CN114172143B - Direct-current system equivalent modeling method based on voltage and current double-loop control - Google Patents

Direct-current system equivalent modeling method based on voltage and current double-loop control Download PDF

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CN114172143B
CN114172143B CN202111496895.9A CN202111496895A CN114172143B CN 114172143 B CN114172143 B CN 114172143B CN 202111496895 A CN202111496895 A CN 202111496895A CN 114172143 B CN114172143 B CN 114172143B
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CN114172143A (en
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赵学深
朱琳
郭力
李霞林
卢浩
王成山
王智
李鹏飞
张可心
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Tianjin 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
    • H02J1/00—Circuit arrangements for dc mains or dc distribution networks
    • H02J1/10—Parallel operation of dc sources
    • 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
    • H02J1/00—Circuit arrangements for dc mains or dc distribution networks
    • H02J1/10—Parallel operation of dc sources
    • H02J1/102—Parallel operation of dc sources being switching converters
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M1/00—Details of apparatus for conversion
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02M—APPARATUS FOR CONVERSION BETWEEN AC AND AC, BETWEEN AC AND DC, OR BETWEEN DC AND DC, AND FOR USE WITH MAINS OR SIMILAR POWER SUPPLY SYSTEMS; CONVERSION OF DC OR AC INPUT POWER INTO SURGE OUTPUT POWER; CONTROL OR REGULATION THEREOF
    • H02M3/00—Conversion of dc power input into dc power output
    • 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
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • 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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  • Power Engineering (AREA)
  • Control Of Voltage And Current In General (AREA)
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Abstract

The invention relates to a direct current system equivalent modeling method based on voltage and current double-loop control, which comprises the following steps: aiming at a direct current system based on voltage and current double-loop control, equivalently converting output filter inductive current state variables of a plurality of converters in the direct current system into output filter inductive current state variables of one equivalent single converter; equivalently converting the current control integral link state variables of a plurality of converters in the direct current system into the current control integral link state variable of one equivalent single converter; equivalently converting the voltage control integral link state variables of a plurality of converters in the direct current system into the voltage control integral link state variable of one equivalent single converter; the droop control loops of a plurality of converters in a direct current system are equivalently converted into the droop control loop of an equivalent single converter, and the plurality of converters based on voltage and current double-loop control are connected in parallel with the direct current system to be modeled into the equivalent single converter.

Description

Direct-current system equivalent modeling method based on voltage and current double-loop control
Technical Field
The invention belongs to the field of direct current system equivalent modeling, and particularly relates to a direct current system equivalent modeling method based on voltage and current double-loop control.
Background
With global warming caused by fossil energy power generation such as coal and the like, all countries in the world are now vigorously developing renewable energy power generation. The direct current system has the advantages of high energy efficiency, large power distribution capacity and the like, can not only consume high-proportion renewable energy power generation equipment such as photovoltaic power generation and fuel cells, but also can allow a large amount of constant power loads such as electric vehicles and data centers to be accessed. However, the strong fluctuation of the constant power load power with the negative resistance characteristic brings great challenges to the safe and stable operation of a plurality of converters in parallel connection with a direct current system. When the constant power load has large power fluctuation, the transient stability of the direct current system before and after the fluctuation cannot be predicted by the linear model-based direct current system small-disturbance stability analysis, so the direct current system large-disturbance stability analysis considering the interaction among a plurality of converters is more and more important. The main problem of the analysis of the large-disturbance stability of the direct-current system with a plurality of converters connected in parallel is that the number of state variables is too large, and the interaction between the state variables and how the interaction affects the large-disturbance stability of the direct-current system are difficult to clearly understand. The existing equivalent modeling method of the direct current system is only suitable for a direct current system with a plurality of parallel converters controlled by a single voltage ring. For a direct-current system with a plurality of converters controlled by voltage and current double rings connected in parallel, an equivalent modeling method suitable for the direct-current system is still lacked.
In summary, in order to reduce the problem of large number of state variables in a dc system with multiple parallel converters based on voltage-current double-loop control and fully exert the advantages of the dc system, an equivalent modeling method for the dc system based on voltage-current double-loop control is required.
Disclosure of Invention
In order to solve the equivalent modeling problem of a direct-current system with a plurality of converters connected in parallel, the invention provides a direct-current system equivalent modeling method aiming at voltage and current double-loop control. The technical scheme is as follows:
a direct current system equivalent modeling method based on voltage and current double-loop control comprises the following steps:
step 1: aiming at a direct current system based on voltage and current double-loop control, output filter inductive current state variables of a plurality of converters in the direct current system are equivalently converted into output filter inductive current state variables of one equivalent single converter. The method comprises the following steps:
setting the output filter inductive current of the y converter as I y Y =1,2, …, n, n is the total number of all converters in the dc system, the output filter inductor currents of all converters are summed with each other, the sum is equal to the output filter inductor current I of a single converter, and I is equal to the output filter inductor current I of a single converter y Y =1,2, …, n, and I as state variables;
step 2: the method is characterized in that the current control integral link state variables of a plurality of converters in a direct current system are equivalently converted into the current control integral link state variables of one equivalent single converter, and the method comprises the following steps:
the state variable of the current control integral link of the y-th converter is assumed to be [ [ integral ] (I ] ry -I y ) dt, let us say that the current control integral link state variable of the equivalent single converter is ^ (I) r -I) dt, further obtaining ^ integral (I) based on the equivalent transformation relation of the output filter inductor current state variable obtained in step 1 ry -I y ) dt and: (I) r -I) the equivalence transformation relationship between dt, as shown in
Figure BDA0003400273780000021
Wherein k is piy And k iiy Proportional and integral coefficients, I, of the current control loop of the y-th converter y And I ry For the y stage conversionOutput filter inductor current reference value, k, of the device pi And k ii Proportional and integral coefficients, I, of the current control loop of the equivalent single converter r Is the output filter inductance current reference value, L, of the equivalent single converter fy And L f Output filter inductances of the y-th converter and the equivalent single converter, respectively, where ^ integral, d, and t are integral sign, differential operator, and time, respectively;
and step 3: the method is characterized in that the voltage control integral link state variables of a plurality of converters in a direct current system are equivalently converted into the voltage control integral link state variables of one equivalent single converter, and the method comprises the following steps:
let the voltage control integral element state variable of the y-th converter be [ U ] ] [ [ integral ] factor refy -U) dt, and the voltage control integral link state variable of the equivalent single converter is ^ Uj (U) ref U) dt, since each converter is given I by a voltage control loop ry The equivalent single converter obtains I through a voltage control loop r Based on the equivalent transformation relation of the state variable of the current control integral link obtained in the step 2, integral factor (U) is further obtained refy -U) dt and & (U) ref -U) dt is equal to the transformation relation, as shown in the following equation:
Figure BDA0003400273780000022
wherein, U refy And U ref Output voltage reference values of the y-th converter and the equivalent single converter respectively, U is the direct current bus voltage of the direct current system, k puy And k iuy Proportional and integral coefficients, k, of the voltage control loop of the y-th converter pu And k iu The proportional coefficient and the integral coefficient of the voltage control loop of the equivalent single converter are respectively.
And 4, step 4: the droop control loops of a plurality of converters in a direct current system are equivalently converted into the droop control loop of an equivalent single converter, and the plurality of converters based on voltage and current double-loop control are connected in parallel with the direct current system to be modeled into the equivalent single converter.
Drawings
FIG. 1 is a control topology for a multiple converter parallel DC system;
FIG. 2 is a control topology of an equivalent single converter;
FIG. 3 is a waveform diagram of a state variable of a current control integration element;
FIG. 4 is a waveform diagram of a state variable of a voltage control integration element;
FIG. 5 is a transient voltage stabilization waveform of the DC bus of the DC system and its equivalent single converter;
FIG. 6 is a transient instability waveform of the DC bus voltage of the DC system and its equivalent single converter;
Detailed Description
The dc system equivalent modeling method based on voltage and current dual-loop control according to the present invention will be described in detail with reference to the accompanying drawings and specific implementations.
(1) The output filter inductance current state variables of a plurality of converters in the direct current system are equivalently converted into the output filter inductance current state variables of one equivalent single converter.
Let the output filter inductor current of the y converter be I y Y =1,2, …, n, n is the total number of all converters in the dc system, and the output filter inductor current of the equivalent single converter is set as I. The output filter inductance currents of all converters are mutually accumulated, and I is y And I as state variables, the following relational expressions exist
Figure BDA0003400273780000031
Further, the following differential form can be obtained
Figure BDA0003400273780000032
Where d and t are the differential operator and time, respectively.
(2) The current control integral link state variables of a plurality of converters in the direct current system are equivalently converted into the current control integral link state variables of one equivalent single converter.
After considering the duty ratio signal, the DC system and the equivalent single machine can be represented by the following formulas
Figure BDA0003400273780000033
Wherein D is y 、L fy And U sy Duty cycle, output filter inductance and input dc voltage of the y converter, D, L f And U s The duty ratio, the output filter inductance and the input direct-current voltage of the equivalent single converter are respectively.
Further, the following formula can be obtained
Figure BDA0003400273780000034
When U is turned s ＝U sy When it is established, then
Figure BDA0003400273780000035
From the above formula, the output filter inductance L of each converter in the DC system can be known fy Output filter inductor L of sum-equivalent single converter f A relational expression between them. In addition, the output filter capacitance C of each converter fy In parallel with each other, there is also the following equation
Figure BDA0003400273780000036
Wherein, C f The output filter capacitance of the equivalent single converter. Because each converter and the equivalent single converter obtain the duty ratio through the current control loop, the following formula can be obtained
Figure BDA0003400273780000041
Wherein k is piy And k iiy Proportional and integral coefficients, I, of the current control loop of the y-th converter y And I ry Respectively the output filtered inductor current of the y converter and its reference value, k pi And k ii Proportional and integral coefficients, I and I, respectively, of the current control loop of the equivalent single converter r The output filter inductor current of the equivalent single converter and the reference value thereof respectively, wherein ^ integral is an integral sign, and ^ integral (I) ry -I y ) dt and ^ j (I) r I) dt is the current control integral link state variable of the y converter and the equivalent single converter respectively.
Because each converter has a droop control link, the output filtering current of each converter presents a proportional relation. Suppose p y As the current sharing factor of the y-th converter, then there is ∑ p y =1 holds, where Σ is the sum sign. Then ^ f (I) ry -I y ) dt and: (I) r The relationship between-I) dt and-I) dt is shown in the following formula
Figure BDA0003400273780000042
(3) The voltage control integral link state variables of a plurality of converters in the direct current system are equivalently converted into the voltage control integral link state variables of one equivalent single converter.
Because each converter (or equivalent single converter) obtains I through a voltage control loop ry (or I) r ) And when U is ref ＝U refy When the formula is satisfied, the following two formulas can be obtained
Figure BDA0003400273780000043
Figure BDA0003400273780000044
Wherein, U refy And U ref Output voltage reference values of the y-th converter and the equivalent single converter respectively, U is the direct current bus voltage of the direct current system, k puy And k iuy Proportional and integral coefficients, k, of the voltage control loop of the y-th converter pu And k iu Proportional coefficient and integral coefficient of the voltage control loop of the equivalent single converter respectively, [ integral ] factor (U [ integral ] factor [ ]) refy -U) dt and & (U) ref -U) dt are the voltage control integral link state variables of the kth converter and the equivalent single converter respectively. Then ^ n ^ (U) refy -U) dt and: (U) ref The relationship between-U) dt and-dt is shown in the following equation.
Figure BDA0003400273780000045
(4) Equivalently converting the droop control loops of a plurality of converters in the direct current system into the droop control loop of one equivalent single converter.
k dy And k d Droop coefficients of the y-th converter and the equivalent single converter respectively, and the following relationship exists
Figure BDA0003400273780000046
Based on the above formula, considering the droop control loop, the following two formulas can be obtained
Figure BDA0003400273780000051
Figure BDA0003400273780000052
Therefore, equivalent transformation of all state variables in the multi-converter parallel direct current system is completed, and an equivalent single converter model of the multi-converter parallel direct current system is established.
In order to verify the effectiveness of the direct current system equivalent modeling method based on voltage and current double-loop control, the invention develops experimental verification work on a loop experiment platform based on RT-BOX hardware, and builds a direct current system with a plurality of parallel converters and an equivalent single converter thereof, wherein the topological structures of the direct current system are respectively shown in figures 1 and 2.
In the experimental results shown in fig. 3, the current control integral element state variable waveforms of the first and second converters are completely identical. And the first converter and the second converter are respectively 50% of the state variable waveform of the current control integral link of the equivalent single converter. Similarly, in fig. 4, the state variable waveforms of the voltage control integration sections of the two converters and the equivalent single converter are completely consistent.
Based on the verification result of the state variable experiment waveform, the verification work of the DC bus voltage experiment waveform can be further carried out. In fig. 5, the power of the constant power load is suddenly increased from 10MW to 12MW, and it can be observed that the transient stability waveforms of the dc bus voltage of the multiple-converter parallel dc system and the equivalent single converter are substantially consistent. In fig. 6, the power of the constant power load is suddenly increased from 10MW to 16.8MW, and it can be observed that transient instability waveforms of the dc bus voltage of the multiple-converter parallel dc system and the equivalent single converter are also substantially consistent. It can be known from fig. 5 and fig. 6 that the equivalent single converter established based on the invention can reflect not only the small-disturbance transient characteristics of the dc system, but also the large-disturbance transient characteristics of the dc system. The accuracy of the direct-current system equivalent modeling method based on voltage and current double-loop control provided by the invention is verified through the experimental result.
In summary, the dc system equivalent modeling method based on voltage and current double-loop control provided by the invention can provide convenience for reducing dc system equivalent modeling. Subsequently, a Lyapunov function can be established based on the equivalent single converter, the maximum estimation attraction domain of the direct current system is carved, and the influence of the voltage and current double-loop control parameters on the maximum estimation attraction domain of the direct current system is analyzed.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting the same, and although the present invention is described in detail with reference to the above embodiments, those of ordinary skill in the art should understand that: modifications and equivalents may be made to the embodiments of the invention without departing from the spirit and scope of the invention, which is to be covered by the claims.

Claims (1)

1. A direct current system equivalent modeling method based on voltage and current double-loop control comprises the following steps:
step 1: aiming at a direct current system based on voltage and current double-loop control, the output filter inductive current state variables of a plurality of converters in the direct current system are equivalently converted into the output filter inductive current state variables of one equivalent single converter, and the method comprises the following steps:
let the output filter inductor current of the y converter be I y Y =1,2, …, n, n is the total number of all converters in the dc system, the output filter inductor currents of all converters are summed with each other, the sum is equal to the output filter inductor current I of a single converter, and I is equal to the output filter inductor current I of a single converter y Y =1,2, …, n, and I as state variables;
step 2: the method is characterized in that the current control integral link state variables of a plurality of converters in a direct current system are equivalently converted into the current control integral link state variables of one equivalent single converter, and the method comprises the following steps:
let current control integral element state variable of the y-th converter be [ integral ] as ry -I y ) dt, let us say that the current control integral link state variable of the equivalent single converter is ^ (I) r -I) dt, further obtaining ^ integral (I) based on the equivalent transformation relation of the output filter inductor current state variable obtained in step 1 ry -I y ) dt and: (I) r -I) the equivalence transformation relationship between dt, as shown in
Figure FDA0003400273770000011
Wherein k is piy And k iiy Proportional and integral coefficients, I, of the y-th converter current control loop, respectively ry For filtering the inductor current reference, k, for the output of the y-th converter pi And k ii Proportional and integral coefficients, I, of the current control loop of the equivalent single converter r Is the output filter inductance current reference value, L, of the equivalent single converter fy And L f Output filter inductances of the y-th converter and the equivalent single converter respectively, wherein ^ integral, d and t are integral sign, differential operator and time respectively;
and step 3: the method is characterized in that the voltage control integral link state variables of a plurality of converters in a direct current system are equivalently converted into the voltage control integral link state variables of one equivalent single converter, and the method comprises the following steps:
let the voltage control integral element state variable of the y-th converter be [ U ] ] [ [ integral ] factor refy -U) dt, the voltage control integral link state variable of the equivalent single converter is [ integral ] ([ integral ] U) ref -U) dt, since each converter gets I through the voltage control loop ry The equivalent single converter obtains I through a voltage control loop r Based on the equivalent transformation relation of the state variable of the current control integral link obtained in the step 2, integral factor (U) is further obtained refy -U) dt and & (U) ref -U) dt is equal to the transformation relation, as shown in the following equation:
Figure FDA0003400273770000012
wherein, U refy And U ref Output voltage reference values of the y-th converter and the equivalent single converter respectively, U is the direct current bus voltage of the direct current system, k puy And k iuy Proportional and integral coefficients, k, of the voltage control loop of the y-th converter pu And k iu Proportional system of voltage control loops of equivalent single converters respectivelyNumber and integral coefficients;
and 4, step 4: the droop control loops of a plurality of converters in a direct current system are equivalently converted into the droop control loop of an equivalent single converter, and the plurality of converters based on voltage and current double-loop control are connected in parallel with the direct current system to be modeled into the equivalent single converter.
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