JPS6315811B2 - - Google Patents

Description

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

Protective relay devices (hereinafter referred to as relays) that protect power systems are used to expand power systems, increase power supply capacity and short-circuit capacity, make power transmission lines ultra-high voltage, extend distances,
With the use of cables, etc., there was a demand for improvements in relay performance, that is, accident determination speed and accuracy, and as technology progressed, relays evolved from the 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, including traditional analog relays,
Most of the digital protection methods proposed so far have been 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 occur, 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. Logically, a filter transient delay of one period of the fundamental frequency (20 ms at 50 Hz) is generated, and this is 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.

The present invention was made in view of these points,
Conventional relays based on AC theory based on a single frequency had a limited operating time.
By deriving a new principle based on time, the present invention aims to provide a high-speed, high-precision differential protection relay system that is essentially suitable for digital computer type relays. will be explained in detail while comparing with the 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 line. In the figure, e(0,
t) and i(0, t) are voltage and current at position x=0 and time t, and are known quantities 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 0, and setting the relay installation point at point x = 0, this solution describes the behavior of voltage e (x, t) and current i (x, t) at point x = x. It is expressed by the voltage e (0, t) and the current i (0, t) at the relay installation point.

In equation (1), let the time partial differential operator ∂/∂t be p. If we express it as a matrix, we get the following.

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

−d/dxu(x, t)=(A+Bp)u(x, t)...(3
) Solving equation (3) taking into account the boundary conditions yields the following equation.

u(x, t)=ε ^-(A+Bp) u(0, t) ...(4) Here, ε ^-(A+Bp) When u is (Taylor expanded and substituted into equation (4)), the following equation is obtained. Become.

u(x,t)=u(0,t)−(A+Bp)u(0,t)
x+(A+Bp) ² u(0, t)x ² /2! -(A+Bp) ³ u (0, t) x ³ /3! +…… Also, (A+Bp) ² =A ² +(AB+BA)p+B ² p ² (A+Bp) ³ =A ³ +(A ² B+ABA+BA ² )p+(AB ²
+BAB+B ² A)p ² +B ³ p ³ , so by substituting this into the previous equation, u(x, t)=u(0, t)−{Au(0, t)+B∂/
∂tu(0,t)}x+{A ² u(0,t)+(AB+BA)∂
/∂tu
(0, t) +B ² ∂ ² /∂t ² u(0, t)}x ² /2! −{A ³ u(0,
t) + (A ² B + ABA + BA ² ) ∂ / ∂tu (0, t) + (AB ² + BAB + B ² A) ∂ ² / ∂t ² u (0, t) + B ³ ∂ ³
/∂t ³ u(0, t)}x ³ /3! +…………(5) becomes.

From the above, the solution to the partial differential equation (5) was obtained. In addition, in equation (5), terms of the third or higher order of x are small and can be ignored, so the following equation is obtained.

By focusing on the current i(x, t) from equation (6) and reversing its sign, the following equation, which is the principle equation of the present invention, is obtained.

i(x,t)+i(0,t)−{Ge(0,t)+C∂/
∂te(0, t)}x+{GRi(0, t)+(CR+GL)∂
/∂ti(0,
t) +CL∂ ² /∂t ² i(0, t)}x ² /2! =0...(7) Further, by partially differentiating equation (7) with respect to time t, the following equation, which is another principle equation of the present invention, is obtained.

∂/∂ti(x,t)+∂/∂ti(0,t)−{C∂/
∂te(0,t)+C∂/∂te(0,t)}x+{GR∂
/∂ti(0,t)+(CR+GL) ^∂2 / ^∂t2i (0,t)+ ^CL∂3 / ^∂t3i
(0, t)}x ² /2! =0...(8) The process of obtaining equations (7) and (8), which are the principle equations of the present invention, has been described above.

On the other hand, in conventional AC theory, when integrating Equation (1) above, a method of integration is used in which time t is replaced with frequency ω by Fourier transform, and the result is Equation (9) below. is well known.

I〓(x,ω)＋I〓(0,ω)−(G+jωc)
xE〓(0, ω)=0……(9) However, the quadratic term of x is omitted, and T is one period, I〓(x, ω)=1/T∫ ^T ₀ −i(x, t) ε ^-j 〓 ^t dt I〓(0, ω)=1/T∫ ^T ₀ i(0, t)ε ^-j 〓 ^t dt E〓(0, ω)=1/T∫ ^T ₀ e(0, t) ε ^-j 〓 ^t dt.

A block diagram of a conventional relay based on such conventional AC theory is shown in FIG. This conventional relay inputs the voltage e(t) and current i(t) at the relay installation point obtained with respect to time t, and converts them into single frequency quantities E〓(ω), I〓( ω), and the next determination circuit 22 determines whether or not an accident has occurred using various relay principles.

A conventional relay based on such conventional 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, if the frequency of interest is the fundamental frequency (for example, 50
Hz, 60Hz), the transient response time of this filter is about one cycle, and no matter how fast the processing time of the determination circuit 22 is, there is a limit to the overall operating time of the relay.

In order to improve the disadvantage of the limited operating time of conventional 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 high speed relays. The present invention provides a differential protective relay system that is accurate and essentially suitable for digital computer type relays.

FIG. 3 shows an embodiment of the differential protection relay system according to the present invention, in which 31 indicates a protected power transmission line;
32 is a current transformer, 33 is a voltage transformer, 34 is a current transformer, 35a to 35c are analog-to-digital converters, 36 is a transmitter for transmitting the output of the analog-to-digital converter 35c, and 37 is a receiver. hand,
Current i ₂ (t) information is transmitted from the transmitter 36 to the receiver 37 using microwaves or the like. here,
Although a case is shown in which microwaves or the like are used as the information transmission path, optical fibers or the like may also be used. 38 is an analog-digital converter 35
A, 35b and the output of the receiver 37 are supplied to the computer relay. Here, current transformer 3
2 and voltage transformer 33 are respectively i ₁ (t) and e ₁ (t), and the current of the other electrical station obtained by current transformer 34 is
i ₂ (t), these are sampled by analog-digital converters 35a to 35c and sent as digital quantities to computer relay 38.
is input. This computer relay 38 has built-in functional blocks as shown in FIG. As can be seen from FIG. 4, the voltage e ₁ (t) and currents i ₁ (t) and i ₂ are applied to the computer relay 38 as described above.
When each piece of digital information (t) is input, first, the differentiating circuit 41 partially differentiates each piece of digital information with respect to time t, and the time partial differential value necessary for the judgment operation in the judgment circuit 42 is determined by the judgment circuit. 42, the determination circuit 42 determines the presence or absence of an accident using various relay principles, and outputs the determination result.

Next, depending on which judgment formula is used in the judgment circuit 42 for operation calculations based on the program of the differentiation circuit 41 and the judgment circuit 42 in the computer relay 38, the following [] to
The case [] will be explained separately.

[] In equation (7), if x=l, i ₁ (t)=i
(0, t), e ₁ (t) = e (0, t), i ₂ (t) = i
(l, t), d/dti ₁ (t) = ∂/∂ti ₁ (t), d/dte ₁ (t) = ∂/∂te ₁ (t), so the differential amount I _A is ( 10) It can be found as shown in the formula.

I _A = i ₂ (t) + i ₁ (t) - {Ge ₁ (t) + Cd/dte ₁
(t)}l+{GRi ₁ (t)+(CR+GR)d/dtd ₁ (t)
+CLd ² /dt ² i ₁ (t)}l ² /2! ...(10) Therefore, L, R, C, and G are distribution constants per unit length of the power transmission line, L is inductance, R is resistance, C is capacitance, and G is conductance. Also, l is the distance of the protected power transmission line.

If there is no accident inside the transmission line, I _A = 0 ... (11) If there is an internal accident, I _A ≠ 0 ... (12) Therefore, with K ₀ as a constant, ｜I _A ｜≧K ₀ ... (13), it is determined that it is an internal accident.

Therefore, when the determination circuit 42 applies equation (13), the computer relay 38 first inputs e ₁ (t), i ₁ by the program in the differentiating circuit 41.
(t), i ₂ (t) time differential values d/dte ₁ (t), d/dti ₁ (t), d ² /dt ² i ₁ (t), and these differential values and e ₁ ( t), i ₁
(t) and i ₂ (t) are input to the determination circuit 42 as shown in the figure, and the determination circuit 42 calculates the operating amount I _A of the equation (10) using a program,
When the magnitude of the absolute value of this calculation result is greater than or equal to a predetermined value _K0 , that is, when formula (13) is satisfied, it is determined that there is an internal fault in the power transmission line, and a trip command is output. In other words, the computer relay 38 performs the calculation of equation (10), and the magnitude of the absolute value of the calculation result is a predetermined value.
When K _{is 0} or more, the computer relay determines that there is an internal fault in the power transmission line and outputs a trip command.

[] When the above equation (10) is partially differentiated with respect to time t, we get
The next differential amount I _B is found as shown in equation (14).

I _B = d/dti ₂ (t) + d/dti ₁ (t) - {Gd/dte ₁ (
t)+Cd ² /dt ² e ₁ (t)}l+{GRd/dti ₁ (t) + (CR+GL)d ² /dt ² i ₁ (t)+CLd ³ /dt ³ i ₁ (t)}
l ² /2! ...(14) In this case, as in the case [], when |I _B |>K ₁ ...(15) with K ₁ as a constant, it is determined that it is an internal fault in the power transmission line.

Therefore, in the computer relay 38, e ₁ is first set by the program in the differentiating circuit 41.
(t), i ₁ (t), i ₂ (t) time differential value d/dte ₁ (t), d ² /dt ² e ₁ (t), d/dti ₁ (t), d ² /dt ² i ₁ (t), d ³ /dt ³ i ₁ (t), and d/dti ₂ (t) are calculated, and their differential values are output to the determination circuit 42. In the determination circuit 42, the differential amount I _B of the above equation (14) is calculated by the program, and when the magnitude of the absolute value of the calculation result is larger than the predetermined value _K1 , that is, when the equation (15) is satisfied, the transmission is stopped. It determines that there is an internal wire accident and outputs a trip command. In other words, the computer relay 38 performs the calculation of equation (14), and when the magnitude of the absolute value of the calculation result is greater than the predetermined value _K1 , the computer relay 38
determines an internal fault in the power transmission line and outputs a trip command.

[] From the differential amount I _A in equation (10) above and the differential amount I _B in equation (14) above, the sum of their absolute values is K ₃ and K ₄ as constants, |I _A |+K ₃ | I _B ｜K ₄ ……(16) When it is determined that there is an internal accident in the power transmission line. According to the judgment formula (16), the value at the time of an internal accident is smoothed, so it is possible to judge an internal accident with higher reliability than the above-mentioned judgment formulas (13) and (15). .

Therefore, in the computer relay 38, e ₁ is first set by the program in the differentiating circuit 41.
(t), i ₁ (t), i ₂ (t) time differential values d/dte ₁ (t), d ² /dt ² e ₁ (t), d/dti ₁ (t), d ² /dt ² i ₁ (t), d ³ /dt ³ i ₁ (t), d/dti ₂ (t), and their differential values and e ₁ (t), i ₁
(t) and i ₂ (t) are input to the judgment circuit 42, and the judgment circuit 42 uses the above (10) according to the program.
Calculate the differential amounts I _A and I _B of the formula and the above formula (14), and further calculate the sum of their respective absolute values, that is, the left side of formula (16), and when the result of the calculation is greater than or equal to the predetermined value _K4 , That is, when formula (16) is satisfied, it is determined that there is an internal fault in the power transmission line, and a trip command is output. In other words, the computer relay 38 calculates equations (10) and (14), and when the sum of the absolute values of the differential amounts I _A and I _B (the left side of equation (16)) is greater than or equal to the predetermined value _K4 , , determines that there is an internal fault in the power transmission line, and outputs a trip command.

[] From the differential amount I _A of the above equation (10) and the differential amount I _B of the above equation (14), the sum of the respective square values is I _A ² +K ₅ I _B with K ₅ and K ₆ as constants. ² K ₆ ...(17) When it is determined that there is an internal accident in the power transmission line. When using the judgment formula of equation (17), the value at the time of an internal accident is smoothed as in the case of [], so it is more reliable than the judgment equations of equations (13) and (15) above. It is possible to determine internal accidents with a high degree of accuracy.

Therefore, in the computer relay 38, e ₁ is first set by the program in the differentiating circuit 41.
(t), i ₁ (t), i ₂ (t) time differential values d/dte ₁ (t), d ² /dt ² e ₁ (t), d/dti ₁ (t), d ² /dt ² i ₁ (t), d ³ /dt ³ i ₁ (t), d/dti ₂ (t) are calculated, and these partial differential values and e ₁ (t), i ₁
(t) and i ₂ (t) are input to the determination circuit 42, and the determination circuit 42 determines the above by a program.
Calculate the differential amounts I _A and I _B of equations (10) and (14) above, and then calculate the sum of their respective squares, that is, the left side of equation (17), and if the calculation result is a predetermined value K ₆ or more. In other words, when formula (17) is satisfied, it is determined that there is an internal fault in the power transmission line, and a trip command is output. In other words, the computer relay 38 calculates equations (10) and (14), and when the sum of the squares of the differential amounts I _A and I _B is greater than or equal to a predetermined value _K6 , it is determined that there is an internal fault in the power transmission line. , outputs a trip command.

In the above [] to [], if the conductance G can be ignored depending on the type of transmission line, G=
0, and if the line length is short, 2 of l of I _A and I _B
Since the next term can be ignored, it can be done in a simplified form without any calculations. Furthermore, in order to avoid malfunctions due to proportional errors in current transformers, etc. when large currents pass during an external fault, it is also possible to determine the amount of suppression using a judgment formula.

Finally, the differential circuit 41 built in the computer relay 38 has a voltage e ₁ (t), a current i ₁ (t),
It calculates the time differential value of i ₂ (t), and the time width required for the differential calculation does not depend on the fundamental frequency of the system and can be relatively short, so the transient response time in the differentiator circuit 41 is also short. Therefore, the total relay operation time can be significantly shortened.

Below, in the differentiating circuit 41, voltage e ₁ (t) and current
The differential calculation method for deriving the time partial differential values of i ₁ (t), i ₂ (t) is generally applied digitally with respect to f(t) instead of e ₁ (t), i ₁ (t), i ₂ (t). It is shown in the method.

In Figure 5a, the sampling interval time is τ _s , and an odd number of sampled n (= 2m _-1 ; m is a natural number)
This shows how the data is approximated by an (n _-1 )th order curve.

Now, (n _-1 )th curve f(t)=a _o-1 t ^n-1 +a _o-2 t ^n-2 +......+ait+a
₀ ...(18) is the time -(m- ¹ ) as shown by the dashed line in the figure.
τ _s , ......, −τ _s , 0, τ _s , ......, (m _-1 ) with τ _s
A _-(n-1) , ......, A _-1 , A ₀ , A ₁ , ......, A _(n-1)
If we take the value of So, there are n (=2m _-1 ) unknowns (a ₀ , a ₁ ,...
..., a _o-1 ), and there are (2m _-1 ) equations,
a ₀ , a ₁ , ......, a _o-1 can be determined.
The differential value of f(t) at time t=0 is d/dtf(t) | _t=0 = a ₁ , d ^k /dt ^k f(t) | _t=0 = k! _ak ,
......,d ^n-1 /dt ^n-1 f(t) | _t=0 = (n _-1 )! a _o-1 .

Figure 5b shows the approximation by an (n _-1 )th order curve from an even number of sampling data n = (2m), but the difference from Figure 5a is that (n _{- 1} ) As shown in the dashed line in the figure, the following curve shows the time −(m−1/2)τ _s , ……, −τ _s /2, τ _s /
2, ......, (m-1/2) τ _s to take the value of A-m, ......, A _-1 , A ₁ , ......, A _n . In this case as well, the differential value at t=0 is found in the same manner as described above.

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

Quadratic curve approximation Cubic curve approximation These calculations are performed for each input quantity e ₁ (t), i ₁ (t), i ₂
(t) may be applied.

The differential value required for the present invention is ∂/∂te ₁ (t) | _t=0 , ∂ ²
/∂t ² e ₁ (t) | _t=0 , ∂/∂ti ₁ (t) | _t=0 , ∂ ² /∂t ² i ₁ (
t) | _t=0 , ∂ ³ /∂t ³ i ₁ (t) | _t=0 , ∂/∂ti ₂ (t) | _t=0 , so the quadratic curve approximation of equation (20) may be used. It turns out.

In this way, the transition time of the differentiating circuit 41 is determined by the number of samples required for differential operation, and the method using three-point approximation (quadratic curve approximation) is 3τ _s , and the method using four-point approximation (cubic curve approximation) is 4τ _s . τ _s is determined by the sampling frequency, but 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 4τ _s =3.332 ms. However, the transient response time of the low-pass filter is approximately 1.66ms.
is added. On the other hand, conventional relays have a transient response time of about 20 ms (when the fundamental frequency is 50 Hz) due to digital filters and the like.

As can be seen from this design example, the relay of the present invention is capable of very high-speed determination.

By using the present invention described above, it is possible to provide a digital differential protective relay system having the following high performance.

(1) There is no need for a frequency conversion circuit (filter) as in the past, and therefore high-speed accident determination is possible.

(2) Highly accurate accident determination is possible.

(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) A digital filter that uses complicated calculations is no longer necessary, and the algorithm is simplified.

[Brief explanation of the drawing]

Fig. 1 is an equivalent circuit diagram of a distributed constant line, Fig. 2 is a basic block diagram of a conventional differential relay, Fig. 3 is a configuration diagram showing an embodiment of the differential protection relay system according to the present invention, and Fig. 4 The figure is a functional block diagram showing the configuration of the computer relay in FIG. 3, and FIGS. 32 and 34 are current transformers; 33 is a voltage transformer; 35 is an analog-to-digital converter; 36 is a transmitter; 37 is a receiver;
is a computer relay, 41 is a differentiation circuit, 42 is a judgment circuit, L is inductance, R is resistance, C is capacitance, G is conductance, l is the length of the power transmission line, i ₁ (t), i ₂ (t) are The current, e ₁ (t) is the voltage, and I _A and I _B are the differential amounts, respectively.

Claims (1)

[Claims] 1. A voltage e ₁ (t) obtained with respect to time t by converting an analog quantity of the own electric power station obtained from a protected power transmission line of the power system into a digital quantity in an analog-digital converter, Input the current i ₁ (t) and the current i ₂ (t) related to time t of the other electric station transmitted by the transmission means and converted into a digital amount by the analog-digital converter, and calculate each input value. The time differential values of voltage e ₁ (t), current i ₁ (t), i ₂ (t) are derived from this differentiation circuit, and these and the From the distributed constants inductance L, resistance R, capacitance C, conductance G, and transmission line length l, the following differential amount I _A is determined in the determination circuit, i.e., i ₂ (t) + i ₁ (t) − {G _e1 (t)+Cd/dte ₁ (t)
}l + {GRi ₁ (t) + (CR + GL) d/dti ₁ (t) + CLd ² /
dt ² i ₁ (t)}l ² /2! At the same time, the differential amount I _A is partially differentiated to obtain the differential amount I _B of the following formula, that is, d/dti ₂ (t) + d/dti ₁ (t) − {Gd/dte ₁ (t)
+Cd ² /dt ² e ₁ (t)}l+{GRd/dti ₁ (t) +(CR+GL)d ² /dt ² i ₁ (t)+CLd ³ /dt ³ i ₁ (t)}
l ² /2! , and from the differential amounts I _A and I _B , when the magnitude of I _A ² + K′I _B ² (here, K′ is a constant) is greater than a predetermined value,
A differential protection relay system that is characterized by determining an internal fault in a power transmission line.