CN112202185B - SVC control method of high-power supply system based on Lyapunov function - Google Patents

SVC control method of high-power supply system based on Lyapunov function Download PDF

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CN112202185B
CN112202185B CN202011108917.5A CN202011108917A CN112202185B CN 112202185 B CN112202185 B CN 112202185B CN 202011108917 A CN202011108917 A CN 202011108917A CN 112202185 B CN112202185 B CN 112202185B
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陶骏
贾登格
邓天白
朱明星
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Anhui 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
    • H02J3/18—Arrangements for adjusting, eliminating or compensating reactive power in networks
    • H02J3/1821—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators
    • H02J3/1835—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators with stepless control
    • H02J3/1864—Arrangements for adjusting, eliminating or compensating reactive power in networks using shunt compensators with stepless control wherein the stepless control of reactive power is obtained by at least one reactive element connected in series with a semiconductor switch
    • 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
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    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
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    • Y02E40/10—Flexible AC transmission systems [FACTS]

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Abstract

The invention discloses an SVC control method of a high-power supply system based on a Lyapunov function, which comprises the following steps: 1. performing mathematical modeling on the joint operation of a high-power supply system and a Static Var Compensator (SVC); 2. the method comprises the steps of utilizing a system identification method to obtain model parameters of a research object in advance, and combining a control framework of joint operation of a high-power phase-controlled rectification power supply system and a reactive compensation device, so as to establish an equivalent transfer function model and an electromagnetic transient simulation model; 3. based on the Lyapunov second method and the large-range asymptotic stability theory, an error energy function about actual output reactive power and load reference reactive power of the static reactive power compensator is constructed, and a closed-loop feedback control rule is designed by a reverse step method. The invention can effectively reduce the reactive power impact value of the network side and enhance the robustness of the bus voltage of the alternating current side, thereby improving the operation reliability of a high-power rectification power supply system.

Description

SVC control method of high-power supply system based on Lyapunov function
Technical Field
The invention belongs to the technical field of electric energy quality control of high-power rectifier power supplies, and particularly relates to a Lyapunov function control method of a Static Var Compensator (SVC) applied to a high-power thyristor phase-controlled rectifier power supply system.
Background
The safe and reliable operation of the power grid determines the long-term stable development of power engineering and industry. In an electric power system, a large number of impact loads exist, such as nuclear fusion devices, rolling mills, electric arc furnaces, cranes, high-power electrolysis devices and the like, the loads threaten the safety and stability of a power grid and damage the normal operation of electric power equipment, so that an electric energy quality control device needs to be additionally arranged in the power grid. Common Power quality control devices in Power networks include Static Var Compensators (SVC), static Var Generators (SVG), active Power Filters (APF), and the like, wherein the SVC is widely used since the early appearance because of the advantages of simplicity, economy, mature control, and the like. The control target of the static var compensator (SVC, TCR + FC, thyristor controlled reactor + fixed capacitor) is to control the output reactive power of the static var compensator to be equal to the load consumption reactive power, and different SVC reactive power control schemes determine the quality of the electric energy quality control effect and finally show the network side reactive power impact level and the stability and robustness of the bus voltage.
The conventional control scheme (QMV method) of the Static Var Compensator (SVC) is an open loop control based on bus side reactive power detection, and its control effect is generally limited by the delay of the detection link, the response lag of the TCR, and the uncertainty perturbation of the model parameters. When the load is in an impact working condition, the compensation effect of a reactive compensation device (SVC) under the traditional open-loop control scheme cannot adapt to the rapid change of the reactive demand of the load. Meanwhile, the voltage value of the bus is seriously fluctuated beyond a safety range due to the fact that the network side bears large reactive impact. Therefore, it is necessary to newly search a control method of the reactive power compensator (SVC).
The existing reactive control scheme cannot greatly reduce the influence of the delay characteristic of a reactive compensation device (SVC) and bus voltage fluctuation introduced by an impact load. The principle of the second lyapunov method is widely applied to power electronic devices such as active power filters, static synchronous compensators and the like, but the application of the static reactive compensator in the scene of a high-power rectification power supply is still to be discovered.
Disclosure of Invention
The invention aims to overcome the defects in the prior art, and provides a static var compensator control method of a high-power supply system based on a Lyapunov function, so that the reactive impact value of a network side can be effectively reduced, the robustness of the bus voltage of an alternating current side is enhanced, and the operation reliability of the high-power rectification power supply system can be improved.
In order to achieve the purpose, the invention adopts the following technical scheme:
the invention relates to an SVC control method of a high-power supply system based on a Lyapunov function, which is characterized by comprising the following steps:
step 1: according to the characteristics of the thyristorThe mathematical models of the high-power supply system and the Static Var Compensator (SVC) are respectively simplified by using the formula (1) and the formula (2), and the transfer function G of the high-power supply system is correspondingly obtained conv And transfer function G of static var compensator SVC SVC ：
Figure BDA0002727927620000021
Figure BDA0002727927620000022
In the formulae (1) and (2), T dc Delay of dead zone of synchronous signal for triggering of thyristor in high-power supply system d Delay of a dead zone of a synchronous signal triggered by a thyristor for the SVC; t is L Control delay for thyristor triggering, T, for high-power supply systems b Control delay for the static var compensator SVC with respect to thyristor triggering; s is a differential operator;
step 2: according to the principle of 'system identification', four delay parameter values in the formula (1) and the formula (2) are obtained in advance;
and step 3: constructing an equivalent circuit model according to the joint operation topology of the high-power supply system and the Static Var Compensator (SVC);
and 4, step 4: calculating reference reactive Q of SVC by using equation (3) conv ：
Figure BDA0002727927620000023
In the formula (3), P conv Obtaining the active power consumption of a current conversion unit in the high-power supply system by using a formula (4), wherein alpha is a trigger angle of the thyristor device and is obtained by using a formula (5); gamma is the commutation overlap angle of the converter unit and is obtained by the formula (6); q m Reactive power for transformer excitation;
Figure BDA0002727927620000024
Figure BDA0002727927620000025
Figure BDA0002727927620000026
in formula (4) -formula (6), U d Is the DC side voltage of the converter cell, I d Is the direct side current of the converter unit, U abc_rms Is the root mean square value, L, of the bus-side voltage of the converter cell tra And R tra Is the inductance and resistance of the transformer, f is the grid frequency;
and 5: according to the transfer function G of the SVC SVC The corresponding differential equation is obtained by using equation (7):
Figure BDA0002727927620000031
in the formula (7), x is the actual output reactive power of the SVC,
Figure BDA0002727927620000032
being the first derivative of the actual output reactive power of the static var compensator SVC,
Figure BDA0002727927620000033
the second derivative of the actual output reactive power of the static var compensator SVC is u, and the control input quantity of the static var compensator SVC is u;
step 6: selecting the actual output reactive x of the SVC as a state variable x 1 Choosing the first derivative of x as the state variable x 2 Thereby establishing the equation of state as shown in equation (8) and equation (9):
Figure BDA0002727927620000034
Figure BDA0002727927620000035
in the formulae (8) and (9),
Figure BDA0002727927620000036
is a state variable x 1 The first derivative of (a) is,
Figure BDA0002727927620000037
is a state variable x 2 The first derivative of (a);
and 7: according to the lyapunov second method, the error e and its derivative δ and the error energy function V with respect to the actual output reactive power of the static var compensator SVC and the load-side reference reactive power are constructed using equations (10) -12 by the state equations shown in equations (8) and (9):
e＝x 1d -x 1 ＝x 1d -Q SVC (10)
Figure BDA0002727927620000038
Figure BDA0002727927620000039
in the formulae (10) to (12), x 1d Desired reactive output for a static var compensator, x 2d Derivative, Q, of the reactive output desired for a static var compensator, SVC SVC For the actual output of the static var compensator SVC,
Figure BDA00027279276200000310
outputting a reactive first-order derivative for the SVC actually;
and 8: the general control target is constructed using equation (13):
e,δ→0,t→∞ (13)
in formula (13), t is time;
and step 9: according to the Lyapunov function and the large-range asymptotic stability theory, obtaining conditional equations of the formulas (14) and (15):
Figure BDA00027279276200000311
Figure BDA00027279276200000312
in formulae (14) to (15), k 1 ,k 2 To control the gain factor, a function representing the rate of decay with respect to the error e;
step 10: the control input u shown in the formula (16) is obtained by a backstepping method, so that the actual output reactive Q of the SVC is SVC Can realize the reference reactive Q conv Tracking:
Figure BDA0002727927620000041
compared with the prior art, the invention has the beneficial effects that:
1. the invention is based on the safety and stability consideration of the combined operation of the reactive power compensation device (SVC) of the high-power system, constructs an energy function about compensation errors according to the Lyapunov second method, and utilizes a backstepping method to newly design a control scheme (called QLC control below) of the static var compensator, and the method can effectively improve the compensation precision and the dynamic characteristic of the static var compensator, thereby improving the voltage stability and the robustness of the system network side and providing powerful support for the optimization control aspect of the combined operation of the high-power system based on the thyristor phase control technology and the static var compensator thereof;
2. according to the method, on the basis of the design of a controller of the static var compensation device, delay parameters are embedded into a control rule based on the consideration of the delay characteristic of the static var compensation device (SVC), and the method can realize the accurate tracking of the reference reactive instruction by the SVC through a backstep method, so that the adverse effect caused by impact load introduction under the uncertain delay factors is well reduced;
3. the control method provided by the invention is based on a large-range asymptotic stability theory, has a good constraint effect on compensation errors, can effectively inhibit other interference errors, obviously improves the compensation effect, and further greatly reduces the reactive impact influence of impact load on the network side.
Drawings
FIG. 1 is a block diagram of the joint operation control of a high-power system and a Static Var Compensator (SVC) of the present invention;
FIG. 2 is a block diagram of a static var compensator SVC control strategy (QLC) based on the Lyapunov function according to the present invention;
fig. 3 is a control block diagram of a conventional control method (QMV) of the static var compensator according to the present invention;
FIG. 4 is a diagram of reactive power control effect under the transfer function model of the present invention;
FIG. 5 is a diagram of reactive power control effect under the electromagnetic transient simulation model of the present invention;
fig. 6 is a diagram of bus voltage stabilization control effect under the electromagnetic transient simulation model of the present invention.
Detailed Description
In the embodiment, an SVC control method of a high-power supply system based on a Lyapunov function is an optimization control strategy for joint operation with a reactive power compensator (SVC) under the working conditions of high power performance and high impact load of a thyristor phase-controlled rectification power supply. Firstly, a Lyapunov second method is introduced, delay parameters of a reactive compensation controller are determined by combining a system identification theory, secondly, a control rule of a reactive compensation device (SVC) about a Lyapunov function is obtained by a backstepping method design, and finally, a simplified equivalent model and an electromagnetic transient model of the combined operation of a corresponding high-power rectification power supply system and the reactive compensation device (SVC) are built on MATLAB/Simulink software to perform optimal control of reactive compensation. Through a comparative simulation experiment, the result verifies the feasibility and effectiveness of the Lyapunov control method.
The high-power rectification power supply system is mainly designed to simulate high-impact characteristic parameters of devices such as nuclear fusion device operation, direct-current electric arc furnace and high-power electrolysis, and a newly-proposed Lyapunov function scheme is applied to achieve cooperative operation optimization control with a reactive power compensation device SVC. The specific control framework is shown in fig. 1 and is performed according to the following steps:
step 1: according to the characteristics of the thyristor device, mathematical models of a high-power supply system and a Static Var Compensator (SVC) are respectively simplified by using the formula (1) and the formula (2), and a transfer function G of the high-power supply system is correspondingly obtained conv And transfer function G of static var compensator SVC SVC ：
Figure BDA0002727927620000051
Figure BDA0002727927620000052
In the formulae (1) and (2), T dc Delay of dead zone of synchronous signal for triggering of thyristor in high-power supply system d Delay of a dead zone of a synchronous signal triggered by a thyristor for the SVC; t is L Control delay for thyristor triggering, T, for high-power supply systems b Control delay for the static var compensator SVC with respect to thyristor triggering; s is a differential operator;
step 2: according to the principle of 'system identification', four delay parameter values in the formula (1) and the formula (2) are obtained in advance;
and step 3: constructing an equivalent circuit model according to the joint operation topology of the high-power supply system and the Static Var Compensator (SVC);
and 4, step 4: calculating reference reactive Q of SVC using equation (3) conv ：
Figure BDA0002727927620000053
In the formula (3), P conv Obtaining the active power consumption of a current transformation unit in the high-power supply system by using a formula (4), wherein alpha is a trigger angle of the thyristor device and is obtained by using a formula (5); gamma is the commutation overlap angle of the converter unit and is obtained by the formula (6); q m Reactive power for transformer excitation;
Figure BDA0002727927620000054
Figure BDA0002727927620000055
Figure BDA0002727927620000061
in formula (4) -formula (6), U d Is the DC side voltage of the converter cell, I d Is the direct side current of the converter unit, U abc_rms Is the root mean square value, L, of the bus side voltage of the converter unit tra And R tra Is the inductance and resistance of the transformer, f is the grid frequency;
and 5: according to the transfer function G of the static var compensator SVC SVC The corresponding differential equation is obtained by using equation (7):
Figure BDA0002727927620000062
in the formula (7), x is the actual output reactive power of the SVC,
Figure BDA0002727927620000063
the first derivative of the actual output reactive of the static var compensator SVC,
Figure BDA0002727927620000064
the second derivative of the actual output reactive power of the static var compensator SVC is u, and the control input quantity of the static var compensator SVC is u;
and 6: selecting the actual output reactive x of the SVC as a state variable x 1 Choosing the first derivative of x as the state variable x 2 Thereby establishing the equation of state as shown in equation (8) and equation (9):
Figure BDA0002727927620000065
Figure BDA0002727927620000066
in the formulae (8) and (9),
Figure BDA0002727927620000067
is a state variable x 1 The first derivative of (a) is,
Figure BDA0002727927620000068
is a state variable x 2 The first derivative of (a);
and 7: according to the lyapunov second method, the error e and its derivative δ and the error energy function V with respect to the actual output reactive power of the static var compensator SVC and the load-side reference reactive power are constructed using equations (10) to (12) by the state equations shown in equations (8) and (9):
e＝x 1d -x 1 ＝x 1d -Q SVC (10)
Figure BDA0002727927620000069
Figure BDA00027279276200000610
in the formulae (10) to (12), x 1d Desired reactive output for a static var compensator, x 2d Derivative, Q, of the reactive output desired for a static var compensator, SVC SVC For the actual output of the static var compensator SVC,
Figure BDA00027279276200000611
a first derivative of the real output reactive power of the static var compensator SVC;
and 8: the general control objective is constructed using equation (13):
e,δ→0,t→∞ (13)
in the formula (13), t is time;
and step 9: according to the Lyapunov function and the large-range asymptotic stability theory, the conditional equations of the formulas (14) and (15) are obtained:
Figure BDA0002727927620000071
Figure BDA0002727927620000072
in formulae (14) to (15), k 1 ,k 2 To control the gain factor, a function is expressed with respect to the error e;
step 10: the control input u shown in the formula (16) is obtained by a backstepping method, so that the actual output reactive power Q of the Static Var Compensator (SVC) SVC Can realize the reference reactive Q conv Tracking:
Figure BDA0002727927620000073
examples
According to the method, an optimal control scheme for the joint operation of a high-power rectification power supply system and a reactive compensation device (SVC) is established based on a control block diagram shown in figure 1. The power supply side is only provided with a 66kV bus, a double-winding transformer (66 kV/1.05 kV) supplies power for the converter unit, and the bus is connected with a reactive power compensation device (SVC, TCR + FC) in side and the capacity of the bus is 250Mvar.
With reference to the thyristor phase control principle and its delay characteristics, delay parameter settings, T, of converter units and reactive compensation devices (SVC) dc ＝1.667ms,T d =1.667ms; then, the rest delay parameters, T, are obtained according to the system identification method L ＝1.5406ms,T b =3.5103ms. QLC controller design refers to equation (16) above to derive control command Q input QLC controller gain factor k 1 ＝k 2 =390. The simulation verification of the controller QLC of the static var compensator is designed by using the control block diagram as shown in fig. 2, and the QMV scheme is designed by referring to fig. 3 for comparing the control effect with the traditional scheme (QMV).
For the impact load working condition, the total reactive impact is as high as 180Mvar, and the change rate is 180Mvar/0.015s. The compensation effect of the reactive compensation device SVC is as shown in fig. 4 to fig. 6, and the network side reactive power surge and the bus voltage stability under the combined operation of the high-power system and the reactive compensation device SVC under different control schemes are significantly different. FIG. 4 and FIG. 5 show control strategy verification under a transfer function model and an electromagnetic transient simulation model, respectively, and use the reactive power impact value Q of the network side grid As a control effect evaluation index, fig. 6 shows control strategy verification regarding bus voltage stability under an electromagnetic transient simulation model. When the QMV scheme is adopted, because of the influences of reactive compensator (SVC) delay characteristics, model parameter uncertainty perturbation and bus side reactive measurement delay, the system network side reactive impact is the most serious at the moment and the bus voltage fluctuation is larger; when the QLC scheme is adopted, because the selected control error and the derivative thereof are Lyapunov functions, once the output reactive power of the reactive compensation device SVC deviates from the expected reactive power of the load, the control instruction Q derived by a backstepping method is limited by a large-range asymptotic stability theory input The deviation value is corrected, the reactive impact of the network side is greatly reduced, and meanwhile, the stability and robustness of the bus voltage are also obviously improved.
In summary, the invention designs a novel control method for the static var compensator SVC of the high-power rectification power supply system under the condition of the impact load from the perspective of the lyapunov function of the error between the expected reactive power and the actual output reactive power of the reactive power compensation device and the change rate thereof. The experiment result verifies that the combined operation of the high-power rectification power supply system and the static reactive compensator can effectively improve the reactive compensation precision and the dynamic response characteristic when the Lyapunov function control method is adopted, thereby enhancing the stability and the robustness of the bus voltage.

Claims (1)

1. A SVC control method of a high-power supply system based on a Lyapunov function is characterized by comprising the following steps:
step 1: according to the characteristics of the thyristor device, mathematical models of a high-power supply system and a Static Var Compensator (SVC) are respectively simplified by using the formula (1) and the formula (2), and a transfer function G of the high-power supply system is correspondingly obtained conv And transfer function G of SVC SVC ：
Figure FDA0002727927610000011
Figure FDA0002727927610000012
In the formulae (1) and (2), T dc Delay of dead zone of synchronous signal for triggering thyristor in high-power supply system d Delay of a dead zone of a synchronous signal triggered by a thyristor for the SVC; t is a unit of L Control delay for thyristor triggering, T, for high-power supply systems b Control delay for the static var compensator SVC with respect to thyristor triggering; s is a differential operator;
step 2: according to the principle of 'system identification', four delay parameter values in the formula (1) and the formula (2) are obtained in advance;
and step 3: constructing an equivalent circuit model according to a combined operation topology of a high-power supply system and a Static Var Compensator (SVC);
and 4, step 4: calculating reference reactive Q of SVC by using equation (3) conv ：
Figure FDA0002727927610000013
In formula (3), P conv Obtaining the active power consumption of a current conversion unit in the high-power supply system by using a formula (4), wherein alpha is a trigger angle of the thyristor device and is obtained by using a formula (5); gamma is the commutation overlap angle of the converter unit and is obtained by the formula (6); q m Reactive power for transformer excitation;
Figure FDA0002727927610000014
Figure FDA0002727927610000015
Figure FDA0002727927610000016
in formula (4) -formula (6), U d Is the DC side voltage of the converter cell, I d Is the direct side current of the converter unit, U abc_rms Is the root mean square value, L, of the bus side voltage of the converter unit tra And R tra Is the inductance and resistance of the transformer, f is the grid frequency;
and 5: according to the transfer function G of the SVC SVC The corresponding differential equation is obtained by using equation (7):
Figure FDA0002727927610000021
in the formula (7), x is the actual output reactive power of the SVC,
Figure FDA0002727927610000022
the first derivative of the actual output reactive of the static var compensator SVC,
Figure FDA0002727927610000023
the second derivative of the actual output reactive power of the SVC is u, and the control input quantity of the SVC is u;
and 6: selecting the actual output reactive x of the SVC as a state variable x 1 Choosing the first derivative of x as the state variable x 2 Thereby establishing the equation of state as shown in equation (8) and equation (9):
Figure FDA0002727927610000024
Figure FDA0002727927610000025
in the formulae (8) and (9),
Figure FDA0002727927610000026
is a state variable x 1 The first derivative of (a) is,
Figure FDA0002727927610000027
is a state variable x 2 The first derivative of (a);
and 7: according to the lyapunov second method, the error e and its derivative δ and the error energy function V with respect to the actual output reactive power of the static var compensator SVC and the load-side reference reactive power are constructed using equations (10) to (12) by the state equations shown in equations (8) and (9):
e＝x 1d -x 1 ＝x 1d -Q SVC (10)
Figure FDA0002727927610000028
Figure FDA0002727927610000029
in the formulae (10) to (12), x 1d Desired reactive output for a static var compensator, x 2d Derivative, Q, of the reactive output desired for a static var compensator, SVC SVC For the actual output of the static var compensator SVC,
Figure FDA00027279276100000210
a first derivative of the real output reactive power of the static var compensator SVC;
and 8: the general control target is constructed using equation (13):
e,δ→0,t→∞ (13)
in the formula (13), t is time;
and step 9: according to the Lyapunov function and the large-range asymptotic stability theory, obtaining conditional equations of the formulas (14) and (15):
Figure FDA00027279276100000211
Figure FDA0002727927610000031
in formulae (14) to (15), k 1 ,k 2 To control the gain factor, a function representing the rate of decay with respect to the error e;
step 10: the control input u shown in the formula (16) is obtained by a backstepping method, so that the actual output reactive power Q of the Static Var Compensator (SVC) SVC Can realize the reference reactive Q conv Tracking:
Figure FDA0002727927610000032
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CN107240921A (en) * 2017-06-13 2017-10-10 李昊昊 Based on the SVC sliding-mode controls for integrating adaptive backstepping

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US8060349B2 (en) * 2007-03-16 2011-11-15 Chang Gung University Method of designing a static synchronous compensator based on passivity-based control
CN104471816B (en) * 2012-06-01 2019-01-15 香港大学 It inputs AC voltage and controls bi-directional power converter

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CN107240921A (en) * 2017-06-13 2017-10-10 李昊昊 Based on the SVC sliding-mode controls for integrating adaptive backstepping

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