JPS6217452B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a digital protective relay system for protecting power transmission lines of a power system.

Protective relay devices (hereinafter referred to as relays) that protect power systems are becoming more and more important due to the expansion of power systems, increases in power supply capacity and short-circuit capacity, ultra-high voltage of power transmission lines, longer distances, cables, etc. Improvements in judgment speed and accuracy were required, and as technology progressed, relays evolved from early electromagnetic relays to transistor relays. Currently, with the advent of microcomputers, computer relays are being developed in various fields using a digital method, which is different from the conventional analog method, and various digital protection methods are being proposed.

However, most of the digital protection systems that have been proposed so far, including conventional analog relays, have a protection principle based on AC theory that focuses on a single fundamental frequency component. Therefore, if other frequency components are superimposed on the input, a large error will result, leading to malfunction or malfunction. To avoid this, it is necessary to install a filter at the input stage to remove components other than the fundamental frequency, and logically, an excessive filter delay of one period of the fundamental frequency (20 ms at 50 Hz) is generated, which is caused by the delay of the relay. This was the main cause of delay in operation time. Furthermore, since the filter is the main factor that determines the accuracy of the relay, the design of the filter determines the performance of the relay in terms of operating speed and operating accuracy.

On the other hand, in electric power systems, due to the ultra-high voltage of power transmission lines and the increase in capacitance due to the expansion of cable systems, extremely severe transient phenomena occur when an accident occurs. Moreover, this transient phenomenon tends to last for quite a long time because the system time constant has become longer due to the decrease in line resistance. For this reason, the voltage and current input to the relay at the time of an accident will have a distorted waveform with a long time constant and a large distortion factor, and in order to accurately identify an accident, it is unavoidable to install a filter that faithfully passes only the fundamental wave. .

However, as short-circuit capacity increases and power transmission lines become longer distances, faster fault removal is required to maintain and improve transient stability, and relays are also required to operate at higher speeds. . Therefore, the conventional relay principle based on AC theory has an essential defect in satisfying such requirements because it has a transient delay of the filter corresponding to one period of the fundamental wave.

Further, in a conventional distance relay, impedance has been expressed as Z=R+jωL, where resistance is R and inductance is L in a distributed constant circuit. However, ignoring the capacitance C,
Especially in long-distance overhead lines and cable systems, distance relays have large errors and are undesirable.

The present invention has been made in view of the above points, and is based on a new principle based on time, which has a limited operating time in conventional distance relays based on AC theory based on a single frequency. By deriving this, the present invention is applied to provide a high-speed, high-precision distance relaying method without neglecting capacitance.The present invention will be explained in detail below in comparison with a conventional example.

First, we will discuss partial differential equations for power transmission lines with distributed constants.

Figure 1 is an equivalent circuit diagram for a single power transmission line, and shows the inductance L, which is a distributed constant per unit length.
[H/Km], resistance R [Ω/Km], capacitance C
It shows how [H/Km] and conductance G [/Km] are distributed along the track. In the figure e(o,
t), i(o, t) are voltage and current at position x=0 and time t, and are known or measured quantities with respect to time t. e(x, t) and i(x, t) are the voltage and current at the power transmission line position x=x and time t, and it is well known that these satisfy the following partial differential equation.

A solution is obtained by integrating this partial differential equation with respect to x and taking into account the boundary conditions of x. As a boundary condition x=
Using the voltage and current at point o, and assuming position x = point o as the relay installation point, this solution describes the behavior of voltage e (x, t) and current i (x, t) at position x = x. Voltage e (o, t) and current i (o, t) at the relay installation point
t).

In equation (1), if the time partial differential operator ∂/∂ _t is expressed as a matrix by P, the following is obtained.

here Then, for u, the first-order ordinary differential equation of x is as follows.

−d/d _x u(x, t)=(A+BP)u(x, t)... (3) When equation (3) is solved taking into account the boundary conditions, the following equation is obtained.

u (x, t) = ε ^{- (A + BP)} u (O, t) ... (4) Here, when ε ^{- (A + BP)} is expanded by Taylor and substituted into equation (4), the following equation is obtained. .

u (x, t) = u (o, t) - (A + BP) u (o, t) x + (A + BP) ² u (o, t) x ² /2〓 - (A + BP) ³ u
^{( o , t ) _ _ _ _ _ _} )P ² +B ³ P ³ , so by substituting this into the previous equation, u(x, t) = u(O, t) - {Au(O, t) + B∂/∂ _t u(O, t)}x + {A ² u(O, t)+(AB+BA)∂/∂ _t u(O, t)+B ² ∂ ² /∂ _t2 u(O, t)}x ² /2〓 −{A ³ u(O, t) + (A ² B+ABA+BA ² ) ∂/∂ _t u(O, t) + (AB ² +BAB+B ² A) ∂ ₂ /∂ _t u(O, t)+B ³ ∂ ₃ /∂ _t3 u(O, t)}x ³ /3〓+......(5).

From the above, we obtained the solution to the partial differential equation (5). Also
From equation (5), the third-order term or higher of x can be ignored, and the normal conductance can also be ignored, so the following equation is obtained.

e(x, t)=e(o, t)−{Ri((o, t)+L(∂/∂ _t i(o, t))}x +1/2{RC(∂/∂ _t e(t ))+LC(∂ ₂ /∂ _t2 e(t))}x ² ...(6) The present invention relates to a distance relay method, where the voltage is 0 at the fault point and the time partial differential of the voltage is also 0. Since it is based on the failure condition that (6)
From the equation, the following equation, which is the principle equation of the present invention, is obtained.

The process of obtaining equation (7), which is the principle equation of the present invention, has been described above.

On the other hand, the conventional AC theory uses an integration method in which time t is replaced by frequency ω when integrating equation (1).

A block diagram of a conventional distance relay based on such conventional AC theory is shown in FIG. This conventional distance relay inputs the voltage e(t) and current i(t) at the relay installation point obtained with respect to time, and converts these into the single frequency quantity E〓(ω) by the frequency conversion circuit 21.
The signal is Fourier-transformed into I〓(ω), and the next determination circuit 22 determines whether or not there is an accident using various relay principles.

A conventional distance relay based on such AC theory is composed of a frequency conversion circuit 21 and a determination circuit 22, and the frequency conversion circuit 21 is indispensable. For this reason, analog relays such as electromagnetic relays or transistor relays are equipped with frequency conversion circuits using LCR filters, and digital computer relays are equipped with digital filters. However, since the frequency of interest is the fundamental frequency (for example, 50 Hz, 60 Hz), the transient response time of this filter is about one cycle, and no matter how fast the processing time of the judgment circuit 22 is, there is a limit to the overall operating time of the relay. It was hot.

In order to improve the drawback of the limited operating time of conventional distance relays based on AC theory, the present invention introduces a new principle based on time as described above, and applies this to high speed and The object of the present invention is to provide a distance relay method that is highly accurate without neglecting capacitance, and is essentially suitable for digital computer type relays.

FIG. 3 is a basic block diagram of the distance relay method according to the present invention.
The voltage e(t) and current i(t) measured by a transformer and current transformer installed at an electric station are input, and a differentiation circuit 31 calculates e(t) and its time partial differential value ∂/∂ _t e (t), ∂ ² /∂ _t2 e(t), ∂ ³ /∂ _t3 e(t
); i(t) and its time partial differential value ∂/∂ _t i(t), ∂ ² /∂ _t2 i(
t), a determination circuit 32 determines the presence or absence of an accident using various relay principles, and an arithmetic circuit 33 calculates the distance x to the failure point. omitted.

Next, the arithmetic circuit 33 that calculates the distance x will be explained.

By combining the two equations (7), the following method of calculating the distance x is given.

(e ₀ i ₁ - e ₁ i ₀ ) - L (i ² ₁ - i ₀ i ₂ ) x + 1/2 {RC (e ₁ i ₁ - e ₂ i ₀ ) + LC (e ₂ i ₁ - e ₃ i ₀ )}x ² = 0 ...(8) (e ₁ i ₁ −e ₀ i ₂ )−R(i ₁ ² −i ₀ i ₂ )X+1/2 {RC(e ₂ i ₁ −e ₁ i ₂ ) +LC(e ₃ i ₁ −e ₂ i ₂ )}X ² = 0 ...(9) However, e ₀ = e (o, t) = e (t) i ₀ = i (o, t) =
i(t) e _o = ∂n/∂ _t ne(o, t) = ∂n/∂
_t te(t) i _o =∂n/∂ _t ni(o, t)=∂n/∂ _t ni(t
) n=1, 2, 3 Here, perform the following replacement.

By the above substitution, equations (8) and (9) are simplified to become equations (11) and (12), respectively.

a ₀ −a ₁ x＋a ₂ x ² =0 ……(11) b ₀ −b ₁ x＋b ₂ x ² =0 ……(12) Now, in the current distance relay, on the impedance plane, the horizontal axis is the resistance component ( It is well known that the vertical axis represents the reactance component (ωLx). Here, if we ignore the quadratic term of x in equations (12) and (12), equations (13) and (14) are obtained, respectively.

Lx= _a0 / _a1L ...(13) Rx= _b0 / _b1R ...(14) Furthermore, if _i0 =Isinωt and _e0 =Esin(ωt+θ), ωLx=IEsinθ/ ^I2 ... ...(15) Rx=IEcosθ/I ² ...(16)

As mentioned above, it can be seen that the current distance relay ignores the quadratic term of x in equations (11) and (12).

The present invention provides a highly accurate distance relay method by considering the quadratic term of x, that is, capacitance, and applies the principle equations (11) and (12). In addition, in order to correspond to the current distance relay, the solution (x _L ) of equation (10) is changed to the distance of the reactance component considering capacitance, and the solution (x _R ) of equation (11) is
Let be the distance of the resistance component considering capacitance.

To solve equations (11) and (12), use Newton's method or the like to obtain the following stable approximate solution.

x _L =a ₀ /a ₁ +a ₀ ² a ₂ /a ₁ (a ₁ ² -2a
₂ a ₀ )...(17) x _R =b ₀ /b ₁ +b ₀ ² b ₂ /b ₁ (b ₁ ² -2b
₂ b ₀ )...(18) The second term on the right side of equations (17) and (18) is a correction term based on consideration of capacitance.

Equations (17) and (18) are used as arithmetic expressions in the arithmetic circuit 33 of the present invention, and the distance x to the failure point is calculated from these.

Next, the determination circuit 32 that determines the presence or absence of an accident will be explained.

In equations (11) and (12), a ₂ and b ₂ are smaller than a ₁ and b ₁ , respectively, and the quadratic term of x serves as a correction term.

The determination formula for a reactance relay having the characteristics shown in FIG. 4 is expressed by the following determination formula (19) using formula (10).

a ₀ −a ₁ x ₁ + a ₂ x ₁ ² ≦0 ...(19) The determination formula for a resistance relay having the characteristics shown in Figure 5 is expressed by the following determination formula (20) using formula (11). .

b ₀ −b ₁ x ₁ +b ₂ x ₁ ² ≦0 (20) However, x ₁ is a setting value.

Equations (19) and (20) are used as the determination formulas in the determination circuit 32 of the present invention, and the presence or absence of an accident is determined based on these.

Finally, the differentiation circuit 31 will be explained.

The differentiating circuit 31 receives input data e(t), i(t)
Therefore, its time partial differential value i ₁ = ∂/∂ _t i (t), i ₂ = ∂ ²
/∂ _t2 i (t), e ₁ =∂/∂ _t e(t), e ₂ =∂ ² /∂ _t2 e(
t), e ₃ = ∂ ³ /∂ _t3 e(t), and calculate these time partial differential values as i ₀ =
i(t), e ₀ =e(t), and in this differentiation circuit 31, the time width required for this differentiation operation does not depend on the fundamental frequency of the system,
Since it can be relatively short, this differentiator circuit 3
The transient response time in No. 1 is also shortened, and the total relay operation time can be greatly shortened. Below is the differential circuit 3
1, the differential calculation method for deriving the time partial differential values of voltage e(t) and current i(t) is described as e(t), i
Instead of (t), we generally denote f(t) in digital form.

FIG. 6a shows that the sampling interval time is τ _s and that an odd number n (=2m−1; m is a natural number) of sampled data is approximated by an (n−1)th order curve.

Now, the (n-1)th order curve f(t)=a _o-1 t ^n-1 + a _o-2 t ^n-2 +...+a ₁ t+a ₀ ...(21) is shown by the dashed line in the figure. So time - (m-1)
τ _s , ..., −τ _s , 0, τ _s , ..., (m-1) τ _s
So A _-(n-1) , ..., A _-1 , A ₀ , A ₁ , ..., A _(n-1
) , then A _-(n-1) = f(-(m-1)τ _s : A _-1 = f(-τ _s ) A ₀ = f(o) A ₁ = f(τ _s ) 〓 A _(n-1) = f((m-1)τ _s ), and there are n (=2m-1) unknowns (a ₀ , a ₁ ,...
..., _ao-1 ), and there are (2m-1) equations, and _a0 , _a1 , ..., _ao-1 can be determined.

The differential value of f(t) at time t=0 is d/d _t f (t) | _t=0 = a ₁ , ..., d ^k /d _t kf(t) | _t=0 =
k 〓a _k ,..., dn-1/d _t n-1f(t) | _t=0 =(
n-1) 〓a _o-1 .

Figure 6b shows the approximation by an (n-1)th order curve from an even number n (= 2m) sampling data, but the difference from Figure 6a is that (n- 1) As shown in the dashed line in the figure, the following curve shows time - (m-1/2)τ _s , ..., -τ _s /2,
It _is to take the values of A _-n , ..., A _-1 , A ₁ , ..., A _n at τ s /2, . . . , (m-1/2) τ _s . In this case too, t=
The differential value at 0 is found in the same manner as described above.

Next, cubic curve approximation and quartic curve approximation will be shown as examples.

Cubic curve approximation 4 Indicative curve approximation Such calculations are performed for each input quantity e(t), i
It should be applied to (t).

The differential values necessary for the present invention are e ₀ = e(o), i ₀ = i
(o), e ₁ = ∂/∂ _t e(t) | _t=0 i ₁ = ∂/∂ _t i
(t) | _{t =0} , e ₂ = ∂ ² /∂ _t2 e(t) | _t=0 i ₂ =∂ ² /∂ _t
2 i(t) | _{t =0} , e ₃ = ∂ ₃ /∂ _t3 e(t) | Since _t=0 (21)
This means that the equation may be a cubic curve.

In this way, the transition time of the differentiating circuit 31 is determined by the number of samples required for differential operation, and the method using four points approximation (cubic curve approximation) is 4τ _s , and the method using five points approximation (quartic curve approximation) is 5τ _s becomes. Although τ _s is determined by the sampling frequency, f _s is determined by the reduction of aliasing errors associated with digital sampling and the sampling theorem. Now, when performing digital protection by pre-installing a low-pass filter that attenuates frequencies above 600Hz and performing 1200Hz sampling,
τ _s =1/f _s ≒0.833ms. Therefore, in the method of the present invention, the transient response time is at most 5τ _s =4.165 ms.
However, the transient response time of the low-pass filter is approximately 1.66 m.
s is added. In contrast, conventional distance relays have a transient response time of approximately 20 ms (provided the fundamental frequency is 50 Hz) due to digital filters and the like. As can be seen from this design example, the distance relay of the present invention is capable of very high-speed determination.

FIG. 7 shows a specific example to which the present invention is applied, and in particular, a case will be described using the above-mentioned cubic curve approximation as an example.

The analog input amount e(t) is passed through the low-pass filter 7.
1. Input to multiplexer 73 through sample hold circuit 72, and analog input amount i
(t) is input to the multiplexer 73 through the low-pass filter 74 and sample hold circuit 75, and the output of this multiplexer 73 is input to the analog
A digital conversion section 76 digitizes the data. Then, in the storage circuit 77, the digital values of the voltage and current from 3τ _s ago are stored as E _-2 , I _-2 , and the digital value from 2τ _s ago by the output of the analog-to-digital converter 76 .
E _-1 , I _-1 , τ _s The previous digital values E ₁ , I ₁ and the current digital values E ₂ , I ₂ are stored, and the differentiating circuit 78 converts the digital values stored in the storage circuit 77 into the (22 ) equation to determine e ₀ , i ₀ , e ₁ , i ₁ , e ₂ , i ₂ , e ₃ by calculation, and input these to the conversion circuit 79 , where the differentiation circuit 78 calculates Applying the calculated differential values to equation (10), a ₀ , b ₀ , a ₁ ,
b ₁ , a ₁ , b ₁ , a ₂ , b ₂ are determined, the arithmetic circuit 80 calculates the distance x to the accident point using equation (17) or (18), and the determination circuit 81 calculates the distance x from (19) or ( 20)
The presence or absence of an accident is determined using the following formula.

By using the distance relay method according to the present invention described above, the following dramatic improvements in performance can be achieved.

(1) Unlike conventional methods, a frequency conversion circuit (filter) is not required, and therefore high-speed accident determination is possible.

(2) Highly accurate accident determination is possible by considering the capacitance C, which is a distribution constant of the power transmission line, without ignoring it.

(3) Accurate response even if the input waveform is a distorted wave.

(4) Accurate response even when there is an attenuated DC component.

(5) It can also be installed in DC power transmission systems, in which case it can accurately respond to transient phenomena that occur during accidents.

(6) There is no need for a digital filter that requires complex calculations, and the algorithm is simplified.

[Brief explanation of the drawing]

Figure 1 is an equivalent circuit diagram of a distributed constant line, Figure 2 is a basic block diagram of a conventional distance relay, Figure 3 is a basic block diagram of a distance relay system according to the present invention, and Figure 4 is a basic block diagram of a distance relay system according to the present invention.
Figure 5 is a characteristic diagram of a reactance relay, Figure 5 is a characteristic diagram of a resistance relay, Figures 6a and b are diagrams for explaining differential operations when the number of samples is odd and even, respectively. This is a block diagram showing a specific example to which the present invention is applied, in which 31 is a differentiation circuit, 32 is a determination circuit, 33 is an arithmetic circuit, 71 and 74 are low-pass filters, and 72, 7
5 is a sample hold circuit, 73 is a multiplexer, 76 is an analog-digital converter, 77 is a storage circuit, 78 is a differentiation circuit, 79 is a conversion circuit, 8
0 is an arithmetic circuit, 81 is a determination circuit, L is an inductance, R is a resistance, C is a capacitance, x is a distance to a failure point, e(t) is a voltage, and i(t) is a current.

Claims (1)

[Claims] 1. An analog quantity obtained from a protected power transmission line of a power system is converted into a digital quantity by an analog-digital converter, and the voltage e obtained with respect to time t is
(t), and a differentiation circuit for differentiating the digital values of current i(t), and this differentiation circuit derives the time partial differential value from the voltage e(t) and current i(t), and calculates In the circuit, voltage e(t) and current i
(t), its derived time partial differential value, and the inductance L, which is the distribution constant per unit length of the power transmission line,
From the resistance R and capacitance C, the following equations (1) and (2) are obtained: e(t)−{Ri(t)+L(∂/∂ _t i(t))}x+1/2{RC(∂/∂ _t e(t)) +LC(∂ ₂ /∂ _t2 e(t))}x ² =0 ...(1) ∂/∂ _t e(t)−{R(∂/∂ _t i(t))+L( ∂ ₂ /∂ _t2 i(t))}x+1/2{RC(∂ ₂ /∂ _t2 e(
t)) +LC(∂ ₃ /∂ _t3 e(t))}x ² =0 ...(2) is used to calculate the distance x to the failure point or define the range in which the distance x exists. Distance relay method characterized by: 2 The following equation (3) obtained by combining equations (1) and (2),
Equation (4), that is, {e(t)(∂/∂ _t i(t))−(∂/∂ _t e(t))i(t)}−L{(∂/∂ _t i(t)) ² −i(t) (∂ ² /∂ _t2 i(t))}x+1/2[RC{(∂/∂ _te (t))(∂/∂ _t i(t))−(∂ ² /∂ _t2 e(
t))i(t)} +LC{(∂ ² /∂ _t2 e(t))(∂/∂ _t i(t))−(∂ ³ /∂ _t3 e(t))i(t)}]x ² = 0 ...(3) {(∂/∂ _t e(t))(∂/∂ _t i(t))-e(t)(∂ ² /∂ _t2 i(t))}-R{( ∂/∂ _t i(t))
² −i(t) (∂ ² /∂ _t2 i(t)}x+1/2[RC{(∂ ² /∂ _t2 e(t))(∂/∂ _t i(t)) −(∂/∂ _t e(t))(∂ ₂ /∂ _t2 i(t))}+LC{(∂ ³ /∂ _t3 e(t))(∂/∂ _t i(t)) −(∂ ₂ /∂ _t2 e(t )) (∂ ₂ /∂ _t2 i(t))}] x ² = 0...Using (4), calculate the distance x to the failure point and define the range in which the distance x exists. 3. When deriving the time partial differential values of voltage e(t) and current i(t), n values sampled at equal intervals are used. From the digital signals f ₁ , f ₂ , ..., f _o , the following (5)
formula, i.e. Here, d ^k /dt ^k f(t) | _t=0 : k-th at time t=0
A patent claim characterized in that the time partial differential value of f(t) is determined using the following time partial differential values b _k , C _kJ : constant k=0, 1, ..., n-1. range 1
Distance relay method described in Section 2 or Section 2.