CN109672182B - Coordination control method among multiple power converters - Google Patents

Coordination control method among multiple power converters Download PDF

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CN109672182B
CN109672182B CN201910065310.4A CN201910065310A CN109672182B CN 109672182 B CN109672182 B CN 109672182B CN 201910065310 A CN201910065310 A CN 201910065310A CN 109672182 B CN109672182 B CN 109672182B
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coordinate
alternating
power converter
voltage
current
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CN109672182A (en
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李鹏
郭天宇
殷云星
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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
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected 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
    • H02J3/24—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
    • 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]

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Abstract

A coordination control method among a plurality of power converters comprises the following steps: establishing a mathematical model of a power converter, selecting direct current as an interference variable, and converting the mathematical model into an affine nonlinear form of the power converter; constructing n coordination controllers for coordination control among the n power converters, wherein each coordination controller comprises an outer ring and an inner ring; constructing a self-adaptive droop controller considering the dynamic allowance of each power converter aiming at an outer ring, wherein the outer ring adaptively adjusts the droop coefficient of the power converter through the corresponding self-adaptive droop controller according to the dynamic allowance of the corresponding power converter, coordinates and distributes the transmission power of an alternating current-direct current power flow section, and respectively constructs a voltage compensation unit of each coordination controller based on a first-order inertia link; and constructing a nonlinear controller of the inner ring of each coordination controller aiming at the inner ring, and realizing the decoupling of the output quantity to the interference quantity. The invention can maintain the voltage stability of the direct current bus and realize the decoupling of the output quantity to the interference quantity.

Description

Coordination control method among multiple power converters
Technical Field
The invention relates to a control method of a power converter. In particular to a coordination control method among a plurality of power converters.
Background
The alternating current-direct current hybrid micro-grid can fully utilize the advantages of the alternating current micro-grid and the direct current micro-grid, and the permeability and the operation efficiency of the distributed power supply are improved; meanwhile, an alternating current-direct current complementary power supply and utilization mode is adopted, so that the alternating current-direct current conversion link can be reduced, the energy loss of multi-stage conversion is reduced, and the power quality and the power supply reliability are improved. The alternating current area and the direct current area in the alternating current-direct current hybrid micro-grid are generally formed by a plurality of power converters which are operated in parallel, power interconnection and mutual support among the alternating current-direct current areas can be realized by reasonably regulating and controlling the transmission power through coordinately controlling the plurality of power converters, dynamic balance of internal power of the alternating current-direct current hybrid micro-grid is maintained, and the electric energy quality of the alternating current-direct current hybrid micro-grid is improved.
Disclosure of Invention
The invention aims to solve the technical problem of providing a coordination control method among a plurality of power converters capable of coordinately distributing alternating current-direct current power flow section transmission power.
The technical scheme adopted by the invention is as follows: a coordination control method among a plurality of power converters comprises the following steps:
1) establishing a mathematical model of a power converter, selecting direct current as an interference variable, and converting the established mathematical model of the power converter into an affine nonlinear form of the power converter according to the interference variable;
2) respectively constructing n coordination controllers for coordination control among the n power converters, wherein each coordination controller comprises an outer ring and an inner ring; respectively constructing self-adaptive droop controllers considering the dynamic allowance of each power converter aiming at the outer ring of each coordination controller, wherein the outer ring of each coordination controller self-adaptively adjusts the droop coefficient of the power converter through the corresponding self-adaptive droop controller according to the dynamic allowance of the corresponding power converter, and coordinates and distributes the transmission power of the alternating current/direct current power flow section;
3) aiming at the outer ring of each coordination controller, respectively constructing a voltage compensation unit of each coordination controller based on a first-order inertia link, and ensuring the voltage quality of a direct-current bus;
4) aiming at each internal ring of the coordination controller, the nonlinear controller of each internal ring of the coordination controller is respectively constructed according to the affine nonlinear form of one power converter, so that the decoupling of the output quantity to the interference quantity is realized, and the dynamic response performance of the transmission power of each power converter is improved.
The mathematical model of the power converter in the step 1) is as follows:
Figure BDA0001955492900000011
idis alternating direct axis current; i.e. iqIs alternating quadrature axis current; u. ofdIs an alternating direct axis voltage; u. ofqIs an alternating quadrature axis voltage; e.g. of the typedThe direct-axis component of the three-phase voltage at the alternating current side is obtained; e.g. of the typeqIs the alternating-current side three-phase voltage alternating-axis component; u. ofdcIs a dc bus voltage; i isLIs direct current;
Figure BDA0001955492900000021
is the derivative of the AC direct axis current;
Figure BDA0001955492900000022
is the derivative of the AC quadrature axis current;
Figure BDA0001955492900000023
is the derivative of the dc bus voltage; r is an alternating current side filter loss equivalent resistance; l is an alternating current side filter inductor; c is a direct current bus capacitor; ω is the angular frequency.
Converting the mathematical model of the power converter into an affine nonlinear form of the power converter in the step 1) is as follows:
Figure BDA0001955492900000024
Figure BDA0001955492900000025
Figure BDA0001955492900000026
wherein X is a state variable under an X coordinate;
Figure BDA0001955492900000027
is the derivative of the state variable in the X coordinate; x is the number ofTIs the transpose of the state variable in the X coordinate; u is a control variable under an X coordinate; u. ofTIs the transpose of the control variable in the X coordinate; p is an interference variable under an X coordinate; y is an output variable under an X coordinate; i.e. idrefIs a reference value of alternating direct axis current; i.e. iqrefIs a reference value of AC quadrature axis current; (X) is a vector field directly related to the state variable in the X coordinate; g (X) is a vector field directly related to the control variable in X coordinate; d (X) is directly related to the disturbance variable in X coordinateAn off vector field; h (X) is a vector field directly related to the output variable in X coordinate; hT(x) Is a transpose of the vector field directly related to the output variable in X coordinates; i.e. idIs alternating direct axis current; i.e. iqIs alternating quadrature axis current; u. ofdIs an alternating direct axis voltage; u. ofqIs an alternating quadrature axis voltage; e.g. of the typedThe direct-axis component of the three-phase voltage at the alternating current side is obtained; e.g. of the typeqIs the alternating-current side three-phase voltage alternating-axis component; u. ofdcIs a dc bus voltage; i isLIs direct current; r is an alternating current side filter loss equivalent resistance; l is an alternating current side filter inductor; c is a direct current bus capacitor; ω is the angular frequency.
The control law of the self-adaptive droop controller in the step 2) is as follows:
ΔP(i)＝m(i)×Δudc
Figure BDA0001955492900000031
Δudc＝udcref-udc
Figure BDA0001955492900000032
the positive direction of power transmission is specified to be from an alternating current area to a direct current area;
wherein, Δ P(i)Dynamic power borne by the ith power converter; m is(i)The droop coefficient of the ith power converter is obtained; Δ udcThe voltage deviation value of the direct current bus is obtained; delta P(i)maxThe maximum deviation amount of the power of the ith power converter is obtained; Δ udcmaxThe maximum deviation value of the direct current bus voltage is obtained; u. ofdcIs a dc bus voltage; pre(i)A dynamic power allowance of the ith power converter; u. ofdcrefIs a direct current bus voltage reference value; pN(i)Rated power of the ith power converter; p(i)The measured power of the ith power converter is obtained; p0(i)The initial power of the ith power converter; Δ udcmaxThe maximum deviation value of the direct current bus voltage is obtained; u. ofdcmaxIs the voltage upper limit value of the direct current bus; u. ofdcminIs the dc bus voltage lower limit.
Step 3) the mathematical model of the voltage compensation unit is as follows:
Figure BDA0001955492900000033
wherein G(s) is the ratio of the output to the input of a defined first-order inertia element; s is a laplace operator; k is a radical ofΔuIs the voltage gain; t is a first-order inertia time constant;
reference value u of DC bus voltagedcrefAnd the DC bus voltage udcAfter the difference value of (2) passes through the voltage compensation unit, the compensation amount delta u 'of the direct current bus voltage is obtained'dc。
The step 4) comprises the following steps:
(1) selecting coordinate transformation:
Figure BDA0001955492900000034
(2) converting an affine nonlinear form of a power converter into a Brinell standard form of the power converter as follows:
Figure BDA0001955492900000041
Figure BDA0001955492900000042
wherein: phi (X) is a local differential homoembryo under an X coordinate; z is a state variable in a Z coordinate; z is a radical of1Is a first state variable in the Z coordinate; z is a radical of2Is a second state variable in the Z coordinate;
Figure BDA0001955492900000043
as a state in the Z coordinateA derivative of the variable; h is1(x) Is a first output variable in the X coordinate; h is2(x) Is a second output variable in the X coordinate; eta (X) is an dimension-increasing state variable under an X coordinate; eta is the dimension-increasing state variable under the Z coordinate;
Figure BDA0001955492900000044
is the derivative of the dimension-increasing state variable in the Z coordinate; v is a pre-control variable under a Z coordinate; a is a coefficient matrix directly related to the state variable under the Z coordinate; b is a coefficient matrix directly related to a pre-control variable under a Z coordinate; q is a coefficient matrix directly related to the dimension-increasing state variable under the Z coordinate; s is a coefficient matrix directly related to an interference variable under an X coordinate;
(3) giving a nonlinear control law u of each nonlinear controllerkComprises the following steps:
uk＝E-1(x)[v-A(x)]
by taking the derivative of lie, we get:
Figure BDA0001955492900000045
by solving the linear optimal control problem of the quadratic performance index, the following results are obtained:
v＝-M-1BTPz
p is obtained by a Riccati equation of a linear optimal control problem of quadratic performance indexes, wherein the Riccati equation is as follows:
ATP+PA-PBM-1BTP+Q＝0
wherein: a (X) is the lie derivative vector field in X coordinates with respect to the state variable; e (X) is the lie derivative vector field in X coordinates for the output variable; e-1(x) Is the inverse of the lie derivative vector field in X coordinates with respect to the output variable; m-1Is the inverse of the weight matrix of the control variable in the X coordinate; q is a weight matrix of the state variable under the X coordinate; a. theTIs the transpose of the coefficient matrix directly related to the state variable in the Z coordinate; b isTAs a matrix of coefficients directly related to the pre-controlled variable in the Z coordinateTransposing; p is a solution vector of the Riccati equation under the Z coordinate; i.e. idIs alternating direct axis current; i.e. iqIs alternating quadrature axis current; e.g. of the typedThe direct-axis component of the three-phase voltage at the alternating current side is obtained; e.g. of the typeqIs the alternating-current side three-phase voltage alternating-axis component; r is an alternating current side filter loss equivalent resistance; l is an alternating current side filter inductor; ω is the angular frequency.
The coordination control method for the plurality of power converters has the following effects:
(1) the method can adaptively adjust the droop coefficient of each power converter according to the dynamic allowance of each power converter when power disturbance occurs, and coordinate and distribute the transmission power of the alternating current-direct current tidal current section;
(2) the method can maintain the voltage stability of the direct current bus, and ensure the voltage quality of the direct current bus through the constructed coordination controller containing the voltage compensation unit;
(3) the method can realize the decoupling of the output quantity to the interference quantity and improve the dynamic response performance of the transmission power of each power converter.
Drawings
FIG. 1 is a power converter topology;
FIG. 2 is an outer loop control block diagram of each coordinating controller;
fig. 3 is an ac/dc hybrid microgrid topology
Fig. 4 is a transmission power variation curve of three power converters;
FIG. 5 is a graph of current change for a power converter;
FIG. 6 is a graph of a variation of a DC reference value and a DC differential value of a power converter;
FIG. 7 is a DC bus voltage variation curve without a voltage compensation unit;
fig. 8 is a dc bus voltage variation curve with and without the voltage compensation unit.
Detailed Description
The following describes a method for coordinating and controlling multiple power converters according to the present invention in detail with reference to the following embodiments and accompanying drawings
The invention discloses a coordination control method among a plurality of power converters, which comprises the following steps:
1) as shown in fig. 1, a mathematical model of a power converter is established, a direct current is selected as an interference variable, and the established mathematical model of the power converter is converted into an affine nonlinear form of the power converter according to the interference variable; wherein the content of the first and second substances,
the mathematical model of the power converter is as follows:
Figure BDA0001955492900000051
idis alternating direct axis current; i.e. iqIs alternating quadrature axis current; u. ofdIs an alternating direct axis voltage; u. ofqIs an alternating quadrature axis voltage; e.g. of the typedThe direct-axis component of the three-phase voltage at the alternating current side is obtained; e.g. of the typeqIs the alternating-current side three-phase voltage alternating-axis component; u. ofdcIs a dc bus voltage; i isLIs direct current;
Figure BDA0001955492900000052
is the derivative of the AC direct axis current;
Figure BDA0001955492900000053
is the derivative of the AC quadrature axis current;
Figure BDA0001955492900000054
is the derivative of the dc bus voltage; r is an alternating current side filter loss equivalent resistance; l is an alternating current side filter inductor; c is a direct current bus capacitor; ω is the angular frequency.
In FIG. 1, eaIs the voltage of the a phase at the alternating current side; e.g. of the typebB phase voltage at the alternating current side; e.g. of the typecIs the alternating side c phase voltage; i.e. iaA phase current of an alternating side a; i.e. ibB phase current on the alternating current side; i.e. icThe current of the alternating side c phase; e is the equivalent voltage of the direct-current microgrid; q1For power converters of number 1Closing; q2A switch No. 2 of the power converter; q3A switch No. 3 of the power converter; q4A switch number 4 of the power converter; q5A switch No. 5 of the power converter; q6Is the switch No. 6 of the power converter.
The method for converting the mathematical model of the power converter into the affine nonlinear form of the power converter comprises the following steps:
Figure BDA0001955492900000061
Figure BDA0001955492900000062
Figure BDA0001955492900000063
wherein X is a state variable under an X coordinate;
Figure BDA0001955492900000064
is the derivative of the state variable in the X coordinate; x is the number ofTIs the transpose of the state variable in the X coordinate; u is a control variable under an X coordinate; u. ofTIs the transpose of the control variable in the X coordinate; p is an interference variable under an X coordinate; y is an output variable under an X coordinate; i.e. idrefIs a reference value of alternating direct axis current; i.e. iqrefIs a reference value of AC quadrature axis current; (X) is a vector field directly related to the state variable in the X coordinate; g (X) is a vector field directly related to the control variable in X coordinate; d (X) is a vector field directly related to the disturbance variable in the X coordinate; h (X) is a vector field directly related to the output variable in X coordinate; hT(x) Is a transpose of the vector field directly related to the output variable in X coordinates; i.e. idIs alternating direct axis current; i.e. iqIs alternating quadrature axis current; u. ofdIs an alternating direct axis voltage; u. ofqIs an alternating quadrature axis voltage; e.g. of the typedFor ac side three-phase voltage straight-axis componentAn amount; e.g. of the typeqIs the alternating-current side three-phase voltage alternating-axis component; u. ofdcIs a dc bus voltage; i isLIs direct current; r is an alternating current side filter loss equivalent resistance; l is an alternating current side filter inductor; c is a direct current bus capacitor; ω is the angular frequency.
2) Respectively constructing n coordination controllers for coordination control among the n power converters, wherein each coordination controller comprises an outer ring and an inner ring; respectively constructing self-adaptive droop controllers considering the dynamic allowance of each power converter aiming at the outer ring of each coordination controller, wherein the outer ring of each coordination controller self-adaptively adjusts the droop coefficient of the power converter through the corresponding self-adaptive droop controller according to the dynamic allowance of the corresponding power converter, and coordinates and distributes the transmission power of the alternating current/direct current power flow section;
the control law of the self-adaptive droop controller is as follows:
ΔP(i)＝m(i)×Δudc
Figure BDA0001955492900000071
Δudc＝udcref-udc
Figure BDA0001955492900000072
the positive direction of power transmission is specified to be from an alternating current area to a direct current area;
wherein, Δ P(i)Dynamic power borne by the ith power converter; m is(i)The droop coefficient of the ith power converter is obtained; Δ udcThe voltage deviation value of the direct current bus is obtained; delta P(i)maxThe maximum deviation amount of the power of the ith power converter is obtained; Δ udcmaxThe maximum deviation value of the direct current bus voltage is obtained; u. ofdcIs a dc bus voltage; pre(i)A dynamic power allowance of the ith power converter; u. ofdcrefIs a direct current bus voltage reference value; pN(i)Rated power of the ith power converter; p(i)The measured power of the ith power converter is obtained; p0(i)The initial power of the ith power converter; Δ udcmaxThe maximum deviation value of the direct current bus voltage is obtained; u. ofdcmaxIs the voltage upper limit value of the direct current bus; u. ofdcminIs the dc bus voltage lower limit.
3) Aiming at the outer ring of each coordination controller, respectively constructing a voltage compensation unit of each coordination controller based on a first-order inertia link, and ensuring the voltage quality of a direct-current bus; the mathematical model of the voltage compensation unit is as follows:
Figure BDA0001955492900000073
wherein G(s) is the ratio of the output to the input of a defined first-order inertia element; s is a laplace operator; k is a radical ofΔuIs the voltage gain; t is a first-order inertia time constant;
reference value u of DC bus voltagedcrefAnd the DC bus voltage udcAfter the difference value of (2) passes through the voltage compensation unit, the compensation amount delta u 'of the direct current bus voltage is obtained'dc。
The outer loop control block diagram of each coordinating controller is shown in FIG. 2, where Pref(i)The power reference value of the ith power converter is obtained; i.e. idref(i)The reference value is the AC direct axis current reference value of the ith power converter.
4) Aiming at each internal ring of the coordination controller, the nonlinear controller of each internal ring of the coordination controller is respectively constructed according to the affine nonlinear form of one power converter, so that the decoupling of the output quantity to the interference quantity is realized, and the dynamic response performance of the transmission power of each power converter is improved. The method comprises the following steps:
(1) selecting coordinate transformation:
Figure BDA0001955492900000086
(2) converting an affine nonlinear form of a power converter into a Brinell standard form of the power converter as follows:
Figure BDA0001955492900000081
Figure BDA0001955492900000082
wherein: phi (X) is a local differential homoembryo under an X coordinate; z is a state variable in a Z coordinate; z is a radical of1Is a first state variable in the Z coordinate; z is a radical of2Is a second state variable in the Z coordinate;
Figure BDA0001955492900000083
is the derivative of the state variable in the Z coordinate; h is1(x) Is a first output variable in the X coordinate; h is2(x) Is a second output variable in the X coordinate; eta (X) is an dimension-increasing state variable under an X coordinate; eta is the dimension-increasing state variable under the Z coordinate;
Figure BDA0001955492900000084
is the derivative of the dimension-increasing state variable in the Z coordinate; v is a pre-control variable under a Z coordinate; a is a coefficient matrix directly related to the state variable under the Z coordinate; b is a coefficient matrix directly related to a pre-control variable under a Z coordinate; q is a coefficient matrix directly related to the dimension-increasing state variable under the Z coordinate; s is a coefficient matrix directly related to an interference variable under an X coordinate;
(3) giving a nonlinear control law u of each nonlinear controllerkComprises the following steps:
uk＝E-1(x)[v-A(x)]
by taking the derivative of lie, we get:
Figure BDA0001955492900000085
by solving the linear optimal control problem of the quadratic performance index, the following results are obtained:
v＝-M-1BTPz
p is obtained by a Riccati equation of a linear optimal control problem of quadratic performance indexes, wherein the Riccati equation is as follows:
ATP+PA-PBM-1BTP+Q＝0
wherein: a (X) is the lie derivative vector field in X coordinates with respect to the state variable; e (X) is the lie derivative vector field in X coordinates for the output variable; e-1(x) Is the inverse of the lie derivative vector field in X coordinates with respect to the output variable; m-1Is the inverse of the weight matrix of the control variable in the X coordinate; q is a weight matrix of the state variable under the X coordinate; a. theTIs the transpose of the coefficient matrix directly related to the state variable in the Z coordinate; b isTIs the transposition of a coefficient matrix directly related to a pre-control variable under a Z coordinate; p is a solution vector of the Riccati equation under the Z coordinate; i.e. idIs alternating direct axis current; i.e. iqIs alternating quadrature axis current; e.g. of the typedThe direct-axis component of the three-phase voltage at the alternating current side is obtained; e.g. of the typeqIs the alternating-current side three-phase voltage alternating-axis component; r is an alternating current side filter loss equivalent resistance; l is an alternating current side filter inductor; ω is the angular frequency.
Examples are given below:
and (3) building a simulation model by referring to fig. 3, wherein 3 power converters run in parallel in the alternating current-direct current flow section. The voltage of an alternating current power grid is 10kV, the rated voltage of a direct current bus is 560V, the transformation ratio of a transformer is 10kV/380V, the rated capacity of a power converter is 250kVA, the filtering loss equivalent resistance of an alternating current side is 0.5m omega, the filtering inductance of the alternating current side is 160uH, and the direct current load is 450 kW.
1) Before 0.6 second, the system was operating at steady state with a dc load of 450 kW. When 0.6 second, the load is 200kW on the direct current side; when 0.7 second, the load on the direct current side is cut off by 200 kW; when 0.8 second, the load on the direct current side is cut off by 250 kW; at 0.9 second, the load on the DC side was 250 kW.
As can be seen from fig. 4, when a load is put in (0.6 second) or a load is cut off (0.8 second) on the basis of the initial operating condition, the three power converters distribute transmission power according to the dynamic power margins of the three power converters, and the borne power difference is gradually reduced; when the total load on the direct current side is larger than the initial operation working condition, the load is cut off (0.7 seconds), or when the total load on the direct current side is smaller than the initial operation working condition, the load is put in (0.9 seconds), the three power converters distribute the transmission power according to the dynamic power allowance of the three power converters, and the difference of the born transmission power is gradually increased. The simulation result verifies the function of the outer ring of the designed coordination controller. Each power converter can coordinate and distribute the transmission power of the alternating current-direct current tidal current section.
2) Before 0.6 second, the system was operating at steady state with a dc load of 450 kW. At 0.6 second, a 200kW load was applied to the DC side.
As can be seen from FIG. 5, when the DC side is loaded, the AC direct axis current reference value i is causeddrefVarying, alternating direct axis current idCan quickly track the reference value i of the upper alternating current direct axis currentdrefIn the transient process, the transmission power oscillation of each power converter is small, the adjusting time is short, and the good dynamic response characteristic is embodied.
As can be seen from FIG. 6, the AC direct axis current reference value idrefWith alternating direct axis current idDifference i ofdref-idWhen the direct current load has step disturbance, the direct current load does not change, and decoupling of output to interference is achieved.
As can be seen from fig. 7, when a load is placed on the dc side, the coordination control method among the power converters can maintain the dc bus voltage stable, and make the dc bus voltage dynamic adjustment time short, without oscillation, and the dynamic response performance good.
3) Before 1 second, the system was operating at steady state with a dc load of 450 kW. When the time is 1 second, a 200kW load is input to the direct current side; at 2 seconds, the direct current side cuts the load of 350 kW; at 3 seconds, the direct current side cuts off a load of 150 kW;
as can be seen from fig. 8, when step disturbance occurs to the dc-side load, the voltage compensation unit is not included, and the voltage deviation amount of the dc bus is large; the voltage compensation unit is included, and the voltage deviation amount of the direct current bus is reduced.

Claims (3)

1. A coordination control method among a plurality of power converters is characterized by comprising the following steps:
1) establishing a mathematical model of a power converter, selecting direct current as an interference variable, and converting the established mathematical model of the power converter into an affine nonlinear form of the power converter according to the interference variable;
the method for converting the mathematical model of the power converter into the affine nonlinear form of the power converter comprises the following steps:
Figure FDA0002929634100000011
Figure FDA0002929634100000012
Figure FDA0002929634100000013
wherein X is a state variable under an X coordinate;
Figure FDA0002929634100000014
is the derivative of the state variable in the X coordinate; x is the number ofTIs the transpose of the state variable in the X coordinate; u is a control variable under an X coordinate; u. ofTIs the transpose of the control variable in the X coordinate; p is an interference variable under an X coordinate; y is an output variable under an X coordinate; i.e. idrefIs a reference value of alternating direct axis current; i.e. iqrefIs a reference value of AC quadrature axis current; (X) is a vector field directly related to the state variable in the X coordinate; g (X) is a vector field directly related to the control variable in X coordinate; d (X) is a vector field directly related to the disturbance variable in the X coordinate; h (X) is a vector field directly related to the output variable in X coordinate; hT(x) Is a transpose of the vector field directly related to the output variable in X coordinates; i.e. idIs alternating direct axis current; i.e. iqIs alternating quadrature axis current; u. ofdIs an alternating direct axis voltage; u. ofqIs a crossA current quadrature axis voltage; e.g. of the typedThe direct-axis component of the three-phase voltage at the alternating current side is obtained; e.g. of the typeqIs the alternating-current side three-phase voltage alternating-axis component; u. ofdcIs a dc bus voltage; i isLIs direct current; r is an alternating current side filter loss equivalent resistance; l is an alternating current side filter inductor; c is a direct current bus capacitor; omega is angular frequency;
2) respectively constructing n coordination controllers for coordination control among the n power converters, wherein each coordination controller comprises an outer ring and an inner ring; respectively constructing self-adaptive droop controllers considering the dynamic allowance of each power converter aiming at the outer ring of each coordination controller, wherein the outer ring of each coordination controller self-adaptively adjusts the droop coefficient of the power converter through the corresponding self-adaptive droop controller according to the dynamic allowance of the corresponding power converter, and coordinates and distributes the transmission power of the alternating current/direct current power flow section;
the control law of the self-adaptive droop controller is as follows:
ΔP(i)＝m(i)×Δudc
Figure FDA0002929634100000021
Δudc＝udcref-udc
Figure FDA0002929634100000022
the positive direction of power transmission is specified to be from an alternating current area to a direct current area;
wherein, Δ P(i)Dynamic power borne by the ith power converter; m is(i)The droop coefficient of the ith power converter is obtained; Δ udcThe voltage deviation value of the direct current bus is obtained; delta P(i)maxThe maximum deviation amount of the power of the ith power converter is obtained; Δ udcmaxThe maximum deviation value of the direct current bus voltage is obtained; u. ofdcIs a dc bus voltage; pre(i)A dynamic power allowance of the ith power converter; u. ofdcrefIs a DC busA voltage reference value; pN(i)Rated power of the ith power converter; p(i)The measured power of the ith power converter is obtained; p0(i)The initial power of the ith power converter; Δ udcmaxThe maximum deviation value of the direct current bus voltage is obtained; u. ofdcmaxIs the voltage upper limit value of the direct current bus; u. ofdcminIs the voltage lower limit value of the direct current bus;
3) aiming at the outer ring of each coordination controller, respectively constructing a voltage compensation unit of each coordination controller based on a first-order inertia link, and ensuring the voltage quality of a direct-current bus;
4) aiming at each internal ring of the coordination controller, respectively constructing the nonlinear controller of the internal ring of each coordination controller according to the affine nonlinear form of one power converter, thereby realizing the decoupling of the output quantity to the interference quantity and improving the dynamic response performance of the transmission power of each power converter; the method comprises the following steps:
(1) selecting coordinate transformation:
Figure FDA0002929634100000023
(2) converting an affine nonlinear form of a power converter into a Brinell standard form of the power converter as follows:
Figure FDA0002929634100000031
Figure FDA0002929634100000032
wherein: phi (X) is a local differential homoembryo under an X coordinate; z is a state variable in a Z coordinate; z is a radical of1Is a first state variable in the Z coordinate; z is a radical of2Is a second state variable in the Z coordinate;
Figure FDA0002929634100000033
is the derivative of the state variable in the Z coordinate; h is1(x) Is a first output variable in the X coordinate; h is2(x) Is a second output variable in the X coordinate; eta (X) is an dimension-increasing state variable under an X coordinate; eta is the dimension-increasing state variable under the Z coordinate;
Figure FDA0002929634100000034
is the derivative of the dimension-increasing state variable in the Z coordinate; v is a pre-control variable under a Z coordinate; a is a coefficient matrix directly related to the state variable under the Z coordinate; b is a coefficient matrix directly related to a pre-control variable under a Z coordinate; q is a coefficient matrix directly related to the dimension-increasing state variable under the Z coordinate; s is a coefficient matrix directly related to an interference variable under an X coordinate;
(3) giving a nonlinear control law u of each nonlinear controllerkComprises the following steps:
uk＝E-1(x)[v-A(x)]
by taking the derivative of lie, we get:
Figure FDA0002929634100000035
by solving the linear optimal control problem of the quadratic performance index, the following results are obtained:
v＝-M-1BTPz
p is obtained by a Riccati equation of a linear optimal control problem of quadratic performance indexes, wherein the Riccati equation is as follows:
ATP+PA-PBM-1BTP+Q＝0
wherein: a (X) is the lie derivative vector field in X coordinates with respect to the state variable; e (X) is the lie derivative vector field in X coordinates for the output variable; e-1(x) Is the inverse of the lie derivative vector field in X coordinates with respect to the output variable; m-1Is the inverse of the weight matrix of the control variable in the X coordinate; q is a weight matrix of the state variable under the X coordinate; a. theTIs the transpose of the coefficient matrix directly related to the state variable in the Z coordinate; b isTIn the Z coordinateTransposing a coefficient matrix directly related to the pre-control variable; p is a solution vector of the Riccati equation under the Z coordinate; i.e. idIs alternating direct axis current; i.e. iqIs alternating quadrature axis current; e.g. of the typedThe direct-axis component of the three-phase voltage at the alternating current side is obtained; e.g. of the typeqIs the alternating-current side three-phase voltage alternating-axis component; r is an alternating current side filter loss equivalent resistance; l is an alternating current side filter inductor; ω is the angular frequency.
2. The method of claim 1, wherein the mathematical model of the power converter in step 1) is:
Figure FDA0002929634100000041
idis alternating direct axis current; i.e. iqIs alternating quadrature axis current; u. ofdIs an alternating direct axis voltage; u. ofqIs an alternating quadrature axis voltage; e.g. of the typedThe direct-axis component of the three-phase voltage at the alternating current side is obtained; e.g. of the typeqIs the alternating-current side three-phase voltage alternating-axis component; u. ofdcIs a dc bus voltage; i isLIs direct current;
Figure FDA0002929634100000042
is the derivative of the AC direct axis current;
Figure FDA0002929634100000043
is the derivative of the AC quadrature axis current;
Figure FDA0002929634100000044
is the derivative of the dc bus voltage; r is an alternating current side filter loss equivalent resistance; l is an alternating current side filter inductor; c is a direct current bus capacitor; ω is the angular frequency.
3. The method of claim 1, wherein the mathematical model of the voltage compensation unit in step 3) is:
Figure FDA0002929634100000045
wherein G(s) is the ratio of the output to the input of a defined first-order inertia element; s is a laplace operator; k is a radical ofΔuIs the voltage gain; t is a first-order inertia time constant;
reference value u of DC bus voltagedcrefAnd the DC bus voltage udcAfter the difference value of (2) passes through the voltage compensation unit, the compensation amount delta u 'of the direct current bus voltage is obtained'dc。
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