CN105119318A - Grid-connected converter anti-interference capability-based similar synchronous machine additional damping control method - Google Patents

Abstract

The invention relates to a grid-connected converter anti-interference capability-based similar synchronous machine additional damping control method and belongs to the technical field of static stability analysis and control in a grid-connected converter-containing power system. According to the method, the stability of the system is prejudged; when the system is unstable, extreme point mirror image configuration is adopted to make the system stable; under a stable condition, the characteristic root of a PSS-containing synchronous machine system is selected as a target characteristic root, and the damping characteristic of the grid-connected converter-containing system can achieve a damping characteristic similar to that of the synchronous machine system, and therefore, the problems of small damping and poor anti-interference ability of the grid-connected converter-containing system can be solved; and under an unstable condition, controllability judgment is performed on the system, uncontrollable state variables are separated, and then, extreme point mirror image configuration is adopted. The invention provides a target characteristic root selection method when the extreme point configuration method is adopted. When the system is instable, the extreme point mirror image configuration is adopted to adjust an instable extreme point, and therefore, through the extreme point configuration method, system damping of the grid-connected converter-containing system can be increased, and the anti-interference performance of the grid-connected converter-containing system can be improved.

Description

Based on the homochronousness machine additional longitudinal forces method of grid-connected converter interference rejection ability

Technical field

The invention belongs in electric power system containing static stability analysis & control technical field during grid-connected converter.Relate to stability analysis and the automation field correlation theory of electric power system, be related specifically to when controlled device is unstable, additional mirror improves power system steady-state stability as POLE PLACEMENT USING.

Background technology

At present, grid-connected converter Main Function has been transmission, the operation of guarantee stability of grid connection of power.Distributed power source, time as grid-connected by current transformer in the device such as wind power generation, photovoltaic generation, the direct-coupling relation between itself and electrical network is isolated by power electronic equipment, does not reach as synchronous motor as the low-frequency oscillation of system provides corresponding damping.

Document P. elder brother moral (U.S.), KundurP. power system stability and control: English copy [M]. China Electric Power Publishing House, 2001. stability index and the control strategies describing electric power system in detail, propose a kind of pole-assignment improving power system steady-state stability.But target signature root during antipodal points configuration is selected not launch research, target signature root be not Left half-plane from the imaginary axis more away from better, need to determine according to the situation of system total damping and performance index.In addition, when unstable limit appears in system, it is still unstable directly to carry out POLE PLACEMENT USING system, and one-sided to improve system damping nonsensical.

Summary of the invention

The object of this invention is to provide a kind of homochronousness machine additional longitudinal forces method based on grid-connected converter interference rejection ability.When proposing high order system employing Method of Pole Placement, need anticipation system stability situation, utilize limit mirror configuration to make system stability for time-dependent system, the characteristic root of the Synchronous Motor System selected containing PSS under stable condition is target signature root.Make the damping characteristic containing grid-connected converter system convergence synchronous motor.Solve containing grid-connected converter system damping little, the problem of interference rejection ability difference.

Technical scheme of the present invention is:

Step 1. sets up the state-space expression containing grid-connected converter system according to formula (1), obtains ssystem transfer function G (s).

$\left\{\begin{array}{c}px=Ax+Bu\\ y=Cx\end{array}\right.---\left(1\right)$

The characteristic root of step 2. according to state-space expression factor arrays or the limit of transfer function G (s), judge the stability of system.If system stability, turn to step 6.

When step 3. system is unstable, ask for System Controllability matrix Q _c(Q _c=[BAB...A ^n-1b], n is the exponent number of equation group) order (rank (Q _c)), decision-making system controllability.As rank (Q _cduring)=n, system is completely controlled, turns to step 5; As 0<rank (Q _c) <n time, system is not exclusively controlled carry out step 4.

Step 4., according to PBH order criterion, is determined uncontrollable state variable, is isolated out original system, obtain controllable system.

Positive limit unstable in controllable system is mirrored to S Left half-plane by step 5., and utilization state feedback is carried out POLE PLACEMENT USING and obtained stable system.

Step 6. pair systems stabilisation, adopt Method of Pole Placement design additional damping controller, controller is made up of gain and a series of lead-lag link, basic structure is such as formula shown in (2), and transfer function H (s) forms closed-loop control as between feedback element and original system G (s).

$H\left(s\right)=K_D\&CenterDot;\frac{{\mathrm{sT}}_w}{1+{\mathrm{sT}}_w}\frac{1+{\mathrm{sT}}_1}{1+{\mathrm{sT}}_2}...\frac{1+{\mathrm{sT}}_{2n-1}}{1+{\mathrm{sT}}_{2n}}---\left(2\right)$

Wherein, K _d, T _w, T ₁, T ₂..., T _2nit is controller parameter.

Step 7. sets up the Synchronous Motor System state equation containing PSS controller, the characteristic root of design factor matrix, and the target signature root λ using this characteristic root as POLE PLACEMENT USING ₀.

Step 8. is by target signature root λ ₀substitute into following phase place and amplitude expression:

$\left|H\left({\mathrm{\&lambda;}}_0\right)\right|=\frac{1}{\left|G\left({\mathrm{\&lambda;}}_0\right)\right|}$

arg(H(λ ₀))＝180°-arg(G(λ ₀))(3)

Determine controller H (s) parameter, complete the design of additional damping controller.

Effect of the present invention and benefit are: the system of selection proposing target signature root when Method of Pole Placement is applied.For the unstable situation of system, propose mirror image POLE PLACEMENT USING and adjust unstable limit, make the system containing grid-connected converter increase system damping by Method of Pole Placement, strengthen anti-interference.

Accompanying drawing explanation

Fig. 1 is the double-fed blower fan grid-connected system structure chart containing grid-connected converter.

Fig. 2 is the homochronousness machine additional longitudinal forces method flow diagram based on grid-connected converter interference rejection ability.

Fig. 3 is synchronous motor PSS System Small Disturbance transfer function block diagram.In figure, M is generator amature inertia time constant, and D is damping coefficient, T ' _do, T _a, T _r, T _lthe time constant of excitation regulation part, K _r, K ₁, K ₂, K ₃, K ₄, K ₅, K ₆proportionality coefficient, T, T _1a, T _2apSS part-time constant, K _cbe PSS fraction coefficient, Δ ω is system frequency variable quantity, and Δ δ is generator torque angle variable quantity, Δ U _tvoltage variety, Δ E _fdthe no-load emf variable quantity determined by exciting voltage, Δ E _q' be transient potential variable quantity.

Fig. 4 (a) be containing grid-connected converter double-fed blower fan grid-connected system stable case under unit-step nsponse curve figure, Fig. 4 (b) be under stable case containing grid-connected converter double-fed blower fan grid-connected system additional damping controller after unit-step nsponse curve figure.

Fig. 5 (a) is that Fig. 5 (b) is containing the unit-step nsponse curve figure after the double-fed blower fan grid-connected system additional damping controller of grid-connected converter in unstable situation containing the unit-step nsponse curve figure in the unstable situation of double-fed blower fan grid-connected system of grid-connected converter.

Embodiment

The specific embodiment of the present invention is described in detail below in conjunction with technical scheme and accompanying drawing.

According to Fig. 1, double-fed blower fan is by wind energy conversion system, and gear box, generator and current transformer form.Grid-connected converter is divided into pusher side current transformer and net side converter, and net side converter accesses electrical network by transformer.Flow process according to Fig. 2, ignores the input power change of wind energy conversion system, sets up the Mathematical Modeling of each several part.Mechanical drive shaft system model is as follows:

$\left\{\begin{array}{c}{\mathrm{p\&Delta;\&theta;}}_b={\mathrm{\&omega;}}_0({\mathrm{\&Delta;\&omega;}}_w-{\mathrm{\&Delta;\&omega;}}_g)\\ {\mathrm{p\&Delta;\&omega;}}_w=-\frac{k_{hg}}{2H_w}{\mathrm{\&Delta;\&theta;}}_b-\frac{D_w+D_{hg}}{2H_w}{\mathrm{\&Delta;\&omega;}}_w+\frac{D_{hg}}{2H_w}{\mathrm{\&Delta;\&omega;}}_g\\ {\mathrm{p\&Delta;\&omega;}}_g=\frac{k_{hg}}{2H_g}{\mathrm{\&Delta;\&theta;}}_b+\frac{D_{hg}}{2H_g}{\mathrm{\&Delta;\&omega;}}_w-\frac{D_{hg}}{2H_g}{\mathrm{\&Delta;\&omega;}}_g-\frac{1}{2H_g}{\mathrm{\&Delta;T}}_g\end{array}\right.---\left(4\right)$

Wherein, ω _w, ω _gthe angular speed of wind energy conversion system and double-fed generator (DFIG) respectively; H _w, H _gthe inertia time constant of wind energy conversion system and DFIG respectively; θ _bit is axle system torsion angle; k _ghaxis rigidity coefficient, D _w, D _hgtwo self damping coefficients of equivalent mass block respectively; T _w, T _gmachine torque and electromagnetic torque.The differential equation of generator electromagnetic torque is as follows:

${\mathrm{\&Delta;T}}_g=\frac{3}{2}{n}_p(i_{qs0}{\mathrm{\&Delta;i}}_{dr}-i_{ds0}{\mathrm{\&Delta;i}}_{qr})---\left(5\right)$

N in formula _pit is power generator electrode logarithm.

According to double-fed blower voltage and flux linkage equations, set up voltage magnetic linkage differential equation group:

$\left\{\begin{array}{c}{\mathrm{p\&Delta;\&psi;}}_{ds}=-\frac{R_s}{l_s}{\mathrm{\&Delta;\&psi;}}_{ds}+l_2{R}_s{\mathrm{\&Delta;i}}_{dr}+{\mathrm{\&omega;}}_{10}{\mathrm{\&Delta;\&psi;}}_{qs}+{\mathrm{\&psi;}}_{qs0}{\mathrm{\&Delta;\&omega;}}_1\\ {\mathrm{p\&Delta;\&psi;}}_{qs}=-\frac{R_s}{l_s}{\mathrm{\&Delta;\&psi;}}_{qs}+l_2{R}_s{\mathrm{\&Delta;i}}_{qr}-{\mathrm{\&omega;}}_{10}{\mathrm{\&Delta;\&psi;}}_{qs}-{\mathrm{\&psi;}}_{ds0}{\mathrm{\&Delta;\&omega;}}_1\\ {\mathrm{p\&Delta;i}}_{dr}=-\frac{R_r}{l_1}{\mathrm{\&Delta;i}}_{dr}+\frac{1}{l_1}\mathrm{\&Delta;}\stackrel{*}{u_{dr}}-\frac{l_2}{l_1}{\mathrm{p\&Delta;\&psi;}}_{ds}\\ {\mathrm{p\&Delta;i}}_{qr}=-\frac{R_r}{l_1}{\mathrm{\&Delta;i}}_{qr}+\frac{1}{l_1}\mathrm{\&Delta;}\stackrel{*}{u_{dr}}-\frac{l_2}{l_1}{\mathrm{p\&Delta;\&psi;}}_{qs}\end{array}\right.---\left(6\right)$

L in formula _s, l _rand l _mstator and rotor self-induction and mutual inductance; r _s, R _rit is stator and rotor resistance parameters; ω ₁and ω ₁₀it is the initial value of synchronous speed and synchronous speed; with it is the output variable of current transformer control loop.

Grid-connected converter adopts double circle controling mode, and outer shroud to be compared with reference power by the generated output of collection double-fed blower fan and forms power closed loop; Inner ring calculates through corresponding the current closed-loop formed by rotor and stator current.Double-loop control strategy, is realized by four control loops, respectively: meritorious loop current ring, idle loop current ring, active power ring, reactive power ring.Four corresponding four PI controllers of control loop are:

$\left\{\begin{array}{c}\stackrel{*}{u_{dr}}=\left(\stackrel{*}{i_{dr}}-i_{dr}\right)\left(K_Q+\frac{K_{QI}}{s}\right)\\ \stackrel{*}{u_{qr}}=\left(\stackrel{*}{i_{qr}}-i_{qr}\right)\left(K_P+\frac{K_{PI}}{s}\right)\end{array}\right.---\left(7\right)$

$\left\{\begin{array}{c}\stackrel{*}{i_{ds}}=(Q_{ref}-Q)\left(c_Q+\frac{c_{QI}}{s}\right)\\ \stackrel{*}{i_{qs}}=(P_{ref}-P)\left(c_P+\frac{c_{PI}}{s}\right)\end{array}\right.---\left(8\right)$

According to formula (7), (8), obtain following state equation:

$\left[\begin{array}{c}{\mathrm{p\&Delta;x}}_1\\ {\mathrm{p\&Delta;x}}_2\\ {\mathrm{p\&Delta;x}}_3\\ {\mathrm{p\&Delta;x}}_4\end{array}\right]=\left[\begin{array}{cccc}-1& 0& \frac{1}{l_m}& 0\\ 0& -1& 0& \frac{1}{l_m}\\ \frac{l_m*u_{qs0}}{l_s}& 0& -\frac{u_{qs0}}{l_s}& 0\\ 0& \frac{l_m*u_{qs0}}{l_s}& 0& -\frac{u_{qs0}}{l_s}\end{array}\right]\left[\begin{array}{c}{\mathrm{\&Delta;i}}_{dr}\\ {\mathrm{\&Delta;i}}_{qr}\\ {\mathrm{\&Delta;\&psi;}}_{ds}\\ {\mathrm{\&Delta;\&psi;}}_{qs}\end{array}\right]+\left[\begin{array}{cc}-\frac{l_s}{l_m}& 0\\ 0& -\frac{l_s}{l_m}\\ 0& 0\\ 0& 0\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;}\stackrel{*}{i_{ds}}\\ \mathrm{\&Delta;}\stackrel{*}{i_{qs}}\end{array}\right]---\left(9\right)$

$\left[\begin{array}{c}\mathrm{\&Delta;}\stackrel{*}{i_{ds}}\\ \mathrm{\&Delta;}\stackrel{*}{i_{qs}}\end{array}\right]=\left[\begin{array}{cc}-c_Q& 0\\ 0& -c_P\end{array}\right]\left[\begin{array}{c}\mathrm{\&Delta;}Q\\ \mathrm{\&Delta;}P\end{array}\right]+\left[\begin{array}{cccc}0& 0& c_{QI}& 0\\ 0& 0& 0& c_{PI}\end{array}\right]\left[\begin{array}{c}{\mathrm{\&Delta;x}}_1\\ {\mathrm{\&Delta;x}}_2\\ {\mathrm{\&Delta;x}}_3\\ {\mathrm{\&Delta;x}}_4\end{array}\right]---\left(10\right)$

Wherein, $x_1=\frac{\stackrel{*}{i_{dr}}-i_{dr}}{s},x_2=\frac{\stackrel{*}{i_{qr}}-i_{qr}}{s},x_3=\frac{(Q_{ref}-Q)*c_{QI}}{s},x_4=\frac{(P_{ref}-P)*c_{PI}}{s}$ Be respectively intermediate variable.

Simultaneous formula (4), (6), (9), (10) obtain 11 rank state equations of system, and state variable is Δ ω _w, Δ ω _g, Δ θ _b, Δ ψ _ds, Δ ψ _qs, Δ i _dr, Δ i _qr, Δ x ₁, Δ x ₂, Δ x ₃, Δ x ₄.Known by Li Yapuluofu First Law, if the characteristic root of factor arrays has negative real part, then system is systems stabilisation.

Bring double-fed fan motor machine set system parameter into: R _r=0.005, R _s=0.0071, l _m=2.9, l _s=3.071, l _r=3.056, H _w=4.54, H _g=0.5, k _s=0.3, D _w=2, D _hg=1, D _g=1, n _p=2.After magnetic linkage d axle orientation, each initial value is: u _ds0=0, u _qs0=1, ψ _ds0=1, u _qs0=0, ω ₁₀=1.Grid-connected converter parameter: 1. K _q=0.001, K _qI=0.5, K _p=0.001, K _pI=0.5, c _p=0.003, c _pI=-0.003, c _q=0.003, c _qI=-0.003, system stability; 2. K _q=0.1, K _qI=0.5, K _p=0.1, K _pI=0.5, c _p=0.3, c _pI=0.3, c _q=0.3, c _qI=0.3, system is unstable.Try to achieve characteristic root as shown in table 1.

Containing grid-connected converter double-fed blower fan system characteristic root in table 1 two kinds of situations

In unstable situation, System Controllability rank of matrix rank (Q _c)=10<11, illustrative system is not exclusively controlled, containing a uncontrollable state variable.According to PBH order criterion, by characteristic root λ _isubstitute into rank ([λ successively _ii-AB]), wherein rank ([λ ₉i-AB])=10, λ is described ₉for uncontrollable point.Select non-singular transformation matrix P, formula (1) is transformed to following formula:

$\left[\begin{array}{c}{\mathrm{px}}_c\\ {\mathrm{px}}_{\stackrel{\&OverBar;}{c}}\end{array}\right]={\mathrm{PAP}}^{-1}\left[\begin{array}{c}{x}_c\\ c_{\stackrel{\&OverBar;}{c}}\end{array}\right]+PBu---\left(11\right)$

$y={\mathrm{CP}}^{-1}\left[\begin{array}{c}{x}_c\\ x_{\stackrel{\&OverBar;}{c}}\end{array}\right]---\left(12\right)$

X _c, represent controlled state variable and uncontrollable state variable respectively.Formula (11), (12) are launched, obtains x respectively _ccorresponding controllable system with corresponding uncontrollable system, carries out mirror configuration limit by the controllable system utilization state obtained feedback, obtains stabistor system.

Because the maximum compensation rate of damping controller single lead-lag link phase place is 60 °, two-stage compensates and is up to 120 °, and meet the compensation condition of double-fed blower fan system, damping controller selects following form:

$H\left(s\right)=K_D\frac{{\mathrm{sT}}_w}{1+{\mathrm{sT}}_w}\frac{1+{\mathrm{sT}}_1}{1+{\mathrm{sT}}_2}---\left(13\right)$

The Synchronous Motor System spatial expression containing PSS is set up, factor arrays A according to Fig. 3 ₀expression formula as follows:

$A_0=\left[\begin{array}{cccccc}0& {\mathrm{\&omega;}}_0& 0& 0& 0& 0\\ -\frac{K_1}{M}& 0& 0& -\frac{K_2}{M}& 0& 0\\ -\frac{K_4}{T_{d0}^{\&prime;}}& 0& -\frac{1}{T_{d0}^{\&prime;}{K}_3}& -\frac{1}{T_{d0}^{\&prime;}}& 0& 0\\ 0& 0& 0& -\frac{K_1}{T_L}& \frac{1}{T_L}& 0\\ 0& 0& 0& -\frac{1}{T_A}& -\frac{1}{T_A}& \frac{1}{T_A}\\ \frac{K_R{K}_5}{T_R}& 0& \frac{K_R{K}_6}{T_R}& 0& 0& -\frac{1}{T_R}\end{array}\right]---\left(14\right)$

The excitation parameter of synchronous motor: M=9.26, T ' _do=7.76s, T _a=0.05s, T _r=0.06s, T _l=0.002 ~ 0.05s, K _r=1.0, K ₁=0.5542, K ₂=1.2120, K ₃=0.6584, K ₄=0.7037, K ₅=0.0945, K ₆=0.8150, ω ₀=1; The factor arrays characteristic root of trying to achieve containing PSS Synchronous Motor System is as shown in table 2.

Table 2 is containing the characteristic value of PSS Synchronous Motor System

	Characteristic root	Damping ratio	Nature frequency of oscillation
				λ 01	-18.0633	1.00e+000	1.81e+001
λ 02	-4.7573+8.8833i	4.72e-001	1.01e+001
				λ 03	-4.7573-8.8833i	4.72e-001	1.01e+001
λ 04	-1.3952+3.9881i	3.30e-001	4.23e+000
				λ 05	-1.3952-3.9881i	3.30e-001	4.23e+000
λ 06	-0.3393	1.00e+000	3.39e-001

When real root is as target signature root, the arg (H)=± 180 ° of feedback element transfer function, cannot carry out lead-lag rectification to system.Therefore λ is selected ₀₂~ λ ₀₅bring transfer function formula (3) into as target signature root, obtain proportionality constant K _dand controller parameter T _w, T ₁, T ₂.After additional damping controller, ssystem transfer function is as follows:

$G_1\left(s\right)=\frac{G\left(s\right)}{1+H\left(s\right)G\left(s\right)}---\left(15\right)$

Additional control after system features root situation and system damping as shown in table 3.

Table 3 adjusts the characteristic root situation of latter two situation

Table 3, Fig. 4, Fig. 5 illustrate that homochronousness machine additional longitudinal forces method can improve the damping of original system, effective equally to time-dependent system.

Claims (1)

1. the homochronousness machine additional longitudinal forces method based on grid-connected converter interference rejection ability, after anticipation system stability situation, limit mirror configuration is utilized to make system stability for time-dependent system, under stable condition, selection contains the pole-assignment that the characteristic root of the Synchronous Motor System of PSS is target signature root, and its characterization step is as follows:

Step 1. sets up the state-space expression containing grid-connected converter system, obtains ssystem transfer function G (s);

The characteristic root of step 2. according to state-space expression factor arrays or the limit of transfer function G (s), judge the stability of system, if system stability, turns to step 6;

When step 3. system is unstable, according to System Controllability rank of matrix decision-making system controllability, when System Controllability rank of matrix is full rank, system is completely controlled, turns to step 5, and system is not exclusively controlled carry out step 4;

Step 4., according to PBH order criterion, is determined uncontrollable state variable, is isolated out original system, obtain controllable system;

Positive limit unstable in controllable system is mirrored on the left of S plane by step 5., and utilization state feedback is carried out POLE PLACEMENT USING and obtained stable system;

Step 6. pair systems stabilisation, adopt Method of Pole Placement design additional damping controller, controller is made up of gain and a series of lead-lag link, and its transfer function H (s) forms closed-loop control as between feedback element and original system G (s);

Step 7. sets up the Synchronous Motor System state equation containing PSS controller, the characteristic root of design factor matrix, and the target signature root λ using this characteristic root as POLE PLACEMENT USING ₀;

Step 8. is by target signature root λ ₀determine controller parameter in the phase place of substitution controller H (s) and amplitude expression, complete the design of additional damping controller.