Calculation of amplitudes of sinusoidal waves

(54) Name: Device for calculating the amplitude value of a sinusoidal wave

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The present invention relates to an apparatus for calculating the amplitude value of a sinusoidal wave by sampling at a predetermined interval a sinusoidal voltage or current and subsequently calculating the amplitude value of the voltage or current from a digital signal, which. corresponds to the sampled value.

Calculating devices of this kind are used for remote control of switches, measuring instruments, machines and apparatus in an electric power system. The digital signal corresponding to the sampled value is encoded and then transmitted to a device installed in a receiving station for calculating the amplitude value.

The following three calculation methods have been used in the calculation device.

The first method is an addition method, in which the absolute values ​​of a plurality of sampled data, which are sampled in a half period of a sinusoidal voltage or current (hereinafter referred to as an incoming alternating current), are added and the result of the addition is multiplied by a predetermined constant, whereby the amplitude value of the incoming alternating current is determined, as shown in Fig. 1 of the accompanying drawings.

When an incoming alternating current according to Fig. 1 with a frequency

7609520-7 of 50 Hz is sampled at a sampling frequency of 600 Hz, the sampling period is 30, so the amplitude value can be determined by the following equation:

I = __i— HI ^x 3,798 ^Lk = m-5 ^ k¹ (1) where m represents a time series and i ^ an instantaneous value, expressed by the following equation (2).

ik = I sin ωt (2)

Using m-5 as a reference for the sampling points and assuming that the phase of the incoming alternating current is ωt, the right term in equation (1) can be expressed as follows:

{| sin ωt | + | sin (+t + -π) | + 2o + | sin (ωϋ + $ π) | + | sin (wt + ^ ir) | + + sin (wt + ^ π) I -t Isin (ωt + —π) 1} (3) • b · · b ·

In equation (3), the range of ωt is limited by:

Oäcot έ-L 12 why the right term according to equation (3) has the following appearance by considering the periodicity of the incoming alternating current.

79q · (cos π + cos π + cos yj ^π) * sin ^{+ π}) ⁼

- - I · sin (ωt + π) (5)

This equation shows that the error in the addition method, caused by the variation in the sampling phase is less than + 1.7%.

The second method is a peak value detection method, in which data with the largest absolute value is selected from sampled data obtained for a half period or more, and the selected data value is used as the amplitude value. The selected maximum data value shows the amplitude value of the incoming AC current with an error within a certain range. Thus, for example, when an incoming AC with a frequency of 50 Hz s is amplified at a sampling frequency of 600 Hz in the same manner as in the addition method described above, the phase of the data sample thus extends with the maximum absolute value from sin to sin yir. in the sampling phase the error caused is less than + 1.7% in the same way as described above.

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The third method is the square method. This is based on the following trigonometric relationships:

its² 0 + cos² 0 = sin² 0 + sin² (0 + —) =1 (6)

By taking advantage of the fact that the sum of the squares of two sampling data with a phase difference of 90 ° is equal to the square of the amplitude value of the incoming alternating current, the amplitude value can be determined from the square root of the sum.

For example, when, like Fig. 1, the incoming AC of 50 Hz is sampled at a sampling frequency of 600 Hz_z the square of the amplitude value can be determined by the following equation:

¹ “M ⁺ ^-3 ⁽⁷⁾

This square method is basically free from errors due to the variation in the sampling phase.

Of these three methods, the square method is thus the most advantageous in that it is not accompanied by errors caused by the variation in the sampling phase, but this method is disadvantageous because it is necessary to calculate a square root according to equation (7). When calculating a square root by means of an electronic computer, much longer time is required than for an addition operation.

Although the addition method or the peak value detection method does not require any such mathematical operation, these are accompanied by errors due to the variation in sampling phase.

Accordingly, an object of the present invention is to provide a new device for calculating a sinusoidal current or voltage amplitude value, which device does not require calculation of a square root and which device can greatly reduce the error due to the variation in sampling phase compared to the prior art addition method. and peak value detection method.

According to the present invention there is provided an apparatus for calculating the amplitude value of a sinusoidal wave, which apparatus comprises means for sampling the instantaneous value of the sinusoidal wave, a data sample sampling circuit connected to the output of the data sampling means for sampling a first data sample obtained by sampling immediately before a peak value. , and a second data sample, obtained by sampling immediately after a peak value, and an operation circuit, which is connected to the output of the sample sampling circuit for calculating the amplitude value of the sinusoidal wave from the first and second data samples. ·

The invention will be described in more detail in the following with reference to the accompanying drawings. Fig. 1 is a diagram showing a method of sampling an incoming alternating current by means of a sampler

7609520-7 charging frequency of 600 Hz. Fig. 2 is a block diagram showing an embodiment of the device according to the invention for calculating the amplitude value of a sinusoidal wave. Fig. 3 is a graph used to explain the operation of the device of Fig. 2. Fig. 4 is a block diagram showing an example of the operating circuit shown in Fig. 2. Fig. 5 is a vector diagram showing the variation of the amplitude value. FIG. 6 is a block diagram showing a modification of the sampling circuit for sampled data. Fig. 7 is a graph used to explain the operation of the modified sampling circuit for sampling data in Fig. 6. Fig. 8 is a block diagram showing another embodiment of the present invention. Figs. 9, 10 and 11 show modified operating circuits. Fig. 12 is a graph showing a modified method for generating two sampled data. FIG. 13 and 14 show further modifications of the operating circuits. The preferred embodiment, in which an incoming alternating current with a frequency of 50 Hz is sampled at a sampling frequency of 600 Hz similar to Fig. 1, will now be described in detail.

In Fig. 2, the current I flowing through a power system 1 is sensed by means of a current transformer 2. The output current I from the current transformer is sampled at some sampling frequency by means of a sampling holding circuit 3. Assuming that the frequency of the power system 1 is 50 Hz and the sampling frequency is 600 Hz, then the sampling period becomes 30 °. The sampled data is fed to a zero point detector 4. In response to successive, sampled data, the zero point detector 4 compares the sign of a current, sampled data with the sign of a sampling immediately preceding said current data. When the signs of the two data are not equal, the zero point detector 4 generates a zero point detection signal SZ, which means that the waveform of the incoming alternating current has passed through a zero point.

A data memory circuit 5 is provided, which stores the current sampled data together with a predetermined number of data for more than half a period before the current data, which data is transmitted from the sampling hole circuit 3. When a zero point detection signal SZ is applied, the data memory circuit 5 outputs two sampled data in and which were sampled in a phase position 90 ° before the two sampled data, which were sampled before and after a zero point, i.e. said current data and the immediately preceding data, as shown in Fig. 3. For this reason, the two data output from the memory circuit 5 represent in and in the sampled data before and after the peak value of the incoming AC current. The zero point detector 4 and the data memory circuit 5 form

7609520-7 thus a sampling circuit 6 for sampled data.

As the data memory circuit 5, a shift register can be used, in which case the sampling period is set to a fraction of 90 ° of the frequency of the incoming alternating current. An operation circuit 7 is arranged for calculating the amplitude value from the two output signals i and i - from the data memory circuit 5. m m-1

Fig. 4 shows an example of the operating circuit 7, which comprises an adder 11, which adds the absolute values ​​Ii I and Ii _Ί| »M^{J 1} m-1 »of the two input signals i and i to generate the sum | i_m| + | i ^ -i | . The output signal from the adder 11 is multiplied by a coefficient by means of a first coefficient multiplier 13 to produce an output signal {| i ^ | + |} / which is fed to an adder 15. The input signals i and i_Ί is also supplied with a subm m-1 tractor 12, which calculates the absolute value of the difference between Ii I ¹ m¹and | im_ I^to always give a positive output signal. The output signal || \ J - from the subtractor 12 is multiplied by a coefficient K2 by means of a second coefficient multiplier 14, and the output signal K ~] | i I - Ii -.I from the second coefficient multiplier 2 i¹ m^{1 1} m-1¹| is added to the second input of the adder 15.

The output signal generated at an output terminal 16 is thus the amplitude value to be determined.

y = k. {I i I + I i I} + k „11 i I - I i, II 'ni ¹ ml '2 I ¹ m^{1 1} m-1 '| (3) where m represents a time series and and K₂ are constants, including 1.

To examine the variation range of the amplitude value Y, set:

ΤΓ i _Ί = I sin ωt and i = I sin (ωt + 7 ·) (9) m— ± mo

Because in and in _Ί is data, which is sampled before and after the peak value of the m m-1 incoming alternating current, the phase ωt varies in an area:

i (Jt £ 1 (10)

XM

Equation (8) can be modified as follows:

Y = (Κ_χ + K₂) I sin ω € + (Κ_χ - K₂) I sin (+t + £) = = (K ^ + K₂) I sin ωt +

ΤΓ7Γ + (Κ_Ί - Κ_π) I (cos sin +t + sin _Έ cos wt) = = (^{2 K}1 ^{+ 2} ~2^ ^κ2^{5 1 sin ut +} + I (Kj - K₂) I cos ωt (11)

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By inserting the following k 2 and k 2 into equation (11)

I (12) ^k2 ⁼ 2 ^(K1 ^K2^JJ, equation (11) can be rewritten as:

Y = k ^ I sin cot + k₂ I cos ωt = = · 4_χ² + k₂² In sin (ωΐ + α) (13) where a = sin¹ - - = cos¹ — ¹ (14). Λ_χ² + k₂²

However, the variation in the amplitude value Y expressed by equation (13), caused by the variation in the sampling phase, expressed by equation (10), is represented by a variation component d = · I along the ordinate, as indicated in the vector diagram shown in Fig. 5.

When and K₂ are chosen to satisfy a relation K ^ / J ^ = 2.03, for example k₁/ k₂ - 7.60, α = 7.5 (15) and the minimum value of the variation d can be expressed by:

d = + k₂² 'I · sin (90 ° -7,5 °) (16)

This time the error is + 0.43%.

This result was obtained by selecting the ratio K 2 / K 2 2.0 3 to minimize the error, but for a practical purpose an approximate solution can be obtained by choosing the ratio

Although in the embodiment shown in Fig. 2, the sampled data supplied to the operating circuit 7 was data, which was sampled in one. phase position 90 ° before the point in which the zero point detection signal SZ was generated, it is also possible to use data sampled in a phase position 90 ° after the point for detecting the zero point detection signal SZ.

For this purpose, a modified sampling circuit for sampled data, as shown in Fig. 6, can be used, a gate signal shaping circuit 8 being triggered by the zero point detection signal SZ from

7609520-7 zero point detector 4. The gate signal shaping circuit 8 comprises a counter which counts the number of sampled data supplied to its input 8a. Thus, the gate signal shaping circuit 8 generates a gate signal GT when it receives the second and third data samples after receiving a zero point detection signal SZ, which is generated at a time t1 when a data sample reaches the zero point detector 4 after the zero point detection interval 7, as shown in Figs. The gate signal GT is applied to a gate circuit 9 to cause it to supply to the operation circuit 7 only two sampled data in and in_mbefore and after a phase position 90 ° after a point in which the incoming alternating current has passed through a zero point, as shown in Fig. 7.

With the modification shown in Fig. 6, it is possible to calculate the amplitude value with a maximum error of + 0.43% in the same way as with the embodiment shown in Fig. 2.

The gate signal shaping circuit 8 shown in Fig. 6 may be constructed so that after receiving a zero point detection signal SZ it counts the pulses generated by a clock pulse generator (not shown) included in the gate signal shaping circuit and thus forms a gate signal for the two, before and after peak data.

A memory circuit similar to the data memory circuit 5 in Fig. 2 may replace the gate pulse shaping circuit 8 and the gate circuit 9 in Fig. 6.

Another embodiment of the present invention is shown in Fig. 8, wherein the sampling circuit 6 for sampled data comprises a comparator 25, which stores the data relating to the previous half period among a plurality of sampled data, which reaches the input connection of the comparator 25, and which generates its output signal. a data signal with a maximum absolute value and a data signal with an absolute value closest to said maximum absolute value. The two outputs in_m_^ ^ocl1i from the comparator 25 the operating circuit 7 is supplied.

The two data signals emitted by the comparator and i ^ are equal to the data sampled before and after the peak value in the previous half period of the incoming alternating current. For this reason, with the amplitude value calculation device shown in Fig. 8, it is also possible to obtain the result with an error of + 0.43%, as discussed with reference to Fig. 2.

The operating circuit used in the above embodiments is not limited to the one without modified operating circuits shown in Fig. 4, shown in Figs. 9-11, can also be used.

The operating circuit 7 shown in Fig. 9 comprises a comparator 31, which compares the absolute values ​​of two sampled data | i_m| ^ochrs

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Ii J for supply of the larger absolute value max {I i I. Ii, 1}¹ m-1 ' ¹ m * ' ¹ ml^{, J} to a coefficient multiplier 32 for multiplication by a coefficient The comparator 31 also outputs the smaller value min {| i_m| t | i_m_^|} ^{a second} coefficient multiplier 33 for multiplication by a coefficient K₂₂The output signals from the two coefficient multipliers are added by an adder 34 to provide an output signal:

Y = K₂₁ · Max {| i_m| , + ^K₂₂ · Mm {| in_m| , [i ^ l) (17)

The variation in the sampling phase in this case can be determined in the same way as discussed in connection with equation (10). Equation (17) can thus be modified as follows: 'TT *

Y = Κ_ηΊ sin ωt + sin (ωt + =

Zl. zz □

ZT1 = (Κ_9Ί + - = · K₉₉) sin ωt + - K₉₉ cos ωt · (18)

By introducing:

^kl ^K21 . 71 _K⁺ 2 ^K22 ^k2 2 ^K22 (19), equation (18) can be converted to the same form as equation (13).

By selecting the values ​​of the coefficients K₂₁ and K₂₂ for fulfillment of the relation = 7.60, ie K_?1/ K₉₉ = 2.93, it is therefore possible to calculate the amplitude value with an error of + 0.43%. The modified operating circuit shown in Fig. 10 includes a comparator 42 which supplies the less min {| i_mlt of the absolute values ​​of two sampled data I i_m I / | i 1 to a coefficient multiplier 41, and an adder 44 for feeding the sum of the absolute values ​​of the two sampled data, | i | + / to a coefficient multiplier 43. The output signals from the two coefficient multipliers are added by means of an adder 45 to produce an output signal:

^{Y =} Κβΐ '^ ίη {| i_m | r 1 i^{+ K}32 * ^ nJ ⁺ ^ ml। ⁼ = K₃₂-max {| i_m| , (K₃₁ + K₃₂) -mm {| i_m| , ₍₂₀₎

By introducing:

^K32 ^{= K}21 ^{and K}31 ^{+ K}32 ^{= K}22 equation (20) can be converted to the same form as. equation (17).

With the circuit shown in Fig. 10 it is thus also possible that

7609520-7 calculate the amplitude value with an error of + 0.43%. However, in order to obtain the result of this error, it is necessary to select the ratio ^ 1 ^ 32 ~

The operating circuit 7 shown in Fig. 11 comprises a comparator 52 for supplying the larger max (I i_m I / 1 ^ -1 ^ ^{of a}^^solutThe values ​​of two sampled data | i ^ | and | i_ma coefficient multiplier 51 and an adder 54 for calculating and adding the sum of the absolute values, | i ^ | + | I r^of the two sampled data to a coefficient multiplier 53- The output signals from the coefficient multipliers 51 and 52 are added by an adder 54 to provide an output signal:

Y = K₄₁-max {I i_m| , + ^κ42 Π ^xml + l^x_m-iU = = (K₄₁ + K₄₂) max {| i_m| , I⁺ K₄₂^my < 1^-1^ ⁽²²⁾

By putting K._T + = Κ_ΟΊ and K._O = K_oo

42 Equation (22) can be transferred to a form similar to equation (17). Consequently, with the modification shown in Fig. 11, it is also possible to calculate the amplitude value with an error of + 0.43%. To obtain a calculation result with this error, it is necessary to select the ratio ^ 4 ^ / ^ 43 ~^1/93*

Although in the above embodiments two data immediately before and after the peak value of an incoming AC are used as the sampled data, by using the periodicity of the incoming AC, a first data sample on one side of the peak value in a half period and a second data sample in a corresponding phase position in a second half period, which second data sample is more than 90 ° apart from the first data sample, may also be used. As shown in FIG. 12, where the first data sample is expressed by ⁼ In sin, for example, a data sample 1 ^ = 1 sin (ωt + - - j) is used as the second data sample.

The sampling frequency can be any frequency, but when the sampling frequency is four times as high as the frequency of the incoming alternating current, ie when the sampling is done at an interval of 90? for the waveform of the incoming AC current, two adjacent data samples comprise in particular two data samples immediately before and after the peak value of the incoming sine waveform or two data samples with the same absolute values ​​as the two data samples, why the data samples can be easily extracted without the use of any special means.

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Fig. 13 shows yet another operation circuit Ί _t comprising a comparator 71_z which compares the absolute values ​​I i_m[and li ^ -J of two data amps i and for delivering the smaller min {| i_m| _t | i ^ |} as its output signal, which is multiplied by a coefficient of a coefficient multiplier 72 to produce an output signal K, -min {Ii | _r | i _ | }, and a subtractor 74, which generates the absolute value of the difference between the two sampled values ​​i and i The output signal Ii I - | i -.1 from the subtractor 74 is multiplied by a coefficient K₂ of a second coefficient multiplier 75 to provide an output signal K_O{| i I - Ii _Ί I}, which is supplied to an adder 71 together with the output signal from the first coefficient multiplier 72 for generating an output signal:

Y, = K. -min {I i I, | i - |} + K {| i | - | i, | } (23)

1 ¹ m * m-1¹ 2 ¹ No. 'm — 1'

This output can be modified according to

Y = K₂-max {| i | , | ij_n_₁| J + (K - K _) 'min {| iJ, | i _χ| } (24)

By setting K₂ = K 2 and = equation (24) can be modified to the same form as equation (17). With the circuit shown in Fig. 13, it is also possible to calculate the amplitude value with an error of ± 0.43%.

Fig. 14 shows yet another modification of the operating circuit 7, which includes a comparator 76 for outputting the larger max {| i_m| , | i ^ -jJ J of the absolute values ​​of two data samples in_m and in_m-1· The output signal from the comparator is applied to a first coefficient multiplier 77 for generating an output signal K * max {Ii I, Ii, |}_z which is supplied to an adder 73. The operating circuit 7 further comprises a subtractor 74, which generates. the absolute value of the difference Ii I - Ii. |, which value is multiplied by a coefficient of a second coefficient multiplier 78 and then applied to the adder 73. The adder thus generates an output signal:

Y = K, «max {I i I, I i, |} + K. {| i - i, |} (25)^J m¹ ' ¹ m-1 4 m ml^r

This equation can be modified according to:

Y = (K₃ + K₄) · Max {ii_m| , li ^ D - V^my ^ ml 'IVl^{11 (26)}

By setting = K₂₁ and - = k₂₂ equation (26) can be converted to the same form as equation (17). With the one in Fig. 14

7609520-7, it is thus also possible to calculate the amplitude value with an error of + 0.43%.

As described above, the present invention provides an apparatus for calculating the amplitude value of a sinusoidal wave with an error much smaller than the prior art addition method and peak value detection method, without calculating any square root, thereby simplifying the operation circuit and reducing the operation time.

The operating circuit can have several different shapes, such as a comparator or a combination of a comparator and an adder or subtractor.