CN106646146A - Method for calculating maximum voltage withstanding position of zero load high voltage power cable - Google Patents

Abstract

The invention discloses a method for calculating a maximum voltage withstanding position of a zero load high voltage power cable. The method comprises the following steps: resistance per unit length, inductance, capacitance and admittance parameters of a cable loop are calculated according to cable structure parameters; an attenuation coefficient and a phase position coefficient per unit length of the cable are calculated based on the resistance, inductance, capacitance and admittance parameters; the attenuation coefficient and the phase position coefficient are applied to a sine wave function, a sine wave propagation function is built, a calculating model for maximum voltage withstanding capability of all points along the cable is built via a sine wave propagation rule based on the sine wave propagation function, and the maximum voltage withstanding position of the cable can be calculated. The method can help solve a problem that currently no method for calculating the maximum voltage withstanding position of the zero load high voltage power cable is available; analysis guidance can be provided for cable transient breakdown faults in high voltage power frequency operation, variable frequency voltage withstanding tests, damping oscillatory wave tests and the like in a long distance zero load cable line; a data basis can be provided for fault cable line breakdown accident simulation tests.

Description

It is a kind of to calculate the method that unloaded high voltage power cable highest bears voltage location

Technical field

The present invention relates to a kind of calculate the method that unloaded high voltage power cable highest bears voltage location, belong to power technology Field.

Background technology

At present for long distance transmission line, sine voltage along transmission line of electricity voltage calculating more than joined using steady-state distribution The method that number circuit is derived, calculates the attenuation coefficient and phase coefficient of circuit, so as to calculate the steady state voltage of each point along the line, but It is the computational problem that cannot solve sinusoidal traveling wave transient voltage on transmission line of electricity.For sinusoidal traveling wave is along cable transmission line, Each point along the line is most in long-distance cable transmission line of electricity to there is presently no the sinusoidal traveling wave caused with regard to maloperation and failure etc. The computational methods of the transient voltage that height bears.

The content of the invention

In order to solve above-mentioned technical problem, the invention provides a kind of zero load high voltage power cable highest that calculates bears voltage The method of position.

In order to achieve the above object, the technical solution adopted in the present invention is：

It is a kind of to calculate the method that unloaded high voltage power cable highest bears voltage location, comprise the following steps：

Cable loop resistance per unit length, inductance, electric capacity and admittance parameter are calculated according to construction of cable parameter；

According to resistance, inductance, electric capacity and admittance parameter, the attenuation coefficient and phase coefficient of cable unit length are calculated；

Attenuation coefficient and phase coefficient are combined with sinusoidal wave function, sine wave propagation function is built；

According to sine wave propagation function, build cable each point highest along the line with sine wave propagation law and bear voltage calculating Model, calculates cable highest and bears voltage location.

The computing formula of cable resistance, inductance, electric capacity and admittance parameter is

R_θ=[R₁+R₂+(R₁κ₁+R₂κ₂)(θ-20)]/n

G=ω ' C × tan δ

Wherein, R_θFor D.C. resistance of the cable loop at temperature θ, R₁It is that, in temperature θ, unit length cable core is led Body D.C. resistance, R₂It is the unit length cable cover(ing) conductor DC resistance in temperature θ, κ₁For each absolute temperature θ when cable The corresponding temperature coefficient of cable core conductor material, κ₂For each absolute temperature θ when the corresponding temperature coefficient of cable cover(ing) conductor material, N is circuit number in parallel in loop；

L be cable loop unit length inductance, μ₀For space permeability, s is the mean geometrical distance between cable core, D_co For cable conductor external diameter；

C be cable loop capacitance per unit length, ε₀For permittivity of vacuum, ε_rFor the relative dielectric constant of insulating materials, D_i By examination cable metal sheath internal diameter, D_nFor in cable loop with other parallel line distances, D_cFor cable core external diameter；

G is cable loop unit length conductance, and ω ' is power frequency angular frequency, and tan δ are the loss factor of material.

The computing formula of attenuation coefficient and phase coefficient is,

Wherein, α, β represent respectively attenuation coefficient and phase coefficient, and ω is angular frequency.

Sine wave propagation function U₊(x, t) is,

0≤t≤t_m

Wherein, t is the propagation time, t_mFor the time of waveform, A is waveforms amplitude, and x is sine wave from the beginning of cable incidence end Displacement on cable termination direction,For the initial phase that sine wave sources produces waveform, g (t-x/v) is the function of definition,V represents velocity of wave.

Along the line each point voltage is cable,

U (x, t)=U_-(x,t)+U₊(x,t)

Wherein, U_-(x, t) is reflection wave function,

Wherein, l is cable length.

Work as t_mDuring >=(2l+ λ)/v：

Cable any point all experiences sine wave and back wave at least a cycle simultaneously, then

0≤δ≤π

X '=l-x

Wherein, x ' is the distance of wave travel positional distance cable termination, and λ represents wavelength,

When U (x, t) is maximum, the x for solving is cable highest and bears voltage location；

Work as t_m<During (2l+ λ)/v：

When sine wave is transmitted to cable termination from cable head-end for the first time, wave function U is reflected_{_}(x, t)=0；

0≤t≤t_m

0≤x≤vt

Wherein,

If 0≤x '≤t_mV/2- λ, interval inner cable any point all experiences sine wave and back wave at least one week simultaneously Phase；

0≤δ≤π

X '=l-x

Wherein,

If 0 ＜ t_mV/2- λ ＜ x '≤t_mV/2 or 0 ＜ x '≤t_mV/2 ＜ λ, sine wave on interval inner cable any point With (t of the back wave experience less than 2 π_mV-2x') β/2 phase angle variations；

(l-x)/v+t_m/2+x/v≤t≤t_m+x/v

0≤δ≤π

X '=l-x

Wherein,

As max [U₁(x,t),U₂(x,t),U₃(x, t)] it is maximum when, the x for solving is cable highest and bears voltage location.

The beneficial effect that the present invention is reached：The present invention is solved and held currently without the unloaded high voltage power cable highest of calculating Can be the operation of high pressure power frequency, frequency conversion pressure test, damping in long range non-loaded cable circuit by the problem of voltage location method The cable transient state breakdown fault analysis of the appearance such as Sasser test provides analysis and guidance, and can puncture for simulated failure cable run Accident test provides data foundation.

Description of the drawings

Fig. 1 is the flow chart of the present invention.

Fig. 2 is cable distribution Simplified analysis figure.

Specific embodiment

Below in conjunction with the accompanying drawings the invention will be further described.Following examples are only used for clearly illustrating the present invention Technical scheme, and can not be limited the scope of the invention with this.

As shown in figure 1, a kind of calculate the method that unloaded high voltage power cable highest bears voltage location, including following step Suddenly：

1) cable loop resistance per unit length, inductance, electric capacity and admittance parameter are calculated according to construction of cable parameter.

Specific formula for calculation is as follows：

R_θ=[R₁+R₂+(R₁κ₁+R₂κ₂)(θ-20)]/n

Wherein, R_θFor D.C. resistance of the cable loop at temperature θ, R₁It is that, in temperature θ, unit length cable core is led Body D.C. resistance, R₂It is the unit length cable cover(ing) conductor DC resistance in temperature θ, κ₁For each absolute temperature θ when cable The corresponding temperature coefficient of cable core conductor material, κ₂For each absolute temperature θ when the corresponding temperature coefficient of cable cover(ing) conductor material, N is circuit number in parallel in loop.

Wherein, L be cable loop unit length inductance, μ₀For space permeability, s be geometric average between cable core away from From D_coFor cable conductor external diameter.

Wherein, C is cable loop in capacitance per unit length, ε₀For permittivity of vacuum, ε_rFor the relative dielectric of insulating materials Constant, D_iBy examination cable metal sheath internal diameter, D_nFor in cable loop with other parallel line distances, D_cFor cable core External diameter.

G=ω ' C × tan δ

Wherein, G is cable loop unit length conductance, and ω ' is power frequency angular frequency, and tan δ are the loss factor of material.

2) according to resistance, inductance, electric capacity and admittance parameter, attenuation coefficient and the phase place system of cable unit length is calculated Number.

Calculated according to distributed constant circuit principle and be derived from：

Wherein, α, β represent respectively attenuation coefficient and phase coefficient, and ω is angular frequency.

3) attenuation coefficient and phase coefficient are combined with sinusoidal wave function, is built sine wave propagation function.

Sinusoidal wave function f (t) is：

0≤t≤t_m

Wherein, t is the propagation time, t_mFor the time of waveform, A is waveforms amplitude,The initial of waveform is produced for sine wave sources Phase place.

Therefore sine wave propagation function U₊(x, t) is：

0≤t≤t_m

Wherein, x starts to the displacement on cable termination direction for sine wave from cable incidence end, and g (t-x/v) is definition Function,V=ω/β represents velocity of wave.

4) according to sine wave propagation function, build cable each point highest along the line with sine wave propagation law and bear potentiometer Model is calculated, cable highest is calculated and is born voltage location.

Sine wave is propagated in the cable with following features：

1st, the sinusoidal waveform time was less than at the propagation time of double length cable, and cable is unloaded it is believed that cable two Terminal impedance is infinitely great, and sine wave can occur multiple reflections in cable, due to there is waveform attenuating, when cable attenuation coefficient it is big, Cable ceiling voltage point possibly be present at the head end position of cable；And it is little to work as cable attenuation coefficient, cable ceiling voltage point may There is the overlapping portion of incidence wave and back wave, due to there is waveform attenuating, therefore incidence wave and back wave maximum superimposed voltage When occurring in secondary reflection at the beginning of cable termination, the superposition of incidence wave and back wave is interval on cable termination to incident extreme direction.

2nd, it is more than in the propagation time of double length cable when the sinusoidal waveform time, cable any point all experiences just simultaneously String ripple and back wave at least a cycle, cable end piece is unloaded, it is believed that impedance is infinitely great, and incidence end connection power supply, impedance It is believed that be zero, therefore, sine wave is propagated in the cable, when voltage reflection ripple reaches cable incidence end and reflects again from terminal, Voltage reflection coefficient is 0, so maximum voltage need to only consider that sine wave passes to terminal along cable from incidence end, back wave is from terminal The cable maximum voltage along the line passed in incidence end this period.

To sum up, cable maximum voltage along the line bears and a little possibly be present at cable incidence end or cable termination to incidence end side Upwards the superposition of incidence wave and back wave is interval.

Definition cable length is l, and cable distribution Simplified analysis figure is as shown in Fig. 2 due to cable end piece zero load, it is believed that resistance Anti- infinity, therefore terminal voltage refraction coefficient is 0, voltage reflection coefficient is 1.Therefore, wave function U is reflected_{_}(x, t) is：

Wherein, 0≤x≤l.

Along the line each point voltage is cable：

U (x, t)=U_{_}(x,t)+U₊(x,t)

Work as t_mDuring >=(2l+ λ)/v：

Cable any point all experiences sine wave and back wave at least a cycle simultaneously, then

0≤δ≤π

X '=l-x

Wherein, x ' is the distance of wave travel positional distance cable termination, and λ represents wavelength, T is the cycle,

When U (x, t) is maximum, the x for solving is cable highest and bears voltage location.

Work as t_m<During (2l+ λ)/v：

When sine wave is transmitted to cable termination from cable head-end for the first time, wave function U is reflected_{_}(x, t)=0；

0≤t≤t_m

0≤x≤vt

Wherein,

If 0≤x '≤t_mV/2- λ, interval inner cable any point all experiences sine wave and back wave at least one week simultaneously Phase；

0≤δ≤π

X '=l-x

Wherein,

If 0 ＜ t_mV/2- λ ＜ x '≤t_mV/2 or 0 ＜ x '≤t_mV/2 ＜ λ, sine wave on interval inner cable any point With (t of the back wave experience less than 2 π_mV-2x') β/2 phase angle variations；

(l-x)/v+t_m/2+x/v≤t≤t_m+x/v

0≤δ≤π

X '=l-x

Wherein,

As max [U₁(x,t),U₂(x,t),U₃(x, t)] it is maximum when, the x for solving is cable highest and bears voltage location.

In order to further illustrate said method, following case is analyzed.

Target cable structural parameters are as shown in Table 1；

The target cable structural parameters of table one

Wherein, D₁And D₂The distance that cable and other two shunt cables are tried in loop is represented respectively.

Formula in method can solve following parameter, specifically as shown in Table 2：

Parameter of the table two according to construction of cable gain of parameter

Sinusoidal wave function f (t) is：

F (t)=1.28 × 10³sin(2000πt+90^°)

0≤t≤1.5×10^-3

It can be seen from sinusoidal wave function：

0≤x≤5.3×10⁴

t_mV/2- λ=- 0.25 λ ＜ 0, therefore U need not be calculated₂(x,t)；

As 0 ＜ x'≤t_mDuring v/2=0.75 λ, then

max[U₁(x,t),U₂(x,t),U₃(x, t)]=1.28 × 10⁵。

Said method is the attenuation coefficient and phase coefficient by calculating cable unit length circuit, sinusoidal with reference to cable Waveform parameter sets up the propagation function that sinusoidal traveling wave is propagated in the cable, sets up with regard to cable axle with trigonometric function operation method To the Mathematical Modeling for bearing voltage, so as to calculate the position that cable highest bears electrical voltage point.

Said method solves the problems, such as to bear voltage location method currently without the unloaded high voltage power cable highest of calculating, It can be the cable of the appearance such as the operation of high pressure power frequency, frequency conversion pressure test, the test of damped vibration ripple in long range non-loaded cable circuit The analysis of transient state breakdown fault provides analysis and guidance, and can provide data foundation for the test of simulated failure cable run breakdown accident.

The above is only the preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art For member, on the premise of without departing from the technology of the present invention principle, some improvement and deformation can also be made, these improve and deform Also should be regarded as protection scope of the present invention.

Claims (6)

1. It is 1. a kind of to calculate the method that unloaded high voltage power cable highest bears voltage location, it is characterised in that：Comprise the following steps,

   Cable loop resistance per unit length, inductance, electric capacity and admittance parameter are calculated according to construction of cable parameter；

   According to resistance, inductance, electric capacity and admittance parameter, the attenuation coefficient and phase coefficient of cable unit length are calculated；

   Attenuation coefficient and phase coefficient are combined with sinusoidal wave function, sine wave propagation function is built；

   According to sine wave propagation function, build cable each point highest along the line with sine wave propagation law and bear voltage calculating mould Type, calculates cable highest and bears voltage location.
2. 2. the method that a kind of unloaded high voltage power cable highest of calculating according to claim 1 bears voltage location, it is special Levy and be：The computing formula of cable resistance, inductance, electric capacity and admittance parameter is,

   R_θ=[R₁+R₂+(R₁κ₁+R₂κ₂)(θ-20)]/n

   $L=\frac{{\mathrm{\&mu;}}_0}{8\mathrm{\&pi;}}+\frac{{\mathrm{\&mu;}}_0}{2\mathrm{\&pi;}}ln\frac{2s}{D_{co}}$

   $C=\frac{2\&times;\mathrm{\&pi;}\&times;{\mathrm{\&epsiv;}}_0\&times;{\mathrm{\&epsiv;}}_r}{ln\frac{D_i}{D_C}}+{\mathrm{\&Sigma;}}_{n=1}^{n-1}\frac{{\mathrm{\&epsiv;}}_0\&times;{\mathrm{\&epsiv;}}_r}{ln\frac{D_n}{D_C}}$

   G=ω ' C × tan δ

   Wherein, R_θFor D.C. resistance of the cable loop at temperature θ, R₁It is that, in temperature θ, unit length cable core conductor is straight Leakage resistance, R₂It is the unit length cable cover(ing) conductor DC resistance in temperature θ, κ₁For each absolute temperature θ when cable core The corresponding temperature coefficient of conductor material, κ₂For each absolute temperature θ when the corresponding temperature coefficient of cable cover(ing) conductor material, n is Circuit number in parallel in loop；

   L be cable loop unit length inductance, μ₀For space permeability, s is the mean geometrical distance between cable core, D_coFor electricity Cable conductor diameter；

   C be cable loop capacitance per unit length, ε₀For permittivity of vacuum, ε_rFor the relative dielectric constant of insulating materials, D_iFor institute The internal diameter of examination cable metal sheath, D_nFor in cable loop with other parallel line distances, D_cFor cable core external diameter；

   G is cable loop unit length conductance, and ω ' is power frequency angular frequency, and tan δ are the loss factor of material.
3. 3. the method that a kind of unloaded high voltage power cable highest of calculating according to claim 1 bears voltage location, it is special Levy and be：The computing formula of attenuation coefficient and phase coefficient is

   $\mathrm{\&alpha;}=\sqrt{\frac{1}{2}\&lsqb;\sqrt{(R^2+{\mathrm{\&omega;}}^2{L}^2)(G^2+{\mathrm{\&omega;}}^2{C}^2)}-({\mathrm{\&omega;}}^{2}LC-RG)\&rsqb;}$

   $\mathrm{\&beta;}=\sqrt{\frac{1}{2}\&lsqb;\sqrt{(R^2+{\mathrm{\&omega;}}^2{L}^2)(G^2+{\mathrm{\&omega;}}^2{C}^2)}+({\mathrm{\&omega;}}^{2}LC-RG)\&rsqb;}$

   Wherein, α, β represent respectively attenuation coefficient and phase coefficient, and ω is angular frequency.
4. 4. the method that a kind of unloaded high voltage power cable highest of calculating according to claim 1 bears voltage location, it is special Levy and be：Sine wave propagation function U₊(x, t) is,

   0≤t≤t_m

   Wherein, t is the propagation time, t_mFor the time of waveform, A is waveforms amplitude, and x starts to electricity for sine wave from cable incidence end The displacement upwards of cable terminal side,For the initial phase that sine wave sources produces waveform, g (t-x/v) is the function of definition,V represents velocity of wave.
5. 5. the method that a kind of unloaded high voltage power cable highest of calculating according to claim 4 bears voltage location, it is special Levy and be：Along the line each point voltage is cable,

   U (x, t)=U_-(x,t)+U₊(x,t)

   Wherein, U_-(x, t) is reflection wave function,

   Wherein, l is cable length.
6. 6. the method that a kind of unloaded high voltage power cable highest of calculating according to claim 5 bears voltage location, it is special Levy and be：

   Work as t_mDuring >=(2l+ λ)/v：

   Cable any point all experiences sine wave and back wave at least a cycle simultaneously, then

   $\mathrm{\&delta;}=ar\cos \frac{e^{{\mathrm{\&alpha;x}}^{\&prime;}}+cos\left(2\mathrm{\&beta;}x\right)e^{-{\mathrm{\&alpha;x}}^{\&prime;}}}{\sqrt{{\&lsqb;e^{{\mathrm{\&alpha;x}}^{\&prime;}}+cos\left(2\mathrm{\&beta;}x\right)e^{-{\mathrm{\&alpha;x}}^{\&prime;}}\&rsqb;}^2+{\&lsqb;e^{-{\mathrm{\&alpha;x}}^{\&prime;}}sin\left(2\mathrm{\&beta;}x\right)\&rsqb;}^2}}$

   0≤δ≤π

   X '=l-x

   Wherein, x ' is the distance of wave travel positional distance cable termination, and λ represents wavelength,

   When U (x, t) is maximum, the x for solving is cable highest and bears voltage location；

   Work as t_m<During (2l+ λ)/v：

   When sine wave is transmitted to cable termination from cable head-end for the first time, wave function U is reflected_-(x, t)=0；

   0≤t≤t_m

   0≤x≤vt

   Wherein,

   If 0≤x '≤t_mV/2- λ, interval inner cable any point all experiences sine wave and back wave at least a cycle simultaneously；

   $\mathrm{\&delta;}=ar\cos \frac{e^{{\mathrm{\&alpha;x}}^{\&prime;}}+cos\left(2\mathrm{\&beta;}x\right)e^{-{\mathrm{\&alpha;x}}^{\&prime;}}}{\sqrt{{\&lsqb;e^{{\mathrm{\&alpha;x}}^{\&prime;}}+cos\left(2\mathrm{\&beta;}x\right)e^{-{\mathrm{\&alpha;x}}^{\&prime;}}\&rsqb;}^2+{\&lsqb;e^{-{\mathrm{\&alpha;x}}^{\&prime;}}sin\left(2\mathrm{\&beta;}x\right)\&rsqb;}^2}}$

   0≤δ≤π

   X '=l-x

   Wherein,

   If 0 ＜ t_mV/2- λ ＜ x '≤t_mV/2 or 0 ＜ x '≤t_mV/2 ＜ λ, sine wave and anti-on interval inner cable any point (t of the ejected wave experience less than 2 π_mV-2x') β/2 phase angle variations；

   (l-x)/v+t_m/2+x/v≤t≤t_m+x/v

   $\mathrm{\&delta;}=ar\cos \frac{e^{{\mathrm{\&alpha;x}}^{\&prime;}}+cos\left(2\mathrm{\&beta;}x\right)e^{-{\mathrm{\&alpha;x}}^{\&prime;}}}{\sqrt{{\&lsqb;e^{{\mathrm{\&alpha;x}}^{\&prime;}}+cos\left(2\mathrm{\&beta;}x\right)e^{-{\mathrm{\&alpha;x}}^{\&prime;}}\&rsqb;}^2+{\&lsqb;e^{-{\mathrm{\&alpha;x}}^{\&prime;}}sin\left(2\mathrm{\&beta;}x\right)\&rsqb;}^2}}$

   0≤δ≤π

   X '=l-x

   Wherein,

   As max [U₁(x,t),U₂(x,t),U₃(x, t)] it is maximum when, the x for solving is cable highest and bears voltage location.