JP3099377B2 - Power calculation method and protection relay using the method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a power calculation method used for a protection relay or the like that detects and responds to power flowing through a power system, and a protection relay using the power calculation method.

[0002]

2. Description of the Related Art A protection relay which receives power flowing through a power system as an input is adapted to respond only to a fundamental wave component so as not to perform unnecessary operations due to harmonic components included in current and voltage. As one method for detecting the fundamental wave component, a Fourier integration method is sometimes applied. In other words, assuming that the current is a current, the current i (t) is represented by an effective value I1 of the fundamental component and an effective value In (n = 2,
3,…)

[0003]

(Equation 1)

[0004] The fundamental cosine component of the current I1c = I1cosθ1 can be expressed by the following Fourier series:

[0005]

(Equation 2)

The fundamental sine component of current I1s = I1sin θ1
Is

[0007]

(Equation 3)

Can be calculated by Here, i (t) is the time tm (m = 0, 1,...,
Assuming that sampling is performed every 2k-1), the above integral equation is expressed as follows.

[0009]

(Equation 4)

[0010]

(Equation 5)

Here, im is a sampling value at time tm. The above is the description of the current, but the voltage can be similarly expressed. The results are as follows:

[0012]

(Equation 6)

[0013]

(Equation 7)

## EQU1 ## Generally, complex power Pa is represented by Pa = VI ^*, where ^* represents complex conjugate. Since V and I are expressed as V = Vc + jVs I = Ic + jIs and are decomposed into a real part and an imaginary part, the complex power is Pa = (Vc + jVs) (Ic-jIs) = (VcIc + VsIs) + j (VsIc-VcIs) Is calculated. The first term on the right side of the above equation represents active power P, and the second term represents reactive power Q. P = VcIc + VsIs Q = VsIc−VcIs Considering only the fundamental wave, P = V1cI1c + V1sI1ss (5) Q = V1sI1c−V1cI1s ‥‥ (6)

[0015]

However, according to the method of calculating the active power and the reactive power, when the frequency fluctuates despite the fact that the sampling period is fixed, the above (1) to (4) There is a drawback that the error is increased depending on the condition when calculated by the formula. If the frequency fluctuates, the instantaneous value of the current i (t) is

[0016]

(Equation 8)

## EQU1 ## Here, I1 is the effective value of the fundamental wave, ω is the nominal angular frequency, Δω is its variation, and θ1 is the phase. However, it is assumed that the current i (t) mainly includes a fundamental wave component, and higher-order terms are ignored. Here, one period 2π
When i (t) is sampled at each time point where / ω is divided into 2k equal parts,

[0018]

(Equation 9)

## EQU1 ## Where ρ is

[0020]

(Equation 10)

Defined by By substituting im in equation (7) into equations (1) and (2),

[0022]

[Equation 11]

[0023]

(Equation 12)

## EQU1 ## here,

[0025]

(Equation 13)

[0026]

[Equation 14]

## EQU1 ## The same applies to voltage,

[0028]

(Equation 15)

[0029]

(Equation 16)

## EQU1 ## The active power P and the reactive power Q are

[0031]

[Equation 17]

[0032]

(Equation 18)

## EQU2 ## The third in [] of equation (12)
The term changes according to ρ, and the range of change (error) is

[0034]

[Equation 19]

Is as follows. If there is no frequency change, Δω = 0, so ρ = 1, and

[0036]

(Equation 20)

[0037]

(Equation 21)

Therefore,

[0039]

(Equation 22)

[0040]

(Equation 23)

Thus, the definition formula is as follows. However, as Δω increases or decreases, in other words, as ρ departs from 1, the amplitude expressed by the equation (14) cannot be ignored, and the error increases. Of course, if the sampling frequency is changed in accordance with the change in the frequency to make apparently Δω = 0, this problem is eliminated, but a device for constantly monitoring the frequency, for example, a PLL (phase locked loop)
Therefore, the circuit of the protection relay is inevitably complicated.

Accordingly, the present invention provides a power calculation method and a power calculation method which do not cause an error even when the frequency is changed, when the fundamental wave components of the voltage and the current are obtained by the Fourier integration method and the power is calculated based on them. It is an object to provide a protection relay using the method.

[0043]

In order to achieve the above object, a power calculation method according to the present invention comprises:
With respect to the nominal angular frequency ω of the fundamental wave included in the current, the target wave is sampled at each time point tm (m = 0, 1,...) Obtained by equally dividing one cycle by 2 k, and based on each sampled value im, vm The cosine components V1c, I1c of the fundamental waves of the obtained voltage and current,
The sine components V1s and I1s of the fundamental wave and the sampling value i
sampling value i at 90 ° phase shift from m, vm
c, V1c ', I1c' of the fundamental wave obtained from m and vm,
Using the sine components V1s 'and I1s' of the fundamental wave, the cosine components <V1c> and <I1c of the fundamental wave averaged by the following equation
>, The sine components <V1s> and <I1s> of the fundamental wave are obtained. <I1c> = 0.5 (I1c + I1s ′) <I1s> = 0.5 (I1s−I1c ′) <V1c> = 0.5 (V1c + V1s ′) <V1s> = 0.5 (V1s-V1c ') The power is calculated using the averaged value.

The protection relay of the present invention obtains power using the above-described power calculation method, and operates when a certain gap occurs between the power value and a reference level.

[0045]

[Operation] If the sampling value im of the target wave is written as shown in equation (7),

[0046]

(Equation 24)

Is as follows. Also, the value sampled shifted by k / 2 samples (90 °)

[0048]

(Equation 25)

Is as follows. By substituting into the above equations (1) and (2), we can write the following form.

[0050]

(Equation 26)

[0051]

[Equation 27]

Especially when there is no frequency change, since ρ = 1,

[0053]

[Equation 28]

[0054]

(Equation 29)

Therefore, a kind of averaging calculation method of <I1c> = 0.5 (I1c + I1s ') <I1s> = 0.5 (I1s-I1c') is conceivable. It is conceivable that the voltage V is averaged according to the following equation: <V1c> = 0.5 (V1c + V1s ') <V1s> = 0.5 (V1s-V1c')

As a result, using the equations (5) and (6), the active power <
P> and reactive power <Q>,

[0057]

[Equation 30]

[0058]

(Equation 31)

Is as follows. Considering the variation term of the averaged active power <P>, its amplitude is

[0060]

(Equation 32)

Is as follows. As described above, since the average value with the fundamental wave component obtained by using the sampling values im and vm having the 90 ° cut-out phases different from each other is taken, a factor of cos (ρπ / 2) is compared with the above-mentioned equation (14). Has occurred. | Cos (ρπ / 2) | can be ρ ≒ 1 in the range where the error Δω of the angular frequency ω is small, so | cos (ρπ / 2) | ≒ cos (π / 2) = 0, which is extremely close to 0. I can expect that. Therefore, the error of the active power <P> becomes very small. Therefore, it is possible to reduce an error due to frequency fluctuation of the active power <P>.

Considering the variation term of the reactive power <Q>,

[0063]

[Equation 33]

Is obtained. In this case, a factor called sin (ρπ / 2) occurs. sin (ρπ / 2) is slightly smaller than 1 in a range where the error Δω of the angular frequency ω is small, and the effect of improving the frequency fluctuation is slightly recognized. Active power at Δω / ω = 0 Po = V1 I1 co
s (φ1-θ1), reactive power Qo = V1 I1 sin (φ1-θ1), active power P obtained by the conventional method, reactive power Q, active power obtained by employing the averaging method <P> , Reactive power <Q
>, P / Po, Q /
Table 1 shows the calculation results of Qo, <P> / Po, and <Q> / Qo. However, k = 60 (3 ° sampling), cos (φ
1-θ1) is assumed to be close to 1.

[0065]

[Table 1]

FIGS. 1 (a) and 1 (b) are graphs of P / Po in Table 1. FIG. FIG. 1 (a) shows a graph of P / Po,
FIG. 1B shows a graph of <P> / Po. It can be seen that the graph of FIG. 1B has a smaller error due to frequency fluctuation. As can be seen from Table 1 and FIG.
It can be seen that even if the frequency fluctuates, the fluctuation in the detected power value can be sufficiently suppressed.

Further, according to the protection relay of the present invention, which obtains a power value by using the above power calculation method and operates when a certain gap occurs between the power value and the reference level, the accuracy of the power calculation is improved. As a result, more accurate judgment can be made.

[0068]

BRIEF DESCRIPTION OF THE DRAWINGS FIG. FIG. 2 is a block diagram showing a digital relay to which the power calculation method of the present invention is applied. Power system line 1
The current flowing in 1 (its fundamental wave frequency is 60 Hz) is detected by the CT 12, insulated and level-converted by the auxiliary CT 13, and then passed through the low-pass filter 1 to reduce high-frequency components. Then, in the sample and hold circuit 2, a certain time (for example, 1/720 second;
(Equivalent to °) (see FIG. 2). The analog value sampled and held is A / D
The digitally converted sampling value (referred to as im) in the converter 3 is stored in the memory 4.
It is taken in.

On the other hand, the voltage of the power system
After being detected, insulated and stepped down, the high frequency component is reduced through the low pass filter 15. Then, the sample-and-hold circuit 16 performs sample-and-hold at the predetermined time intervals. The sampled and held analog value is digitally converted in the A / D converter 17, and the digitally converted sampled value (vm
Is also taken into the memory 4.

Each value im, vm taken into the memory 4 is
The CPU 5 is used to calculate active power and reactive power. That is, the fundamental cosine components V1c and I1c of the voltage and current and the fundamental sine components V1s and I1s of the voltage and the current are obtained based on the sampling values im and vm, and the voltage / current , The fundamental cosine components V1c 'and I1c', and the fundamental sine component V1
s 'and I1s' are determined, and the averaged active power <P> and reactive power <Q> are determined using the averaging method of the present invention.

Description will be made by taking the current waveform of FIG. 3 as an example.
At a certain time t1, the past sampling values i0 to i
Using 11

[0072]

(Equation 34)

[0073]

(Equation 35)

Is calculated, and sampling values i3 to i14 shifted by 90 ° are calculated.

[0075]

[Equation 36]

[0076]

(37)

Is calculated. The averaged fundamental wave component <I1c> = 0.5 (I1c + I1s ') <I1s> = 0.5 (I1s-I1c') <V1c> = 0.5 (V1c + V1s ') <V1s> = 0.5 (V1s-V1c') Then, the active power <P> and the reactive power <Q> are obtained using the equations (5) and (6).

By this calculation, the power value can be calculated using the data values in the past about 1.25 cycles. As already described by using equations (18) to (21),
Even if the frequency (60 Hz) of the current flowing through the power supply changes to, for example, 63 Hz or 57 Hz, the averaged power calculation using the sampling value shifted by 90 ° as described above is performed, so that the power with less error is obtained. Value can be obtained. The power thus obtained is compared with the reference level in the comparator 6, and an operation signal is output when the distance from the reference level becomes equal to or more than a certain value. In this case, a timed relay may be attached to output an operation signal only when the above state continues for a certain period of time.

It should be noted that the present invention is not limited to the above-described embodiment. For example, the sampling interval is not limited to 30 ° and can be set to an arbitrary interval. Various other design changes can be made without departing from the scope of the present invention.

[0080]

As described above, according to the power calculation method of the present invention, each time tm (m = m) obtained by dividing one cycle by 2k with respect to the nominal angular frequency ω of the fundamental wave included in the wave to be calculated. 0,
Each of the target waves is sampled at every 1,...), And the fundamental wave cosine components V1c and I1c, the fundamental sine components V1s and I1s of the voltage and current obtained based on each sampling value im and vm, and the sampling values im and vm The fundamental cosine components averaged using the fundamental cosine components V1c 'and I1c' and the fundamental sine components V1s 'and I1s' obtained from the sampling values im and vm at the time when the phase is shifted by 90.degree. <V1c>, <I1c
>, The fundamental wave sine components <V1s>, <V1s> are determined, and the powers <P>, <Q> are calculated based on these averaged components. Even if it occurs, an extremely accurate power calculation method can be realized.

Further, when the present invention is applied to a protection relay which operates by detecting a power value, a stable operation can be performed even with a change in frequency.

[Brief description of the drawings]

FIG. 1 is a graph showing a result of performing a power calculation of the present invention and a conventional power calculation with respect to a frequency variation of ± 5%.

FIG. 2 is a block diagram showing a protection relay to which the power calculation method of the present invention is applied.

FIG. 3 is a waveform chart showing a sampling method.

[Explanation of symbols]

 2 Sample hold circuit 3 A / D converter 4 Memory 5 CPU 6 Comparator 16 Sample hold circuit 17 A / D converter

──────────────────────────────────────────────────続 き Continued on the front page (58) Field surveyed (Int. Cl. ⁷ , DB name) H02H 3/42 G01R 21/133 H02J 3/00

Claims (2)

(57) [Claims] An object wave is sampled at each time point when one cycle is equally divided into 2k, where ω is a nominal angular frequency of a fundamental wave included in a voltage i and a current v to be calculated. vm (m = 0,1,...), the cosine components V1c and I1c and the sine components V1s and I1s of the fundamental wave of the voltage and current.
And the cosine components V1c 'and I1c' of the fundamental wave and the sine component V1s', which are obtained by using the sampling values im and vm at the time when the phase is shifted by 90 degrees from the sampling values im and vm.
Using I1s', cosine components <V1c> and <I1c> and sine components <V1s> and <
<I1c> = 0.5 (I1c + I1s ') <I1s> = 0.5 (I1s-I1c') <V1c> = 0.5 (V1c + V1s ') <V1s> = 0.5 (V1s-V1c') A power calculation method comprising calculating power using a cosine component and a sine component of a fundamental wave. 2. Setting a nominal angular frequency ω of a fundamental wave included in a voltage v and a current i to be calculated, and setting one cycle to 2
Sampling means for sampling the target wave at each time point divided into k equal parts, and cosine components of the fundamental wave of the voltage and current obtained by each sampling value im, vm (m = 0,1,...) sampled by the sampling means V1c, I1c, sine components V1s, I1s, and 9
Sampling value im, v at the time of 0 ° cut-out phase shift
Using the cosine components V1c 'and I1c' and the sine components V1s 'and I1s' of the fundamental wave obtained from m, the cosine components <V1c> and <I1c> of the fundamental wave, <Is> = 0.5 (I1c + I1s ′) <I1s> = 0.5 (I1s−I1c ′) <V1c> = 0.5 (V1c + V1s ′) <V1s> = 0.5 (V1s−) V1c ') comprising power calculating means for calculating power using the averaged fundamental wave component, and comparing means for comparing a value output by the power calculating means with a reference level. A protection relay using a power calculation method, wherein the protection relay operates when a value output from the result power calculation means deviates from the reference level by a certain distance.