CN110417003B - STATCOM and excitation robust coordination method based on double-parameter self-adaption - Google Patents

STATCOM and excitation robust coordination method based on double-parameter self-adaption Download PDF

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CN110417003B
CN110417003B CN201910614918.8A CN201910614918A CN110417003B CN 110417003 B CN110417003 B CN 110417003B CN 201910614918 A CN201910614918 A CN 201910614918A CN 110417003 B CN110417003 B CN 110417003B
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CN110417003A (en
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张蕾
杜超凡
朱家豪
李鹏飞
景军峰
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Xian Polytechnic 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
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02E—REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION
    • Y02E40/00—Technologies for an efficient electrical power generation, transmission or distribution
    • Y02E40/10—Flexible AC transmission systems [FACTS]

Abstract

The invention discloses a double-parameter self-adaptive STATCOM and excitation robust coordination method, which comprises the steps of firstly, establishing a four-order mathematical model of a STATCOM and generator excitation coordination control system with uncertain double parameters and unknown disturbance; then adopts an immersion and invariance self-adaptive algorithmDesigning a double-parameter self-adaptive estimation law for uncertain parameters; finally, the obtained two-parameter self-adaptive estimation law and the backstepping method are combined to derive the excitation control law u of the generatorfAnd control law u of STATCOMsDesigning a robust coordination controller according to L2The gain robust control method constructs an energy function of disturbance input, and the dissipation theory proves that the designed coordination control method can ensure that the system has robust suppression capability, and realizes the excitation coordination control of the static synchronous compensator and the generator. The method disclosed by the invention can simultaneously estimate two parameters in the aspect of parameter self-adaptation in the system, and is superior to the traditional backstepping method in the convergence speed and the estimation precision of parameter estimation.

Description

STATCOM and excitation robust coordination method based on double-parameter self-adaption
Technical Field
The invention belongs to the technical field of power systems, and particularly relates to a STATCOM and excitation robust coordination method based on double-parameter self-adaptation.
Background
At present, the scale of a power grid in China is increasingly large, the power grid system is more complex, and a power transmission system is developed into a large-capacity, long-distance and ultrahigh-voltage power transmission mode. The stability problem of the power system is increasingly highlighted, and the practical problem in engineering can be solved more quickly and effectively by using a Flexible Alternating Current Transmission (FACTS) device. While a static synchronous compensator (STATCOM) has significant advantages as a main FACTS device, most notably low loss, voltage stabilization, power regulation, transient stability improvement of a power system, and the like. The generator excitation system is one of the most mature systems of all power system models, and plays a prominent role in solving the stability problem of the power system. Therefore, the design of the STATCOM and generator excitation coordinated controller has great research value and significance.
Disclosure of Invention
The invention aims to provide a double-parameter adaptive STATCOM and excitation robust coordination method, which solves the problem that the stability of a power system is influenced by multiple parameter uncertainty and unknown disturbance in a STATCOM and generator excitation coordination control system.
The technical scheme adopted by the invention is that a STATCOM and excitation robust coordination method based on double-parameter self-adaptation, the specific operation process comprises the following steps:
step 1, establishing a fourth-order mathematical model of a STATCOM and generator excitation coordination control system with uncertain double parameters and unknown disturbance in a power system;
step 2, designing a double-parameter adaptive estimation law for uncertain parameters by adopting an immersion and invariant adaptive algorithm;
step 3, combining the double-parameter self-adaptive estimation law obtained in the step 2 and a backstepping method to derive a generator excitation control law ufAnd control law u of STATCOMsDesigning a robust coordination controller according to L2The gain robust control method constructs an energy function of disturbance input, eliminates the influence of unknown disturbance on the system, and proves that the designed coordination control method can ensure that the system has robust inhibition capability through a dissipation theory, so that excitation coordination control of the static synchronous compensator and the generator is realized.
Yet another feature of the present invention is that,
the specific process of step 1 is as follows:
step 1.1, not considering the action of the speed regulator, and on the premise of neglecting the influence of the stator loop resistance and the rotor damping winding, adopting a three-order nonlinear differential equation of the generator and a STATCOM first-order controllable current source model, and then the nonlinear system equation of a single-machine infinite system comprising the STATCOM is shown as a formula (1):
Figure BDA0002123612630000021
wherein:
Figure BDA0002123612630000022
xdΣ＝xd+XL+XT，XL＝XL1+XL2，x′dΣ＝x′d+XL+XT
in the formula, xdAnd x'dRespectively a d-axis equivalent reactance and a transient equivalent reactance of the generator; x is the number ofdΣAnd x'dΣThe equivalent total reactance and the equivalent transient total reactance of the system; xTIs the transformer impedance; xL1、XL2Is the equivalent reactance of the transmission line; is the generator power angle; ω is generator angular velocity, ω0Is the rated synchronous angular velocity of the generator; eq' is the generator q-axis transient potential; vsIs the STATCOM installation point bus voltage; i isqIs the controllable power supply output current equivalent to the STATCOM; d is the generator damping coefficient; h is the moment of inertia of the generator rotor; p is a radical ofmIs the mechanical power of the prime mover; t isqIs the inertial time constant of the STATCOM; u. ofsIs a control input signal of the STATCOM; u. offA control input signal of a generator excitation system; p is a radical ofeIs the electromagnetic power of the generator; w is a1、w2、w3Is L2Unknown function of space, w ═ w1 w2 w3]TFor the uncertain disturbances suffered by the generator rotor, admittance and STATCOM controllers;
step 1.2, selecting the state variable as [ x ]1 x2 x3 x4]T＝[-0 ω-ω0 E′q-E′q0 Iq-Iq0]TWherein, in the step (A),0、ω0、E′q0、Iq0respectively corresponding initial values of all variables;
parameter replacement is performed on the constant in the formula (1):
Figure BDA0002123612630000031
Figure BDA0002123612630000032
taking into account uncertainty in generator damping and prime mover mechanical power
Figure BDA0002123612630000033
And theta2＝PmThen, a fourth-order mathematical model of the excitation coordination control system of the STATCOM and the generator is shown as formula (2):
Figure BDA0002123612630000034
wherein, theta1And theta2To not determine the parameters, w1、w2、w3Is an uncertain disturbance; (ii) a
Assuming that the system output is as shown in equation (3):
y＝[q1x1 q2x2]T (3)
wherein q is1、q2Is a non-negative weight coefficient represented by x1And x2The weighted proportion of (c).
Preferably, the specific process of step 2 is as follows:
step 2.1, defining the estimation error of the uncertain parameters as shown in the formula (4):
Figure BDA0002123612630000041
in the formula (I), the compound is shown in the specification,
Figure BDA0002123612630000042
and
Figure BDA0002123612630000043
is theta1And theta2Estimate of beta1(x1,x2) And beta2(x1,x2) A smoothing function is to be designed;
step 2.2, derivation is carried out on the formula (4), and the derivative of the uncertain parameter estimation error obtained after the formula (2) is substituted is shown as a formula (5):
Figure BDA0002123612630000044
constructing a differential function containing z, and designing an adaptive parameter replacement law as shown in the formula (6):
Figure BDA0002123612630000045
substituting formula (6) for formula (5) to obtain:
Figure BDA0002123612630000046
step 2.3, in order to make the parameter estimation error Z index converge and achieve stable performance, constructing a Lyapunov function V (Z) as shown in a formula (8):
Figure BDA0002123612630000051
v (z) then its derivative with respect to time is given by equation (9):
Figure BDA0002123612630000052
get
Figure BDA0002123612630000053
Where ρ > 0, and the substitution (9) has
Figure BDA0002123612630000054
V (z) is positive from the formulae (8) and (10),
Figure BDA0002123612630000055
is negative, obtained according to the LaSalle's theorem: the double-parameter adaptive law can ensure that the dynamic of parameter estimation errors is asymptotically stable.
Preferably, the specific process of step 3 is as follows:
step 3.1, designing a robust coordination controller, firstly, reducing a high-order system of the formula (2) into a low-order subsystem, and defining a state error function of the system as a formula (11) to a formula (14):
e1＝x1 (11)
Figure BDA0002123612630000056
Figure BDA0002123612630000057
Figure BDA0002123612630000058
in the formula (I), the compound is shown in the specification,
Figure BDA0002123612630000059
representing a virtual control quantity;
according to equation (2), equation (11) is derived:
Figure BDA00021236126300000510
for this first order system, will
Figure BDA00021236126300000511
As a virtual control quantity, will
Figure BDA00021236126300000512
The design is as follows:
Figure BDA00021236126300000513
in the formula, c1＞0；
Step 3.2, solving e according to the formula (2)2The derivative of (c) is represented by the formula (17):
Figure BDA0002123612630000061
then according to L2-dissipation control theory in gain suppression represents the disturbance w1Energy supply and dissipation relation function S1As shown in equation (18):
Figure BDA0002123612630000062
the following formula (18) is substituted for the output formula (3) and the formulae (15) to (17):
Figure BDA0002123612630000063
in the formula:
Figure BDA0002123612630000064
in order to make the first and second order subsystems of the system (2) to the disturbance w1Is gamma-dissipative, with virtual control quantities being designed
Figure BDA0002123612630000065
So that formula (19) satisfies S1Is less than or equal to 0, therefore, according to the uncertain double-parameter estimation law obtained in the step 2, the method can be used for estimating the parameters of the target object
Figure BDA0002123612630000066
Designed as shown in formula (20):
Figure BDA0002123612630000067
in the formula, in the following formula,
Figure BDA0002123612630000068
η1more than 0 is the designed parameter;
substituting the formula (20) into the formula (19), and arranging the formula (20) according to the uncertain biparametric estimation error defined by the formula (4) to obtain the formula (21):
Figure BDA0002123612630000069
to ensure S1Less than or equal to 0, then the parameter estimation law
Figure BDA00021236126300000610
And
Figure BDA00021236126300000611
in the virtual control quantity
Figure BDA00021236126300000612
Under the action of the disturbance control system, the first 2-stage subsystem in the coordinated control system of the STATCOM and the generator excitation is dissipated, and the disturbance w1Gamma-dissipative with respect to output response;
step 3.3, adopting a reverse step method and L for a three-order system represented by the formula (2)2-gain suppression design control law ufAnd eliminating the uncertain disturbance w1And w2Influence on the transient stability responsiveness of the system;
first, e is obtained3The derivative of (c) is as shown in equation (22):
Figure BDA0002123612630000071
then according to L2-dissipation control theory in gain suppression to represent the disturbance w1、w2Energy supply and dissipation relation function S2As shown in equation (23):
Figure BDA0002123612630000072
obtained by the formula (1): v has a corresponding equivalence functional relationship with the equivalent current of the STATCOM,
Figure BDA0002123612630000073
designing generator excitation controlInput ufAs shown in equation (24):
Figure BDA0002123612630000074
in the formula, v*Defining intermediate variables for the association between the generator dynamics and the STATCOM first order dynamics model as:
Figure BDA0002123612630000081
and (23) putting the formula (3), the formula (24) and the formula (25) into a formula (23) to obtain:
Figure BDA0002123612630000082
wherein eta is2More than 0 is the designed parameter;
due to S2Is less than or equal to 0, indicating an uncertain disturbance w of the system (2)1And w2Gamma-dissipative is satisfied for both regulated output responses;
step 3.4, construct the new state variable according to equation (2) and input the control variable x according to equation (14)4Intermediate control law of
Figure BDA0002123612630000083
Designed as shown in formula (27):
Figure BDA0002123612630000084
derivation of equation (14):
Figure BDA0002123612630000085
representing the disturbance w according to dissipation control theory1、w2And w3Energy supply and dissipation relation function S3As shown in equation (29):
Figure BDA0002123612630000086
and STATCOM control law usDesigned as shown in formula (30):
Figure BDA0002123612630000087
substituting formula (3) and formulae (28) and (30) into formula (29) yields:
Figure BDA0002123612630000091
in the formula eta3More than 0 is the designed parameter;
control law usMake S3Less than or equal to 0 to obtain the uncertain disturbance w of the system (2)1、w2And w3Has L not more than gamma2And (4) gain to ensure the robustness of the system to uncertain disturbance.
The method has the advantages that a double-parameter self-adaptive identification STATCOM-generator excitation robust coordination control strategy based on immersion and invariance (I & I) is provided for solving the problem that double-parameter uncertainty and unknown disturbance in a generator excitation and STATCOM coordination control system affect the transient stability of the system, and the effectiveness is verified through a simulation example. In the aspect of parameter self-adaption in the system, two parameters can be estimated simultaneously, the convergence rate and the estimation precision of the parameter estimation are superior to those of the traditional self-adaption backstepping method, and compared with the traditional backstepping method, the method is small in amplitude and short in response time, the nonlinear characteristic of the system is reserved, and the transient stability of the system is improved. The method of the invention can also be simultaneously applied to the adaptive robust control of the nonlinear system containing a plurality of uncertain parameters.
Drawings
FIG. 1 is a diagram of a SMIB system including a STATCOM according to the present invention;
FIG. 2 is a graph of the power angle response of a generator according to an embodiment of the present invention;
FIG. 3 is a graph of angular velocity response in an embodiment of the present invention;
FIG. 4 is a graph of a response of a transient potential of a generator in an embodiment of the present invention;
FIG. 5 is a graph of a STATCOM access point equivalent current response in an embodiment of the present invention;
FIG. 6 is a graph of uncertain parameter damping coefficient estimation response in an embodiment of the present invention;
FIG. 7 is a response graph of uncertain parameter mechanical power estimation in an embodiment of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention discloses a double-parameter self-adaptive STATCOM and excitation robust coordination method, which comprises the following specific operation processes of:
step 1: establishing a fourth-order mathematical model of a STATCOM and generator excitation coordination control system with uncertain double parameters and unknown disturbance in a power system;
the specific process of step 1 is as follows:
step 1.1, not considering the action of the speed regulator, and on the premise of neglecting the influence of the stator loop resistance and the rotor damping winding, adopting a three-order nonlinear differential equation of the generator and a STATCOM first-order controllable current source model, and then the nonlinear system equation of a Single Machine Infinite (SMIB) system comprising the STATCOM is shown as a formula (1):
Figure BDA0002123612630000101
wherein:
Figure BDA0002123612630000102
xdΣ＝xd+XL+XT，
Figure BDA0002123612630000103
x′dΣ＝x′d+XL+XTin the formula, xdAnd x'dRespectively a d-axis equivalent reactance and a transient equivalent reactance of the generator; x is the number ofdΣAnd x'dΣThe equivalent total reactance and the equivalent transient total reactance of the system; xTIs the transformer impedance; xL1、XL2Is the equivalent reactance of the transmission line; is the generator power angle; ω is generator angular velocity, ω0Is the rated synchronous angular velocity of the generator; e'qIs the generator q-axis transient potential; vsIs the STATCOM installation point bus voltage; i isqIs the controllable power supply output current equivalent to the STATCOM; d is the generator damping coefficient; h is the moment of inertia of the generator rotor; p is a radical ofmIs the mechanical power of the prime mover; t isqIs the inertial time constant of the STATCOM; u. ofsIs a control input signal of the STATCOM; u. offA control input signal of a generator excitation system; p is a radical ofeIs the electromagnetic power of the generator; w is a1、w2、w3Is L2Unknown function of space, w ═ w1w2 w3]TAre the uncertain disturbances experienced at the generator rotor, admittance and STATCOM controllers.
Step 1.2, selecting the state variable as [ x ]1 x2 x3 x4]T＝[-0 ω-ω0 E′q-E′q0 Iq-Iq0]TWherein, in the step (A),0、ω0、E′q0、Iq0respectively corresponding initial values of all variables;
parameter replacement is performed on the constant in the formula (1):
Figure BDA0002123612630000111
Figure BDA0002123612630000112
taking into account uncertainty in generator damping and prime mover mechanical power
Figure BDA0002123612630000113
And theta2＝PmThen, a fourth-order mathematical model of the excitation coordination control system of the STATCOM and the generator is shown as formula (2):
Figure BDA0002123612630000114
wherein, theta1And theta2To not determine the parameters, w1、w2、w3Is an uncertain disturbance;
assuming that the system output is as shown in equation (3):
y＝[q1x1 q2x2]T (3)
wherein q is1、q2Is a non-negative weight coefficient represented by x1And x2The weighted proportion of (c).
The control targets are: for a system (2) with uncertain double parameters and unknown disturbance, firstly, an adaptive law is designed to identify an uncertain damping coefficient theta1And mechanical power theta2Then, the excitation control law u is obtained through the nonlinear robust control law designfAnd STATCOM control law usWhen the system is disturbed by the outside, the variable in the system (2) is bounded and can be converged to the original balance point quickly.
Step 2, designing an adaptive parameter estimation law for uncertain double parameters by adopting an immersion and invariant (I & I) adaptive algorithm;
the specific process of step 2 is as follows:
step 2.1, defining the estimation error of the uncertain parameters as shown in the formula (4):
Figure BDA0002123612630000121
in the formula (I), the compound is shown in the specification,
Figure BDA0002123612630000122
and
Figure BDA0002123612630000123
is theta1And theta2Estimate of beta1(x1,x2) And beta2(x1,x2) A smooth function is to be designed.
Step 2.2, derivation is carried out on the formula (4), and the derivative of the uncertain parameter estimation error obtained after the formula (2) is substituted is shown as a formula (5):
Figure BDA0002123612630000124
then, a differential function containing z is constructed, and an adaptive parameter replacement law is designed as shown in formula (6):
Figure BDA0002123612630000125
substituting formula (6) for formula (5) to obtain:
Figure BDA0002123612630000131
step 2.3, in order to converge the parameter estimation error and achieve stable performance, constructing a Lyapunov function V (z) as shown in formula (8):
Figure BDA0002123612630000132
v (z) then its derivative with respect to time is given by equation (9):
Figure BDA0002123612630000133
get
Figure BDA0002123612630000134
Where ρ > 0, and the substitution (9) has
Figure BDA0002123612630000135
V (z) is positive from the formulae (8) and (10),
Figure BDA0002123612630000136
is negative, obtained according to the LaSalle's theorem: the designed double-parameter adaptive law can ensure that the dynamic of parameter estimation errors is asymptotically stable.
Compared with the traditional self-adaptive control method, I&The I self-adaptive method has the following advantages: (1) due to the introduction of beta in the law of parameter estimation1(x1,x2) And beta2(x1,x2) The function does not need to construct a Lyapunov function, and the determinacy-equivalence principle is broken through; (2) the introduction of the two functions can design the self-adaptive estimation errors of two uncertain parameters at the same time, and the dynamic characteristics of the parameter estimation errors can be adjusted through the configuration of the functions.
Step 3, adopting the designed I&I self-adaptive parameter estimation law and backstepping method for deriving power generator excitation and STATCOM robust coordination control law uf、usCombining and constructing an energy function of the disturbance input according to an L2 gain robust control method; finally, the designed coordination control method is proved to have the robust suppression capability according to the dissipation theory, and the STATCOM and the generator excitation coordination control is realized.
The specific process of step 3 is as follows:
step 3.1, designing a robust coordination controller, firstly, reducing a high-order system of a formula (2) into a low-order subsystem, and defining a state error function of the system as shown in a formula (11) to a formula (14):
e1＝x1 (11)
Figure BDA0002123612630000141
Figure BDA0002123612630000142
Figure BDA0002123612630000143
in the formula (I), the compound is shown in the specification,
Figure BDA0002123612630000144
representing a virtual control quantity;
according to equation (2), equation (11) is derived:
Figure BDA0002123612630000145
for this first-order system, the first-order system,
Figure BDA0002123612630000146
as a virtual control quantity, can be
Figure BDA0002123612630000147
The design is as follows:
Figure BDA0002123612630000148
in the formula, c1＞0；
Step 3.2, first, e is corrected according to formula (2)2The derivative of (c) is represented by the formula (17):
Figure BDA0002123612630000149
then according to L2-dissipation control theory in gain suppression to represent the disturbance w1Energy supply and dissipation relation function S1As shown in equation (18):
Figure BDA00021236126300001410
the following formula (18) is substituted for the output formula (3) and the formulae (15) to (17):
Figure BDA00021236126300001411
in the formula:
Figure BDA0002123612630000151
in order to make the first and second order subsystems of the system (2) to the disturbance w1Is gamma-dissipative and can be controlled virtually by design
Figure BDA0002123612630000152
So that formula (19) satisfies S1Is less than or equal to 0, therefore, according to the uncertain double-parameter estimation law obtained in the step 2, the method can be used for
Figure BDA0002123612630000153
Designed as shown in formula (20):
Figure BDA0002123612630000154
in the formula (I), the compound is shown in the specification,
Figure BDA0002123612630000155
η1more than 0 is the designed parameter;
substituting the formula (20) into the formula (19), and arranging the formula (20) according to the uncertain double-parameter estimation law defined by the formula (4) to obtain the formula (21):
Figure BDA0002123612630000156
to make S1Less than or equal to 0, then the parameter estimation law
Figure BDA0002123612630000157
And
Figure BDA0002123612630000158
in deficiencyAmount to be controlled
Figure BDA0002123612630000159
Under the action of the disturbance control system, the first 2-stage subsystem in the coordinated control system of the STATCOM and the generator excitation is dissipated, and the disturbance w1Gamma-dissipative to the output response.
Step 3.3, adopting a reverse step method and L for a three-order system represented by the formula (2)2-gain suppression design control law ufAnd eliminating the uncertain disturbance w1And w2Influence on the transient stability responsiveness of the system;
first, e is obtained3The derivative of (c) is as shown in equation (22):
Figure BDA00021236126300001510
then according to L2-dissipation control theory in gain suppression to represent the disturbance w1、w2Energy supply and dissipation relation function S2As shown in equation (23):
Figure BDA0002123612630000161
obtained by the formula (1): v has a corresponding equivalence functional relationship with the equivalent current of the STATCOM,
Figure BDA0002123612630000162
designing generator excitation control input ufAs shown in equation (24):
Figure BDA0002123612630000163
in the formula, v*Defining intermediate variables for the association between the generator dynamics and the STATCOM first order dynamics model as:
Figure BDA0002123612630000164
and (23) putting the formula (3), the formula (24) and the formula (25) into a formula (23) to obtain:
Figure BDA0002123612630000165
wherein eta is2More than 0 is the designed parameter;
control law ufCan be designed such that S2Is ≦ 0, which indicates an uncertain disturbance w of the system (2)1And w2The gamma-dissipative is satisfied for both regulated output responses.
Step 3.4, construct the new state variable according to equation (2) and input the control variable x according to equation (14)4Intermediate control law of
Figure BDA0002123612630000171
Designed as shown in formula (27):
Figure BDA0002123612630000172
first, formula (14) is derived:
Figure BDA0002123612630000173
the disturbance w is then expressed according to dissipation control theory1、w2And w3Energy supply and dissipation relation function S3As shown in equation (29):
Figure BDA0002123612630000174
and STATCOM control law usDesigned as shown in formula (30):
Figure BDA0002123612630000175
substituting formula (3) and formulae (28) and (30) into formula (29) yields:
Figure BDA0002123612630000176
in the formula eta3More than 0 is the designed parameter;
control law usCan be designed such that S3Is less than or equal to 0, and the uncertain disturbance w of the system (2) can be obtained1、w2And w3Has L not more than gamma2And (4) gain to ensure the robustness of the system to uncertain disturbance.
Examples of embodiment
The algorithm verifies that an I & I-based double-parameter self-adaptive identification STATCOM-generator excitation robust coordination control strategy is provided for the problem that double-parameter uncertainty and unknown disturbance in a generator excitation and STATCOM coordination control system affect the transient stability of the system, and the effectiveness of the provided algorithm is verified through a simulation example. In the aspect of parameter self-adaptation in the system, two parameters can be estimated simultaneously, and the convergence rate and the estimation precision of the parameter estimation are superior to those of the traditional self-adaptive backstepping method. The algorithm can also be applied to the adaptive robust control of a nonlinear system containing a plurality of uncertain parameters.
Infinite system parameters and STATCOM-generator excitation coordination control parameters designed by the invention are selected as follows: h ═ 1.94 and E'q＝1.08、ω0＝314.15、0＝50°、Tq＝1、XT＝0.32、XL1＝0.1、XL2＝0.3、γ＝1、q1＝0.4、q2＝0.6、η1＝η2＝110、η3＝80、c1＝c26. The initial state point of the system state input is selected as [ x ]1 x2 x3x4]T＝[0.68 0 -0.08 -8000]With uncertain damping coefficient set to D ═ 1 and uncertain parameter mechanical power set to PmWhen 1.0, the parameter is not determined
Figure BDA0002123612630000181
And theta2The estimator initial value is set to 0, 1.0. Modeling uncertain disturbances L2The spatial function is set as: w is a1＝e-2tsin(5t)、w2＝e-2tcos(5t)、w3＝e-2tsin(5t)。
The simulation scenario is as follows: the system initially operates at steady state. When t is 0.1s, a three-phase earth fault occurs at the outlet of the generator on the transmission line, the fault is removed after 0.1s, and the system rapidly restores to a stable state and is kept at an equilibrium point. In this process, the control method (IABCC) of the present invention is compared with the simulation results based on the conventional adaptive backstepping coordination controller (taccc) under the same initial conditions.
x1(power angle of generator), x2(angular velocity), x3(transient potential of generator), x4Transient response curves for (equivalent current of STATCOM access system) and uncertain two-parameter estimation are shown in fig. 2-6.
From fig. 2 and 3, it follows: when the system is in 1s, the transmission line is in fault and the fault is removed after 0.1s, compared with the traditional TABCC, the designed IBACC control method can quickly respond, so that the power angle and the angular speed of the generator can respond in a very short time, the response time of the power angle and the angular speed is about 1.5s, the amplitude is small, the curve convergence speed is high, and the transient stability performance of the system is improved.
From fig. 4 and fig. 5, it follows that: x is the number of3And x4Compared with the traditional TABCC method, the transient response curve is more quickly converged to a stable running state before the fault, the response time of the system is shortened by about 1s and 2s respectively, the oscillation amplitude of the system is small, the transient stability performance of the system is improved, and the transient response curve has better robustness to disturbance and the fault.
FIG. 6 is a graph of the response of uncertain parameter identification under the designed IBACC controller, and it can be seen from the graph that compared with the conventional TABCC, the response is fast1The estimated true value can be quickly stabilized at-0.516 within 0.1s, and the graph of FIG. 7 shows that theta is2The estimation truth value can be quickly stabilized at 1.0 only by about 0.5 s. Both parameter estimates are substantially in accordance with the set true values, so that the use of I can be obtained&The parameter self-adaptation law designed by I can effectively identify uncertain parameters.

Claims (3)

1. A STATCOM and excitation robust coordination method based on double-parameter self-adaptation is characterized in that the specific operation process comprises the following steps:
step 1, establishing a fourth-order mathematical model of a STATCOM and generator excitation coordination control system with uncertain double parameters and unknown disturbance in a power system;
the specific process of the step 1 is as follows:
step 1.1, not considering the action of the speed regulator, and on the premise of neglecting the influence of the stator loop resistance and the rotor damping winding, adopting a three-order nonlinear differential equation of the generator and a STATCOM first-order controllable current source model, and then the nonlinear system equation of a single-machine infinite system comprising the STATCOM is shown as a formula (1):
Figure FDA0002623315550000011
wherein:
Figure FDA0002623315550000012
xdΣ＝xd+XL+XT，XL＝XL1+XL2，x′dΣ＝x′d+XL+XT
in the formula, xdAnd x'dRespectively a d-axis equivalent reactance and a transient equivalent reactance of the generator; x is the number ofdΣAnd x'dΣThe equivalent total reactance and the equivalent transient total reactance of the system; xTIs the transformer impedance; xL1、XL2Is the equivalent reactance of the transmission line; is the generator power angle; ω is generator angular velocity, ω0Is the rated synchronous angular velocity of the generator; e'qIs hairMotor q-axis transient potential; vsIs the STATCOM installation point bus voltage; i isqIs the controllable power supply output current equivalent to the STATCOM; d is the generator damping coefficient; h is the moment of inertia of the generator rotor; p is a radical ofmIs the mechanical power of the prime mover; t isqIs the inertial time constant of the STATCOM; u. ofsIs a control input signal of the STATCOM; u. offA control input signal of a generator excitation system; p is a radical ofeIs the electromagnetic power of the generator; w is a1、w2、w3Is L2Unknown function of space, w ═ w1 w2 w3]TFor the uncertain disturbances suffered by the generator rotor, admittance and STATCOM controllers;
step 1.2, selecting the state variable as [ x ]1 x2 x3 x4]T＝[-0 ω-ω0 E′q-E′q0 Iq-Iq0]TWherein, in the step (A),0、ω0、E′q0、Iq0respectively corresponding initial values of all variables;
parameter replacement is performed on the constant in the formula (1):
Figure FDA0002623315550000021
Figure FDA0002623315550000022
taking into account uncertainty in generator damping and prime mover mechanical power
Figure FDA0002623315550000023
And theta2＝PmThen, a fourth-order mathematical model of the excitation coordination control system of the STATCOM and the generator is shown as formula (2):
Figure FDA0002623315550000024
wherein, theta1And theta2To not determine the parameters, w1、w2、w3Is an uncertain disturbance; (ii) a
Assuming that the system output is as shown in equation (3):
y＝[q1x1 q2x2]T (3)
wherein q is1、q2Is a non-negative weight coefficient represented by x1And x2The weighted specific gravity of (a);
step 2, designing a double-parameter adaptive estimation law for uncertain parameters by adopting an immersion and invariant adaptive algorithm;
step 3, combining the double-parameter self-adaptive estimation law obtained in the step 2 and a backstepping method to derive a generator excitation control law ufAnd control law u of STATCOMsDesigning a robust coordination controller according to L2The gain robust control method constructs an energy function of disturbance input, eliminates the influence of unknown disturbance on the system, and proves that the designed coordination control method can ensure that the system has robust inhibition capability through a dissipation theory, so that excitation coordination control of the static synchronous compensator and the generator is realized.
2. The method for coordinating STATCOM and excitation robustness based on two-parameter self-adaptation as claimed in claim 1, wherein the specific process of the step 2 is as follows:
step 2.1, defining the estimation error of the uncertain parameters as shown in the formula (4):
Figure FDA0002623315550000031
in the formula (I), the compound is shown in the specification,
Figure FDA0002623315550000032
and
Figure FDA0002623315550000033
are each theta1And theta2Estimate of beta1(x1,x2) And beta2(x1,x2) To be waited forCalculating a smooth function;
step 2.2, derivation is carried out on the formula (4), and the derivative of the uncertain parameter estimation error obtained after the formula (2) is substituted is shown as a formula (5):
Figure FDA0002623315550000034
constructing a differential function containing z, and designing an adaptive parameter replacement law as shown in the formula (6):
Figure FDA0002623315550000041
substituting formula (6) for formula (5) to obtain:
Figure FDA0002623315550000042
step 2.3, in order to make the parameter estimation error Z index converge and achieve stable performance, constructing a Lyapunov function V (Z) as shown in a formula (8):
Figure FDA0002623315550000043
v (z) then its derivative with respect to time is given by equation (9):
Figure FDA0002623315550000044
get
Figure FDA0002623315550000045
Where ρ > 0, and the substitution (9) has
Figure FDA0002623315550000046
V (z) is positive from the formulae (8) and (10),
Figure FDA0002623315550000047
is negative, obtained according to the LaSalle's theorem: the double-parameter adaptive law can ensure that the dynamic of parameter estimation errors is asymptotically stable.
3. The method for coordinating STATCOM and excitation robustness based on two-parameter adaptation as claimed in claim 2, wherein the specific process of step 3 is as follows:
step 3.1, designing a robust coordination controller, firstly, reducing a high-order system of the formula (2) into a low-order subsystem, and defining a state error function of the system as a formula (11) to a formula (14):
e1＝x1 (11)
Figure FDA0002623315550000051
Figure FDA0002623315550000052
Figure FDA0002623315550000053
in the formula (I), the compound is shown in the specification,
Figure FDA00026233155500000513
representing a virtual control quantity;
according to equation (2), equation (11) is derived:
Figure FDA0002623315550000054
for this first order system, will
Figure FDA0002623315550000055
As a virtual control quantity, will
Figure FDA0002623315550000056
The design is as follows:
Figure FDA0002623315550000057
in the formula, c1＞0；
Step 3.2, solving e according to the formula (2)2The derivative of (c) is represented by the formula (17):
Figure FDA0002623315550000058
then according to L2-dissipation control theory in gain suppression represents the disturbance w1Energy supply and dissipation relation function S1As shown in equation (18):
Figure FDA0002623315550000059
the following formula (18) is substituted for the output formula (3) and the formulae (15) to (17):
Figure FDA00026233155500000510
in the formula:
Figure FDA00026233155500000511
in order to make the first and second order subsystems of the system (2) to the disturbance w1Is gamma-dissipative, with virtual control quantities being designed
Figure FDA00026233155500000512
So that formula (19) satisfiesS1Is less than or equal to 0, therefore, according to the uncertain double-parameter estimation law obtained in the step 2, the method can be used for estimating the parameters of the target object
Figure FDA0002623315550000061
Designed as shown in formula (20):
Figure FDA0002623315550000062
in the formula (I), the compound is shown in the specification,
Figure FDA0002623315550000063
η1more than 0 is the designed parameter;
substituting the formula (20) into the formula (19), and arranging the formula (20) according to the uncertain biparametric estimation error defined by the formula (4) to obtain the formula (21):
Figure FDA0002623315550000064
to ensure S1Less than or equal to 0, then the parameter estimation law
Figure FDA0002623315550000065
And
Figure FDA0002623315550000066
in the virtual control quantity
Figure FDA0002623315550000067
Under the action of the disturbance control system, the first 2-stage subsystem in the coordinated control system of the STATCOM and the generator excitation is dissipated, and the disturbance w1Gamma-dissipative with respect to output response;
step 3.3, adopting a reverse step method and L for a three-order system represented by the formula (2)2-gain suppression design control law ufAnd eliminating the uncertain disturbance w1And w2Influence on the transient stability responsiveness of the system;
first, e is obtained3Derivative of (2)As shown in equation (22):
Figure FDA0002623315550000068
then according to L2-dissipation control theory in gain suppression to represent the disturbance w1、w2Energy supply and dissipation relation function S2As shown in equation (23):
Figure FDA0002623315550000069
obtained by the formula (1): v has a corresponding equivalence functional relationship with the equivalent current of the STATCOM,
Figure FDA0002623315550000071
designing generator excitation control input ufAs shown in equation (24):
Figure FDA0002623315550000072
in the formula, v*Defining intermediate variables for the association between the generator dynamics and the STATCOM first order dynamics model as:
Figure FDA0002623315550000073
and (23) putting the formula (3), the formula (24) and the formula (25) into a formula (23) to obtain:
Figure FDA0002623315550000074
wherein eta is2More than 0 is the designed parameter;
due to S2Is less than or equal to 0, indicating an uncertain disturbance w of the system (2)1And w2For the regulationThe output responses all satisfy gamma-dissipative;
step 3.4, construct the new state variable according to equation (2) and input the control variable x according to equation (14)4Intermediate control law of
Figure FDA0002623315550000075
Designed as shown in formula (27):
Figure FDA0002623315550000076
derivation of equation (14):
Figure FDA0002623315550000081
representing the disturbance w according to dissipation control theory1、w2And w3Energy supply and dissipation relation function S3As shown in equation (29):
Figure FDA0002623315550000082
and STATCOM control law usDesigned as shown in formula (30):
Figure FDA0002623315550000083
substituting formula (3) and formulae (28) and (30) into formula (29) yields:
Figure FDA0002623315550000084
in the formula eta3More than 0 is the designed parameter;
control law usMake S3Less than or equal to 0 to obtain the uncertain disturbance w of the system (2)1、w2And w3Has L not more than gamma2And (4) gain to ensure the robustness of the system to uncertain disturbance.
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