CN106786715A - A kind of multiterminal VSC HVDC system droop control coefficients determine method - Google Patents

Abstract

The present invention discloses a kind of multiterminal VSC HVDC system droop control coefficients and determines method, and the mean value model for being primarily based on VSC establishes the straight-flow system state-space model containing droop control, and the mechanism of action of droop control is analyzed with this；Sagging coefficient is determined that problem is converted to the optimization problem with system Mixed Sensitivity Frobenius Hankel Norm minimums as target based on system model again, the constraint of closed-loop system characteristic value and steady-state error constraint are considered simultaneously, are optimal the stability of system and robustness.The method of the present invention can at utmost ensure stability of the system under disturbance, and system is had certain fault ride-through capacity；Can also determine that method is combined with other sagging coefficients, increase constraints or change optimization aim, design the droop control device for meeting different requirements or realizing difference in functionality.

Description

A kind of multi-end VSC-HVDC system droop control coefficient determines method

Technical field

The present invention relates to Coordinated Control field between current conversion station in power grid construction, specially a kind of multiterminal VSC-HVDC systems System droop control coefficient determines method.

Background technology

Multiterminal voltage source converter based HVDC system (voltage source converter based High voltage direct current, VSC-HVDC) it is increasingly becoming power grid construction new trend.Preferably to play many The regulating power of VSC-HVDC systems is held, the research coordinated control mode between current conversion station is essential, the wherein sagging control of voltage Combination property processed is to apply coordinated control mode between more station at present preferably, and voltage droop control coefficient determines the change of current Power and voltage-regulation task proportion that station undertakes, and then determine the stability of system, thus sagging coefficient determination most It is important.

At present research in sagging coefficient be mainly according to current conversion station capacity and power margin be configured with dynamic regulation, For example have research consider current conversion station capacity on the basis of meter and current conversion station power margin come determine sagging coefficient (Zhu Rui can, Lee Xing Yuan, Wu Feng consider that the VSC-MTDC systems of power margin improve droop control strategy [J] Sichuan Universitys journal (engineering science Version), 2015,47 (3)：137-143.), there is research and consider the influence of real-time working condition on this basis, in system operation work Condition change when automatically adjust sagging coefficient, make imbalance power in system obtain an equitable breakdown (Zhu Rui can, Wang Yuhong, Li Xingyuan, Deng .VSC-MTDC system dc voltage adaptive slop control strategy [J] Automation of Electric Systems, 2015,39 (4)：63- 68.).But the current rare research to droop control Mathematical Modeling, and it is determined that also have ignored based on number during sagging coefficient Learn the stability analysis of model.To weigh influence of the controller to the stability of a system, generally propose that different parameters refer to as evaluation Mark, wherein S/T Mixed Sensitivities have proven to a kind of ripe determination of stability index, can be used to evaluate droop control device The stability of a system is influenceed.

The content of the invention

Regarding to the issue above, system can be made still to keep stability under disturbance it is an object of the invention to provide one kind Multi-end VSC-HVDC system droop control coefficient with robustness determines method, and technical scheme is as follows：

A kind of multi-end VSC-HVDC system droop control coefficient determines method, it is characterised in that comprise the following steps：

Step 1：Mean value model according to VSC decouples ac and dc systemses, and Converter DC-side is equivalent into direct current Stream source, DC line carries out π types equivalence, obtains multi-end VSC-HVDC system equivalent model；

Step 2：Its state-space model is set up according to multi-end VSC-HVDC system equivalent model：

In formula, x is state variable；ω is disturbance variable, and u is control variables, and ω and u are input variable；Y and z are Output variable；A、B_ω、B_u、C_yAnd C_zIt is state matrix；And

X=[U₁,...U_i,...,U_n,i_L1,...,i_Lk,...,i_Lm]^T (2)

Wherein, n is transverter quantity, U_iIt is i-th transverter DC voltage, m is DC line quantity, i_LkTo flow through line Road L_kElectric current；i_kIt is i-th transverter DC current, n_cIt is the quantity at DC voltage control end, n_ncFor non-dc voltage is controlled The quantity at end；

Specific topology according to system obtains its steady-state operation equation, substitutes into the transmission that formula (1)-(4) arrange the system that obtains Jacobian matrix is：

And

Step 3：The closed-loop system state-space model containing droop control device is set up, is asked for by Constrained Optimum Theory Sagging coefficient optimal value, specific method is：

1) closed-loop system characteristic value constraint：By droop control device u=K (y-U_dcmin) formula (1) is substituted into, obtain adding sagging control Closed-loop system state matrix after device processed is A_c=A+B_uKC_y；

Wherein, the matrix expression of droop control device isK in formula₁It is using the transverter 1 of droop control Sagging coefficient, k₂It is the sagging coefficient using the transverter 2 of droop control；A_cTo add the closed-loop system after droop control device State matrix；U_dcminFor the voltage minimum that straight-flow system is allowed；

To make closed-loop system keep stabilization, then the characteristic value real part of closed-loop system all takes negative value, corresponding constraints For：

real(λ_i(A_c))<0 (i=1 ..., n_eig) (7)

In formula：λ_i(A_c) it is A_cCharacteristic value；n_eigIt is characterized value quantity；

2) steady-state error constraint：The degree of each end DC voltage offset voltage minimum value is set to be maintained at certain restriction range Interior, then the constraint of y passages steady-state error and z passage steady-state error constraint expression formulas are：

E (s)=y (s)-U_dcmin(s)=[S (s) G_yω(s) -S(s)]v(s) (8)

e_z(s)=[G_zω(s)+G_zu(s)KS(s)G_yω(s)-G_zu(s)KS(s)-I]v(s) (9)

In formula, v (s)=[ω (s) U_dcmin(s)]^TIt is input variable, including disturbance variable and control variables minimum value；

S (s)=(I-KG_yu(s))^-1It is narrow sense controlled device G_yuSensitivity function；

The ratio between two norms with variable assess influence of the input variable to output variable and control variables, by steady-state error Analysis is converted to the odd value analysis of transfer function matrix, and steady-state error constraint is then converted into the singular value of transmission function about Beam；

3) the sensitivity function S and mending sensitivity function T of controlled device G are defined as

H is feedback controller in formula；

Make the FH Norm minimums of system sensitivity function and mending sensitivity function, i.e.,：

In formula, J_optIt is the optimal value of S/T Mixed Sensitivity performance indications, K_stabTo meet the constraint of S/T Mixed Sensitivities PID controller parameter domain；

The optimization problem is solved, the droop control coefficient for being optimal the stability of a system is obtained.

The beneficial effects of the invention are as follows：The present invention determines problem for multi-end VSC-HVDC system droop control coefficient, carries Go out a kind of sagging coefficient for considering the stability of a system and determine method, the mean value model for being primarily based on VSC is established containing sagging control The straight-flow system state-space model of system, the mechanism of action of droop control is analyzed with this；Then, based on system model by sagging system Number determination problem is converted to the optimization problem with system Mixed Sensitivity Frobenius-Hankel Norm minimums as target, together When consider the constraint of closed-loop system characteristic value and steady-state error constraint, be optimal the stability of system and robustness；The method Stability of the system under disturbance can at utmost be ensured, and make system that there is certain fault ride-through capacity；Can also be with it His sagging coefficient determines that method is combined, and increases constraints or changes optimization aim, designs and meets different requirements or realize not The droop control device of congenerous.

Brief description of the drawings

Fig. 1 is to add the closed-loop system schematic diagram after droop control device.

Fig. 2 is four end VSC-HVDC system topology schematics.

Fig. 3 is four end VSC-HVDC system equivalent model schematic diagrames.

Fig. 4 a for marine wind electric field exert oneself change when each end DC voltage dynamic response figure.

Fig. 4 b for marine wind electric field exert oneself change when each end active power dynamic response figure (VSC1, VSC2).

Fig. 4 c for marine wind electric field exert oneself change when each end active power dynamic response figure (VSC3, VSC4).

Fig. 4 d for marine wind electric field exert oneself change when each end DC current dynamic response figure (VSC1, VSC2).

Fig. 4 e for marine wind electric field exert oneself change when each end DC current dynamic response figure (VSC3, VSC4).

Each end DC voltage dynamic response figure when Fig. 5 a are ac bus three-phase shortcircuit earth fault.

Each end active power dynamic response figure (VSC1, VSC2) when Fig. 5 b are ac bus three-phase shortcircuit earth fault.

Each end active power dynamic response figure (VSC3, VSC4) when Fig. 5 c are ac bus three-phase shortcircuit earth fault.

Each end DC voltage dynamic response figure (VSC3) when Fig. 5 d are ac bus three-phase shortcircuit earth fault.

Each end DC voltage dynamic response figure (VSC4) when Fig. 5 e are ac bus three-phase shortcircuit earth fault.

Specific embodiment

Technical scheme and technique effect are described in further details with specific embodiment below in conjunction with the accompanying drawings.

A kind of multi-end VSC-HVDC system droop control coefficient determines method, comprises the following steps：

Step 1：Mean value model based on VSC decouples ac and dc systemses, and Converter DC-side is equivalent into direct current Stream source, DC line carries out π types equivalence, obtains the equivalent model of VSC-HVDC systems.

Step 2：Its state-space model is set up based on multi-end VSC-HVDC system equivalent model.Specially：

The state-space model for making multi-end VSC-HVDC system is

In formula：X is state variable；ω is disturbance variable；U is control variables；Y and z is output variable；A, B_ω, B_u, C_y, C_z It is state matrix.

1) state variable, its value is：

X=[U₁,...U_i,...,U_n,i_L1,...,i_Lk,...,i_Lm]^T (2)

In formula：N is transverter quantity, U_iIt is i-th transverter DC voltage, m is DC line quantity, i_LkTo flow through line Road L_kElectric current.

2) disturbance variable and control variables, they are all input variable, and its value is：

In formula：i_kIt is i-th transverter DC current, n_cIt is the quantity at DC voltage control end, n_ncIt is non-dc voltage The quantity of control end

3) output variable, its value is：

In formula：U_iIt is i-th transverter DC voltage, n_cIt is the quantity at DC voltage control end, n_ncIt is non-dc voltage The quantity of control end.

Specific topology according to system obtains its steady-state operation equation, substitutes into the transmission that formula (1)-(4) arrange the system that obtains Jacobian matrix is：

Wherein

Transfer function matrix is divided into four parts, and the transitive relation between two inputs and two outputs is represented respectively, its Middle G_yuIt is the transfer matrix between control variables u and output variable y, namely controlled device in the narrow sense.Make droop control device Matrix expression is K, then add the closed-loop system after droop control device as shown in figure 1, so far obtaining closing containing droop control device Loop systems state-space model.

Step 3：According to closed-loop system state-space model, sagging coefficient is asked for by Constrained Optimum Theory optimal Value, wherein constraints are the constraint of closed-loop system characteristic value and steady-state error constraint, and optimization aim is that the S/T for making closed-loop system is mixed Close the Frobeniu-Hankel Norm minimums of sensitivity.Specially：

1) closed-loop system characteristic value constraint：

By droop control device u=K (y-U_dcmin) formula (1) is substituted into, obtain adding the closed-loop system state after droop control device Matrix is A_c=A+B_uKC_y.Wherein, the matrix expression of droop control device isK in formula₁It is to use droop control Transverter 1 sagging coefficient, k₂It is the sagging coefficient using the transverter 2 of droop control；A_cAfter adding droop control device Closed-loop system state matrix；U_dcminFor the voltage minimum that straight-flow system is allowed.

Closed-loop system is set to keep stabilization, then the characteristic value real part of closed-loop system must be all negative value, namely closed-loop system Limit needs to be entirely located in Left half-plane, and a corresponding constraints is：

real(λ_i(A_c))<0 (i=1 ..., n_eig) (7)

In formula：λ_i(A_c) it is A_cCharacteristic value；n_eigIt is characterized value quantity.

2) steady-state error constraint：

Refer to that the degree of each end DC voltage offset voltage minimum value is maintained in certain restriction range, because closed-loop system is deposited In output variable y and z, droop control end DC voltage and non-droop control end DC voltage, therefore steady-state error are corresponded to respectively Constraint can be divided into the constraint of y passages steady-state error and the constraint of z passages steady-state error.Each error variance expression formula can obtain by Fig. 1：

E (s)=y (s)-U_dcmin(s)=[S (s) G_yω(s) -S(s)]v(s) (8)

e_z(s)=[G_zω(s)+G_zu(s)KS(s)G_yω(s)-G_zu(s)KS(s)-I]v(s) (9)

V (s)=[ω (s) U in formula_dcmin(s)]^TIt is input variable, including disturbance variable and control variables minimum value；S (s)=(I-KG_yu(s))^-1It is narrow sense controlled device G_yuSensitivity function.The Concept Evaluation energy of introducing norm is between variable The gain of transmission, assesses influence of the input variable to output variable and control variables, by stable state with the ratio between two norms of variable Error analysis is converted to the odd value analysis of transfer function matrix, and steady-state error constraint is then converted into the singular value of transmission function Constraint.

3) optimization aim based on S/T Mixed Sensitivity functions：

The sensitivity function S and mending sensitivity function T of controlled device G are defined as：

H is feedback controller in formula.

S/T mixed sensitivity problem overall thoughts are to make the FH norms of system sensitivity function and mending sensitivity function most It is small, i.e.,：

J in formula_optIt is the optimal value of S/T Mixed Sensitivity performance indications, K_stabExpression meets the constraint of S/T Mixed Sensitivities PID controller parameter domain.

Solve above optimization problem, you can obtain the droop control coefficient for being optimal the stability of a system, also obtain final product To desired droop control device.

To detect the beneficial effect of the inventive method, verified using realistic model emulation.

Four end VSC-HVDC systems are chosen as simulation example, its structure is as shown in Figure 2.In fig. 2, VSC1 and VSC2 connects Marine wind electric field is connect, using double-fed blower fan, VSC3 and VSC4 connects land AC network, it is assumed that all AC networks are all heavily fortified point Forceful electric power net.VSC1 and VSC2 is used and is determined alternating voltage and determine FREQUENCY CONTROL, and VSC3 and VSC4 uses voltage droop control.

1) according to system topological and parameter, the equivalent model for obtaining four end VSC-HVDC systems is as shown in Figure 3.

2) according to the equivalent model of four end VSC-HVDC systems, its steady-state operation equation is obtained based on Kirchhoff's law For：

Wherein：

The state variable of system, disturbance variable, control variables and two output variables are respectively：

Formula (14) is substituted into formula (12), arrangement obtains system state space model.

3) the sagging coefficient select permeability based on Optimum Theory, its object function are proposed for four end VSC-HVDC systems As shown in formula (11), its characteristic value is constrained as shown in formula (7), and its y channel error is constrained to：

Its z channel error is constrained to：

Above-mentioned optimization problem is solved, obtaining sagging coefficient optimal solution is：

Now the y channel error variables steady-state error of system is for 38.6621, z channel error variable steady-state errors 39.9869, S/T Mixed Sensitivities are 0.3920.

After obtaining optimal sagging coefficient, different disturbance and failures are applied in systems, checking system is in droop control device Stability under effect.The perturbation scheme of Digital Simulation is：

(1) WF1 to exert oneself and be reduced to 75MW by 100MW during 5s；WF2 to exert oneself and increase to 125MW by 100MW during 6s；WF1 during 7s Exert oneself recovery rated value；WF2 exerts oneself recovery rated value during 9s.Marine wind electric field exert oneself change when each electrical quantity of system response feelings Condition is as shown in Fig. 4 a- Fig. 4 e.

(2) there is three-phase shortcircuit earth fault during 5s at VSC4 current conversion stations ac bus, cut off after 0.1s.Ac bus three The response condition of each electrical quantity of system is as shown in Fig. 5 a- Fig. 5 e during phase short circuit grounding failure.

Simulation result shows, can at utmost ensure system under disturbance based on the droop control device designed by this method Stability, and make system that there is certain fault ride-through capacity.In addition, this method can also determine method with other sagging coefficients With reference to, increase constraints or change optimization aim, design the droop control device for meeting different requirements or realizing difference in functionality.

Claims (1)

1. a kind of multi-end VSC-HVDC system droop control coefficient determines method, it is characterised in that comprise the following steps：

Step 1：Mean value model according to VSC decouples ac and dc systemses, and Converter DC-side is equivalent into DC current source, DC line carries out π types equivalence, obtains multi-end VSC-HVDC system equivalent model；

Step 2：Its state-space model is set up according to multi-end VSC-HVDC system equivalent model：

$\left\{\begin{array}{c}\frac{dx}{dt}=Ax+B_{u}u+B_{\mathrm{\&omega;}}\mathrm{\&omega;}\\ y=C_{y}x\\ z=C_{z}x\end{array}\right.---\left(1\right)$

In formula, x is state variable；ω is disturbance variable, and u is control variables, and ω and u are input variable；Y and z is output Variable；A、B_ω、B_u、C_yAnd C_zIt is state matrix；And

X=[U₁,...U_i,...,U_n,i_L1,...,i_Lk,...,i_Lm]^T (2)

$\left\{\begin{array}{c}u={\&lsqb;i_1,i_2,\mathrm{...},i_k,\mathrm{...},i_{n_c}\&rsqb;}^T\\ \mathrm{\&omega;}={\&lsqb;i_1,i_2,\mathrm{...},i_k,\mathrm{...},i_{n_{nc}}\&rsqb;}^T\end{array}\right.---\left(3\right)$

$\left\{\begin{array}{c}y={\&lsqb;U_1,U_2,\mathrm{...},U_{n_c}\&rsqb;}^T\\ z={\&lsqb;U_1,U_2,\mathrm{...},U_{n_{nc}}\&rsqb;}^T\end{array}\right.---\left(4\right)$

Wherein, n is transverter quantity, U_iIt is i-th transverter DC voltage, m is DC line quantity, i_LkTo flow through circuit L_k Electric current；i_kIt is i-th transverter DC current, n_cIt is the quantity at DC voltage control end, n_ncIt is non-dc voltage controling end Quantity；

Specific topology according to system obtains its steady-state operation equation, substitutes into the arrangement of formula (1)-(4) and obtains system transter Matrix is：

$G\left(s\right)=\left[\begin{array}{cc}{G}_{yu}\left(s\right)& G_{y\mathrm{\&omega;}}\left(s\right)\\ G_{zu}\left(s\right)& G_{z\mathrm{\&omega;}}\left(s\right)\end{array}\right]---\left(5\right)$

And

$\left\{\begin{array}{c}{G}_{yu}\left(s\right)=C_y{(sI-A)}^{-1}{B}_u\\ G_{y\mathrm{\&omega;}}\left(s\right)=C_y{(sI-A)}^{-1}{B}_{\mathrm{\&omega;}}\\ G_{zu}\left(s\right)=C_z{(sI-A)}^{-1}{B}_u\\ G_{z\mathrm{\&omega;}}\left(s\right)=C_z{(sI-A)}^{-1}{B}_{\mathrm{\&omega;}}\end{array}\right.---\left(6\right)$

Step 3：The closed-loop system state-space model containing droop control device is set up, is asked for by Constrained Optimum Theory sagging Coefficient optimal value, specific method is：

1) closed-loop system characteristic value constraint：By droop control device u=K (y-U_dcmin) formula (1) is substituted into, obtain adding droop control device Closed-loop system state matrix afterwards is A_c=A+B_uKC_y；

Wherein, the matrix expression of droop control device isK in formula₁Under being the transverter 1 using droop control Hang down coefficient, k₂It is the sagging coefficient using the transverter 2 of droop control；A_cTo add the closed-loop system state after droop control device Matrix；U_dcminFor the voltage minimum that straight-flow system is allowed；

To make closed-loop system keep stabilization, then the characteristic value real part of closed-loop system all takes negative value, and corresponding constraints is：

real(λ_i(A_c))<0 (i=1 ..., n_eig) (7)

In formula：λ_i(A_c) it is A_cCharacteristic value；n_eigIt is characterized value quantity；

2) steady-state error constraint：The degree of each end DC voltage offset voltage minimum value is set to be maintained in certain restriction range, then y Passage steady-state error is constrained and z passage steady-state error constraint expression formulas are：

E (s)=y (s)-U_dcmin(s)=[S (s) G_yω(s) -S(s)]v(s) (8)

e_z(s)=[G_zω(s)+G_zu(s)KS(s)G_yω(s)-G_zu(s)KS(s)-I]v(s) (9)

In formula, v (s)=[ω (s) U_dcmin(s)]^TIt is input variable, including disturbance variable and control variables minimum value；

S (s)=(I-KG_yu(s))^-1It is narrow sense controlled device G_yuSensitivity function；

The ratio between two norms with variable assess influence of the input variable to output variable and control variables, by analysis of steady-state error The odd value analysis of transfer function matrix are converted to, steady-state error constraint is then converted into the singular value constraint of transmission function；

3) the sensitivity function S and mending sensitivity function T of controlled device G are defined as

$\left\{\begin{array}{c}S\left(s\right)=\frac{1}{1+H\left(s\right)G\left(s\right)}\\ T\left(s\right)=\frac{H\left(s\right)G\left(s\right)}{1+H\left(s\right)G\left(s\right)}\end{array}\right.---\left(10\right)$

H is feedback controller in formula；

Make the FH Norm minimums of system sensitivity function and mending sensitivity function, i.e.,：

$J_{opt}=\underset{K_{stab}}{\min }\left|\right|\begin{array}{c}S\\ T\end{array}|{|}_{FH}---\left(11\right)$

In formula, J_optIt is the optimal value of S/T Mixed Sensitivity performance indications, K_stabTo meet the PID controls of S/T Mixed Sensitivities constraint Device parameter field processed；

The optimization problem is solved, the droop control coefficient for being optimal the stability of a system is obtained.