JPH0445788B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Technical Field of the Invention] The present invention relates to a method for determining power flow direction in a power system used in a digital ground fault directional relay or a ground fault directional overcurrent relay.

[Prior art]

The following is an arithmetic formula for calculating the active power in the power flow of the power system using digital data.

A _i・B _i +A _i-1・B _i-1 >0 ...(1) However, A _i is current data, B _i is voltage data, i
represents sampling steps every 90°. t=
0, the current data at t=0 step is A _i =A ₀ , and the data one step before is A _i-1
Or expressed as A _-1 .

where θ is the sampling step angle of 90°,
k=f/f ₀ is the frequency conversion rate, f ₀ is the rated frequency (60
Hz), f is an arbitrary frequency, Ap and Bp are the peak values of current data and voltage data, and ψ is the phase difference between them.

Now A _i = Ap sin (ωtk), B _i = Bp sin (ωtk + ψ)
Then, A _i-1 = Ap sin(ωtk−θk), B _i-1 = Bp
sin((ωtk+ψ−θk).

Therefore, the left side of equation (1) =Ap・Bp{sin((ωtk)sin(ωtk+ψ) +sin(ωtk−θk)sin(ωtk+ψ−θk)} =1/2Ap・Bp{cosψ−cos(2ωtk+ψ) +cosψ −cos (2ωtk+ψ−2θk)} =1/2Ap・Bp{2cosψ−2cos1/2(4ωtk −2θk+2ψ)cos1/2(2θk)} =Ap・Bp{cosψ−cos(2ωtk +ψ−θk)cos(θk) } ...(2) In equation (2), cos (2ωtk + ψ−θk) cos (θk)
is an error term containing a double frequency component. f = f ₀ = 60
In the case of Hz, since k = 1.0, cos (θk) = cos90° = 0, so the error term disappears, and the left side of equation (1) = Ap・
Bp cosψ, indicating the correct active component power value.
Therefore, equation (1) corresponds to determining that AP·Bp cosψ>0, and the correct direction can be determined at the rated frequency.

In equation (2), the frequency of 60Hz is ±3Hz ((±5%)
If it changes, k=1.05 or k=0.95. Therefore, cos(θk)=cos94.5° or cos85.5°, both of which are 0.0875. Also, cos in equation (2)
The maximum and minimum values of the double frequency component of (2ωtk + ψ - θk) are +1.0 and -1.0, respectively, so when the operating limit angle of equation (2), that is, ψ = ±90°, cosψ = cos ((±
Since 90°)=0, an angular error of ApBp(0〓0087) will occur. That is, Ap・Bp
An angular error that fluctuates between cos94.5° and Ap・Bp cos85.5° occurs at double frequency, and the calculation output at each step is not constant. In other words, there is a discrimination angle variation of ±4.5° at the limit point.

[Summary of the invention]

This invention was made to eliminate the drawbacks of the conventional ones as described above, and uses current and voltage data obtained by sampling the current and voltage of an AC power system at a predetermined sampling period. It is an object of the present invention to provide a power flow direction determination method that can determine the power flow direction by calculation without being affected by frequency fluctuations in a power system.

[Embodiments of the invention]

In Figure 1, current data A _i and voltage data
The sum x _i and the difference y _i of B _i are respectively x _i =A _i +B _i (3) y _i =A _i −B _i (4). Similarly, x _i-1 , x _i-2 , y _i-1 , y _i-2 are x _i-1 =
A _i-1 + B _i-1 , x _i-2 = A _i-2 + B _i-2 and y _i-1 = A _i-1 −
B _i-1 , y _i-2 = A _i-2 − B _i-2 . Here, if the squared amplitude values of x _i and y _i are respectively X ² _p and Y ² _p , then x _i = X _p sin(ωt), x _i-1 = X _p sin((ωt−θK), Since x _i-2 = X _p sin ( _ωt ^- 2θK), x ² _i-1 = X ² _p sin ² (ωt-θK) = x _i・x _i-2 =X ² _p sin(ωt) ・sin(ωt−2θK)=−X ² _p 1/2 {cos(2ωt−2θK)−cos(2θK)} Therefore, x ² _{i− 1} −x _i・x _i-2 =X ² _p 1/2 {1−cos(2θK)} =X ² _p sin ² (θK) ……(5) Similarly, y ² _i-1 −y _i・There is the following relationship: y _i-2 = Y ² _p sin ² (θK) ...(6) As shown in Figure 2 a, b, and c,
Compare the sum Xp and the difference Yp of peak values Ap and Bp of alternating current and voltage, and (a) If Xp>Yp, ψ<90° (b)
If Xp′=Yp′, then ψ′=90°, and if (c) This holds even if both sides are squared. Therefore, by comparing the magnitudes of equations (5) and (6), the effective direction can be determined using equation (7) below.

x ² _i-1 −x _i・x _i-2 ＞y ² _i-1 −y _i・y _i-2 ……(7) ∴X ² _p sin ² (θk)＞Y ² _p sin ² (θk) (θk=n・180
゜ is excluded. n = 1, 2, 3, ...) ∴X ² _p > Y ² _p ... (8) Since these do not include terms related to frequency, their errors are also not included. Also, since sinθk reaches its maximum value at θk = 90°, both sides of equation (7) also reach a maximum when θk = 90°, and therefore, when comparing both sides, the accuracy is highest when θk = 90°. (Comparing large values is easier than comparing small values.) From equation (8), it can be seen that the sampling interval can be arbitrary (for example,
45°, 30°, 15°, 10°, etc.).

Next, we will prove that the correct effective direction can be determined using equation (7). Now, Xp and Yp in Figure 2a are taken out separately and shown in Figures 3a and 3b. When the law of the first cosine of a plane triangle is applied to the squared Xp value X ² _p in FIG. 3a, equation (9) holds true.

X ² _p = A ² _p + B ² _p −2Ap・Bp cos(180°−ψ) cos((180°−ψ) = −cosψ, so X ² _p = A ² _p +B ² _p +2Ap.Bp cosψ … ...(9) Next, by similarly applying the law of the first cosine to Yp squared value Y ² _p in Figure 3 b, equation (10) is obtained: Y ² _p = A ² _p + B ² _p −2AP・Bp cosψ ...(10) By substituting equations (9) and (10) into equation (8), we obtain the relationship shown in equation (11) below.

A ² _p +B ² _p +2Ap・Bp cosψ ＞A ² _p +B ² _p −2AP・Bp cosψ ∴4Ap・Bp cosψ＞0 ...(11) In other words, solving equation (7) is It can be seen that the polarity of the active component power value is being determined. The phase characteristic of equation (11) is as shown in FIG. 4, and the shaded side is the operating range.

[Effects of the Invention] As described above, according to the present invention, it is possible to obtain a digital arithmetic expression for effective direction determination without a determination angular frequency error.

[Brief explanation of drawings]

1, 2, 3 and 4 are vector diagrams of current and voltage. A _i , A _i-1 , A _i-2 , ... current data, B _i , B _i-1 ,
B _i-2 ... Voltage data.

Claims (1)

[Claims] 1. Three mutually consecutive current data (A _i , A _i-1 , A _i-2 ) and voltage data obtained by sampling the current and voltage of the power system at a predetermined sampling period. Using (B _i , B _i-1 , B _i-2 ), the sum x _i =
A _i + B _i and the difference y _i = A _i −B _i are calculated, and the discriminant x ² _i-1 −
A method for determining the direction of power flow in an electric power system, in which it is determined that the above current and voltage have an in-phase relationship when x _i・x _i-2 >y ² _i-1 −y _{i ・y} i-2 holds. 2. The method for determining power flow direction in a power system according to claim 1, wherein the predetermined sampling period is set by an arbitrary sampling frequency selected to include a phase position of 90 degrees.