CN110417003A - Based on two-parameter adaptive STATCOM and excitation Robust Coordinated method - Google Patents
Based on two-parameter adaptive STATCOM and excitation Robust Coordinated method Download PDFInfo
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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
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- Y02E40/10—Flexible AC transmission systems [FACTS]
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Abstract
It is disclosed by the invention a kind of based on two-parameter adaptive STATCOM and excitation Robust Coordinated method, firstly, establishing the coordinated control system quadravalence mathematical model for not knowing two-parameter and unknown disturbance STATCOM and generator excitation；Then it uses immersion to design two-parameter ART network with constant adaptive algorithm for uncertain parameter to restrain；Obtained two-parameter ART network rule and Backstepping is finally combined to derive generator excitation control rule ufWith the control law u of STATCOMs, Robust coordinated control device is designed, according to L2Gain robust control method constructs the energy function of disturbance input, proves that designed control method for coordinating can guarantee that system has robust rejection ability by Dissipative Theory, realizes static synchronous compensator and generator excitation coordinated control.Method disclosed by the invention in terms of parameter adaptive, can estimate two parameters simultaneously and be better than traditional Backstepping techniques in the convergence rate of parameter Estimation and estimated accuracy in systems.
Description
Technical field
The invention belongs to technical field of power systems, and in particular to it is a kind of based on two-parameter adaptive STATCOM with encourage
Magnetic Robust Coordinated method.
Background technique
Currently, China's power grid scale is more and more huger and network system is more complicated, transmission system has evolved into great Rong
Amount, remote, super-pressure transmission of electricity form.The stability problem of its electric system becomes increasingly conspicuous, and uses flexible AC transmission
(FACTS) device can practical problem in rapider effective solution engineering.And static synchronous compensator (STATCOM) conduct
A kind of main FACTS device has a significant advantage, it is most outstanding is low loss, burning voltage, regulation power, improve electric power
Power system transient stability etc..Generator excited system is most mature one of the system of all electric power system models, is solving electric power
Play the role of in system instability outstanding.Therefore, the tuning controller of STATCOM and generator excitation, pole are designed
With researching value and meaning.
Summary of the invention
The object of the present invention is to provide a kind of based on two-parameter adaptive STATCOM and excitation Robust Coordinated method, solution
Multiple parameters uncertainty present in STATCOM and generator excitation coordinated control system of having determined and unknown disturbance influence electric power
It is the problem of system stability, adaptive compared to one-parameter, two-parameter Adaptive Identification of the invention have higher precision and
Stability.
The technical scheme adopted by the invention is that a kind of based on two-parameter adaptive STATCOM and excitation Robust Coordinated
Method, specific operation process include the following steps:
Step 1, it establishes to exist in electric system and does not know two-parameter and unknown disturbance STATCOM and generator excitation
Coordinated control system quadravalence mathematical model；
Step 2, it uses immersion to design two-parameter ART network with constant adaptive algorithm for uncertain parameter to restrain；
Step 3, generator excitation control rule u is derived with Backstepping in conjunction with the two-parameter ART network rule that step 2 obtainsf
With the control law u of STATCOMs, Robust coordinated control device is designed, according to L2The energy of gain robust control method construction disturbance input
Flow function eliminates influence of the unknown disturbance to system, then proves that designed control method for coordinating can guarantee by Dissipative Theory
System has robust rejection ability, realizes static synchronous compensator and generator excitation coordinated control.
Other features of the invention also reside in,
Detailed process is as follows for step 1:
Step 1.1, the influence premise of stator loop resistance and rotor Damper Winding is ignored in the effect for not considering governor
Under, it then include the list of STATCOM using generator Third-Order Nonlinear Differential Equations and STATCOM single order controllable current source model
Shown in the nonlinear system equation such as formula (1) of machine Infinite bus system:
Wherein:
xdΣ=xd+XL+XT, XL=XL1+XL2, x 'dΣ=x 'd+XL+XT
In formula, xdWith x 'dRespectively generator d axis equivalent reactance and transient state equivalent reactance；xdΣWith x 'dΣFor system etc.
Imitate total reactance and the total reactance of equivalent transient state；XTFor transformer impedance；XL1、XL2For transmission line of electricity equivalent reactance；δ is generator function
Angle；ω is generator angular speed, ω0It is the specified synchronous angular velocity of generator；Eq' it is generator q axis transient potential；VsIt is
STATCOM attachment point busbar voltage；IqIt is the equivalent controllable electric power output electric current of STATCOM；D is Generator Damping coefficient；H
It is the rotary inertia of generator amature；pmIt is prime mover mechanical output；TqIt is the inertia time constant of STATCOM；usFor
The control input signal of STATCOM；ufFor the control input signal of generator excited system；peFor generator electromagnetic power；w1、
w2、w3For L2The unknown function in space, w=[w1 w2 w3]TTo be applied to generator amature, admittance and STATCOM controller institute
The uncertain disturbance being subjected to；
Step 1.2, choosing state variable is [x1 x2 x3 x4]T=[δ-δ0 ω-ω0 E′q-E′q0 Iq-Iq0]T, wherein
δ0、ω0、E′q0、Iq0The corresponding initial value of respectively each variable；
Parameter replacement is carried out to the constant in formula (1): Consider the uncertainty of Generator Damping and prime mover mechanical output, enablesAnd θ2=Pm,
Then shown in the quadravalence mathematical model such as formula (2) of STATCOM and generator excitation coordinated control system:
Wherein, θ1And θ2For uncertain parameter, w1、w2、w3For uncertain disturbance；；
It is assumed that system output is as shown in formula (3):
Y=[q1x1 q2x2]T (3)
Wherein, q1、q2For non-negative weight coefficient, it is expressed as x1And x2Weighting specific gravity.
Preferably, detailed process is as follows for step 2:
Step 2.1, it defines shown in uncertain parameter evaluated error such as formula (4):
In formula,WithFor θ1And θ2Estimated value, β1(x1,x2) and β2(x1,x2) it is smooth function to be designed；
Step 2.2, derivation is carried out to formula (4), obtains the derivative such as formula of uncertain parameter evaluated error after formula (2) are substituted into
(5) shown in:
The differentiation function containing z is constructed, design auto-adaptive parameter replacement rule is as shown in formula (6):
Formula (6) are substituted into formula (5) to obtain:
Step 2.3, in order to make parameter estimating error Z exponential convergence, reach stability, construct Lyapunov function V (z)
As shown in formula (8):
Then V (z) is asked shown in its derivative such as formula (9) for the time:
It takesWherein ρ > 0, substituting into (9) has
Obtaining V (z) from formula (8) and formula (10) is positive definite,It is negative definite, is obtained according to LaSalle's theorem: double
Parameter update law can guarantee that the dynamic of parameter estimating error is asymptotically stable.
Preferably, detailed process is as follows for step 3:
Step 3.1, Robust coordinated control device is designed, firstly, by the high order system depression of order of formula (2) at low order subsystem, it is fixed
The state error function such as formula (11) of adopted system-formula (14):
e1=x1 (11)
In formula,Indicate virtual controlling amount；
According to formula (2), derivation is carried out to formula (11) and is obtained:
It, will for this first-order systemIt is considered as virtual controlling amount, it willDesign are as follows:
In formula, c1> 0；
Step 3.2, e is asked according to formula (2)2Derivation such as formula (17) shown in:
Then, according to L2Dissipative control theory in gain inhibition indicates disturbance w1Energy supply and dissipation relation function
S1As shown in formula (18):
Output type (3) and formula (15)-formula (17) are substituted into formula (18) and obtained:
In formula:
In order to make the preceding second order subsystem of system (2) for disturbing w1It is γ-dissipation, by designing virtual controlling amountSo that formula (19) meets S1≤ 0, therefore, restrained according to the two-parameter estimation that do not know that step 2 obtains, it willIt is designed as such as formula
(20) shown in:
In formula,η1> 0 is designed parameter；
Formula (20) are substituted into formula (19), and do not know two-parameter evaluated error according to what formula (4) defined, formula (20) is whole
Reason obtains formula (21):
In order to ensure S1≤ 0, then parameter Estimation is restrainedWithIn virtual controlling amountUnder the action of, STATCOM and power generation
Preceding 2 rank subsystem is to dissipate, and disturb w in the coordinated control system of machine excitation1For output response γ-dissipation；
Step 3.3, third-order system formula (2) indicated uses Backstepping and L2Gain inhibits design control law uf, and disappear
Except uncertain disturbance w1And w2Influence to power system transient stability responsiveness；
Firstly, seeking e3Derivative such as formula (22) shown in:
Then, according to L2Gain inhibit in dissipative control theory come indicate disturbance w1、w2Energy supply and dissipate close
It is function S2As shown in formula (23):
It is obtained by formula (1): there is corresponding equivalent function relationship between v and the equivalent current of STATCOM,If
It counts generator excitation control and inputs ufAs shown in formula (24):
In formula, v*The associated intermediate variable between generator dynamic and STATCOM first-order dynamic model, is defined as:
Formula (3) and formula (24), formula (25) are arranged to substitute into (23) and obtained:
Wherein, η2> 0 is designed parameter；
Due to S2≤ 0, show the uncertain disturbance w of system (2)1And w2γ-dissipation is all satisfied for adjusting output response
's；
Step 3.4, new state variable is constructed according to formula (2), and will control input variable x according to formula (14)4In
Between control lawIt is designed as shown in formula (27):
To formula (14) derivation:
Disturbance w is indicated according to dissipative control theory1、w2And w3Energy supply and dissipation relation function S3Such as formula (29)
It is shown:
And STATCOM control law usIt is designed as shown in formula (30):
Formula (3) and formula (28) and formula (30) are updated in formula (29) and obtained:
In formula, η3> 0 is designed parameter；
Control law usMake S3≤ 0, obtain the uncertain disturbance w of system (2)1、w2And w3With the L for being not more than γ2Gain, with
Robustness of the guarantee system for uncertain disturbance.
The invention has the advantages that for generator excitation with it is two-parameter present in STATCOM coordinated control system
Uncertain the problem of influencing power system transient stability with unknown disturbance, proposes a kind of double with constant (I&I) based on immersing
Parameter adaptive recognizes STATCOM- generator excitation Robust coordinated control strategy, and is demonstrated effectively by simulation example
Property.In systems in terms of parameter adaptive, two parameters and convergence rate and estimated accuracy in parameter Estimation can be estimated simultaneously
Better than traditional adaptive Backstepping techniques, small compared to traditional Backstepping amplitude, the response time is short, remains the non-of system
Linear characteristic improves the transient stability of system.Method of the invention can also be applied to containing the non-of multiple uncertain parameters simultaneously
In the adaptive robust control of linear system.
Detailed description of the invention
Fig. 1 is that the present invention uses the SMIB system containing STATCOM；
Fig. 2 is the generator's power and angle response curve implemented in example of the invention；
Fig. 3 is the angular speed response curve implemented in example of the invention；
Fig. 4 is the response curve for implementing the generator transient potential in example of the invention；
Fig. 5 is the response curve for implementing the STATCOM access point equivalent current in example of the invention；
Fig. 6 is the uncertain parameter damped coefficient estimation response diagram implemented in example of the invention；
Fig. 7 is the uncertain parameter mechanical output estimation response diagram implemented in example of the invention.
Specific embodiment
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
Of the invention is a kind of based on two-parameter adaptive STATCOM and excitation Robust Coordinated method, specific operation process
Include the following steps:
Step 1: establishing to exist in electric system and do not know two-parameter and unknown disturbance STATCOM and generator excitation
Coordinated control system quadravalence mathematical model；
Detailed process is as follows for step 1:
Step 1.1, the influence premise of stator loop resistance and rotor Damper Winding is ignored in the effect for not considering governor
Under, it then include the list of STATCOM using generator Third-Order Nonlinear Differential Equations and STATCOM single order controllable current source model
Shown in the nonlinear system equation such as formula (1) of machine infinity (SMIB) system:
Wherein:
xdΣ=xd+XL+XT,x′dΣ=x 'd+XL+XTIn formula, xdWith x 'dPoint
It Wei not generator d axis equivalent reactance and transient state equivalent reactance；xdΣWith x 'dΣIt is always electric for equivalent total reactance of system and equivalent transient state
It is anti-；XTFor transformer impedance；XL1、XL2For transmission line of electricity equivalent reactance；δ is generator's power and angle；ω is generator angular speed, ω0
It is the specified synchronous angular velocity of generator；E′qIt is generator q axis transient potential；VsIt is STATCOM attachment point busbar voltage；IqIt is
STATCOM equivalent controllable electric power exports electric current；D is Generator Damping coefficient；H is the rotary inertia of generator amature；pm
It is prime mover mechanical output；TqIt is the inertia time constant of STATCOM；usFor the control input signal of STATCOM；ufFor power generation
The control input signal of machine excitation system；peFor generator electromagnetic power；w1、w2、w3For L2The unknown function in space, w=[w1
w2 w3]TTo be applied to the uncertain disturbance that generator amature, admittance and STATCOM controller are subjected to.
Step 1.2, choosing state variable is [x1 x2 x3 x4]T=[δ-δ0 ω-ω0 E′q-E′q0 Iq-Iq0]T, wherein
δ0、ω0、E′q0、Iq0The corresponding initial value of respectively each variable；
Parameter replacement is carried out to the constant in formula (1): Consider the uncertainty of Generator Damping and prime mover mechanical output, enablesAnd θ2=Pm,
Then shown in the quadravalence mathematical model such as formula (2) of STATCOM and generator excitation coordinated control system:
Wherein, θ1And θ2For uncertain parameter, w1、w2、w3For uncertain disturbance；
It is assumed that system output is as shown in formula (3):
Y=[q1x1 q2x2]T (3)
Wherein, q1、q2For non-negative weight coefficient, it is expressed as x1And x2Weighting specific gravity.
Control target is: for having the two-parameter and unknown disturbance system (2) that do not know, design adaptive law first is come
Recognize uncertain damped coefficient θ1With mechanical output θ2, excitation con-trol rule is then obtained by nonlinear robust control rule design
ufWith STATCOM control law us, when so that this system is by external disturbance, Bounded Variables in system (2), and can promptly receive
Hold back original equalization point.
Step 2, immersion and constant (I&I) adaptive algorithm are used not know two-parameter design adaptive parameter estimation
Rule；
Detailed process is as follows for step 2:
Step 2.1, it defines shown in uncertain parameter evaluated error such as formula (4):
In formula,WithFor θ1And θ2Estimated value, β1(x1,x2) and β2(x1,x2) it is smooth function to be designed.
Step 2.2, derivation is carried out to formula (4), obtains the derivative such as formula of uncertain parameter evaluated error after formula (2) are substituted into
(5) shown in:
Then, the differentiation function containing z is constructed, design auto-adaptive parameter replacement rule is as shown in formula (6):
Formula (6) are substituted into formula (5) to obtain:
Step 2.3, in order to restrain parameter estimating error, reach stability, construct Lyapunov function V (z) such as formula
(8) shown in:
Then V (z) is asked shown in its derivative such as formula (9) for the time:
It takesWherein ρ > 0, substituting into (9) has
Obtaining V (z) from formula (8) and formula (10) is positive definite,It is negative definite, is obtained according to LaSalle's theorem: institute
The two-parameter adaptive law of design can guarantee that the dynamic of parameter estimating error is asymptotically stable.
It is compared compared to traditional self-adaptation control method, I&I adaptive approach has the advantage that (1) due to estimating in parameter
β is introduced in meter rule1(x1,x2) and β2(x1,x2) function, construction Lyapunov function is not needed, certainty-equivalence is breached
Principle；(2) introducing of the two functions can design the ART network error of two uncertain parameters simultaneously, and can pass through
The configuration of function carrys out the dynamic characteristic of adjustment parameter evaluated error.
Step 3, using above-mentioned designed I&I adaptive parameter estimation rule and Backstepping derive generator excitation and
STATCOM Robust coordinated control restrains uf、usIn conjunction with, and according to L2 gain robust control method go construction disturbance input energy letter
Number；It finally proves that designed control method for coordinating can guarantee that system has robust rejection ability according to Dissipative Theory, realizes
STATCOM and generator excitation coordinated control.
Detailed process is as follows for step 3:
Step 3.1, Robust coordinated control device is designed, firstly, by the high order system depression of order of formula (2) at low order subsystem, it is fixed
Shown in the state error function such as formula (11) of adopted system-formula (14):
e1=x1 (11)
In formula,Indicate virtual controlling amount；
According to formula (2), derivation is carried out to formula (11) and is obtained:
For this first-order system,It is considered as virtual controlling amount, can incites somebody to actionDesign are as follows:
In formula, c1> 0；
Step 3.2, firstly, according to formula (2) to e2Derivation such as formula (17) shown in:
Then, according to L2Gain inhibit in dissipative control theory come indicate disturbance w1Energy supply and dissipation relationship letter
Number S1As shown in formula (18):
Output type (3) and formula (15)-formula (17) are substituted into formula (18) and obtained:
In formula:
In order to make the preceding second order subsystem of system (2) for disturbing w1It is γ-dissipation, it can be by designing virtual controlling
AmountSo that formula (19) meets S1≤ 0, therefore, is restrained, can be incited somebody to action according to the two-parameter estimation that do not know that step 2 obtainsIt is designed as
As shown in formula (20):
In formula,η1> 0 is designed parameter；
Formula (20) are substituted into formula (19), and are restrained according to the two-parameter estimation that do not know that formula (4) defines, formula (20) are arranged
Obtain formula (21):
In order to make S1≤ 0, then parameter Estimation is restrainedWithIn virtual controlling amountUnder the action of, STATCOM and generator
Preceding 2 rank subsystem is to dissipate, and disturb w in the coordinated control system of excitation1For output response γ-dissipation.
Step 3.3, third-order system formula (2) indicated uses Backstepping and L2Gain inhibits design control law uf, and disappear
Except uncertain disturbance w1And w2Influence to power system transient stability responsiveness；
Firstly, seeking e3Derivative such as formula (22) shown in:
Then, according to L2Gain inhibit in dissipative control theory come indicate disturbance w1、w2Energy supply and dissipate close
It is function S2As shown in formula (23):
It is obtained by formula (1): there is corresponding equivalent function relationship between v and the equivalent current of STATCOM,If
It counts generator excitation control and inputs ufAs shown in formula (24):
In formula, v*The associated intermediate variable between generator dynamic and STATCOM first-order dynamic model, is defined as:
Formula (3) and formula (24), formula (25) are arranged to substitute into (23) and obtained:
Wherein, η2> 0 is designed parameter；
Control law ufDesign can make S2≤ 0, this shows the uncertain disturbance w of system (2)1And w2It is exported for adjusting
Response is all satisfied γ-dissipation.
Step 3.4, new state variable is constructed according to formula (2), and will control input variable x according to formula (14)4In
Between control lawIt is designed as shown in formula (27):
Firstly, to formula (14) derivation:
Then, disturbance w is indicated according to dissipative control theory1、w2And w3Energy supply and dissipation relation function S3Such as formula
(29) shown in:
And STATCOM control law usIt is designed as shown in formula (30):
Formula (3) and formula (28) and formula (30) are updated in formula (29) and obtained:
In formula, η3> 0 is designed parameter；
Control law usDesign can make S3≤ 0, the uncertain disturbance w of available system (2)1、w2And w3With little
In the L of γ2Gain, to guarantee system for the robustness of uncertain disturbance.
Implement example
The invention of this algorithm demonstrates, for present in generator excitation and STATCOM coordinated control system it is two-parameter not
The problem of certainty and unknown disturbance influence power system transient stability, proposes a kind of two-parameter Adaptive Identification based on I&I
STATCOM- generator excitation Robust coordinated control strategy, and the validity of mentioned algorithm is demonstrated by simulation example.In
The adaptive aspect of system parameters can estimate two parameters simultaneously and be better than in the convergence rate of parameter Estimation and estimated accuracy
Traditional adaptive Backstepping techniques.This algorithm can also apply to the ADAPTIVE ROBUST of the nonlinear system containing multiple uncertain parameters
In control.
Infinite bus system parameter and STATCOM- generator excitation coordinated control parameter designed by the present invention are chosen as follows:
H=1.94, E'q=1.08, ω0=314.15, δ0=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=c2=6.The original state point of system mode input is selected as [x1 x2 x3
x4]T=[0.68 0-0.08-8000], uncertain damped coefficient is set as D=1 and uncertain parameter mechanical output is set as Pm
=1.0, then uncertain parameterAnd θ2=1.0, estimator initial value is set as 0.It will not know
Interference modeling L2Spatial function setting are as follows: w1=e-2tsin(5t)、w2=e-2tcos(5t)、w3=e-2tsin(5t)。
Simulation scenarios are as follows: system initialization is in stable state.As t=0.1s, the exit of generator on transmission line of electricity
Three-phase ground failure occurs, failure removal after 0.1s, system promptly restores stable state, and is maintained at equalization point.At this
In the process, by control method (IABCC) of the invention with based on the adaptive Backstepping tuning controller (TABCC) of tradition same
Primary condition under simulation result be compared.
x1(generator's power and angle), x2(angular speed), x3(transient potential of generator), x4(STATCOM access system etc.
Effect electric current) and the transient response curve of two-parameter estimation is not known as shown in Fig. 2-Fig. 6.
It is obtained from Fig. 2 and Fig. 3: when system is in 1s, transmission line of electricity line failure and the failure removal after 0.1s,
Designed IBACC control method can be responded quickly compared to traditional TABCC, enable generator's power and angle and angular speed
It is responded in the very short time, the response time of generator rotor angle and angular speed is about 1.5s, and amplitude is small, curve convergence speed
Fastly, the transient stability performance of system is improved.
It is obtained from Fig. 4 with Fig. 5: x3And x4Transient response curve converged on faster compared to traditional TABCC method
The response time of system is shortened 1s and 2s or so respectively by the steady operational status before failure, and system oscillation amplitude is small, mentions
The high transient stability performance of system, has preferable robustness to disturbance and failure.
Fig. 6 is that uncertain parameter recognizes the response curve under designed IBACC controller, can from figure
Out, it can quickly be responded compared to traditional TABCC, θ1Estimation true value only need 0.1s or so can it is promptly stable-
0.516, Fig. 7 shows θ2Estimation true value also only needs 0.5s or so rapidly stable 1.0.Two parameter Estimations all with it is set
The true value set is almost the same, therefore can obtain effectively recognizing uncertain parameter using parameter update law designed by I&I.
Claims (4)
1. a kind of based on two-parameter adaptive STATCOM and excitation Robust Coordinated method, which is characterized in that specific operation process
Include the following steps:
Step 1, the coordination for existing in electric system and not knowing two-parameter and unknown disturbance STATCOM and generator excitation is established
Control system quadravalence mathematical model；
Step 2, it uses immersion to design two-parameter ART network with constant adaptive algorithm for uncertain parameter to restrain；
Step 3, generator excitation control rule u is derived with Backstepping in conjunction with the two-parameter ART network rule that step 2 obtainsfWith
The control law u of STATCOMs, Robust coordinated control device is designed, according to L2The energy of gain robust control method construction disturbance input
Function eliminates influence of the unknown disturbance to system, then proves that designed control method for coordinating can guarantee by Dissipative Theory and be
System has robust rejection ability, realizes static synchronous compensator and generator excitation coordinated control.
2. as described in claim 1 a kind of based on two-parameter adaptive STATCOM and excitation Robust Coordinated method, feature
It is, detailed process is as follows for the step 1:
Step 1.1, the effect for not considering governor is adopted under the premise of the influence for ignoring stator loop resistance and rotor Damper Winding
With generator Third-Order Nonlinear Differential Equations and STATCOM single order controllable current source model, then the single machine comprising STATCOM is infinite
Shown in the nonlinear system equation such as formula (1) of big system:
Wherein:
xdΣ=xd+XL+XT,x′dΣ=x 'd+XL+XT
In formula, xdWith x 'dRespectively generator d axis equivalent reactance and transient state equivalent reactance；xdΣWith x 'dΣFor equivalent total electricity of system
The anti-and total reactance of equivalent transient state；XTFor transformer impedance；XL1、XL2For transmission line of electricity equivalent reactance；δ is generator's power and angle；ω is
Generator angular speed, ω0It is the specified synchronous angular velocity of generator；E′qIt is generator q axis transient potential；VsIt is STATCOM dress
Set up an office busbar voltage；IqIt is the equivalent controllable electric power output electric current of STATCOM；D is Generator Damping coefficient；H is generator
The rotary inertia of rotor；pmIt is prime mover mechanical output；TqIt is the inertia time constant of STATCOM；usFor the control of STATCOM
Input signal；ufFor the control input signal of generator excited system；peFor generator electromagnetic power；w1、w2、w3For L2Space
Unknown function, w=[w1 w2 w3]TIt uncertain is disturbed for be applied to that generator amature, admittance and STATCOM controller be subjected to
It is dynamic；
Step 1.2, choosing state variable is [x1 x2 x3 x4]T=[δ-δ0 ω-ω0 E′q-E′q0 Iq-Iq0]T, wherein δ0、
ω0、E′q0、Iq0The corresponding initial value of respectively each variable；
Parameter replacement is carried out to the constant in formula (1): Consider the uncertainty of Generator Damping and prime mover mechanical output, enablesAnd θ2=Pm,
Then shown in the quadravalence mathematical model such as formula (2) of STATCOM and generator excitation coordinated control system:
Wherein, θ1And θ2For uncertain parameter, w1、w2、w3For uncertain disturbance；；
It is assumed that system output is as shown in formula (3):
Y=[q1x1 q2x2]T (3)
Wherein, q1、q2For non-negative weight coefficient, it is expressed as x1And x2Weighting specific gravity.
3. as claimed in claim 2 a kind of based on two-parameter adaptive STATCOM and excitation Robust Coordinated method, feature
It is, detailed process is as follows for the step 2:
Step 2.1, it defines shown in uncertain parameter evaluated error such as formula (4):
In formula,WithRespectively θ1And θ2Estimated value, β1(x1,x2) and β2(x1,x2) it is smooth function to be designed；
Step 2.2, derivation is carried out to formula (4), obtains the derivative such as formula (5) of uncertain parameter evaluated error after formula (2) are substituted into
It is shown:
The differentiation function containing z is constructed, design auto-adaptive parameter replacement rule is as shown in formula (6):
Formula (6) are substituted into formula (5) to obtain:
Step 2.3, in order to make parameter estimating error Z exponential convergence, reach stability, construct Lyapunov function V (z) such as formula
(8) shown in:
Then V (z) is asked shown in its derivative such as formula (9) for the time:
It takesWherein ρ > 0, substituting into (9) has
Obtaining V (z) from formula (8) and formula (10) is positive definite,It is negative definite, is obtained according to LaSalle's theorem: two-parameter
Adaptive law can guarantee that the dynamic of parameter estimating error is asymptotically stable.
4. as claimed in claim 3 a kind of based on two-parameter adaptive STATCOM and excitation Robust Coordinated method, feature
It is, detailed process is as follows for the step 3:
Step 3.1, Robust coordinated control device is designed, firstly, by the high order system depression of order of formula (2) at low order subsystem, definition system
The state error function such as formula (11) of system-formula (14):
e1=x1 (11)
In formula,Indicate virtual controlling amount；
According to formula (2), derivation is carried out to formula (11) and is obtained:
It, will for this first-order systemIt is considered as virtual controlling amount, it willDesign are as follows:
In formula, c1> 0；
Step 3.2, e is asked according to formula (2)2Derivation such as formula (17) shown in:
Then, according to L2Dissipative control theory in gain inhibition indicates disturbance w1Energy supply and dissipation relation function S1Such as
Shown in formula (18):
Output type (3) and formula (15)-formula (17) are substituted into formula (18) and obtained:
In formula:
In order to make the preceding second order subsystem of system (2) for disturbing w1It is γ-dissipation, by designing virtual controlling amountMake
It obtains formula (19) and meets S1≤ 0, therefore, restrained according to the two-parameter estimation that do not know that step 2 obtains, it willIt is designed as such as formula (20) institute
Show:
In formula,η1> 0 is designed parameter；
Formula (20) are substituted into formula (19), and do not know two-parameter evaluated error according to what formula (4) defined, formula (20) is arranged
To formula (21):
In order to ensure S1≤ 0, then parameter Estimation is restrainedWithIn virtual controlling amountUnder the action of, STATCOM and generator excitation
Coordinated control system in preceding 2 rank subsystem be dissipate, and disturb w1For output response γ-dissipation；
Step 3.3, third-order system formula (2) indicated uses Backstepping and L2Gain inhibits design control law uf, and eliminate not
Determine disturbance and w2Influence to power system transient stability responsiveness；
Firstly, seeking e3Derivative such as formula (22) shown in:
Then, according to L2Gain inhibit in dissipative control theory come indicate disturbance w1、w2Energy supply and dissipation relationship letter
Number S2As shown in formula (23):
It is obtained by formula (1): there is corresponding equivalent function relationship between v and the equivalent current of STATCOM,Design hair
Motor excitation control input ufAs shown in formula (24):
In formula, v*The associated intermediate variable between generator dynamic and STATCOM first-order dynamic model, is defined as:
Formula (3) and formula (24), formula (25) are arranged to substitute into (23) and obtained:
Wherein, η2> 0 is designed parameter；
Due to S2≤ 0, show the uncertain disturbance w of system (2)1And w2γ-dissipation is all satisfied for adjusting output response；
Step 3.4, new state variable is constructed according to formula (2), and will control input variable x according to formula (14)4Intermediate control
RuleIt is designed as shown in formula (27):
To formula (14) derivation:
Disturbance w is indicated according to dissipative control theory1、w2And w3Energy supply and dissipation relation function S3As shown in formula (29):
And STATCOM control law usIt is designed as shown in formula (30):
Formula (3) and formula (28) and formula (30) are updated in formula (29) and obtained:
In formula, η3> 0 is designed parameter；
Control law usMake S3≤ 0, obtain the uncertain disturbance w of system (2)1、w2And w3With the L for being not more than γ2Gain, to guarantee
Robustness of the system for uncertain disturbance.
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| CN113985781A (en) * | 2021-10-28 | 2022-01-28 | 广东电网有限责任公司广州供电局 | Emergency power supply vehicle excitation control method based on instruction filtering backstepping controller |
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