CN104333030A - Analysis method for multi-feed DC interaction factors based on reduced order Jacobian matrix - Google Patents

Abstract

The invention discloses an analysis method for multi-feed DC interaction factors based on reduced order Jacobian matrix, and the method comprises the steps as follows: simplifying and equivalently processing the DC- AC system to obtain the equivalent system; building the reduced order Jacobian matrix linearized model of the equivalent system; calculating multi-feed DC interaction factors through the related Jacobian matrix element. An analysis method for multi-feed DC interaction factors based on reduced order Jacobian matrix comprises the steps as follows: simplifying and equivalently processing the DC- AC system to obtain the equivalent system; building the reduced order Jacobian matrix linearized model of the equivalent system; calculating multi-feed DC interaction factors through the related Jacobian matrix element. MIIF can be calculated through Jacobian matrix related element, the existing running state of the system is not changed, the simulation experiment is avoided for calculating MIIF. The essence and impact factor for the MIIF are processed on theoretical derivation and analyzed, the former calculating method for MIIF is improved and the result is more reasonable and accurate.

Description

Based on the analytical method of the multi-infeed HVDC interaction factor of depression of order Jacobian matrix

Technical field

The invention belongs to technical field of HVDC transmission, especially a kind of analytical method of the multi-infeed HVDC interaction factor based on depression of order Jacobian matrix.

Background technology

In ac and dc systems, receiving end AC system rack power is the deciding factor of the stability of a system, in theoretical research and engineer applied, usually adopt the concept of short circuit ratio (SCR) and effective short circuit ratio (ESCR) to assess the relative strong or weak relation between AC system with direct current system.Along with the development of HVDC Transmission Technology, the grid structure that multiple current conversion station electrical distance is close, i.e. multi-infeed HVDC system in electrical network, are there is.Compared with single time direct current system, the voltage in multi-infeed HVDC system between converter interacts and will have an impact to system strength, commutation failure, temporary overvoltage, fault recovery and power/voltage stability.Therefore take into account interactional many feed-ins short circuit ratio (MSCR) between current conversion station to be more suitable for evaluating many feed-ins AC system and the relative strong or weak relation between direct current system.

Utilize many feed-ins interaction factor (MIIF) to take into account the degree that influences each other between multiple current conversion station in the computing formula of many feed-ins short circuit ratio (MSCR), therefore the result of calculation of MIIF directly affects the validity of MSCR.At present, what the calculating of MIIF extensively adopted is the emulation experiment method that CIGRE working group proposes.Although emulation experiment method can react the interaction size between multi-infeed HVDC accurately, single principle inherently not disclosing MIIF.Some research and utilization nodal impedance matrixs have carried out explanation to a certain degree to MIIF, but nodal impedance matrix sometimes (during as system equipment active reactive characteristic changing) still can not describe the problem.Notice that MIIF essence has reacted the interactional relation of voltage, and the interactional essence of voltage is the change of the reactive power distribution of AC network, therefore consider that carrying out research from system load flow distribution aspect to MIIF can inherently explain influencing each other between multi-infeed HVDC.

Summary of the invention

An object of the present invention is to provide a kind of analytical method of the multi-infeed HVDC interaction factor based on depression of order Jacobian matrix, loaded down with trivial details to solve analytical complexity of the prior art, and the multi-infeed HVDC interaction factor reliability obtained and the low problem of accuracy.

In some illustrative embodiment, the analytical method of the described multi-infeed HVDC interaction factor based on depression of order Jacobian matrix, comprising: simplify and equivalent process orthogonal streaming system, obtains equivalent system; Set up the depression of order Jacobian matrix inearized model of described equivalent system; Multi-infeed HVDC interaction factor is calculated by relevant Jacobian matrix element.

Compared with prior art, illustrative embodiment of the present invention comprises following advantage:

The present invention, by setting up equivalent system linearization model, directly utilizes Jacobian matrix coherent element to calculate MIIF, does not need, by the existing running status of change system, to avoid and calculated MIIF by emulation experiment.The present invention has simultaneously carried out theory deduction and analysis to the essence of MIIF and influencing factor, and improves the computational methods of former MIIF, makes the result obtained more rationally with accurate.

Accompanying drawing explanation

Accompanying drawing described herein is used to provide a further understanding of the present invention, and form a application's part, schematic description and description of the present invention, for explaining the present invention, does not form inappropriate limitation of the present invention.In the accompanying drawings:

Fig. 1 is the flow chart according to illustrative embodiment of the present invention

Fig. 2 is the 2 feedback orthogonal streaming systems according to illustrative embodiment of the present invention;

Fig. 3 is the equivalent system of the 2 feedback orthogonal streaming systems according to illustrative embodiment of the present invention.

Embodiment

In the following detailed description, a large amount of specific detail is proposed, so that provide thorough understanding of the present invention.But, person of skill in the art will appreciate that, also can implement the present invention even without these specific detail.In other cases, do not describe well-known method, process, assembly and circuit in detail, in order to avoid affect the understanding of the present invention.

Illustrative embodiment for a better understanding of the present invention, is briefly described the main thought in illustrative embodiment of the present invention below.

The object of the invention is to provide a kind of MIIF based on depression of order Jacobian matrix to improve computational methods for the deficiencies in the prior art, be characterized in changing the existing operating condition of system, directly can calculate MIIF by system load flow distribution, in itself MIIF is explained, and there is higher accuracy.With calculate the method for MIIF based on nodal impedance matrix compared with, the method compensate for the defect that accurately cannot calculate MIIF when system equipment active reactive characteristic changing.The method makes improvement in original computational methods based on depression of order Jacobian matrix simultaneously, further increases efficiency and the accuracy of calculating.

As shown in Figure 1, disclose a kind of analytical method of the multi-infeed HVDC interaction factor based on depression of order Jacobian matrix, comprising:

S11, orthogonal streaming system to be simplified and equivalent process, obtain equivalent system;

S12, set up the depression of order Jacobian matrix inearized model of described equivalent system;

S13, calculate multi-infeed HVDC interaction factor by relevant Jacobian matrix element.

The present invention, by setting up equivalent system linearization model, directly utilizes Jacobian matrix coherent element to calculate MIIF, does not need, by the existing running status of change system, to avoid and calculated MIIF by emulation experiment.The present invention has simultaneously carried out theory deduction and analysis to the essence of MIIF and influencing factor, and improves the computational methods of former MIIF, makes the result obtained more rationally with accurate.

In some illustrative embodiment, for step S11, orthogonal streaming system is simplified and equivalent process, obtains equivalent system and propose a preferably embodiment:

Orthogonal streaming system as shown in Figure 2, carries out equivalence to two feedthrough system generating sets and associated loadings circuit, obtains equivalent system as shown in Figure 3, and the system after equivalence and real system are carried out contrast verification, as shown in table 1 for the result of rectification side.

Wherein, the symbol in Fig. 3 is expressed as follows:

X _i1, X _i2---direct current 1,2 converter transformer converts the impedance of secondary side;

T ₁, T ₂---direct current 1,2 converter transformer no-load voltage ratio;

P _dc1, jQ _dc1, P _dc2, jQ _dc1---direct current 1,2 injects the meritorious, idle of AC system;

P _ac1, jQ _ac1, P _ac2, jQ _ac2---AC system accepts the meritorious, idle of direct current 1,2 injection;

P _i1, P _i2---it is meritorious that direct current 1,2 is carried;

P ₁₂, jQ ₁₂---the contact power between the node 1,2 that calculating is considered;

Z ₁=| Z ₁| ∠ θ ₁, Z ₂=| Z ₂| ∠ θ ₂---direct current 1,2 AC equivalent impedance;

U _s1∠ 0, U _s2∠ 0, U ₁∠ δ ₁, U ₂∠ δ ₂---node 1,2 voltage that the equivalent power supply 1,2 of powering to direct current 1,2 and calculating are considered;

R _l1, R _l2, I _d1, I _d2---DC line resistance and electric current;

Table 1 rectification side trend distributes

As can be seen from Table 1, the system after equivalence and original system basically identical, the result of inverter side is similar, no longer lists result.

In some illustrative embodiment, at the described depression of order Jacobian matrix inearized model setting up described equivalent system, also comprise: under setting up stable situation, DC side linear equation and AC linear equation; According to described DC side linear equation and AC linear equation, set up the depression of order Jacobian matrix inearized model of described equivalent system.

In some illustrative embodiment, described DC side linear equation comprises:

P _dci＝U _diI _di

Wherein, P _dcifor direct current i injects the active power of AC system, U _difor inverter side direct voltage, I _difor the electric current of direct current i;

$\begin{array}{c}{U}_{\mathrm{di}}=U_{\mathrm{doi}}\cos \left({\mathrm{\γ}}_i\right)-\sqrt{2}{K}_m{X}_i{I}_{\mathrm{di}}\\ =1.35E_{\mathrm{LL}}{\mathrm{BT}}_i\cos \left({\mathrm{\γ}}_i\right)-\frac{6B{X}_i{I}_{\mathrm{di}}}{\mathrm{\π}}\end{array}$

Wherein, U _doifor desirable floating voltage, γ _ifor inverter side extinguish angle, K _mfor coefficient, E _lLfor transformer primary voltage effective value, B is bridge number;

$P_{\mathrm{dci}}=1.35E_{\mathrm{LL}}{\mathrm{BT}}_i\cos \left({\mathrm{\γ}}_i\right)I_{\mathrm{di}}-\frac{6B{X}_i{I}_{\mathrm{di}}^2}{\mathrm{\π}}$

$Q_{\mathrm{dci}}=P_{\mathrm{dci}}\frac{2{\mathrm{\μ}}_i+\sin \left(2{\mathrm{\γ}}_i\right)-\sin (2{\mathrm{\γ}}_i+2{\mathrm{\μ}}_i)}{\cos \left(2{\mathrm{\γ}}_i\right)-\cos (2{\mathrm{\γ}}_i+2{\mathrm{\μ}}_i)}$

Wherein, Q _dcifor direct current i inject AC system have reactive power, μ _ifor folded arc angle;

ΔP _dci＝P _Ii-P _dci

Wherein, Δ P _dcithe increment of the active power of AC system is injected, P for direct current i _iifor the active power that direct current i carries, P _dcifor direct current i injects the active power of AC system.

In some illustrative embodiment, described AC linear equation comprises:

$P_{\mathrm{aci}}=\frac{U_i^2\cos \left({\mathrm{\θ}}_i\right)-U_{\mathrm{si}}{U}_i\cos ({\mathrm{\θ}}_i+{\mathrm{\δ}}_i)}{\left|Z_i\right|}$

Wherein, P _acifor AC system accepts the active power of direct current i injection, U _sifor giving the power supply of direct current i, U _ifor node voltage on direct current i, Z ₁for direct current i injects the impedance of AC system;

$Q_{\mathrm{aci}}=\frac{U_i^2\sin \left({\mathrm{\θ}}_i\right)-U_{\mathrm{si}}{U}_i\sin ({\mathrm{\θ}}_i+{\mathrm{\δ}}_i)}{\left|Z_i\right|}$

Wherein, Q _acifor AC system accepts the reactive power of direct current i injection;

ΔP _aci＝P _ij+P _dci-P _aci

Wherein, Δ P _acifor AC system accepts the increment of the active power that direct current i injects, P _ijfor the contact active power between node i, j;

ΔQ _aci＝Q _ij-Q _dci-Q _aci

Wherein, Δ Q _acifor AC system accepts the increment of the reactive power that direct current i injects, Q _ijfor the contact reactive power between node i, j.

In some illustrative embodiment, the described depression of order Jacobian matrix inearized model setting up described equivalent system, specifically comprises:

Choose Δ I _d, Δ δ and Δ U/U is state variable, builds many feedback direct current inearized models:

$\left[\begin{array}{c}{\mathrm{\ΔP}}_{\mathrm{dc}}\\ {\mathrm{\ΔP}}_{\mathrm{ac}}\\ {\mathrm{\ΔQ}}_{\mathrm{ac}}\end{array}\right]=\left[\begin{array}{ccc}{J}_{\mathrm{DI}}& J_{\mathrm{D\δ}}& J_{\mathrm{DU}}\\ J_{\mathrm{PI}}& J_{\mathrm{P\δ}}& J_{\mathrm{PU}}\\ J_{\mathrm{QI}}& J_{\mathrm{Q\δ}}& J_{\mathrm{QU}}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ΔI}}_d\\ \mathrm{\Δ\δ}\\ \mathrm{\ΔU}/U\end{array}\right]$

$\left[\begin{array}{ccc}{J}_{\mathrm{DI}}& J_{\mathrm{D\δ}}& J_{\mathrm{DU}}\\ J_{\mathrm{PI}}& J_{\mathrm{P\δ}}& J_{\mathrm{PU}}\\ J_{\mathrm{QI}}& J_{\mathrm{Q\δ}}& J_{\mathrm{QU}}\end{array}\right]=\left[\begin{array}{ccc}-\∂P_{\mathrm{dc}}/\∂I_d& 0& -\∂P_{\mathrm{dc}}/\∂U\\ \∂P_{\mathrm{dc}}/\∂I_d& -\∂P_{\mathrm{ac}}/\∂\mathrm{\δ}& \∂(P_{\mathrm{dc}}-P_{\mathrm{ac}})/\∂U\\ -\∂Q_{\mathrm{dc}}/\∂I_d& -\∂Q_{\mathrm{ac}}/\∂\mathrm{\δ}& -\∂(Q_{\mathrm{dc}}+Q_{\mathrm{ac}})/\∂U\end{array}\right]$

In some illustrative embodiment, the described process being calculated multi-infeed HVDC interaction factor by relevant Jacobian matrix element, being comprised:

By described many feedback direct current inearized models, derive described multi-infeed HVDC interaction factor.

In some illustrative embodiment, described in derive described multi-infeed HVDC interaction factor, specifically comprise:

1), due to direct current invariable, then Δ I _d=0, described many feedback direct current linearisation model degradation are as follows:

$\left[\begin{array}{c}{\mathrm{\ΔP}}_{\mathrm{ac}}\\ {\mathrm{\ΔQ}}_{\mathrm{ac}}\end{array}\right]=\left[\begin{array}{cc}{J}_{\mathrm{P\δ}}& J_{\mathrm{PU}}\\ J_{\mathrm{Q\δ}}& J_{\mathrm{QU}}\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ\δ}\\ \mathrm{\ΔU}/U\end{array}\right]$

2), because system is in stable state, then make Δ δ=0,1) in described many feedback direct current linearisation model degradation be as follows:

ΔQ _ac＝J _QUΔU

According to 2) in degeneration formulae discovery go out described multi-infeed HVDC interaction factor.

In some illustrative embodiment, described according to 2) in degeneration formulae discovery go out described multi-infeed HVDC interaction factor, specifically comprise:

Described multi-infeed HVDC interaction factor is gone out according to following formulae discovery:

${\mathrm{MIIF}}_{\mathrm{ij}}=\frac{{\mathrm{\ΔU}}_i}{{\mathrm{\ΔU}}_j}=\frac{{\left(J_{\mathrm{QU}}^{-1}\right)}_{i,j}}{{\left(J_{\mathrm{QU}}^{-1}\right)}_{j,j}}$

Wherein, MIIF _ijfor described multi-infeed HVDC interaction factor.

Preferably, be directed to the equivalent system shown in Fig. 3, set up inearized model according to derivation conclusion, and directly utilize the Jacobian matrix element in model to calculate rectification side MIIF.Simultaneously by result of calculation with emulation to MIIF result compare, as shown in table 2.

Table 2MIIF emulation and result of calculation

In table 2, known MIIF12 and MIIF21 distribution represents the interaction factor of rectification side direct current 2 pairs of direct currents 1, direct current 1 pair of direct current 2.As shown in Table 2, based on computational methods of the present invention and simulation result basically identical.

The explanation of above embodiment just understands method of the present invention and core concept thereof for helping; Meanwhile, for one of ordinary skill in the art, according to thought of the present invention, all will change in specific embodiments and applications, in sum, this description should not be construed as limitation of the present invention.

Claims (8)

1., based on an analytical method for the multi-infeed HVDC interaction factor of depression of order Jacobian matrix, it is characterized in that, comprising:

Orthogonal streaming system is simplified and equivalent process, obtains equivalent system;

Set up the depression of order Jacobian matrix inearized model of described equivalent system;

Multi-infeed HVDC interaction factor is calculated by relevant Jacobian matrix element.

2. analytical method according to claim 1, is characterized in that, at the described depression of order Jacobian matrix inearized model setting up described equivalent system, also comprises:

Under setting up stable situation, DC side linear equation and AC linear equation;

According to described DC side linear equation and AC linear equation, set up the depression of order Jacobian matrix inearized model of described equivalent system.

3. analytical method according to claim 2, is characterized in that, described DC side linear equation comprises:

P _dci＝U _diI _di

Wherein, P _dcifor direct current i injects the active power of AC system, U _difor inverter side direct voltage, I _difor the electric current of direct current i;

$\begin{array}{c}{U}_{\mathrm{di}}=U_{\mathrm{doi}}\cos \left({\mathrm{\γ}}_i\right)-\sqrt{2}{K}_m{X}_i{I}_{\mathrm{di}}\\ =1.35E_{\mathrm{LL}}{\mathrm{BT}}_i\cos \left({\mathrm{\γ}}_i\right)-\frac{6{\mathrm{BX}}_i{I}_{\mathrm{di}}}{\mathrm{\π}}\end{array}$

Wherein, U _doifor desirable floating voltage, γ _ifor inverter side extinguish angle, K _mfor coefficient, E _lLfor transformer primary voltage effective value, B is bridge number;

$Q_{\mathrm{dci}}=P_{\mathrm{dci}}\frac{2{\mathrm{\μ}}_i+\sin \left(2{\mathrm{\γ}}_i\right)-\sin (2{\mathrm{\γ}}_i+2{\mathrm{\μ}}_i)}{\cos \left(2{\mathrm{\γ}}_i\right)-\cos (2{\mathrm{\γ}}_i+2{\mathrm{\μ}}_i)}$

Wherein, Q _dcifor direct current i inject AC system have reactive power, μ _ifor folded arc angle;

ΔP _dci＝P _Ii-P _dci

Wherein, Δ P _dcifor direct current i injects the active power increment of AC system, P _iifor the active power that direct current i carries, P _dcifor direct current i injects the active power of AC system.

4. analytical method according to claim 3, is characterized in that, described AC linear equation comprises:

$P_{\mathrm{aci}}=\frac{U_i^2\cos \left({\mathrm{\θ}}_i\right)-U_{\mathrm{si}}{U}_i\cos ({\mathrm{\θ}}_i+{\mathrm{\δ}}_i)}{\left|Z_i\right|}$

Wherein, P _acifor AC system accepts the active power of direct current i injection, U _sifor giving the power supply of direct current i, U _ifor node voltage on direct current i, Z ₁for direct current i injects the impedance of AC system;

$Q_{\mathrm{aci}}=\frac{U_i^2\sin \left({\mathrm{\θ}}_i\right)-U_{\mathrm{si}}{U}_i\sin ({\mathrm{\θ}}_i+{\mathrm{\δ}}_i)}{\left|Z_i\right|}$

Wherein, Q _acifor AC system accepts the reactive power of direct current i injection;

ΔP _aci＝P _ij+P _dci-P _aci

Wherein, Δ P _acifor AC system accepts the increment of the active power that direct current i injects, P _ijfor the contact active power between node i, j;

ΔQ _aci＝Q _ij-Q _dci-Q _aci

Wherein, Δ Q _acifor AC system accepts the increment of the reactive power that direct current i injects, Q _ijfor the contact reactive power between node i, j.

5. analytical method according to claim 4, is characterized in that, the described depression of order Jacobian matrix inearized model setting up described equivalent system, specifically comprises:

Choose Δ I _d, Δ δ and Δ U/U is state variable, builds many feedback direct current inearized models:

$\begin{array}{c}\left[\begin{array}{c}{\mathrm{\ΔP}}_{\mathrm{dc}}\\ {\mathrm{\ΔP}}_{\mathrm{ac}}\\ {\mathrm{\ΔQ}}_{\mathrm{ac}}\end{array}\right]=\left[\begin{array}{ccc}{J}_{\mathrm{DI}}& J_{\mathrm{D\δ}}& J_{\mathrm{DU}}\\ J_{\mathrm{PI}}& J_{\mathrm{P\δ}}& J_{\mathrm{PU}}\\ J_{\mathrm{QI}}& J_{\mathrm{Q\δ}}& J_{\mathrm{QU}}\end{array}\right]\left[\begin{array}{c}{\mathrm{\ΔI}}_d\\ \mathrm{\Δ\δ}\\ \mathrm{\ΔU}/U\end{array}\right]\\ \left[\begin{array}{ccc}{J}_{\mathrm{DI}}& J_{\mathrm{D\δ}}& J_{\mathrm{DU}}\\ J_{\mathrm{PI}}& J_{\mathrm{P\δ}}& J_{\mathrm{PU}}\\ J_{\mathrm{QI}}& J_{\mathrm{Q\δ}}& J_{\mathrm{QU}}\end{array}\right]=\left[\begin{array}{ccc}-{\∂P}_{\mathrm{dc}}/{\∂I}_d& 0& -{\∂P}_{\mathrm{dc}}/\∂U\\ {\∂P}_{\mathrm{dc}}/{\∂I}_d& -{\∂P}_{\mathrm{ac}}/\∂\mathrm{\δ}& \∂(P_{\mathrm{dc}}-P_{\mathrm{ac}})/\∂U\\ -{\∂Q}_{\mathrm{dc}}/{\∂I}_d& -{\∂Q}_{\mathrm{ac}}/\∂\mathrm{\δ}& -\∂(Q_{\mathrm{dc}}+Q_{\mathrm{ac}})/\∂C\end{array}\right]\end{array}.$

6. analytical method according to claim 5, is characterized in that, the described process being calculated multi-infeed HVDC interaction factor by relevant Jacobian matrix element, being comprised:

By described many feedback direct current inearized models, derive described multi-infeed HVDC interaction factor.

7. analytical method according to claim 6, is characterized in that, described in derive described multi-infeed HVDC interaction factor, specifically comprise:

1), due to direct current invariable, then Δ I _d=0, described many feedback direct current linearisation model degradation are as follows:

$\left[\begin{array}{c}{\mathrm{\ΔP}}_{\mathrm{ac}}\\ {\mathrm{\ΔQ}}_{\mathrm{ac}}\end{array}\right]=\left[\begin{array}{cc}{J}_{\mathrm{P\δ}}& J_{\mathrm{PU}}\\ J_{\mathrm{Q\δ}}& J_{\mathrm{QU}}\end{array}\right]\left[\begin{array}{c}\mathrm{\Δ\δ}\\ \mathrm{\ΔU}/U\end{array}\right]$

2), because system is in stable state, then make Δ δ=0,1) in described many feedback direct current linearisation model degradation be as follows:

ΔQ _ac＝J _QUΔU

According to 2) in degeneration formulae discovery go out described multi-infeed HVDC interaction factor.

8. analytical method according to claim 7, is characterized in that, described according to 2) in degeneration formulae discovery go out described multi-infeed HVDC interaction factor, specifically comprise:

Described multi-infeed HVDC interaction factor is gone out according to following formulae discovery:

${\mathrm{MIIF}}_{\mathrm{ij}}=\frac{{\mathrm{\ΔU}}_i}{{\mathrm{\ΔU}}_j}=\frac{{\left(J_{\mathrm{QU}}^{-1}\right)}_{i,j}}{{\left(J_{\mathrm{QU}}^{-1}\right)}_{j,j}}$

Wherein, MIIF _ijfor described multi-infeed HVDC interaction factor.