PL212159B1 - Method and system for measuring of active power - Google Patents

Description

The subject of the invention is a method and system for measuring active power intended for use in various types of measurement systems, in particular in the environment of distorted currents and voltages, and also as one of the elements of power protection automatics systems.

The increasing number and power of non-linear receivers causes that the currents drawn from the electric network, deformed from the sinusoid, result in distorted voltage drops, which leads to distortion of voltage waveforms at nodal points of the power network. Due to the constantly increasing number of receivers sensitive to the quality of electricity, monitoring of electricity parameters with the use of classic measurement systems is burdened with large errors. This is mainly due to the non-linear characteristics of current and voltage transformers, the signals of which are also used to determine energy parameters.

Modern power quality analyzers - among several quantities measured in the environment of distorted waveforms - also measure active power. However, these are very expensive devices, usually using signals provided by current and voltage transformers.

In analog power converters, the values of voltage and current, after initial processing in the input circuits, are multiplied in a system called an analog multiplier. The most common output signal of the multiplier is direct voltage or direct current. In modern measurement technology, sampling power converters are also used. They differ significantly from the analog converters mentioned above.

The input quantities, after initial processing, are subjected to the sampling operation. Obtained at a certain time, e.g. in the period T, the set of samples is a digital (discrete) representation of the values of the input quantities. Then, on the stored sets of samples, an operation is carried out in the microprocessor to multiply the voltage uk and current k samples collected at the same moment tk - consequently obtaining a set of instantaneous values of power p (t). After calculating their mean value in the period T, the active power P τ Ν is obtained

Ρ = - J p (t) dt = - ^ (u _k i _k ),

Ο fc = l where: N - number of collected samples in period T, and k - number of the sample.

The signal sampling method makes it possible to measure not only active power, but also apparent power, reactive power, power factor and many other parameters of the input signals. The method is the basis for the operation of modern measurement systems.

The essence of the method according to the invention consists in the fact that the measured voltage signal is divided by a divider constituting a series-connected choke with the resistor, the reactance of the choke being much greater than the resistance of the resistor, and the instantaneous values of the voltage drop across the resistor and the instantaneous values of the induced electromotive force are measured. in the Rogowski coil under load current. Then the instantaneous values of the voltage drop across the resistor are multiplied by the instantaneous values of the electromotive force induced in the Rogowski coil and the measurement result, which is the measured active power, is averaged.

The essence of the system according to the invention consists in the fact that a voltage circuit and a current circuit are connected to the input terminals, the voltage circuit is a voltage divider in the form of a series-connected choke with a resistor, and the current circuit is equipped with a Rogowski coil, in the window of which a wire with load current. In addition, a resistor and a Rogowski coil connected to the multiplier block.

Preferably, the reactance of the choke is significantly greater than the resistance of the resistor.

The advantage of the method according to the invention is the precise measurement of the mean active power value in systems with periodic, non-sinusoidal voltage and current waveforms. The measurement value may be a criterion value for the operation of power protection automatics systems as well as the measurement and monitoring systems themselves. An additional advantage of the method is the simplicity of the system while maintaining high accuracy of measurements both for linear and non-linear circuits.

The subject of the invention in an embodiment is explained in the drawing, in which Fig. 1 shows the current circuit of the active power measurement system with a Rogowski coil, and Fig. 2 shows the active power measurement system.

PL 212 159 B1

The active power measurement method is based on the fact that the voltage signal measured u (t) is divided by the divider LR which is a series-connected choke L with the resistor R, while the reactance of the choke L is much greater than the resistance of the resistor R, and the instantaneous values of the voltage drop are measured uR (t) on the resistor R and at the same time the instantaneous values of the voltage e (t) induced in the Rogowski coil CR under the load current i (t). Then, the instantaneous values of the voltage drop uR (t) on the resistor R are multiplied by the instantaneous values of the voltage e (t) induced in the Rogowski coil CR and the measurement result, which is the measured active power, is averaged.

The active power measurement system has a voltage circuit and a current circuit connected to the A, N input terminals. The current circuit is equipped with a CR Rogowski coil in the window of which the conductor 1 with the load current i (t) is placed. The voltage circuit has an inductance L connected in series and a resistor R, which is a branch connected to terminals A and N, between which there is a voltage u (t). The multiplier block 2 is fed with the electromotive force e (t) induced in the Rogowski coil CR, and on the other hand the voltage drop uR (t) across the resistor R connected in series with the choke L. The branch thus formed is connected to terminals A and N between which there is a voltage u (t). The output of block 2 is fed to the input of block 3 for determining the average value Ps of both waveforms e (t) and uR (t).

The instantaneous value of the active power p (t) of the circuit with non-sinusoidal voltage u (t) and current i (t) waveforms can be written;

p (t) = u (t) i (t), and the mean value P of the active power of this circuit is determined by the relationship:

TT ^{P =} rf P (t) dt = -fu (t) · i (t) dt, oo

The distorted voltage u (t) and current i (t) waveforms contain higher harmonics. Since the average value of the product of two sinusoidal functions with different frequencies is equal to zero, the dependence describing the average value P of active power will drop the products of all harmonics with different frequencies, and the relationship itself will take the form:

o. o

_Σ ο _ \ '^ ^ km km • COS (p _k

-Σ

U _k -I _k - cos (p _k , where: Pk - mean value of the power of the k-th harmonic,

Uk - RMS value of the k-th voltage harmonic,

Ik - RMS value of the kth current harmonic.

In the Rogowski coil CR with the number of turns z, coupled with the conductor 1 of the current circuit, under the influence of flux changes (φ) caused by the flowing current and (t), the electromotive force e (t) is induced:

φ e (t) = z- ^ = A; -— = M -;

dt 2π ν dt dt where: z - number of turns of the Rogowski coil CR,

- air magnetic permeability,

S - coil cross-sectional area, r - coil axis distance from the primary circuit,

M - mutual inductance.

By distributing the distorted voltage u (t) and current i (t) waveforms into the Fourier series, one can write respectively;

OO u (t) = U _km sin (fc ω t + i // _fc ) k = 0 oo i (t) = I _km sin (fc ω t + ψ _κ - φ) k = 0 where:

k - harmonic order, ω - fundamental harmonic pulsation,

PL 212 159 B1 where:

f _I - frequency of the fundamental harmonic,

Ukm - amplitude of the kth voltage harmonic,

Ikm - amplitude of k-th current harmonic, k - initial phase of k-th voltage harmonic, k - phase shift of k-th current harmonic and k-th voltage harmonic. The current circuit of the active power measurement system has a current sensor consisting of a Rogowski coil CR which includes a conductor 1 with current i (t). The derivative di / dt of the deformed current wave i (t) can be expressed as follows:

and y

- ^Σ k = l co s (k at + ψ _{! (} - φ _k )

The electromotive force ek (t) induced in the Rogowski coil CR from A: -th harmonic of the current i (t) can therefore be written as;

'S dib _o _F ₀ - ^{z e} fc (O - ^z ~ 7 ~ - at 2π

Li, dL

-Γ = ^Μ ~ Γ dt dt

The electromotive force e (t) induced in the Rogowski coil CR from all harmonics of the current can be written as the sum of the electromotive forces induced from individual harmonics:

e (t) = V fc = l di

M— = ω · M dt oo

Σ k = l

Σ

Lfc = l

Finally, the electromotive force e (t) of current i (t) is:

a induced in the Rogowski coil CR from deformation ⁽ t) = L ^u km · S in (k-at + ψ _{] ί} - φ _{] ί} + |) k = l where: u ^l km = ω-Mk-ikm - amplitude k the -th harmonic of the voltage induced in the Rogowski coil CR from the k-th harmonic of the current Ikm.

The waveforms of individual harmonic voltages induced in the CR coil are shifted in relation to the inducing currents by the angle / 2 and their amplitudes are k-times greater than the amplitudes of the respective currents.

The voltage circuit of the active power measurement system consists of a choke L and resistance R connected in series with each other, forming a branch connected in parallel to terminals A and N, between which there is a distorted voltage u (t). Under the condition that the reactance of the choke L is much greater than the resistance of the resistor R, the current iL flowing through this branch is inductive, and the resistor R then acts as a shunt on which a voltage drop uR (t) is generated. The waveform of the current iL (t) can be written as follows:

oo ^eM = Zit '' ^s ' ⁿ ( ^,, ^ ^t + k = l

The voltage drop uR (t) on the shunt R is:

o. o

7? Y ^-1 Uj, ^ / 7T \ ^e - ® = ωτ · Σ— · ™ β · ^ω + ^ψ " ^- μ · k = l

While the amplitudes of individual harmonics of voltage uR (t) decrease with an increase of the order k harmonic Ukm in voltage u (t), the amplitudes of individual harmonics of voltages induced in the CR coil are k times greater than the amplitudes of the corresponding harmonics and km of current i (t).

The product of the electromotive force e (t) induced in the Rogowski coil CR and the voltage drop uR (t) is:

PL 212 159 B1

e (t) ' ^u r (P) = ωΜ o. o ω R ω oo m ( ^k -at + / _fc ^- £) Lfc = i -k = 1 M e (f) -u _R (f) = -R- - • o. O ω -p _k ~) • o. O Y —in (k - ωt + //) -fc = l k = l

The mean value of SR of the product of both these functions is:

Τ

Ρ- * Fm Fcm ί ζ χ Μ γ ^-1 k

SR = ~ J e (t) u _R (t) dt = —R - 2 ^ - y / 2 ky / 2

COS (p _k o Lfc = i

Dividing both sides of the equation by the resistance of the resistor R, we get:

^u r ^ F) M <Χ> η I

Z ^ Ikm ^ km 1 C _z x. z, \ j _{,, COSVk =} . β ₍ ,)., ΛΟΛ

Lfc = l Jo

The average value of Ps of the product of e (t) and iL (t) is;

f M

Ps = yJ e (t) i _LR (t) dt = - - k I _k 72 - U _k 72 cos (p _k k = l

Pr =

2M ~ lt '2 ^ l _k -U _k -COSę _k

2M

P.

Lfc = l

For the known values of the inductance of the choke L and the mutual inductance M, it is possible to accurately determine the real average value of the power P according to the relationship

L.

2M

Denoting by SCR the sensitivity of the Rogowski coil CR for the fundamental harmonic:

^u i

P where; - RMS value of the fundamental harmonic of the voltage induced in the Rogowski coil CR from the fundamental harmonic current of RMS value I1 and using the relationship;

Ukrn = ω-Μ-k- Ikm · one can express the mutual induction M with a more practical parameter, which is the SCR sensitivity of the Rogowski CR coil.

M = = ^ScR , ω 2 π -f 'where f ₁ - frequency of the fundamental harmonic

Finally, it should be stated that the mean value of power P is proportional to the mean value of PS of the product of both waveforms e (t) and uR (t) according to the relationship:

Claims (3)

1. The method of measuring active power, characterized in that the measured voltage signal (u (t)) is divided into a divider (LR) which is a series-connected choke (L) with a resistor (R), while the reactance of the choke (L) is much higher from the resistance of the resistor (R), and the instantaneous values of the voltage drop (uR (t)) across the resistor (R) are measured and at the same time the instantaneous values of the electromotive force (e (t)) induced in the Rogowski coil (CR) under the load current (i (t)), followed by the instantaneous values The voltage drop (uR (t)) across the resistor (R) is multiplied by the instantaneous electromotive force (e (t)) induced in the Rogowski coil (CR) and the measured active power is averaged. 2. Active power measurement system equipped with a multiplier connected to the mean value determining block, characterized in that a voltage circuit and a current circuit are connected to the input terminals (A, N), the voltage circuit being a voltage divider (LR) in the form of a series-connected choke (L) with a resistor (R), and the current circuit is equipped with a Rogowski coil (CR), in the window of which a wire (1) with the load current is placed, moreover a resistor (R) and a Rogowski coil (CR) connected to the multiplier block (2). 3. The system according to p. The method of claim 2, characterized in that the reactance of the choke (L) is significantly greater than the resistance of the resistor (R).