CN104333030B - A kind of analysis method of multi-infeed HVDC interaction factor - Google Patents

Abstract

A kind of analysis method of multi-infeed HVDC interaction factor, including: orthogonal streaming system is simplified and equivalent process, it is thus achieved that equivalent system；Set up the depression of order Jacobian matrix inearized model of equivalent system；Multi-infeed HVDC interaction factor is calculated by relevant Jacobian matrix element.The analysis method of multi-infeed HVDC interaction factor based on depression of order Jacobian matrix, including: orthogonal streaming system is simplified and equivalent process, it is thus achieved that equivalent system；Set up the depression of order Jacobian matrix inearized model of equivalent system；Multi-infeed HVDC interaction factor is calculated by relevant Jacobian matrix element.By utilizing Jacobian matrix coherent element to calculate MIIF, it is not necessary to by changing the existing running status of system, it is to avoid by emulation experiment, MIIF is calculated.The essence of MIIF and influence factor have been carried out theoretical derivation and analysis simultaneously, and the MIIF before improving computational methods so as to get result more rationally with accurately.

Description

A kind of analysis method of multi-infeed HVDC interaction factor

Technical field

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

Background technology

In ac and dc systems, receiving end AC system rack power is the deciding factor of system stability, In theoretical research and engineer applied, generally use short-circuit ratio (SCR) and effective short-circuit ratio (ESCR) Concept assess the relative strong or weak relation between AC system with straight-flow system.Along with HVDC Transmission Technology Development, electrical network occurs in that the grid structure that multiple current conversion station electrical distance is close, i.e. multi-infeed HVDC System.Compared with single time straight-flow system, in multi-infeed HVDC system, the voltage interaction between inverter will System strength, commutation failure, transient overvoltage, fault recovery and power/voltage stability are produced shadow Ring.Therefore count and between current conversion station, interactional many feed-ins short-circuit ratio (MSCR) is more suitable for for evaluating Relative strong or weak relation between many feed-ins AC system and straight-flow system.

The computing formula of many feed-ins short-circuit ratio (MSCR) utilizes many feed-ins interaction factor (MIIF) The degree that influences each other between meter and multiple current conversion station, therefore the result of calculation of MIIF directly affects MSCR's Effectiveness.At present, what the calculating of MIIF was widely used is the emulation experiment method of CIGRE working group proposition. Although emulation experiment method can react the interaction size between multi-infeed HVDC accurately, single not from this The principle of MIIF is disclosed in matter.MIIF has been carried out to a certain degree by some research and utilization nodal impedance matrixs Explanation, but nodal impedance matrix sometimes (during such as system equipment active reactive characteristic changing) still Can not describe the problem.Notice that MIIF essence has reacted the relation that voltage interacts, and voltage is mutual The essence of effect is the change of reactive power distribution of AC network, therefore considers in terms of system load flow distribution pair MIIF carries out research 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 analysis method of multi-infeed HVDC interaction factor, with Solve analytical complexity of the prior art loaded down with trivial details, and the multi-infeed HVDC obtained interacts Factor reliability and the low problem of accuracy.

In some illustrative embodiment, the analysis method of described base multi-infeed HVDC interaction factor, Including: orthogonal streaming system is simplified and equivalent process, it is thus achieved that equivalent system；Set up described equivalent system The depression of order Jacobian matrix inearized model of system；Many feed-ins are calculated straight by relevant Jacobian matrix element Stream interaction factor.

Compared with prior art, the illustrative embodiment of the present invention includes advantages below:

The present invention, by setting up equivalent system linearization model, directly utilizes Jacobian matrix coherent element meter Calculate MIIF, it is not necessary to by changing system existing running status, it is to avoid by emulation experiment to MIIF Calculate.The present invention has carried out theoretical derivation and analysis to essence and the influence factor of MIIF simultaneously, And improve former MIIF computational methods so as to get result more rationally with accurately.

Accompanying drawing explanation

Accompanying drawing described herein is used for providing a further understanding of the present invention, constitutes of the application Point, the schematic description and description of the present invention is used for explaining the present invention, is not intended that the present invention's Improper restriction.In the accompanying drawings:

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

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

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

Detailed description of the invention

In the following detailed description, a large amount of specific detail is proposed, in order to provide the thorough reason to the present invention Solve.However it will be understood by those of ordinary skill in the art that, even if not having these specific detail can implement this yet Bright.In other cases, it is not described in well-known method, process, assembly and circuit, with Exempt to affect the understanding of the present invention.

For the illustrative embodiment being better understood from the present invention, below to illustrative embodiment of the present invention In main thought be briefly described.

It is an object of the invention to provide a kind of based on depression of order Jacobian matrix for the deficiencies in the prior art MIIF improve computational methods, be characterized in changing the existing operating condition of system, can directly lead to Cross system load flow distribution and calculate MIIF, in itself MIIF is explained, and has higher Accuracy.Compared with the method calculating MIIF based on nodal impedance matrix, the method compensate in system The defect of MIIF cannot be accurately calculated during equipment active reactive characteristic changing.The method is original simultaneously Computational methods based on depression of order Jacobian matrix on make improvement, further increase the efficiency of calculating with Accuracy.

As it is shown in figure 1, disclose a kind of multi-infeed HVDC interaction based on depression of order Jacobian matrix because of The analysis method of son, including:

S11, orthogonal streaming system is simplified and equivalent process, it is thus achieved that 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 meter Calculate MIIF, it is not necessary to by changing system existing running status, it is to avoid by emulation experiment to MIIF Calculate.The present invention has carried out theoretical derivation and analysis to essence and the influence factor of MIIF simultaneously, And improve former MIIF computational methods so as to get result more rationally with accurately.

In some illustrative embodiment, for step S11, orthogonal streaming system is simplified and equivalence Process, it is thus achieved that equivalent system proposes a preferred embodiment:

Orthogonal streaming system is as in figure 2 it is shown, carry out two feedthrough system generating sets and associated loadings circuit Value, it is thus achieved that equivalent system as it is shown on figure 3, and the system after equivalence and real system are carried out contrast verification, The result as a example by rectification side is as shown in table 1.

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

X_i1、X_i2Direct current 1,2 converter power transformer converts the impedance of secondary side；

T₁、T₂Direct current 1,2 converter power transformer no-load voltage ratio；

P_dc1、jQ_dc1、P_dc2、jQ_dc1Direct current 1,2 injects the meritorious, idle of AC system；

P_ac1、jQ_ac1、P_ac2、jQ_ac2AC system accepts the meritorious, idle of direct current 1,2 injection；

P_I1、P_I2Gaining merit of direct current 1,2 conveying；

P₁₂、jQ₁₂Calculate the contact power between the node 1,2 considered；

Z₁=| Z₁|∠θ₁、Z₂=| Z₂|∠θ₂Direct current 1,2 AC equivalent impedance；

U_s1∠0、U_s2∠0、U₁∠δ₁、U₂∠δ₂To direct current 1,2 power supply equivalent power supply 1,2 with And calculate node 1,2 voltage considered；

R_l1、R_l2、I_d1、I_d2DC line resistance and electric current；

Table 1 rectification side trend is distributed

As it can be seen from table 1 the system after equivalence is basically identical with original system, the result of inverter side is similar to, No longer list result.

In some illustrative embodiment, at the described depression of order Jacobian matrix line setting up described equivalent system Property model, also includes: set up under stable situation, DC side linear equation and AC linear equation； According to described DC side linear equation and AC linear equation, set up refined gram of the depression of order of described equivalent system Ratio linearization of matrix model.

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

P_dci=U_diI_di

Wherein, P_dciThe active power of AC system, U is injected for direct current i_diFor inverter side DC voltage, I_di Electric current for direct current i；

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

Wherein, U_doiFor preferable floating voltage, γ_iFor inverter side blow-out angle, K_mFor coefficient, E_LLFor transformation Device primary side voltage virtual value, B is bridge number；X_iThe resistance of secondary side is converted for direct current i converter power transformer Anti-；T_iFor direct current i converter power transformer no-load voltage ratio；

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

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

Wherein, Q_dciThe reactive power of AC system, μ is injected for direct current i_iFor folded arc angle；

ΔP_dci=P_Ii-P_dci

Wherein, Δ P_dciThe increment of the active power of AC system, P is injected for direct current i_IiCarry for direct current i Active power, P_dciThe active power of AC system is injected for direct current i.

In some illustrative embodiment, described AC linear equation includes:

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

Wherein, P_aciThe active power that direct current i injects, U is accepted for AC system_siFor the electricity to direct current i Source, U_iFor node voltage, Z on direct current i_iThe impedance of AC system is injected for direct current i；θ_iRefer to direct current i AC equivalent impedance angle；δ_iRefer to node voltage phase angle on direct current i；

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

Wherein, Q_aciThe reactive power that direct current i injects is accepted for AC system；

ΔP_aci=P_ij+P_dci-P_aci

Wherein, Δ P_aciThe increment of the active power that direct current i injects, P is accepted for AC system_ijFor node i, Contact active power between j；

ΔQ_aci=Q_ij-Q_dci-Q_aci

Wherein, Δ Q_aciThe increment of the reactive power that direct current i injects, Q is accepted for AC system_ijFor node i, Contact reactive power between j.

In some illustrative embodiment, the described depression of order Jacobian matrix setting up described equivalent system is linear Change model, specifically include:

Choose Δ I_d, Δ δ and Δ U/U is state variable, builds and presents direct current inearized model more:

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

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

Wherein, Δ I_dIncrement for DC line electric current；Δ δ is node voltage phase angle increment, and Δ U/U is Node voltage increment and the ratio of self；

In some illustrative embodiment, described to calculate many feed-ins by relevant Jacobian matrix element straight The process of stream interaction factor, including:

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, tool Body includes:

1), due to DC current invariable, then Δ I_d=0, described many feedback direct current linearisation model degradation For as follows:

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

2) the described many feedback direct current inearized models in, owing to system is in stable state, then make Δ δ=0,1) Deteriorate to as follows:

ΔQ_ac=J_QUΔU

According to 2) in degeneration formula calculate described multi-infeed HVDC interaction factor.

In some illustrative embodiment, described according to 2) in degeneration formula calculate described many feed-ins Direct current interaction factor, specifically includes:

Described multi-infeed HVDC interaction factor is calculated according to equation below:

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

Wherein, MIIF_ijFor described multi-infeed HVDC interaction factor.

Preferably, it is directed to the equivalent system shown in Fig. 3, sets up inearized model according to derivation conclusion, And rectification side MIIF is calculated by the Jacobian matrix element directly utilized in model.To calculate simultaneously Result with emulation to MIIF result compare, as shown in table 2.

Table 2 MIIF emulation and result of calculation

Table 2 understands MIIF12 Yu MIIF21 distribution and represents that rectification side direct current 2 is to direct current 1, direct current 1 Interaction factor to direct current 2.As shown in Table 2, computational methods based on the present invention and simulation result Basically identical.

The explanation of above example is only intended to help to understand method and the core concept thereof of the present invention；With Time, for one of ordinary skill in the art, according to the thought of the present invention, in detailed description of the invention and should All will change with in scope, in sum, this specification content should not be construed as the present invention's Limit.

Claims (6)

1. the analysis method of a multi-infeed HVDC interaction factor, it is characterised in that including:

Orthogonal streaming system is simplified and equivalent process, it is thus achieved that equivalent system；

Set up under 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 of described equivalent system Jacobian matrix inearized model；

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

Wherein, described DC side linear equation includes:

P_dci=U_diI_di

Wherein, P_dciThe active power of AC system, U is injected for direct current i_diFor inverter side DC voltage, I_di Electric current for direct current i；

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

Wherein, U_doiFor preferable floating voltage, γ_iFor inverter side blow-out angle, K_mFor coefficient, E_LLFor transformation Device primary side voltage virtual value, B is bridge number；X_iThe resistance of secondary side is converted for direct current i converter power transformer Anti-；T_iFor direct current i converter power transformer no-load voltage ratio；

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

Wherein, Q_dciThe reactive power of AC system, μ is injected for direct current i_iFor folded arc angle；

ΔP_dci=P_Ii-P_dci

Wherein, Δ P_dciThe active power increment of AC system, P is injected for direct current i_IiFor direct current i conveying Active power, P_dciThe active power of AC system is injected for direct current i.

Analysis method the most according to claim 1, it is characterised in that described AC linearly side Journey includes:

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

Wherein, P_aciThe active power that direct current i injects, U is accepted for AC system_siFor the electricity to direct current i Source, U_iFor node voltage, Z on direct current i_iThe impedance of AC system is injected for direct current i；θ_iRefer to direct current i AC equivalent impedance angle；δ_iRefer to node voltage phase angle on direct current i；

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

Wherein, Q_aciThe reactive power that direct current i injects is accepted for AC system；

ΔP_aci=P_ij+P_dci-P_aci

Wherein, Δ P_aciThe increment of the active power that direct current i injects, P is accepted for AC system_ijFor node i, Contact active power between j；

ΔQ_aci=Q_ij-Q_dci-Q_aci

Wherein, Δ Q_aciThe increment of the reactive power that direct current i injects, Q is accepted for AC system_ijFor node i, Contact reactive power between j.

Analysis method the most according to claim 2, it is characterised in that described set up described equivalence The depression of order Jacobian matrix inearized model of system, specifically includes:

Choose Δ I_d, Δ δ and Δ U/U is state variable, builds and presents direct current inearized model more:

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

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

Wherein, Δ I_dIncrement for DC line electric current；Δ δ is node voltage phase angle increment, and Δ U/U is Node voltage increment and the ratio of self.

Analysis method the most according to claim 3, it is characterised in that described by relevant refined gram The process of multi-infeed HVDC interaction factor is calculated than matrix element, including:

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

Analysis method the most according to claim 4, it is characterised in that described in derive described many Feed-in direct current interaction factor, specifically includes:

1), due to DC current invariable, then Δ I_d=0, described many feedback direct current linearisation model degradation For as follows:

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

2) the described many feedback direct current inearized models in, owing to system is in stable state, then make Δ δ=0,1) Deteriorate to as follows:

ΔQ_ac=J_QUΔU

According to 2) in degeneration formula calculate described multi-infeed HVDC interaction factor.

Analysis method the most according to claim 5, it is characterised in that described according to 2) in move back Change formula and calculate described multi-infeed HVDC interaction factor, specifically include:

Described multi-infeed HVDC interaction factor is calculated according to equation below:

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

Wherein, MIIF_ijFor described multi-infeed HVDC interaction factor.