CN106786493A - A kind of practical calculation method of multi-infeed HVDC interaction factor - Google Patents

Abstract

The invention discloses a kind of practical calculation method of multi-infeed HVDC interaction factor, its core concept is on the basis of ac and dc systemses Load flow calculation P Q decomposition methods, the alternating current-direct current total system Q V imbalance equations for considering direct-current external characteristic are derived, further abbreviation solves multi-infeed HVDC interaction relative factors.Relative to prior art, the present invention remains the electric network composition of actual motion when many feed-in interaction factor MIIF are calculated, it is not necessary to equivalent treatment is carried out to power network, therefore with stronger practicality and universality；In addition the present invention theoretically derives the practical algorithm of MIIF, with clear and definite physical significance；Finally, when MIIF is calculated, the present invention not only allows for the network parameter of actual AC system, and considers external characteristics of the straight-flow system under different control modes, therefore accuracy is ensured.

Description

A kind of practical calculation method of multi-infeed HVDC interaction factor

Technical field

The invention belongs to technical field of HVDC transmission, and in particular to a kind of reality of multi-infeed HVDC interaction factor Use computational methods.

Background technology

Under the strategic general layout of China's " transferring electricity from the west to the east ", the regional power grid such as East China Power Grid and Guangdong Power Grid have evolved into order to Multi-feed HVDC system, many direct currents concentration drop points have turned into one of key character of China's power network.In multi-feed HVDC system, All direct currents access same AC system, and there is natural circuit coupling by the connection of alternating current circuit between direct current closes It is, therefore there is disturbance and the operation characteristic of other direct currents will be impacted in every direct current.Due to the friendship of multi-feed HVDC system Direct current interacts complicated, direct current feed-in power greatly, and huge challenge, therefore researching DC are brought to Electric Power Network Planning and operation The evaluation index and its computational methods of interphase interaction degree, will provide effective for the planning of multi-feed HVDC system and operation Guidance tool, has important practical significance and engineering practical value.

In multi-feed HVDC system, many feedbacks that the Degree of interaction between direct current is generally proposed with CIGRE working groups Enter interaction factor (Multi-infeed Interaction Factor, MIIF) to weigh, specially：In i-th time direct current Certain capacity reactor is put on system converter station bus so that busbar voltage landing amplitude is about 1%, and other time direct current is changed Stream busbar voltage variable quantity and the i-th time ratio of DC converter station busbar voltage variable quantity.Solution for MIIF, it is main at present There are three kinds of computational methods, be respectively simulation calculation method, the parsing meter based on depression of order Jacobian matrix based on stability Calculation program Algorithm and the approximate calculation method based on depression of order nodal impedance matrix.Wherein, the simulation calculation method based on stability Calculation program System-wide mathematical models are remained, without carrying out equivalence to extensive AC system, for extensive ac and dc systemses Stability analysis for particularly simple practicality, be weigh other numerical computation method result accuracys standard；However, this side Method theoretically cannot strictly parse the sensible factor of many direct current interaction strengths.Therefore, equivalent in many feed-in alternating current-direct currents On the basis of the tide model of system, the Analytic Calculation based on depression of order Jacobian matrix has theoretically derived the resolution table of MIIF Up to formula, and disclosing MIIF is determined by the ac and dc systemses Jacobian matrix coherent element for considering direct-current external characteristic；So And the method is mainly used in the planning construction of multi-feed HVDC system, therefore the AC system that direct current is accessed can be according to effective The parameters such as short-circuit ratio are simulated with Dai Weinan circuit equivalents, and for the multi-feed HVDC alternating current-direct current bulk power grid in actual motion Speech, the Thevenin's equivalence circuit that it is accurately equivalent to multiport is highly difficult, therefore the practicality of the method is not good enough, not The actual bulk power grid research of multi-feed HVDC can be directly applied to；Similarly, on the basis of the valve systems such as many feed-in alternating current-direct currents, Approximation technique based on depression of order nodal impedance matrix is calculated by solving the impedance matrix of AC network change of current tiny node MIIF；But the method does not consider external characteristics of the straight-flow system under different control modes, equivalent exchange system is only considered There is relatively large deviation in the network parameter of system, the result of calculation of the method.Therefore, for the actual electric network of multi-feed HVDC, It is necessary to study the MIIF computational methods for taking into account practicality and accuracy.

The content of the invention

In view of it is above-mentioned, the invention provides a kind of practical calculation method of multi-infeed HVDC interaction factor, the method Remain the electric network composition of actual motion, it is not necessary to which equivalent treatment is carried out to power network, and theoretically give the calculation of MIIF Method, with clear and definite physical significance；The core concept of the method is on the basis of ac and dc systemses Load flow calculation P-Q decomposition methods On, the alternating current-direct current total system Q-V imbalance equations for considering direct-current external characteristic are derived, further abbreviation solves multi-infeed HVDC Interaction relative factors.

A kind of practical calculation method of multi-infeed HVDC interaction factor, comprises the following steps：

(1) the AC network basic parameter of multi-feed HVDC system is obtained, the multi-feed HVDC system includes multiple The exchange PQ nodes (active-power P and reactive power Q of this kind of node are given) of interconnection, these exchange PQ nodes point It is two classes：One class is the current conversion station bus nodes accessed by straight-flow system, and another kind of is pure exchange PQ nodes；

(2) basic parameter and control mode of straight-flow system corresponding to current conversion station bus nodes are obtained, and then is calculated each Sensitivity of the current conversion station bus nodes reactive power to change of current busbar voltage；

(3) the constant coefficient symmetrical matrix of multi-feed HVDC system is set up by calculating according to the AC network basic parameter B, the constant coefficient compensation matrix B' of multi-feed HVDC system is set up according to the sensitivity, makes constant coefficient symmetrical matrix B with often system Number compensation matrix B' is added and obtains revised constant coefficient symmetrical matrix B^*；

(4) according to the revised constant coefficient symmetrical matrix B^*The many feed-ins calculated between current conversion station bus nodes are mutual Acting factor.

Constant coefficient symmetrical matrix B in the step (3) is the square formation of dimension of m m, and m is the friendship in multi-feed HVDC system Stream PQ node numbers, wherein preceding n exchange PQ nodes are current conversion station bus nodes, other exchange PQ nodes are saved for pure exchange PQ Point, n is the current conversion station bus nodes number in multi-feed HVDC system, the expression formula of each element value in constant coefficient symmetrical matrix B It is as follows：

Wherein：B_iiIt is i-th row the i-th column element value in constant coefficient symmetrical matrix B, B_ijFor in constant coefficient symmetrical matrix B I-th row jth column element value, x_ijFor i-th exchange PQ node exchanges the line reactance between PQ nodes with j-th and hands over for i-th Stream PQ nodes exchange PQ nodes with j-th and are joined directly together；If i-th exchange PQ node exchanges the not direct phase of PQ nodes with j-th Connect, then B_ij=0；K is that the exchange PQ node sets that PQ nodes are joined directly together are exchanged with i-th, and k is in exchange PQ node sets K Any exchange PQ nodes, x_ikFor i-th exchange and exchanges the line reactance between PQ nodes k, b at PQ nodes_iIt is i-th exchange The ground connection branch road susceptance of PQ nodes, i and j is natural number and 1≤i≤m, 1≤j≤m.

Constant coefficient compensation matrix B' in the step (3) is the square formation of dimension of m m, and m is the friendship in multi-feed HVDC system Stream PQ node numbers, the expression formula of constant coefficient compensation matrix B' is as follows：

B'₁₁=diag (σ₁,σ₂,...,σ_n)

Wherein：B'₁₁It is the submatrix and B' in the correspondence upper left corner in constant coefficient compensation matrix B'₁₁Be n × n dimension to angular moment Battle array, σ_pThe sensitivity for being p-th current conversion station bus nodes reactive power to change of current busbar voltage, p is natural number and 1≤p≤n, n It is the current conversion station bus nodes number in multi-feed HVDC system.

The expression formula of revised constant coefficient symmetrical matrix B* is as follows in the step (3)：

Wherein：B₁₁、B₁₂、B₂₁And B₂₂Respectively constant coefficient symmetrical matrix B correspondence constant coefficient compensation matrix B' STRUCTURE DECOMPOSITIONs are obtained Four submatrixs for arriving.

The many feed-in interaction factors between current conversion station bus nodes are calculated according to following formula in the step (4)：

Wherein：MIIF_q,pIt is q-th current conversion station bus nodes, p-th relatively many feed-in phase interactions of current conversion station bus nodes With the factor, B_cdIt is intermediary matrix,It is B₂₂Inverse matrix,It is B_cdInverse matrix,It is inverse matrixIn Q row pth column element values,It is inverse matrixIn pth row pth column element value, q be natural number and 1≤q≤n.

Compared with prior art, the Advantageous Effects of computational methods of the present invention are as follows：

(1) present invention remains the electric network composition of actual motion when many feed-in interaction factor MIIF are calculated, and is not required to Equivalent treatment is carried out to power network, therefore with stronger practicality.

(2) present invention theoretically derives the practical algorithm of MIIF, with clear and definite physical significance；Calculating MIIF When, the network parameter of actual AC system is not only allowed for, and consider outer spy of the straight-flow system under different control modes Property, therefore accuracy ensured.

(3) present invention is applicable not only to the MIIF calculating of multi-infeed DC system, and suitable for many direct current transmitting systems MIIF calculate, now only need to the Inverter Station power external characteristics of multi-infeed HVDC system with the rectifications for sending out straight-flow systems more Power external characteristics of standing is replaced, therefore the present invention has universality.

Brief description of the drawings

Fig. 1 is the schematic flow sheet of computational methods of the present invention.

Fig. 2 is the schematic diagram of the actual bulk power system of multi-feed HVDC.

Specific embodiment

In order to more specifically describe the present invention, below in conjunction with the accompanying drawings and specific embodiment is to technical scheme It is described in detail.

As shown in figure 1, the practical calculation method of multi-infeed HVDC interaction factor of the present invention, comprises the following steps：

(1) the AC network basic parameter of multi-feed HVDC system and the basic parameter and controlling party of straight-flow system are obtained Formula；Wherein, the AC network basic parameter of multi-feed HVDC system includes line reactance x and node ground connection branch road susceptance b；Direct current The basic parameter of system includes change of current busbar voltage E, the ideal no-load direct voltage U of current conversion station_d0, straight-flow system number of poles K_p； Straight-flow system control mode determines voltage control and rectification side Given current controller-inverse including rectification side Given current controller-inverter side Hold-off angle control is determined in change side, and both combine control modes.

(2) according to the basic parameter and control mode of straight-flow system, the reactive power of straight-flow system is calculated to change of current bus The sensitivity of voltage：

If 2.1 straight-flow system control modes are rectification side Given current controller, inverter side determines voltage control, for many feed-ins The Inverter Station of straight-flow system, its active and idle external characteristics equation is respectively：

P_di=K_pU_diI_d=K_p(U_ds-I_dsR_dc)I_ds

Wherein：I_ds、U_dsThere are DC current and direct voltage reference value, K respectively_pIt is the number of poles of straight-flow system, U_d0iIt is inversion Stand ideal no-load direct voltage；

Therefore sensitivity of the reactive power of Inverter Station to change of current busbar voltage is：

Wherein：C is ideal no-load direct voltage U_d0iWith change of current busbar voltage E_iThe ratio between coefficient, andT is converter power transformer no-load voltage ratio (voltage on line side is than voltage on valve side).

If 2.2 straight-flow system control modes are rectification side Given current controller, inverter side determines hold-off angle control, for many feedbacks Enter the Inverter Station of straight-flow system, its active and idle external characteristics equation is respectively：

P_di=K_pU_diI_d=K_p(U_d0icosγ_s-d_xiI_ds)I_ds

Wherein：I_ds、γ_sThere are DC current and shut-off angle reference value, K respectively_pIt is the number of poles of straight-flow system, d_xiIt is Inverter Station Commutating resistance, U_d0iIt is Inverter Station ideal no-load direct voltage；

Therefore sensitivity of the reactive power of Inverter Station to change of current busbar voltage is：

Wherein：C is ideal no-load direct voltage U_d0iWith change of current busbar voltage E_iThe ratio between coefficient, andT is converter power transformer no-load voltage ratio (voltage on line side is than voltage on valve side).

(3) sensitivity of the reactive power according to AC network basic parameter and straight-flow system to change of current busbar voltage, Form the total system Q-V update equations comprising dc power external characteristics：

The P-Q decomposition methods of Load flow calculation are alternately directly caused convergence by P- θ iteration and Q-V iteration and realized.In P- θ iteration The coefficient matrix B of update equation " represents that the coefficient matrix of update equation is represented with B in Q-V iteration, and basic characteristics are B " and B It is all permanent symmetrical matrix.Routinely the Q-V update equations of the P-Q decomposition methods of pure AC system Load flow calculation are：

Δ Q/V=B Δs V

The matrix element of B is in formula：

Wherein：x_ijIt is node i and the line reactance of node j, b_iIt is the ground connection branch road susceptance of node i.If in power system Total l node, r PV node, then B is the constant coefficient symmetry square matrix of l-r-1 ranks in Q-V update equations.

Because dc power is unrelated with the phase angle of node voltage, therefore, the introducing of straight-flow system does not have shadow to P- θ iteration Ring, i.e. matrix B " it is constant, but the introducing of straight-flow system can be impacted to Q-V iteration, i.e., matrix B can be caused to change. If multi-feed HVDC system contains n bars direct current and accesses actual electric network, as shown in Fig. 2 by the n numbering of current conversion station bus nodes (represented with subscript cd) before coming most, behind the pure exchange PQ nodes in system come successively, then can form outer special containing direct current The total system Q-V update equations of property are：

In formula, except the matrix in block form in constant coefficient symmetrical matrixNeed the Q-V according to DC converter station outer special Property is modified outer, and remaining element is constant.After considering the Q-V external characteristics of DC converter station, matrix in block formIt is specific Expression formula is：

Wherein：Sensitivity of the reactive power of change of current tiny node to change of current busbar voltageWith DC power transmission system The control mode of system is related, i.e. the sensitivity by the Inverter Station reactive power of step (2) derivation to change of current busbar voltage is determined.

(4) the total system Q-V update equations comprising dc power external characteristics formed according to step (3), derive and only retain The Q-V update equations of DC converter station bus nodes, so as to calculate many feed-in interaction factor MIIF：

Defined according to many direct current interaction factors, certain capacity reactor is put on i-th time DC converter station bus And in holding system other nodes it is idle constant, that is, have：

Then, above formula is substituted into the total system Q-V update equations containing direct-current external characteristic in step (3), and eliminates pure friendship Stream PQ nodes, can derive the Q-V update equations for only retaining DC converter station bus nodes：

Above formula launches to obtain final product：

Finally, defined according to many direct current interaction factors, interaction factor MIIFs of the current conversion station j to current conversion station i_j,i Lower analytic expression is may be used to be expressed as：

Analyzed more than, the sensible factor of multi-infeed HVDC interaction strength depends primarily on the knot of AC system The control mode of structure parameter and straight-flow system.

The above-mentioned description to embodiment is to be understood that and apply the present invention for ease of those skilled in the art. Person skilled in the art obviously can easily make various modifications to above-described embodiment, and described herein general Principle is applied in other embodiment without by performing creative labour.Therefore, the invention is not restricted to above-described embodiment, ability Field technique personnel announcement of the invention, the improvement made for the present invention and modification all should be in protection scope of the present invention Within.

Claims (5)

1. a kind of practical calculation method of multi-infeed HVDC interaction factor, comprises the following steps：

(1) the AC network basic parameter of multi-feed HVDC system is obtained, the multi-feed HVDC system includes multiple mutual The exchange PQ nodes of connection, these exchange PQ nodes are divided into two classes：One class is the current conversion station bus section accessed by straight-flow system Point, another kind of is pure exchange PQ nodes；

(2) basic parameter and control mode of straight-flow system corresponding to current conversion station bus nodes are obtained, and then calculates each change of current Sensitivity of bus nodes of the standing reactive power to change of current busbar voltage；

(3) the constant coefficient symmetrical matrix B of multi-feed HVDC system, root are set up by calculating according to the AC network basic parameter The constant coefficient compensation matrix B' of multi-feed HVDC system is set up according to the sensitivity, constant coefficient symmetrical matrix B is mended with constant coefficient Repay matrix B ' be added obtain revised constant coefficient symmetrical matrix B^*；

(4) according to the revised constant coefficient symmetrical matrix B^*The many feed-ins calculated between current conversion station bus nodes interact The factor.

2. practical calculation method according to claim 1, it is characterised in that：The symmetrical square of constant coefficient in the step (3) Battle array B is the square formation of dimension of m m, and m is the exchange PQ node numbers in multi-feed HVDC system, wherein preceding n exchange PQ nodes are to change Stream station bus nodes, other exchange PQ nodes are pure exchange PQ nodes, and n is the current conversion station bus nodes in multi-feed HVDC system Number, the expression formula of each element value is as follows in constant coefficient symmetrical matrix B：

$\left\{\begin{array}{c}{B}_{ii}=\underset{k\∈K}{\Σ}\frac{1}{x_{ik}}-b_i\\ B_{ij}=-\frac{1}{x_{ij}},i\≠j\end{array}\right.$

Wherein：B_iiIt is i-th row the i-th column element value in constant coefficient symmetrical matrix B, B_ijIt is the i-th row in constant coefficient symmetrical matrix B Jth column element value, x_ijSaved for i-th exchange PQ node exchanges line reactance and i-th exchange PQ between PQ nodes with j-th Point exchanges PQ nodes with j-th and is joined directly together；If i-th exchange PQ node exchanges PQ nodes with j-th and is not joined directly together, B_ij =0；K is that the exchange PQ node sets that PQ nodes are joined directly together are exchanged with i-th, and k is to exchange any friendship in PQ node sets K Stream PQ nodes, x_ikFor i-th exchange and exchanges the line reactance between PQ nodes k, b at PQ nodes_iIt is i-th exchange PQ node Ground connection branch road susceptance, i and j is natural number and 1≤i≤m, 1≤j≤m.

3. practical calculation method according to claim 1, it is characterised in that：Constant coefficient compensation square in the step (3) Battle array B' is the square formation of dimension of m m, and m is the exchange PQ node numbers in multi-feed HVDC system, the expression of constant coefficient compensation matrix B' Formula is as follows：

$\begin{array}{cc}{B}^{\′}=\left[\begin{array}{cc}{B}_{11}^{\′}& 0\\ 0& 0\end{array}\right]& B_{11}^{\′}=diag({\mathrm{\σ}}_1,{\mathrm{\σ}}_2,\mathrm{...},{\mathrm{\σ}}_n)\end{array}$

Wherein：B'₁₁It is the submatrix and B' in the correspondence upper left corner in constant coefficient compensation matrix B'₁₁It is the diagonal matrix of n × n dimensions, σ_p The sensitivity for being p-th current conversion station bus nodes reactive power to change of current busbar voltage, p is natural number and 1≤p≤n, n are many Current conversion station bus nodes number in direct current drop point system.

4. practical calculation method according to claim 3, it is characterised in that：Revised constant coefficient in the step (3) Symmetrical matrix B^*Expression formula it is as follows：

$B^{*}=B+B^{\′}=\left[\begin{array}{cc}{B}_{11}& B_{12}\\ B_{21}& B_{22}\end{array}\right]+\left[\begin{array}{cc}{B}_{11}^{\′}& 0\\ 0& 0\end{array}\right]=\left[\begin{array}{cc}{B}_{11}+B_{11}^{\′}& B_{12}\\ B_{21}& B_{22}\end{array}\right]$

Wherein：B₁₁、B₁₂、B₂₁And B₂₂Respectively constant coefficient symmetrical matrix B correspondence constant coefficient compensation matrix B' STRUCTURE DECOMPOSITIONs are obtained Four submatrixs.

5. practical calculation method according to claim 4, it is characterised in that：According to following formula meter in the step (4) Calculate many feed-in interaction factors between current conversion station bus nodes：

$\begin{array}{cc}{\mathrm{MIIF}}_{q,p}=\frac{{\left(B_{cd}^{-1}\right)}_{q,p}}{{\left(B_{cd}^{-1}\right)}_{p,p}}& B_{cd}=\[B_{11}+B_{11}^{\′}-B_{12}{B}_{22}^{-1}{B}_{21}\]\end{array}$

Wherein：MIIF_q,pFor the relative p-th current conversion station bus nodes of q-th current conversion station bus nodes many feed-in interactions because Son, B_cdIt is intermediary matrix,It is B₂₂Inverse matrix,It is B_cdInverse matrix,It is inverse matrixIn q rows P column element values,It is inverse matrixIn pth row pth column element value, q be natural number and 1≤q≤n.