing all state variables is obtained for analysis and calculation; reducing the order of the small signal model to obtain a reduced order model of the direct-drive fan, and providing convenience for the design of a feedback controller; a feedback controller is designed by utilizing a reduced-order direct-drive fan small-signal model, and a good direct-drive fan subsynchronous oscillation suppression effect is realized.

Description

Model reduced order feedback control method for direct-drive fan subsynchronous oscillation suppression
Technical Field
The invention relates to a control method applied to subsynchronous oscillation suppression of a direct-driven fan, in particular to a feedback control method based on a reduced order model applied to subsynchronous oscillation analysis.
Background
In recent years, wind power generation is rapidly developed and becomes an important component of green new energy. An active oscillation phenomenon in which an oscillation frequency is much higher than 2Hz and lower than 50Hz in an electric power system is called subsynchronous oscillation, and is one of important research subjects of the electric power system. With the increase of the loading amount of the wind power generation, the problem of subsynchronous oscillation of the wind power generation gradually draws attention. In 2011, a certain wind power plant in the north China area generates multiple synchronous oscillation phenomena, and the oscillation frequency of the wind power plant changes in a large range. In 2015, a certain large wind power plant in northwest China generates subsynchronous oscillation, and the oscillation frequency is constantly changed within 16-24 Hz.
Subsynchronous oscillation belongs to oscillation phenomena of non-power frequency, so that the analysis of the subsynchronous oscillation needs to relate to electromagnetic transient characteristics. The wind turbine generator set model is complex, and the linearization model order is higher. Therefore, a high-order linearization model is adopted for the analysis of the subsynchronous oscillation of the wind turbine generator and the design of the controller. This presents significant difficulties in controller design and verification.
The invention provides a linear model order reduction method for subsynchronous oscillation analysis, aiming at the problem of subsynchronous oscillation of a permanent magnet direct-driven wind driven generator. On the basis, based on the order-reduced model obtained by the invention, the structure of the feedback controller for subsynchronous oscillation suppression is provided, and the parameters of the feedback controller are designed by adopting a quadratic time performance index method. The method can greatly reduce the complexity of the linear model of the direct-drive wind turbine generator and bring convenience to the design of the controller. The feedback controller designed on the basis reflects good subsynchronous oscillation suppression effect.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a model order-reduction feedback control method for suppressing subsynchronous oscillation of a direct-drive wind turbine, so that the complexity of a linear model of the direct-drive wind turbine is greatly reduced, convenience is brought to the design of a controller, and a feedback controller designed on the basis has a good subsynchronous oscillation suppression effect.
In order to achieve the above purposes, the technical scheme adopted by the invention is as follows:
the invention adopts a small signal model to design the feedback controller. According to the method, firstly, a small signal model containing all state variables of the direct-drive fan system is established, then the model is reduced, and finally, a feedback controller is designed by using the reduced small signal model, so that a good direct-drive fan subsynchronous oscillation suppression effect is achieved.
A model reduced order feedback control method for suppressing subsynchronous oscillation of a direct-drive fan comprises the following steps:
step 1: and linearizing the mathematical models of the direct-drive fan and the controller thereof, and establishing a small signal model of the direct-drive fan containing all state variables.
Step 2: and reducing the order of the small signal model according to the characteristic value of the complete small signal model, observability of the state variable and the influence degree on the oscillation, and establishing a reduced order model of the direct-drive fan.
And step 3: a feedback controller of the direct-drive fan is designed by utilizing the reduced-order direct-drive fan small-signal model, so that a good direct-drive fan subsynchronous oscillation suppression effect is realized.
The coordinate transformation of the electrical quantity used by the model order-reduction feedback control method is based on two different reference coordinate systems, and when the same electrical quantity is the PCC point voltage UsWhen the directional reference is carried out, c is marked on the upper corner marks of d and q axis components, and if no mark exists, the directional reference is based on infinite power grid voltage UEOrientation of (1); among the electrical quantity symbols used, the initial steady state value is indicated by the lower corner mark 0.
The specific steps of step 1 are as follows:
linearizing each part of the direct-drive fan simplified circuit; the linear model is calculated based on per unit value, and the AC vector rotation angular velocity base value of the system is omegaB100 π rad/s; with infinite network voltage UEWith reference to the orientation of (1), output current IsThe linearization equation is as formula (1):
Figure BDA0002602476660000031
wherein isd、isqAre respectively the output current IsD, q-axis component of (u)sd、usqRespectively, PCC point voltage UsD and q axis components of (1), the value of the transformer equivalent inductance L is Ls；
PCC point voltage UsIs shown in equation (2):
Figure BDA0002602476660000032
wherein u issd、usqRespectively, PCC point voltage UsD, q-axis component of (u)cd、ucqRespectively, the AC side outlet voltage U of the convertercD, q-axis components of (i)gd、igqAre respectively an alternating side current IgD, q-axis components of (1), filter capacitance CgHas a value of cgResistance RgHas a value of rgFilter inductance LgHas a value of lg；
AC side current IgThe small signal linearization equation of (3):
Figure BDA0002602476660000041
the direct-current bus small-signal equation of the grid-side converter is as shown in formula (4):
Figure BDA0002602476660000042
wherein, the DC capacitor CdHas a value of cd，UdcThe lower corner mark 0 represents the initial steady state value when the voltage is direct current voltage;
the coordinate transformation of the controller adopts a phase-locked loop to provide an orientation angle and adopts a power grid voltage orientation mode; the phase-locked loop has a proportionality coefficient of kpIntegral coefficient of phase-locked loop is kiEstablishing auxiliary intermediate variable Z to obtain PCC point voltage UsThe difference between the orientation angle and the orientation angle of the infinite grid voltage E is thetapllAnd s represents a frequency parameter in the complex frequency domain; the phase-locked loop linearization equation is as follows:
Figure BDA0002602476660000043
a grid-side converter of the direct-drive fan controls the voltage of a direct-current bus and the reactive power of a rotor, and a loop of the direct-drive fan comprises an outer ring controller and an inner ring controller; the outer ring controller fixes direct current voltage, and the inner ring controller fixes current; DC voltage command value Udc *As a d-axis outer ring command value; q-axis current command value igq *As a q-axis inner loop command value;
the method comprises the following steps of establishing a network side controller linearization model:
Figure BDA0002602476660000044
is a d-axis inner ring command value, kp1、ki1Respectively is a proportionality coefficient and an integral coefficient of the outer ring controller; establishing an auxiliary intermediate variable Z1And obtaining an equation of the outer ring of the d axis:
Figure BDA0002602476660000051
ucd *outputs a d-axis voltage command value, k, to the controllerp3、ki3Proportional coefficient and integral coefficient of d-axis inner ring controller, and initial value of AC vector rotation angular velocity of system is omega0Establishing an auxiliary intermediate variable Z3And obtaining an equation of the inner ring of the d axis:
Figure BDA0002602476660000052
ucq *outputting a q-axis voltage command value, k, to the controllerp4、ki4Respectively establishing an auxiliary intermediate variable Z for a proportionality coefficient and an integral coefficient of the q-axis inner ring controller4And obtaining an equation of the q-axis outer ring:
Figure BDA0002602476660000053
the magnitude of the converter gain is denoted as kPWMThe switching period of the converter is TThe relationship between the control signal output by the controller and the outlet voltage at the alternating current side of the converter is as follows:
Figure BDA0002602476660000054
the carrier amplitude of the converter is M, and the formula (9) is linearized to obtain:
Figure BDA0002602476660000055
the joint vertical type (1) - (8), (10) can obtain a direct-drive fan linear small-signal model in the standard form as the formula (11):
Figure BDA0002602476660000061
wherein, the state variable X ═ Δ usd,Δusq,Δigd,Δigq,ΔUdc,Δisd,Δisq,Δθpll,ΔZ,ΔZ1,ΔZ3,ΔZ4,Δucd,Δucq]TControl variable U ═ Δ Udc *,Δigq *]TA is a 14-order square matrix, B is a 14 multiplied by 2-order matrix, and the upper corner mark T of the matrix represents the matrix transposition.
The specific steps of step 2 are as follows:
1) matrix reordering and chunking
Carrying out reduced order processing based on the small signal model of the formula (11); firstly, find the systemCharacteristic values of the parameter matrix A are all located on the left half plane of the complex plane; dividing the obtained characteristic values into two groups, wherein the number of the first group of characteristic values is a, the number of the second group of characteristic values is b, and the second group of b characteristic values is required to be far away from the virtual axis compared with the first group of a characteristic values; the characteristic value of A constitutes a characteristic value diagonal matrix Lambda, Lambda has a sub-diagonal matrix Lambda1、Λ2(ii) a The first group of characteristic values after grouping form an a-order matrix Lambda1The second group of characteristic values form a b-order matrix Lambda2。
Figure BDA0002602476660000062
According to the observability of each state quantity and the influence degree on the oscillation, a main a state quantities are taken to form a main state quantity matrix X1The other b state quantities form a secondary state quantity matrix X2(ii) a Order:
Figure BDA0002602476660000063
the order of the state variables of X in the formula (11) and X 'in the formula (13) may be different, so that the matrix A is subjected to symmetrical row transformation and column transformation, and is corresponding to the state variable X', a new coefficient matrix A 'is obtained, and the matrix B is transformed in the same way to obtain B'; the adjusted state equation is obtained as follows:
Figure BDA0002602476660000071
the block processing is performed on the formula (14) according to the formula (13), and the following results are obtained:
Figure BDA0002602476660000072
wherein A is11Is a square matrix of order a, A12Is an a × b order matrix, A21Is a b × a order matrix, A22Is a B-order square matrix, B1Is an a x 2 order matrix, B2Is a b x 2 order matrix, A11，A12，A21，A22，B1，B2Is obtained by directly partitioning an A 'matrix and a B' matrix of an original model formula (14);
A’the eigenvalues of a and a are consistent, so the Λ matrix continues to be used for calculations;
thus, the eigenvector matrix C is obtained by:
A'＝CΛC-1 (16)
for subsequent calculations, C is also blocked:
Figure BDA0002602476660000073
wherein, C11Is a square matrix of order a, C12Is an a × b order matrix, C21Is a b × a order matrix, C22Is a b-order square matrix;
2) and (3) performing system order reduction calculation:
setting auxiliary intermediate variable matrix ZbSo that Z isbSatisfies the following relation:
Figure BDA0002602476660000074
wherein Zb1Is a column vector of order a, Zb2Is a b-order column vector, both of which are ZbDirectly obtaining the product by blocking;
then there is
Figure BDA0002602476660000075
Figure BDA0002602476660000081
The analytic solution of the equation set of equation (20) is:
Figure BDA0002602476660000082
due to Λ2Is a large distance from the imaginary axis, and is approximately considered to be within the time range of the study
Figure BDA0002602476660000086
Is 0, then
Zb2(t)＝0 (22)
By substituting formula (22) for formula (18), it is possible to obtain:
Figure BDA0002602476660000083
using the result of equation (23), the system is reduced by substituting equation (15), and only X is reserved after the reduction1As state variables. Then there are:
Figure BDA0002602476660000084
recording:
H＝A11+A12C21C11 -1 (25)
then the formula (25) is rewritten as
Figure BDA0002602476660000085
Equation (26) is the reduced small signal model; h is an a-order square matrix, B1Is a b x 2 order matrix.
The specific steps of step 3 are as follows:
feedback control input UfWritten in phasor form of formula (27), wherein U* dcfIs a DC voltage feedback quantity command value i* gqfFor the q-axis current feedback amount command value:
Figure BDA0002602476660000091
wherein K is a feedback controller parameter to be designed, and K is a 2 x a order matrix;
the feedback controller parameters are designed based on equation (26), and the following performance indicator functional J is used for equation (26):
Figure BDA0002602476660000092
in the formula (28), t is time, Q is a state quantity weight coefficient matrix, and the size of the element reflects the degree of influence of each corresponding state quantity on oscillation; r is a control quantity weight coefficient matrix, the element size of the control quantity weight coefficient matrix reflects the limitation of the control quantity, and the instability of the system caused by the overlarge feedback control quantity is avoided;
when the performance index functional of equation (28) reaches an extreme value, the ricatt ladder equation should be satisfied:
HTPb+PbH-PbB1R-1B1 TPb+Q＝0 (29)
the unknown matrix solved by equation (29) is PbDetermining Q, R matrix values before solving the equation;
in order to accelerate the convergence speed of the system and improve the improvement effect of the feedback controller on the dynamic characteristics of the system, the value of Q is calculated in an iterative way by using a time optimal control method; simultaneous equations (30) to (32) for optimizing the time index, the Lyapunov function decays at a negative fixed rate and reaches a minimum value; wherein I is an identity matrix, EbControlling characteristic values of closed-loop systems for additional feedback, SbIs a positive definite coefficient matrix;
Eb＝H-B1R-1B1 TPb (30)
Eb TQ+QEb＝-Sb (31)
EbSb -2+Sb -2Eb T＝-I (32)
after obtaining Q matrix, substituting formula (29) to obtain PbFrom PbThe feedback controller parameter K is calculated according to the following formula:
K＝R-1B1 TPb (33)
after obtaining the feedback controller parameter K, substituting K for equation (27) to determine the feedback control input UfAnd a DC voltage command value Udc *And q-axis current command value igq *And finally obtaining the feedback controller of the direct-drive fan.
The invention has the beneficial effects that:
(1) according to the method, through the linearization of mathematical models of the direct-drive fan and the controller thereof, a direct-drive fan small-signal model containing all state variables is obtained for analysis and calculation;
(2) according to the method, the small signal model is reduced according to the characteristic value of the complete small signal model, observability of state variables and influence degree on oscillation, so that a reduced-order model of the direct-drive fan is obtained, and convenience is provided for the design of a feedback controller;
(3) according to the invention, a feedback controller is designed by utilizing a reduced-order direct-drive fan small-signal model, so that a good direct-drive fan subsynchronous oscillation suppression effect is realized.
Drawings
The invention has the following drawings:
FIG. 1 is a schematic structural diagram of a direct-drive wind generating set.
Fig. 2 is a simplified circuit diagram of a direct-drive fan.
FIG. 3 is a schematic diagram of a net-side controller loop.
Fig. 4 is a schematic diagram of feedback control.
FIG. 5 is a schematic diagram of a direct drive fan feedback controller.
FIG. 6Q matrix calculation flow chart.
Fig. 7a scene 1 active power P simulation result
FIG. 7b scene 1 DC Voltage UdcSimulation result
FIG. 7c Scenario 1 output Current IsD-axis component ofisdSimulation result
Fig. 8a scene 2 active power P simulation result
FIG. 8b scene 2 DC Voltage UdcSimulation result
FIG. 8c Scenario 2 output Current IsD-axis component i ofsdSimulation result
Fig. 9a scene 3 active power P simulation result
FIG. 9b scene 3 DC Voltage UdcSimulation result
FIG. 9c Scenario 3 output Current IsD-axis component i ofsdSimulation result
The wind power generation system comprises a wind turbine 1, a permanent magnet synchronous motor 2, a rotor side converter 3, a grid side converter 4, a filter circuit 5, a filter circuit 6 and an alternating current power grid.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
Firstly, establishing a direct-drive fan linearization model
As shown in fig. 1, the direct-drive wind generating set comprises a wind turbine 1, a permanent magnet synchronous motor 2, a rotor-side converter 3, a grid-side converter 4, a grid-side converter controller, a filter circuit 5 and the like.
Because the wind turbine 1, the permanent magnet synchronous motor 2 and the rotor side converter 3 are isolated from the alternating current power grid 6 and have little influence on subsynchronous oscillation, the direct current source is used for replacing the parts, and a simplified circuit diagram of the direct-drive wind turbine is shown in fig. 2. Wherein, the current magnitude I of the direct current sourcedcRepresenting the fan output level, and a DC capacitor CdDC voltage of UdcAC side outlet voltage U of convertercFilter inductance L on the AC sidegAlternating side current Ig(flow through filter inductor LgCurrent of) PCC point voltage of UsPCC point parallel resistance RgAnd a parallel capacitor CgAre connected in series to form a filter. Output current IsAnd the equivalent inductance L of the transformer is incorporated into an infinite alternating current power supply.
The invention uses the coordinate transformation of the electrical quantity based on two different reference coordinate systems, when the same electrical quantity is represented by PVoltage U at point CCsWhen the directional reference is carried out, c is marked on the upper corner marks of d and q axis components, and if no mark exists, the directional reference is based on infinite power grid voltage UEIn the orientation of (c). For example, the AC-side outlet voltage U of a convertercBased on UsDirected d and q axis components of ucd c、ucq cBased on UEDirected d and q axis components of ucd、ucq. Similar symbol changes are not described in detail below.
And linearizing each part of the direct-drive fan simplified circuit. The linear model is calculated based on per unit value, and the AC vector rotation angular velocity base value of the system is omegaB100 pi rad/s. With infinite network voltage UEWith reference to the orientation of (1), output current IsThe linearized equation is given in the following formula (1), where isd、isqAre respectively the output current IsD, q-axis component of (u)sd、usqRespectively, PCC point voltage UsD and q axis components of (1), the value of the transformer equivalent inductance L is Ls。
Figure BDA0002602476660000121
PCC point voltage UsIs given by the following formula (2), wherein usd、usqRespectively, PCC point voltage UsD, q-axis components of (1). u. ofcd、ucqRespectively, the AC side outlet voltage U of the convertercD, q-axis components of (1). i.e. igd、igqAre respectively an alternating side current IgD, q-axis components of (1). Filter capacitor CgHas a value of cgResistance RgHas a value of rgFilter inductance LgHas a value of lg。
Figure BDA0002602476660000122
AC side filter inductor L of convertergCurrent of (I)gThe small signal linearization equation of (3).
Figure BDA0002602476660000131
In the electrical quantity symbols used in the present invention, the following subscript 0 represents the initial steady-state value.
The small signal equation of the direct current bus of the grid-side converter is as follows (4), wherein a direct current capacitor CdSize cdThe lower subscript 0 represents the initial steady state value:
Figure BDA0002602476660000132
the controller coordinate transformation adopts a phase-locked loop to provide a directional angle and adopts a power grid voltage directional mode. The phase-locked loop has a proportionality coefficient of kpIntegral coefficient of phase-locked loop is kiEstablishing auxiliary intermediate variable Z to obtain PCC point voltage UsThe difference between the orientation angle and the orientation angle of the infinite grid voltage E is thetapllAnd s denotes a frequency parameter in the complex frequency domain. The phase-locked loop linearization equation is as follows:
Figure BDA0002602476660000133
a grid-side converter of the direct-drive fan controls the voltage of a direct-current bus and the reactive power of a rotor, and a loop of the direct-drive fan comprises an outer loop controller and an inner loop controller. The outer loop controller fixes DC voltage, and the inner loop controller fixes current. DC voltage command value Udc *As a d-axis outer ring command value; q-axis current command value igq *As the q-axis inner loop command value. The controller loop is shown in fig. 3.
The method comprises the following steps of establishing a network side controller linearization model:
Figure BDA0002602476660000141
is a d-axis inner ring command value, kp1、ki1Respectively are a proportionality coefficient and an integral coefficient of the outer ring controller. In the establishment of assistanceVariable Z1And obtaining an equation of the outer ring of the d axis:
Figure BDA0002602476660000142
ucd *outputs a d-axis voltage command value, k, to the controllerp3、ki3Proportional coefficient and integral coefficient of d-axis inner ring controller, and initial value of AC vector rotation angular velocity of system is omega0Establishing an auxiliary intermediate variable Z3And obtaining an equation of the inner ring of the d axis:
Figure BDA0002602476660000143
ucq *outputting a q-axis voltage command value, k, to the controllerp4、ki4Respectively establishing an auxiliary intermediate variable Z for a proportionality coefficient and an integral coefficient of the q-axis inner ring controller4And obtaining an equation of the q-axis outer ring:
Figure BDA0002602476660000144
the magnitude of the converter gain is denoted as kPWMThe switching period of the converter is T. The relationship between the control signal output by the controller and the voltage at the AC side of the converter is as follows:
Figure BDA0002602476660000145
the carrier amplitude of the converter is M, and the formula (9) is linearized to obtain:
Figure BDA0002602476660000151
the united vertical type (1) - (8), (10) can obtain the direct-drive fan linear small-signal model in the standard form of the formula (11)
Figure BDA0002602476660000152
Wherein, the state variable X ═ Δ usd,Δusq,Δigd,Δigq,ΔUdc,Δisd,Δisq,Δθpll,ΔZ,ΔZ1,ΔZ3,ΔZ4,Δucd,Δucq]TControl variable U ═ Δ Udc *,Δigq *]T. A is a 14-order square matrix, B is a 14 multiplied by 2-order matrix, and the upper corner mark T of the matrix represents the matrix transposition.
Secondly, establishing a reduced-order model of the direct-drive fan
Part of state variables in the small-signal model are not observable, and a feedback controller participated in the full state is too complex, so that the method is unfavorable for engineering application. Therefore, the design calculation of the feedback controller is performed after the complete system is subjected to the order reduction processing.
1. Matrix reordering and chunking
And (4) carrying out reduction processing based on the small signal model of the formula (11). First, the eigenvalue of the system parameter matrix A is solved. The eigenvalues are all located in the left half plane of the complex plane. Dividing the obtained eigenvalues into two groups, wherein the number of the first group of eigenvalues is a, and the number of the second group of eigenvalues is b. The second set of b eigenvalues are required to be much further from the imaginary axis than the first set of a eigenvalues. The characteristic value of A constitutes a characteristic value diagonal matrix Lambda, Lambda has a sub-diagonal matrix Lambda1、Λ2. The first group of characteristic values after grouping form an a-order matrix Lambda1The second group of characteristic values form a b-order matrix Lambda2。
Figure BDA0002602476660000153
According to the observability of each state quantity and the influence degree on the oscillation, a main a state quantities are taken to form a main state quantity matrix X1The other b state quantities form a secondary state quantity matrix X2. Order:
Figure BDA0002602476660000161
since the order of the state variables of X in the formula (11) and X 'in the formula (13) may be different, the matrix a needs to be subjected to symmetrical row transformation and column transformation to correspond to the state variable X' to obtain a new coefficient matrix a ', and similarly, the matrix B needs to be transformed to obtain the matrix B'. Thus, an adjusted equation of state is obtained:
Figure BDA0002602476660000162
the block processing is performed on the formula (14) according to the formula (13), and the following results are obtained:
Figure BDA0002602476660000163
wherein A is11Is a square matrix of order a, A12Is an a × b order matrix, A21Is a b × a order matrix, A22Is a B-order square matrix, B1Is an a x 2 order matrix, B2Is a b x 2 order matrix, A11，A12，A21，A22，B1，B2Is obtained by directly partitioning the A 'matrix and the B' matrix of the original model formula (14).
The eigenvalues of a' and a are consistent and therefore the matrix Λ as previously evaluated can continue to be used for calculations.
Thereby, the feature vector matrix C is obtained. Then there are:
A'＝CΛC-1 (16)
for subsequent calculations, C needs to be blocked as well.
Figure BDA0002602476660000164
Wherein, C11Is a square matrix of order a, C12Is an a × b order matrix, C21Is a b × a order matrix, C22Is of order bAnd (5) square matrix.
2. System reduced order computation
Setting auxiliary intermediate variable matrix ZbSo that Z isbThe following relation is satisfied.
Figure BDA0002602476660000171
Wherein Zb1Is a column vector of order a, Zb2Is a b-order column vector, both of which are ZbDirectly obtaining the product by blocking.
Then there is
Figure BDA0002602476660000172
Namely, it is
Figure BDA0002602476660000173
The analytic solution of the equation set of equation (20) is:
Figure BDA0002602476660000174
due to Λ2Is a large distance from the imaginary axis, and is approximately considered to be within the time range of the study
Figure BDA0002602476660000175
Is 0, then
Zb2(t)＝0 (22)
By substituting formula (22) for formula (18), it is possible to obtain:
Figure BDA0002602476660000176
using the result of equation (23), the system is reduced by substituting equation (15), and only X is reserved after the reduction1As state variables. Then there are:
Figure BDA0002602476660000181
recording:
H＝A11+A12C21C11 -1 (25)
then the formula (25) is rewritten as
Figure BDA0002602476660000182
Equation (26) is the reduced small signal model. H is an a-order square matrix, B1Is a b x 2 order matrix. The reduced system only keeps state variables which have large influence on the system and can be observed. Meanwhile, main characteristic roots of the system are reserved, and main oscillation mode information is reserved, so that the reduced system oscillation mode is consistent with the complete system, and the oscillation suppression problem of the original system can be analyzed and designed.
Third, direct-drive fan subsynchronous oscillation feedback controller design
1. Feedback controller structural design
For a standard linearization system like equation (11), the basic principle of feedback control is to take the linear combination of each state quantity as input feedback and access the input end of the controller. The invention carries out reduced order processing on the state quantity of input feedback, and only takes the main state variable X1Feedback is input as shown in fig. 4.
For the direct-drive fan, the input end of the direct-drive fan is a direct-current voltage instruction value Udc *And q-axis current command value igq *Therefore, the structure of the feedback controller of the direct drive fan is designed as shown in FIG. 5.
Feedback control input UfWritten in phasor form of formula (27), wherein U* dcfIs a DC voltage feedback quantity command value i* gqfFor the q-axis current feedback amount command value:
Figure BDA0002602476660000183
wherein K is the feedback controller parameter to be designed, and K is a 2 x a order matrix.
2. Feedback controller parameter calculation
The design of the feedback controller parameters is based on a reduced order linear system as shown in equation (26). The goal of the feedback controller is to minimize the system performance index functional. The following performance indicator functional J is used for the system of equation (26):
Figure BDA0002602476660000191
in the formula (28), t represents time. Q is a state quantity weight coefficient matrix whose element size reflects the degree of influence of each corresponding state quantity on oscillation. And R is a control quantity weight coefficient matrix, the element size of the control quantity weight coefficient matrix reflects the limitation of the control quantity, and the instability of the system caused by overlarge feedback control quantity is avoided.
When the performance index functional of equation (28) reaches an extreme value, the ricatt ladder equation should be satisfied:
HTPb+PbH-PbB1R-1B1 TPb+Q＝0 (29)
the unknown matrix solved by the equation is Pb. The values of the Q, R matrix need to be determined before solving the equation.
In order to accelerate the convergence speed of the system and improve the improvement effect of the feedback controller on the dynamic characteristics of the system, the value of Q is calculated iteratively by using a time optimal control method. The following equations (30) to (32) are combined to optimize the time index, that is, the lyapunov function decays at a negative constant speed and reaches a minimum value, and the calculation flow for obtaining Q is shown in fig. 6. Wherein I is an identity matrix. EbThe characteristic values of the closed loop system are controlled for additional feedback. SbIs a positive constant coefficient matrix.
Eb＝H-B1R-1B1 TPb (30)
Eb TQ+QEb＝-Sb (31)
EbSb -2+Sb -2Eb T＝-I (32)
After obtaining Q matrix, substituting formula (29) to obtain Pb. From PbAnd calculating a feedback controller parameter K according to the following formula.
K＝R-1B1 TPb (33)
After obtaining the feedback controller parameter K, substituting K for equation (27) to determine the feedback control input UfAnd a DC voltage command value Udc *And q-axis current command value igq *And finally obtaining the feedback controller of the direct drive fan shown in the figure 5.
Fourth, example
In the example, the system parameters used for modeling the system linearization small signal are as follows:
TABLE 1 direct drive Fan System principal parameters
Figure BDA0002602476660000201
And carrying out modeling calculation according to the steps to obtain coefficient matrixes A and B of the small signal model.
And then, carrying out order reduction processing on the matrix to improve the usability of the feedback controller. The eigenvalues of the matrix a are evaluated to obtain 14 eigenvalues of the complete system, and the 14 eigenvalues need to be grouped according to their position from the imaginary axis. Dividing the characteristic values into two groups according to the calculation result, wherein the real part of one group of characteristic values close to the virtual axis is-15.96, -25, -57.95 and-103.23, and the 6 characteristic values in the group form a main characteristic value matrix Lambda of a diagonal matrix forming system1And the order a is 6. The real part of the other 8 characteristic roots is between-1634 and-3000, the distance from the real part to the virtual axis is much larger than that of the former group, and a secondary characteristic value matrix Lambda forming a diagonal matrix forming system2And the order b is 8. Thereby the device is provided withAnd obtaining a system eigenvalue matrix Lambda.
The state variables that need to be processed in order to reduce are then analyzed. Observability was first analyzed. Of the 14 state variables, Δ θpllCannot be observed in practical application. Δ Z, Δ Z1,ΔZ3,ΔZ4Human being is assumed to be an intermediate variable, and is likewise unobservable. The variables do not participate in the feedback.
And secondly, analyzing the influence degree of the variable on the system. DC voltage UdcHas a large influence on the stability of the system, and is added into a feedback variable. Delta i in direct drive fan systemsd,ΔisqAnd Δ igd,ΔigqVery similar in size, taking only Δ i for feedback controller design simplificationsd,ΔisqA feedback controller is designed. Similarly, at Δ usd,Δusq,Δucd,ΔucqIn (1), take only Δ usd,ΔusqThe feedback controller is designed, and since 6 main characteristic values of the system are selected and a state variable is required to be added, the selection of the delta u with large active effectcdFeedback is added.
Taking the state quantity X corresponding to the main characteristic value1Is [ Delta U ]dc,Δucd,Δisd,Δisq,Δusd,Δusq]T. Taking the state quantity X corresponding to the secondary characteristic value2Is [ Delta i ]gd,Δigq,Δθpll,ΔZ,ΔZ1,ΔZ3,ΔZ4,Δucq]T. Due to [ X ]1,X2]TThe sequence of the formed X 'state variables is different from that of X obtained by modeling in the foregoing, and the A matrix needs to be subjected to symmetrical row and column transformation and the B matrix needs to be subjected to row transformation, so that the corresponding state variable sequence of the new A' and B 'matrixes is consistent with X'.
And then calculating a matrix C according to the formulas (15) to (17), partitioning the matrix A ', the matrix B' and the matrix C, and calculating according to a formula (25) to obtain a reduced order small signal model shown in a formula (26).
The convergence criterion is 0.005, and the feedback controller parameter K of the feedback controller is calculated by calculating according to the calculation method shown in fig. 6 and equation (27).
Figure BDA0002602476660000221
Therefore, a subsynchronous oscillation feedback controller based on a reduced order model for the direct-drive wind turbine can be constructed according to the formula (34) and the schematic diagram of the direct-drive wind turbine feedback controller shown in FIG. 5.
Next, the actual effect of the feedback controller is subjected to simulation verification. The direct-drive fan used in the small-signal modeling is utilized to carry out single-machine system simulation. The main investigation indexes comprise active power P and direct current voltage UdcOutput current IsD-axis component i ofsd。
Scene 1: the wind input is reduced by 0.2 pu. The simulation results are shown in fig. 7a-7c, and it can be seen that the system generates a certain degree of subsynchronous oscillation, with an oscillation frequency of 21.27Hz, and the oscillation subsides after a period of time. After the feedback controller is added, the convergence speed of the system is obviously accelerated, the dynamic characteristic is enhanced, the oscillation is quickly eliminated, and the good effect of the feedback controller is reflected.
And in scene 2, after the scene 1 acts, when the system enters a stable state, the reactive output of the fan system is increased by 0.2 pu. The simulation results are shown in fig. 8a-8c, and the system generates serious subsynchronous oscillation, which leads to instability of the system. The addition of the feedback controller enables the system to be rapidly converged, the dynamic characteristic is greatly improved, and the occurrence of system instability accidents is effectively avoided.
Scene 3: scene 1 fan system is in strong alternating current system, and subsynchronous oscillation risk is lower relatively, consequently transfers alternating current system intensity to weak alternating current system, and subsynchronous oscillation risk increases, and wind power reduces 0.2pu under this condition. The simulation results are shown in fig. 9a-9c, and it can be seen from the simulation that the system has serious subsynchronous oscillation, the oscillation amplitude of the oscillation frequency of 20.7Hz is continuously increased, and the system will be unstable. After the feedback controller is added, the system is rapidly converged, no oscillation occurs, and the system is safe and stable to operate.
The comprehensive simulation result shows that the model order reduction and feedback control method for suppressing the subsynchronous oscillation of the direct-drive wind turbine has a good suppression effect on the broadband subsynchronous oscillation of the direct-drive wind turbine generator generated under different operating environments and different system disturbances, the subsynchronous oscillation risk is effectively reduced, and the dynamic characteristic of the system is improved.
The above embodiments are merely illustrative, and not restrictive, and those skilled in the relevant art can make various changes and modifications without departing from the spirit and scope of the invention, and therefore all equivalent technical solutions also belong to the scope of the invention.
Those not described in detail in this specification are within the skill of the art.

Claims (5)

1. A model reduced order feedback control method for suppressing subsynchronous oscillation of a direct-drive fan is characterized by comprising the following steps of:
step 1: linearizing mathematical models of the direct-drive fan and a controller thereof, and establishing a direct-drive fan small signal model containing all state variables;
step 2: reducing the order of the small signal model according to the characteristic value of the complete small signal model, observability of state variables and influence degree on oscillation, and establishing a reduced order model of the direct-drive fan;
and step 3: a feedback controller of the direct-drive fan is designed by utilizing the reduced-order direct-drive fan small-signal model, so that a good direct-drive fan subsynchronous oscillation suppression effect is realized.
2. The model reduced order feedback control method for direct drive fan subsynchronous oscillation suppression as claimed in claim 1, wherein: the coordinate transformation of the electrical quantity used by the model order-reduction feedback control method is based on two different reference coordinate systems, and when the same electrical quantity is the PCC point voltage UsWhen the directional reference is carried out, c is marked on the upper corner marks of the d-axis component and the q-axis component, and if no mark exists, the grid voltage U is based on infinityEOrientation of (1); among the electrical quantity symbols used, the initial steady state value is indicated by the lower corner mark 0.
3. The model reduced order feedback control method for direct drive fan subsynchronous oscillation suppression as claimed in claim 2, wherein the specific steps of step 1 are as follows:
linearizing each part of the direct-drive fan simplified circuit; the linear model is calculated based on per unit value, and the AC vector rotation angular velocity base value of the system is omegaB100 π rad/s; with infinite network voltage UEWith reference to the orientation of (1), output current IsThe linearization equation is as formula (1):
Figure FDA0002602476650000021
wherein isd、isqAre respectively the output current IsD, q-axis component of (u)sd、usqRespectively, PCC point voltage UsD and q axis components of (1), the value of the transformer equivalent inductance L is Ls；
PCC point voltage UsIs shown in equation (2):
Figure FDA0002602476650000022
wherein u issd、usqRespectively, PCC point voltage UsD, q-axis component of (u)cd、ucqRespectively, the AC side outlet voltage U of the convertercD, q-axis components of (i)gd、igqAre respectively an alternating side current IgD, q-axis components of (1), filter capacitance CgHas a value of cgResistance RgHas a value of rgFilter inductance LgHas a value of lg；
AC side current IgThe small signal linearization equation of (3):
Figure FDA0002602476650000023
the direct-current bus small-signal equation of the grid-side converter is as shown in formula (4):
Figure FDA0002602476650000024
wherein, the DC capacitor CdHas a value of cd，UdcThe lower corner mark 0 represents the initial steady state value when the voltage is direct current voltage;
the coordinate transformation of the controller adopts a phase-locked loop to provide an orientation angle and adopts a power grid voltage orientation mode; the phase-locked loop has a proportionality coefficient of kpIntegral coefficient of phase-locked loop is kiEstablishing auxiliary intermediate variable Z to obtain PCC point voltage UsThe difference between the orientation angle and the orientation angle of the infinite grid voltage E is thetapllAnd s represents a frequency parameter in the complex frequency domain; the phase-locked loop linearization equation is as follows:
Figure FDA0002602476650000031
a grid-side converter of the direct-drive fan controls the voltage of a direct-current bus and the reactive power of a rotor, and a loop of the direct-drive fan comprises an outer ring controller and an inner ring controller; the outer ring controller fixes direct current voltage, and the inner ring controller fixes current; DC voltage command value Udc *As a d-axis outer ring command value; q-axis current command value igq *As a q-axis inner loop command value;
the method comprises the following steps of establishing a network side controller linearization model:
Figure FDA0002602476650000032
is a d-axis inner ring command value, kp1、ki1Respectively is a proportionality coefficient and an integral coefficient of the outer ring controller; establishing an auxiliary intermediate variable Z1And obtaining an equation of the outer ring of the d axis:
Figure FDA0002602476650000033
ucd *outputs a d-axis voltage command value, k, to the controllerp3、ki3Proportional coefficient and integral coefficient of d-axis inner ring controller, and initial value of AC vector rotation angular velocity of system is omega0Establishing an auxiliary intermediate variable Z3And obtaining an equation of the inner ring of the d axis:
Figure FDA0002602476650000034
ucq *outputting a q-axis voltage command value, k, to the controllerp4、ki4Respectively establishing an auxiliary intermediate variable Z for a proportionality coefficient and an integral coefficient of the q-axis inner ring controller4And obtaining an equation of the q-axis outer ring:
Figure FDA0002602476650000041
the magnitude of the converter gain is denoted as kPWMThe switching period of the converter is TThe relationship between the control signal output by the controller and the outlet voltage at the alternating current side of the converter is as follows:
Figure FDA0002602476650000042
the carrier amplitude of the converter is M, and the formula (9) is linearized to obtain:
Figure FDA0002602476650000043
the joint vertical type (1) - (8), (10) can obtain a direct-drive fan linear small-signal model in the standard form as the formula (11):
Figure FDA0002602476650000044
wherein, the state variable X ═ Δ usd,Δusq,Δigd,Δigq,ΔUdc,Δisd,Δisq,Δθpll,ΔZ,ΔZ1,ΔZ3,ΔZ4,Δucd,Δucq]TControl variable U ═ Δ Udc *,Δigq *]TA is a 14-order square matrix, B is a 14 multiplied by 2-order matrix, and the upper corner mark T of the matrix represents the matrix transposition.
4. The model reduced order feedback control method for direct drive fan subsynchronous oscillation suppression as claimed in claim 3, wherein the concrete steps of the step 2 are as follows:
1) matrix reordering and chunking
Carrying out reduced order processing based on the small signal model of the formula (11); firstly, solving eigenvalues of a system parameter matrix A, wherein the eigenvalues are all positioned on the left half plane of a complex plane; dividing the obtained characteristic values into two groups, wherein the number of the first group of characteristic values is a, the number of the second group of characteristic values is b, and the second group of b characteristic values is required to be far away from the virtual axis compared with the first group of a characteristic values; the characteristic value of A constitutes a characteristic value diagonal matrix Lambda, Lambda has a sub-diagonal matrix Lambda1、Λ2(ii) a The first group of characteristic values after grouping form an a-order matrix Lambda1The second group of characteristic values form a b-order matrix Lambda2；
Figure FDA0002602476650000051
According to the observability of each state quantity and the influence degree on the oscillation, a main a state quantities are taken to form a main state quantity matrix X1The other b state quantities form a secondary state quantity matrix X2(ii) a Order:
Figure FDA0002602476650000052
the order of the state variables of X in the formula (11) and X 'in the formula (13) may be different, so that the matrix A is subjected to symmetrical row transformation and column transformation, and is corresponding to the state variable X', a new coefficient matrix A 'is obtained, and the matrix B is transformed in the same way to obtain B'; the adjusted state equation is obtained as follows:
Figure FDA0002602476650000053
the block processing is performed on the formula (14) according to the formula (13), and the following results are obtained:
Figure FDA0002602476650000054
wherein A is11Is a square matrix of order a, A12Is an a × b order matrix, A21Is a b × a order matrix, A22Is a B-order square matrix, B1Is an a x 2 order matrix, B2Is a b x 2 order matrix, A11，A12，A21，A22，B1，B2Is obtained by directly partitioning an A 'matrix and a B' matrix of an original model formula (14);
the eigenvalues of A' and A are consistent, so the Λ matrix continues to be used for calculations;
thus, the eigenvector matrix C is obtained by:
A'＝CΛC-1 (16)
for subsequent calculations, C is also blocked:
Figure FDA0002602476650000061
wherein, C11Is a square matrix of order a, C12Is an a × b order matrix, C21Is a b × a order matrix, C22Is a b-order square matrix;
2) and (3) performing system order reduction calculation:
setting auxiliary intermediate variable matrix ZbSo that Z isbSatisfies the following formulaThe relationship is as follows:
Figure FDA0002602476650000062
wherein Zb1Is a column vector of order a, Zb2Is a b-order column vector, both of which are ZbDirectly obtaining the product by blocking;
then there is
Figure FDA0002602476650000063
Figure FDA0002602476650000064
The analytic solution of the equation set of equation (20) is:
Figure FDA0002602476650000065
due to Λ2Is a large distance from the imaginary axis, and is approximately considered to be within the time range of the study
Figure FDA0002602476650000066
Is 0, then
Zb2(t)＝0 (22)
By substituting formula (22) for formula (18), it is possible to obtain:
Figure FDA0002602476650000071
using the result of equation (23), the system is reduced by substituting equation (15), and only X is reserved after the reduction1As a state variable; then there are:
Figure FDA0002602476650000072
recording:
H＝A11+A12C21C11 -1 (25)
then the formula (25) is rewritten as
Figure FDA0002602476650000073
Equation (26) is the reduced small signal model; h is an a-order square matrix, B1Is a b x 2 order matrix.
5. The model reduced order feedback control method for direct drive fan subsynchronous oscillation suppression as claimed in claim 4, wherein the concrete steps of the step 3 are as follows:
feedback control input UfWritten in phasor form of formula (27), wherein U* dcfIs a DC voltage feedback quantity command value i* gqfFor the q-axis current feedback amount command value:
Figure FDA0002602476650000074
wherein K is a feedback controller parameter to be designed, and K is a 2 x a order matrix;
the feedback controller parameters are designed based on equation (26), and the following performance indicator functional J is used for equation (26):
Figure FDA0002602476650000075
in the formula (28), t is time, Q is a state quantity weight coefficient matrix, and the size of the element reflects the degree of influence of each corresponding state quantity on oscillation; r is a control quantity weight coefficient matrix, the element size of the control quantity weight coefficient matrix reflects the limitation of the control quantity, and the instability of the system caused by the overlarge feedback control quantity is avoided;
when the performance index functional of equation (28) reaches an extreme value, the ricatt ladder equation should be satisfied:
HTPb+PbH-PbB1R-1B1 TPb+Q＝0 (29)
the unknown matrix solved by equation (29) is PbDetermining Q, R matrix values before solving the equation;
in order to accelerate the convergence speed of the system and improve the improvement effect of the feedback controller on the dynamic characteristics of the system, the value of Q is calculated in an iterative way by using a time optimal control method; simultaneous equations (30) to (32) for optimizing the time index, the Lyapunov function decays at a negative fixed rate and reaches a minimum value; wherein I is an identity matrix, EbControlling characteristic values of closed-loop systems for additional feedback, SbIs a positive definite coefficient matrix;
Eb＝H-B1R-1B1 TPb (30)
Eb TQ+QEb＝-Sb (31)
EbSb -2+Sb -2Eb T＝-I (32)
after obtaining Q matrix, substituting formula (29) to obtain PbFrom PbThe feedback controller parameter K is calculated according to the following formula:
K＝R-1B1 TPb (33)
after obtaining the feedback controller parameter K, substituting K for equation (27) to determine the feedback control input UfAnd a DC voltage command value Udc *And q-axis current command value igq *And finally obtaining the feedback controller of the direct-drive fan.
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