CN106707752A - Improved algorithm for solving state feedback gain matrix of current source STATCOM (static synchronous compensator) - Google Patents

Improved algorithm for solving state feedback gain matrix of current source STATCOM (static synchronous compensator) Download PDF

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CN106707752A
CN106707752A CN201611187584.3A CN201611187584A CN106707752A CN 106707752 A CN106707752 A CN 106707752A CN 201611187584 A CN201611187584 A CN 201611187584A CN 106707752 A CN106707752 A CN 106707752A
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current source
formula
gain matrix
statcom
matrix
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牟宪民
范永升
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Dalian University of Technology
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    • G05—CONTROLLING; REGULATING
    • G05B—CONTROL OR REGULATING SYSTEMS IN GENERAL; FUNCTIONAL ELEMENTS OF SUCH SYSTEMS; MONITORING OR TESTING ARRANGEMENTS FOR SUCH SYSTEMS OR ELEMENTS
    • G05B13/00—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion
    • G05B13/02—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric
    • G05B13/04—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators
    • G05B13/042—Adaptive control systems, i.e. systems automatically adjusting themselves to have a performance which is optimum according to some preassigned criterion electric involving the use of models or simulators in which a parameter or coefficient is automatically adjusted to optimise the performance

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Abstract

The present invention provides an improved algorithm for solving the state feedback gain matrix of a current source STATCOM (static synchronous compensator) and belongs to the calculation, control and registration table test field. Based on a state feedback control strategy, a genetic algorithm and a linear quadratic regulator (LQR) are combined so as to be applied to the solving of the state feedback gain matrix, so that an ideal state feedback gain matrix can be obtained. According to the improved algorithm of the invention, the genetic algorithm is adopted to globally optimize two weight matrices of the LQR, and obtained optimized weight matrices are substituted into a formula, so that the ideal state feedback gain matrix can be obtained; the ideal state feedback gain matrix can be applied to the state feedback control strategy; and therefore, the controlled current source STATCOM can have good dynamic performance.

Description

A kind of improvement solved for current source type STATCOM feedback of status gain matrix Algorithm
Technical field
The present invention proposes a kind of innovatory algorithm solved for current source type STATCOM feedback of status gain matrix, category In calculating, control and registration form testing field.
Background technology
STATCOM (STATic synchronous COMpensator, STATCOM) have it is continuous, quick, Accurately dynamic compensation performance, extensive research and application have been obtained in power system reactive power compensation field.Current source type (Current Source Conventor, CSC) STATCOM is used as one kind therein, because carrying short-circuit protection function, can be straight Connect and electric current be controlled, high reliability and gather around and have broad application prospects.Control strategy influences and determines electric current Source type STATCOM systematic functions.At present, current source type STATCOM the most frequently used control strategy is STATE FEEDBACK CONTROL, and is used Method of Pole Placement is linearized and decoupled to system, solving state feedback gain matrix.
Solved using Method of Pole Placement and treatment feedback of status gain matrix, the experience of designer is often relied on, by matching somebody with somebody Put the specific diverse location of limit to determine feedback of status gain matrix, and then realize adjustment current source type STATCOM systematicness The control targe of energy, this not only takes more time, while the feedback of status gain matrix for obtaining usually is absorbed in local optimum, Have impact on the dynamic property of whole system.
The content of the invention
For the problem that prior art is present, the present invention provides a kind of for current source type STATCOM feedback of status gains The innovatory algorithm of Matrix Solving, the present invention combines genetic algorithm and LQR methods, it is to avoid calculating feedback of status gain matrix is absorbed in The experience of local optimum simultaneously saves the solution used time；Suitable fitness function is chosen in the application of genetic algorithm and is set Penalty factor is put, system is obtained good dynamic property.
In order to achieve the above object, the technical scheme is that：
A kind of innovatory algorithm solved for current source type STATCOM feedback of status gain matrix, described innovatory algorithm On the basis of STATE FEEDBACK CONTROL strategy, by genetic algorithm and liner quadratic regulator device (Lineal Quadratic Regulator, LQR) combine, apply in solving state feedback gain matrix, obtain preferable feedback of status gain matrix；Change Algorithm after entering carries out global optimizing using genetic algorithm to two the weight matrix Q and R of LQR, the weight after will be optimized Matrix obtains preferable feedback of status gain matrix in being updated to formula, then realizes current source by STATE FEEDBACK CONTROL strategy The performance optimization of type STATCOM systems.Specifically include following steps：
The first step, sets up current source type STATCOM Mathematical Modelings
With reference to side circuit, mathematical modeling, adoption status feedback are carried out to its current source type STATCOM system topologies Control strategy, is processed by state feedback linearization, obtains current source type STATCOM mathematical modelings, such as formula (6) and formula (7) shown in.Detailed process is：According to Kirchhoff's law, the high frequency model of system state equation is obtained：
Wherein, subscript a, b, c respectively in expression system symmetrical three phase circuit a phase；E, v, i represent each phase electricity respectively Phase voltage, capacitance voltage in road, line current；R, L, C represent line resistance, line inductance, electricity in each circuitry phase respectively Hold；idc、Ldc、RdcDC side electric current, DC side inductance, direct current side resistance are represented respectively；SkIt is the three of the switching converter of three-phase six Value Logic switch function, is defined as：
Clark conversion and Park conversion are carried out to formula (1), and to idcComponent carries out state feedback linearization treatment, obtains System state equation under dq coordinate systems：
Wherein, m is three-phase power switch bridge output current fundamental voltage amplitude and DC current Amplitude Ration, and δ is current source type The output current of STATCOM and the phase difference of line voltage.
Formula (3) is rearranged into the matrix form as shown in formula (4)：
The current source type STATCOM systems output quantity deeply concerned in design is direct current lateral current magnitude idcAnd reactive current component iq, therefore design output matrix is：
Described current source type STATCOM Mathematical Modelings are expressed as：
Y=Cx (7)
Wherein, state variableInput variable u=[Mdidc Mqidc]T, controlled input VariableInput variable e=[ed eq]T；Output variableA, B, C, F are specific electricity Road parameter matrix.
Second step, according to the current source type STATCOM mathematical modelings that the first step is obtained, using the electricity suitable for innovatory algorithm Stream source type STATCOM state feedback controller design system control block diagrams, in the Simulink simulated environment of MATLAB softwares Set up its simulation model.
Shown in described current source type STATCOM state feedback controllers, such as formula (8)：
U=-Kx+Tyref+Me (8)
Wherein,It is the reference value of output variable, K is feedback of status gain matrix, and T is second order It is configured to obtain the diagonal matrix of input quantity reference value by constant, M is constant gain vector.
By formula (6), formula (7) and formula (8), the closed loop controller existed between input quantity and output quantity is obtained, such as Shown in formula (9)：
Y=C (sI-A+BK)-1[BTyref+(BM+F)e] (9)
Wherein, I is unit matrix, and s is the general plural number of transmission function.
Operator V is calculated using formula (10)：V=C (BK-A)-1B (10)
By formula (9) and formula (10), (s=0, y are required according to system controlref=y) can obtain：
T=V-1 (11)
M=-V-1C(BK-A)-1F (12)
3rd step, solves preferable feedback of status gain matrix.
3.1) form of liner quadratic regulator device LQR suitable for innovatory algorithm of the design as shown in formula (13) is：
Wherein, t is the time；X and u are respectively state variable and input variable；Q and R are the weight matrix of symmetrical non-negative, are led to Crossing weight matrix can be calculated feedback of status gain matrix K using the formula K=lqr (A, B, Q, R) of MATLAB softwares.
3.2) genetic algorithm fitness function of the design suitable for innovatory algorithm
Genetic algorithm is used to carry out global optimizing to the weight matrix of LQR in innovatory algorithm, and the quality of optimizing result takes Certainly in the selection and design of genetic algorithm fitness function.The present invention proposes the genetic algorithm fitness letter suitable for innovatory algorithm Number is designed as：
Fobj=a*Mp+b*ts+c*tr+d*SSE+f (14)
Wherein, Mp, ts, tr, SSE are respectively output quantity iqOrThe overshoot of curve, stabilization time, rise time and steady State error；Constant a, b, c, d are respectively the coefficient of correspondence of overshoot, stabilization time, rise time and steady-state error；Constant f (one As be taken as positive number) as the penalty factor of fitness function, due to the characteristic of Algorithm for Solving fitness function minimum value, punishment because The bootable genetic groups of son are evolved to the direction for meeting constraints.
3.3) according to actual conditions to step 3.2) in constant be adjusted, the fitness function for being suited the requirements is simultaneously Called in GAs Toolbox, genetic algorithm of reruning is to step 3.1) in liner quadratic regulator device LQR weigh Weight matrix carries out global optimizing, obtains preferable feedback of status gain matrix, and current source is ensured finally by STATE FEEDBACK CONTROL Type STATCOM has good dynamic property.
The beneficial effects of the invention are as follows：Innovatory algorithm is by genetic algorithm and liner quadratic regulator device (LQR) R. concomitans To in solving state feedback gain matrix, obtain preferable feedback of status gain matrix, final optimization pass current source type STATCOM Systematic function, improves many deficiencies that traditional pole-assignment brings by experience, the solution time is saved, while avoiding Solving result is absorbed in local optimum.Meanwhile, the current source type STATCOM that innovatory algorithm is designed has preferably dynamic special Property, faster response time and smaller system overshoot.
Brief description of the drawings
Fig. 1 is current source type STATCOM system topology figures.
Fig. 2 is the STATE FEEDBACK CONTROL block diagram of current source type STATCOM.
Fig. 3 is Genetic Algorithm optimized design LQR controller schematic diagrames.
Specific embodiment
With reference to Figure of description and technical scheme, specific embodiments of the present invention are elaborated.
The first step, sets up current source type STATCOM Mathematical Modelings.
With reference to side circuit, mathematical modeling is carried out to current source type STATCOM system topologies as shown in Figure 1, adopted STATE FEEDBACK CONTROL strategy is used, is processed by coordinate transform and state feedback linearization, can obtain the number of shape such as formula (6) (7) Learn model.
Second step, by Mathematical Modeling, sets up the system simulation model in Simulink.
Current source type STATCOM models are set up and are completed, using the current source type shown in formula in innovatory algorithm (8) STATCOM state feedback controllers design system control block figure as shown in Figure 2, and in the simulated environment of software MATLAB Its simulation model is set up in Simulink.
3rd step, writes the genetic algorithm fitness function of innovatory algorithm.
Fitness function of the invention is write using the m files of software MATLAB, and the emulation obtained with second step is led to Contact is called in assignin () sentence and sim () sentence foundation for crossing MATLAB softwares.
3.1) row write parameters matrix A, B, C, F, because x and u difference comprising variable numbers are 5 and 2, design weight matrix Q, R is respectively the diagonal matrix of five ranks and second order, and LQR method solving states are realized from formula K=lqr (A, B, Q, R) in MATLAB Feedback gain matrix K.
3.2) after K is tried to achieve, operator V, formula (11) and formula (12) are write and tries to achieve matrix T and M, then write out respectively Output response iqOrThe performance index function such as overshoot, stabilization time, rise time and steady-state error.
3.3) when fitness function is designed, adjust the numerical value of constant a, b, c, d to adjust the weight of related performance indicators Size, and then have adjusted the dynamic property of output quantity；Design penalty factor f, filters out inappropriate individuality in genetic algorithm, draws Genetic evolution direction is led, accelerates the calculating speed of algorithm.Finally, the coefficient that will be adjusted is multiplied by correspondence performance indications sues for peace i.e. again Can obtain fitness function, such as formula (14).
3.4)：GAs Toolbox from MATLAB calls the fitness function that writes, completes innovatory algorithm.
In the setting of GAs Toolbox, system includes 7 variables altogether, and bound is respectively provided with to these variables, The weight of each component is distributed targeted specifically.Genetic algorithm other major parameters, such as initial population generation space, population scale, essence English number, aberration rate and algorithm stop condition etc., designer can require flexibly to write with system control according to actual needs.
The process of genetic algorithm optimization LQR controller solving state feedback gain matrix K is as shown in Figure 3.Operation heredity is calculated Method, obtains weight matrix Q, R of LQR, feedback of status gain matrix K and fitness function value successively, and fitness function value is entered Row punishment judges and algorithm stop condition judges that filtering out suitable individual carries out calculating of future generation, and process to be calculated reaches algorithm The stop condition of setting reaches the maximum genetic algebra of algorithm setting, and calculating terminates, it is as a result as optimized after state it is anti- Feedforward gain matrix K, while obtaining each component concrete numerical value of LQR method weight matrix Q and R.
During feedback of status gain matrix K applied into control strategy, current source type STATCOM systematic functions are optimized.

Claims (1)

1. it is a kind of for current source type STATCOM feedback of status gain matrix solve innovatory algorithm, it is characterised in that walk below Suddenly：
The first step, sets up current source type STATCOM Mathematical Modelings
With reference to side circuit, mathematical modeling, adoption status feedback control are carried out to its current source type STATCOM system topologies Strategy, is processed by state feedback linearization, current source type STATCOM mathematical modelings is obtained, such as formula (6) and formula (7) institute Show：
x · = A x + B u + F e - - - ( 6 )
Y=Cx (7)
Wherein, x is state variable；E and u is input variable；Y is output variable；A, B, C, F are physical circuit parameter matrix；
Second step, according to the current source type STATCOM mathematical modelings that the first step is obtained, using the current source suitable for innovatory algorithm Type STATCOM state feedback controller design system control block diagrams, set up its simulation model；
Shown in described current source type STATCOM state feedback controllers, such as formula (8)：
U=-Kx+Tyref+Me (8)
Wherein, yrefIt is the reference value of output variable；K is feedback of status gain matrix；T is that second order is configured to obtain by constant The diagonal matrix of input quantity reference value；M is constant gain vector；
By formula (6), formula (7) and formula (8), the closed loop controller existed between input quantity and output quantity, such as formula are obtained (9) shown in：
Y=C (sI-A+BK)-1[BTyref+(BM+F)e] (9)
Wherein, I is unit matrix, and s is the general plural number of transmission function；
Operator V is calculated using formula (10)：V=C (BK-A)-1B (10)
By formula (9) and formula (10), s=0, y are required according to system controlref=y is obtained：
T=V-1 (11)
M=-V-1C(BK-A)-1F (12)
3rd step, solves preferable feedback of status gain matrix
3.1) according to the liner quadratic regulator device (LQR) for being applied to innovatory algorithm, state is calculated by weight matrix anti- Feedforward gain matrix K, the form of described liner quadratic regulator device (LQR) is：
J = ∫ 0 ∞ x T Q x d t + ∫ 0 ∞ u T R u d t - - - ( 13 )
Wherein, t is the time；X and u are respectively state variable and input variable；Q and R are the weight matrix of symmetrical non-negative；
3.2) genetic algorithm fitness function suitable for innovatory algorithm of the design as shown in formula (14)：
Fobj=a*Mp+b*ts+c*tr+d*SSE+f (14)
Wherein, Mp, ts, tr, SSE are respectively output quantity iqOrThe overshoot of curve, stabilization time, rise time and stable state are missed Difference；Constant a, b, c, d are respectively the coefficient of correspondence of overshoot, stabilization time, rise time and steady-state error；Constant f is adaptation The penalty factor of function is spent, usually positive number；
3.3) according to actual conditions to step 3.2) in constant be adjusted, the fitness function for being suited the requirements simultaneously lose Propagation algorithm is called in tool box, and genetic algorithm of reruning is to step 3.1) in liner quadratic regulator device LQR weight squares Battle array carries out global optimizing, obtains preferable feedback of status gain matrix, and current source type is ensured finally by STATE FEEDBACK CONTROL STATCOM has good dynamic property.
CN201611187584.3A 2016-12-21 2016-12-21 Improved algorithm for solving state feedback gain matrix of current source STATCOM (static synchronous compensator) Pending CN106707752A (en)

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Application publication date: 20170524