CN102201671B - Calculation method for transmission line voltage distribution based on transmission line theory - Google Patents

Abstract

The invention belongs to the field of electrical power systems, particularly relating to a calculation method for transmission line voltage distribution based on the transmission line theory, and comprising the following steps: firstly, converting a two-port transmission parameter matrix of the transmission line to a two-port node admittance matrix so as to obtain a lumped parameter of a transmission line Pi type equivalent model; secondly, filling the lumped parameter in business trend calculation software and carrying out trend calculation on a target power grid containing the transmission line; and finally, taking the trend calculation result as a tail end boundary condition and utilizing the transmission parameter matrix to quickly obtain the voltage distribution in the line. The calculation method can precisely calculate the voltage distribution condition in an extra-high voltage series compensated line, and also can consider the reactive power compensation capacity on both sides of the line, thus having stronger engineering usability.

Description

The computational methods that a kind of transmission line based on transmission line theory voltage along the line distributes

Technical field

The invention belongs to field of power, be specifically related to the computational methods that a kind of transmission line based on transmission line theory voltage along the line distributes.

Background technology

Be accompanied by the development of power industry, string is installed in superhigh pressure (220～765kv) and UHV transmission line and is mended the conveying capacity that (SCs) can significantly improve circuit, but can change the distribution character of line steady-state voltage, and on circuit, each point voltage all should not surpass the highest working voltage of system simultaneously.At present, the research both at home and abroad superhigh pressure serial supplementary line steady state voltage being distributed finds, affect that voltage distributes because have the infield, compensativity, active power etc. of string benefit and high resistance (SR).But the reactive power compensation configuration of circuit both sides in Practical Project is not all considered in these researchs, extra-high voltage series supplementary line is not carried out to particular study yet.

UHV transmission has great application prospect in China.Use extra-high voltage series compensation can significantly promote the ability to transmit electricity of circuit.And the voltage distribution of obtaining on circuit is very important for the mount scheme of determining extra-high voltage series compensation.Meanwhile, the voltage along the line of Obtaining Accurate transmission line distributes and also contributes to the stable state power-frequency overvoltage level on check line road, raising to debug scheme and control measure etc. to the level of control of voltage along the line, the overvoltage level of checking switching nonloaded line and reasonable arrangement circuit.Obtain at present that line voltage distribution distributes related algorithm have electro-magnetic transient algorithm and non-linear power flow algorithm.But the former can not take into account the reactive power compensation ability of extra high voltage line both sides, and and the latter is a kind of approximate data, and zero increase of injecting number of nodes can make the more difficult convergence of trend.

Summary of the invention

In order to overcome now methodical deficiency, the present invention relates to the computational methods that a kind of transmission line (comprising serial supplementary line) based on transmission line theory voltage along the line distributes.First, the two-port transformation parameter matrix of transmission line is converted into two-port node admittance matrix, obtains the lumped parameter of transmission line π type Equivalent Model.Then inserted business Load Flow Calculation Software the target grid containing transmission line is carried out to trend calculating.The result of again trend being calculated, as end boundaries condition, just can show that with transformation parameter matrix the voltage on circuit distributes fast.This algorithm can accurately calculate the voltage distribution situation on extra-high voltage series supplementary line, but also can take into account the reactive power compensation ability of circuit both sides, and engineering adaptability is very strong.

For being illustrated in figure 1 an extra-high voltage series supplementary line, in figure, string cover is in extra high voltage line top, and top high resistance is positioned at bus bar side.This circuit forms by three sections, is followed successively by common-tower double-return line (plains region), common double loop line (mountain area), common-tower double-return line (mountain area), and length is respectively l ₁, l ₂, l ₃, the unit length parameter (z of three sections of circuits ₀y ₀) and propagation constant γ be different.

The fast algorithm that the transmission line based on transmission line theory (the comprising serial supplementary line) voltage along the line that the present invention proposes distributes comprises the steps:

First, the two-port transformation parameter matrix of transmission line is converted into two-port node admittance matrix, obtains the lumped parameter of transmission line π type Equivalent Model; Then inserted business Load Flow Calculation Software the target grid containing transmission line is carried out to trend calculating; The result of again trend being calculated, as end boundaries condition, just can show that with transformation parameter matrix the voltage on circuit distributes fast.

(1) by formula (1)-(4) below, calculated the transformation parameter matrix T of transmission line;

(2) establishing whole piece transmission line is comprised of the circuit of the different unit parameters of n section, the π type Equivalent Model of whole piece transmission line can be regarded as the cascade of the π type Equivalent Model of the different circuits of n section, and total transformation parameter matrix T is this n section circuit transformation parameter matrix (T ₁, T ₂..., T _n) product,

T＝T ₁T ₂…T _n (1)

Wherein,

$T_1=\left[\begin{array}{cc}\mathrm{ch}\left({\mathrm{\γ}}_1{l}_1\right)& j{Z}_{C1}\mathrm{sh}\left({\mathrm{\γ}}_1{l}_1\right)\\ j\frac{1}{Z_{C1}}\mathrm{sh}\left({\mathrm{\γ}}_1{l}_1\right)& \mathrm{ch}\left({\mathrm{\γ}}_1{l}_1\right)\end{array}\right]---\left(2\right)$

$T_2=\left[\begin{array}{cc}\mathrm{ch}\left({\mathrm{\γ}}_2{l}_2\right)& j{Z}_{C2}\mathrm{sh}\left({\mathrm{\γ}}_2{l}_2\right)\\ j\frac{1}{Z_{C2}}\mathrm{sh}\left({\mathrm{\γ}}_2{l}_2\right)& \mathrm{ch}\left({\mathrm{\γ}}_2{l}_2\right)\end{array}\right]---\left(3\right)$

…

$T_n=\left[\begin{array}{cc}\mathrm{ch}\left({\mathrm{\γ}}_n{l}_n\right)& j{Z}_{C3}\mathrm{sh}\left({\mathrm{\γ}}_n{l}_n\right)\\ j\frac{1}{Z_{C3}}\mathrm{sh}\left({\mathrm{\γ}}_n{l}_n\right)& \mathrm{ch}\left({\mathrm{\γ}}_n{l}_n\right)\end{array}\right]---\left(4\right)$

In formula, γ _nbe the propagation constant of n section circuit, Z _cnbe the wave impedance of n section circuit, l _nbe the length of n section circuit;

(3) according to formula (5), calculate the equivalent parameters (Z of whole piece transmission line _eq, Y _eq)

If $T=\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]$

Have:

Z _eq＝B

Y _eq＝(A-1)/B＝(D-1)/B (5)

(D-1)/B and (A-1)/B represent respectively the admittance of branch road over the ground of the left and right sides in the equivalent branch road of π type;

(4) by π type Equivalent Model parameter (Z _eq, Y _eq) insert business Load Flow Calculation Software or stability Calculation software, the target grid containing extra-high voltage series supplementary line is carried out to trend calculating or stability Calculation;

(5) from trend calculate or the result of stability Calculation pick out the terminal voltage of extra-high voltage series supplementary line and electric current as end boundaries condition, extra high voltage line art end load is the summation that flows through the having of line end circuit breaker, reactive power flow and flow through the reactive power flow of line end high resistance, and end current is loaded by end and terminal voltage is calculated;

(6) according to end condition and formula (6), with transformation parameter matrix (T, T ₁, T ₂..., T _n) calculate fast the voltage distribution situation on circuit, wherein, T is used for the voltage at computational scheme top, T ₁, T ₂..., T _nbe used for that voltage on computational scheme distributes and three sections of different condition circuits on boundary voltage;

$\left[\begin{array}{c}{\stackrel{\·}{U}}_1\\ {\stackrel{\·}{I}}_1\end{array}\right]=T\left[\begin{array}{c}{\stackrel{\·}{U}}_2\\ -{\stackrel{\·}{I}}_2\end{array}\right]---\left(6\right)$

Wherein, in described step (1), if circuit comprises string, mend, string is mended to unified taking into account in circuit transmission matrix T and take in, specific as follows:

The equivalent transformation parameter matrix T of the string benefit of " high resistance is arranged in bus bar side scheme " and " high resistance is positioned at line side scheme " and the combinational circuit of high resistance _a, T _bfor:

$T_a=\left[\begin{array}{cc}1& X_C\\ Y_R& 1+Y_R{X}_C\end{array}\right]---\left(7\right)$

$T_b=\left[\begin{array}{cc}1+Y_R{X}_C& X_C\\ Y_R& 1\end{array}\right]---\left(8\right)$

Wherein, Y _rfor high resistance admittance, X _cfor string is mended reactance;

Try to achieve T _a, T _bafter, according to string, mend and the combinational circuit of high resistance and the cascade situation of circuit π type Equivalent Model, T _a, (T _b) with former Transmission Lines parametric array T premultiplication, take advantage of on the right side or combine and multiply each other, and can obtain new transmission matrix T.

Basic principle of the present invention is:

According to the sinusoidal steady-state solutions of uniform transmission line, node voltage and electric current apart from line end apart from l place are shown below:

$\left\{\begin{array}{c}\stackrel{\·}{U}={\stackrel{\·}{U}}_2\mathrm{ch}\left(\mathrm{\γl}\right)+{\stackrel{\·}{I}}_2{Z}_C\mathrm{sh}\left(\mathrm{\γl}\right)\\ \stackrel{\·}{I}={\stackrel{\·}{I}}_2\mathrm{ch}\left(\mathrm{\γl}\right)+\frac{{\stackrel{\·}{U}}_2}{Z_C}\mathrm{sh}\left(\mathrm{\γl}\right)\end{array}\right.---\left(9\right)$

Wherein, $Z_C=\sqrt{\frac{z_0}{y_0}},$ $\mathrm{\γ}=\sqrt{z_0{y}_0}=\mathrm{\α}+\mathrm{j\β}$

In formula, Z _cfor wave impedance, γ is propagation constant, z ₀for unit length impedance, y ₀for unit length admittance.

Constant γ and Z _cit is plural number.The real part of propagation constant γ is called attenuation constant α, and imaginary part is called phase coefficient β.Circuit can be considered as the two-port network shown in Fig. 5.

Formula (9) can be expressed as matrix form:

$\left[\begin{array}{c}{\stackrel{\·}{U}}_1\\ {\stackrel{\·}{I}}_1\end{array}\right]=\left[\begin{array}{cc}\mathrm{ch}\left(\mathrm{\γl}\right)& {\mathrm{jZ}}_C\mathrm{sh}\left(\mathrm{\γl}\right)\\ j\frac{1}{Z_C}\mathrm{sh}\left(\mathrm{\γl}\right)& \mathrm{ch}\left(\mathrm{\γl}\right)\end{array}\right]\left[\begin{array}{c}{\stackrel{\·}{U}}_2\\ -{\stackrel{\·}{I}}_2\end{array}\right]---\left(10\right)$

Transformation parameter matrix is:

$T=\left[\begin{array}{cc}\mathrm{ch}\left(\mathrm{\γl}\right)& {\mathrm{jZ}}_C\mathrm{sh}\left(\mathrm{\γl}\right)\\ j\frac{1}{Z_C}\mathrm{sh}\left(\mathrm{\γl}\right)& \mathrm{ch}\left(\mathrm{\γl}\right)\end{array}\right]---\left(11\right)$

Wherein,

A＝ch(γl)

B＝jZ _Csh(γl)

$C=j\frac{1}{Z_C}\mathrm{sh}\left(\mathrm{\γl}\right)---\left(12\right)$

D＝ch(γl)

According to TWO-PORT NETWORK THEORY, circuit two-port network can be converted into the π type Equivalent Model shown in Fig. 6:

Parameter in Fig. 6 is:

Z _eq＝B

Y _eq＝(A-1)/B＝(D-1)/B (13)

Above π type Equivalent Model and parameter are rigorous equivalences under power frequency, in trend calculating and transient stability calculating, can directly use.In formula (11), the admittance of branch road over the ground of the left and right sides in (D-1)/B and (A-1)/B difference presentation graphs 2.

The invention has the beneficial effects as follows:

The voltage of any point on computational scheme, can obtain thus accurate full line voltage and distribute quickly and accurately; In addition, can accurately take into account the reactive power compensation ability of extra-high voltage series supplementary line both sides, therefore, the engineering adaptability of this algorithm is very strong.

Accompanying drawing explanation

Below in conjunction with accompanying drawing, the present invention is further described.

Fig. 1 is extra-high voltage series compensation transmission line schematic diagram;

Fig. 2 is the UHV transmission line simplified model figure mending with string;

Fig. 3 be extra-high voltage series compensation and and anti-mount scheme figure, wherein, (a) representative " high resistance is positioned at bus bar side scheme ", (b) representative " high resistance is positioned at line side scheme ";

Fig. 4 is the Equivalent Model figure that different strings are mended mount scheme;

Fig. 5 is the two-port network figure of transmission line;

Fig. 6 is the π type Equivalent Model figure of transmission line;

Fig. 7 is that in the embodiment of the present invention, band string is mended " Wan electricity Dong send " UHV Transmission Engineering planning schematic diagram;

Fig. 8 is that in the embodiment of the present invention, voltage distribution map on the circuit of south, Huainan-Anhui occurs after N-1 fault scheme a;

Fig. 9 is that in the embodiment of the present invention, voltage distribution map on the circuit of south, Huainan-Anhui occurs after N-1 fault scheme b;

Figure 10 is that in the embodiment of the present invention, voltage distribution map on the circuit of south, Huainan-Anhui occurs after N-1 fault scheme c;

Figure 11 is the FB(flow block) of computational methods of the present invention.

Embodiment

Below in conjunction with accompanying drawing, computational methods of the present invention are further described in detail.

As shown in figure 11, the computational methods that transmission line based on transmission line theory of the present invention voltage along the line distributes comprise following each step: first, the two-port transformation parameter matrix of transmission line is converted into two-port node admittance matrix, obtains the lumped parameter of transmission line π type Equivalent Model; Then inserted business Load Flow Calculation Software the target grid containing transmission line is carried out to trend calculating; The result of again trend being calculated, as end boundaries condition, just can show that with transformation parameter matrix the voltage on circuit distributes fast.

Be below an embodiment of the present invention, with " Wan electricity Dong send " UHV Transmission Engineering programme, make embodiment, further illustrate as follows:

" Wan electricity Dong send " UHV Transmission Engineering is sent to a large amount of electric power Zhejiang, Shanghai from Anhui, as shown in Figure 7.In planning electrical network in 2012, south, the 1000kV Huainan that band string is mended-Anhui double loop transmission power is about 10000MW.Under which, Huainan and ultra high voltage station, north, Zhejiang are all dropped into 8 groups of 210Mvar secondary capacitors and are carried out reactive power compensation.Trend and the transient stability computing module of application PSD-BPA distribute and study serial supplementary line voltage.

Fig. 5 has provided three kinds of different arrangements: a of string benefit and high resistance, in 40% string supplementary set, is arranged in Huainan side, and high resistance is positioned at bus bar side; B, is arranged in Huainan side in 40% string supplementary set, and high resistance is positioned at line side; C, the string of each dispersed placement 20% of He Wannan both sides, Huainan is mended, and high resistance is all positioned at bus bar side.The π type equivalent parameters that draws circuit according to this paper institute extracting method, then carries out trend calculating, and then obtains the steady state voltage of south, Huainan under normal operating mode-Anhui circuit, lists in table 1 and table 2.

Table 1 " Wan electricity Dong send " UHV Transmission Engineering scheme a), b) circuit working voltage

Voltage unit: kV

Table 2 " Wan electricity Dong send " UHV Transmission Engineering scheme c) line steady-state working voltage

Voltage unit: kV

In above three schemes, while there is N-1 fault on the circuit of south, Huainan-Anhui, due to overload and reactive loss serious, system can not provide enough reactive power compensations, so while there is N-1 fault, trend is calculated and is difficult to adjust convergence.And adopt transient stability to calculate, easily obtain the loading condiction of each busbar voltage and line end after N-1 fault.Then, utilize algorithm in this paper can obtain respectively the line voltage distribution distribution situation of three kinds of schemes: in scheme a and scheme b, after N-1 fault, serial supplementary line side voltage has all surpassed the highest working voltage of system (1100kV), wherein scheme a is 1150kV (Fig. 8), and scheme b is 1130kV (Fig. 9); In scheme C, after N-1 fault, circuit ceiling voltage is 1054kV, lower than 1100kV (Figure 10).

Clearly, under heavy service mode, while being arranged in circuit one side in string supplementary set, no matter high resistance is positioned at bus bar side or line side, and after generation circuit N-1 fault, serial supplementary line side voltage all will be over 1100kV; And if string is mended dispersed placement in circuit two ends, and high resistance is while being positioned at bus bar side, there is circuit N-1 fault after serial supplementary line side voltage will be no more than 1100kV.Therefore, suggested design c, string mend dispersed placement in Huainan-circuit two ends, south, Anhui, high resistance is positioned at bus bar side, this is consistent with EMTPE electromagnetic transient simulation conclusion.

According to specific exemplary embodiment, invention has been described herein.It will be apparent under not departing from the scope of the present invention, carrying out to one skilled in the art suitable replacement or revise.Exemplary embodiment is only illustrative, rather than the restriction to scope of the present invention, and scope of the present invention is defined by appended claim.

Claims (2)

1. the computational methods that the transmission line based on transmission line theory voltage along the line distributes, it is characterized in that: first, the two-port transformation parameter matrix of transmission line is converted into two-port node admittance matrix, obtains the lumped parameter of transmission line π type Equivalent Model; Then inserted business Load Flow Calculation Software the target grid containing transmission line is carried out to trend calculating; The result of again trend being calculated, as end boundaries condition, just can show that with transformation parameter matrix the voltage on circuit distributes fast;

Comprise the steps:

(1) by formula (1)-(4) below, calculated the transformation parameter matrix T of transmission line;

(2) establishing whole piece transmission line is comprised of the circuit of the different unit parameters of n section, the π type Equivalent Model of whole piece transmission line can be regarded as the cascade of the π type Equivalent Model of the different circuits of n section, and total transformation parameter matrix T is this n section circuit transformation parameter matrix (T ₁, T ₂..., T _n) product,

T＝T ₁T ₂…T _n (1)

Wherein,

$T_1=\left[\begin{array}{cc}\mathrm{ch}\left({\mathrm{\γ}}_1{l}_1\right)& j{Z}_{C1}\mathrm{sh}\left({\mathrm{\γ}}_1{l}_1\right)\\ j\frac{1}{Z_{C1}}\mathrm{sh}\left({\mathrm{\γ}}_1{l}_1\right)& \mathrm{ch}\left({\mathrm{\γ}}_1{l}_1\right)\end{array}\right]---\left(2\right)$

$T_2=\left[\begin{array}{cc}\mathrm{ch}\left({\mathrm{\γ}}_2{l}_2\right)& j{Z}_{C2}\mathrm{sh}\left({\mathrm{\γ}}_2{l}_2\right)\\ j\frac{1}{Z_{C2}}\mathrm{sh}\left({\mathrm{\γ}}_2{l}_2\right)& \mathrm{ch}\left({\mathrm{\γ}}_2{l}_2\right)\end{array}\right]---\left(3\right)$

…

$T_n=\left[\begin{array}{cc}\mathrm{ch}\left({\mathrm{\γ}}_n{l}_n\right)& j{Z}_{C3}\mathrm{sh}\left({\mathrm{\γ}}_n{l}_n\right)\\ j\frac{1}{Z_{C3}}\mathrm{sh}\left({\mathrm{\γ}}_n{l}_n\right)& \mathrm{ch}\left({\mathrm{\γ}}_n{l}_n\right)\end{array}\right]---\left(4\right)$

In formula, γ _nbe the propagation constant of n section circuit, Z _cnbe the wave impedance of n section circuit, l _nbe the length of n section circuit;

(3) according to formula (5), calculate the equivalent parameters (Z of whole piece transmission line _eq, Y _eq)

If $T=\left[\begin{array}{cc}A& B\\ C& D\end{array}\right]$

Have:

Z _eq＝B

Y _eq＝(A-1)/B＝(D-1)/B (5)

(D-1)/B and (A-1)/B represent respectively the admittance of branch road over the ground of the left and right sides in the equivalent branch road of π type;

(4) by π type Equivalent Model parameter (Z _eq, Y _eq) insert business Load Flow Calculation Software or stability Calculation software, the target grid containing extra-high voltage series supplementary line is carried out to trend calculating or stability Calculation;

(5) from trend calculate or the result of stability Calculation pick out the terminal voltage of extra-high voltage series supplementary line and electric current as end boundaries condition, extra high voltage line end load is the summation that flows through the having of line end circuit breaker, reactive power flow and flow through the reactive power flow of line end high resistance, and end current load and calculated with terminal voltage by end;

(6) according to end condition and formula (6), with transformation parameter matrix (T, T ₁, T ₂..., T _n) calculate fast the voltage distribution situation on circuit, wherein, T is used for the voltage at computational scheme top, T ₁, T ₂..., T _nbe used for that voltage on computational scheme distributes and three sections of different condition circuits on boundary voltage;

$\left[\begin{array}{c}{\stackrel{\·}{U}}_1\\ {\stackrel{\·}{I}}_1\end{array}\right]=T\left[\begin{array}{c}{\stackrel{\·}{U}}_2\\ -{\stackrel{\·}{I}}_2\end{array}\right]---\left(6\right)$

Wherein,

for the voltage of circuit head end,

for the Injection Current of circuit head end,

for the voltage of line end,

injection Current for line end.

2. the method for claim 1, is characterized in that, in described step (1), if circuit comprises string, mends, and string is mended to unified taking into account in circuit transmission matrix T and takes in, specific as follows:

The string benefit of " high resistance is arranged in bus bar side scheme " and " high resistance is positioned at line side scheme " and high resistance

The equivalent transformation parameter matrix T of combinational circuit _a, T _bfor:

$T_a=\left[\begin{array}{cc}1& X_C\\ Y_R& 1+Y_R{X}_C\end{array}\right]---\left(7\right)$

$T_b=\left[\begin{array}{cc}1+Y_R{X}_C& X_C\\ Y_R& 1\end{array}\right]---\left(8\right)$

Wherein, Y _rfor high resistance admittance, X _cfor string is mended reactance;

Try to achieve T _a, T _bafter, according to string, mend and the combinational circuit of high resistance and the cascade situation of circuit π type Equivalent Model, T _a, T _bwith former Transmission Lines parametric array T premultiplication, take advantage of on the right side or combine and multiply each other, and can obtain new transmission matrix T.

Images