Measuring method for deciding direction to a flickering source

SWEDEN <₁₂) PATENT WRITING (13) C2 in) 525 331

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2005-02-01

2004-06-24

2002-12-23

2002-12-23 (19) SE (51)

International class ⁷G01R 31/08

PATENT AND REGISTRATION (45) (41) (22) (24) (62) (86) (86) (83)

Patent filed Application widely available The patent application was submitted on expiration date

National application number International filing date Filing date for European patent application Deposit of microorganism (21) Patent application number 02038917

Application received as:

ΡΠ Swedish patent application completed international patent application with number □ converted European patent application with number (30) Priority information (73) (72) (74) (54) (56) (57)

PATENT LAW Unipower AB, Box 411 441 28 Alingsås SE

INVENTOR Peler Axelberg, Alingsås SE Jonny Carlsson, Vårgårda SE OMBUD Albihns Göteborg AB

NAME Measurement method for determining direction to flicker source SUBJECT PUBLICATIONS:

EP A2 1,072,897

SUMMARY, The present invention relates to a method for determining the direction of a flicker source in relation to a measuring point in an AC power grid with a mains frequency (f_c) with low frequency amplitude variations from the discharge source. The invention is characterized in that the method comprises the steps;

- receiving an amplitude modulated current signal (i (n)) comprising signals originating from the network frequency (f_c) and the low-frequency amplitude variations in the current signal (i (n));

recording an amplitude modulated voltage signal (u (n)) comprising signals derived from the network frequency (f_c) and the low-frequency amplitude variations in the voltage signal (u (n));

- generating a flicker effect with a character value by multiplying the low-frequency amplitude variations in the current signal and the low-frequency amplitude variations in the voltage signal, and;

-analysis of the character value, the character value indicating in which direction the source of noise is in relation to the measurement point. The method also includes a device intended to be used in carrying out the method.

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The numbers in parentheses indicate the INID code.

SUMMARY

The present invention relates to a method for determining the direction of a flicker source with respect to a measuring point in an AC power network having a mains frequency (f_c) with low-frequency amplitude variations from the drying source.

The invention is characterized in that the method comprises the steps;

- receiving an amplitude modulated current signal (i (n)) comprising signals originating from the network frequency (f_c) and the low frequency amplitude variations in the current signal (i (n));

recording an amplitude modulated voltage signal (u (n)) comprising signals derived from the network frequency (f_c) and the low-frequency amplitude variations in the voltage signal (u (n));

forming a flicker effect with a character value by multiplying the low-frequency amplitude variations in the current signal and the low-frequency amplitude variations in the voltage signal, and;

analysis of the character value, the character value indicating the direction in which the source of interference is in relation to the measurement point. The method also includes a device intended to be used in carrying out the method.

TECHNICAL FIELD

The present invention relates to a method for determining the direction of a flicker noise source relative to a measuring point in an alternating current electrical grid having a grid frequency with low frequency amplitude variations from a noise source. The present invention also relates to a device comprising means for carrying out the method.

BACKGROUND OF THE ART

In electricity generation, generators are used that provide an alternating voltage around a certain frequency. The user of the electricity produced is aware of the frequency that applies and the voltage supplied on the electricity grid. The user of the electricity grid wants to get as clean electricity as possible, ie wants electricity that is well defined at the specified frequency and voltage. However, in conventional electricity grids that supply cities and factories, it is common for the electricity grid to include low-frequency voltage distortions. Voltage distortions occur when various devices are cyclically connected to the network, which include e.g. capacitances and inductances.

Large power-consuming installations such as induction furnaces, compressors, lift motors, pumps etc. help to increase the level of voltage distortion in the electricity grid. These loads often cause low frequencies (&lt;25 Hz) and periodic fluctuations in the voltage's effective value. The phenomenon is usually referred to as flicker. The most noticeable effect of flicker is the irritation that can be experienced from incandescent light bulbs whose light intensity fluctuates with the voltage variations caused by the flicker. Studies have shown that humans are particularly sensitive to light fluctuations with a repetition frequency in the range 0.5Hz to 25Hz. At the maximum sensitivity (about 9Hz), the relative voltage change need only be 0.25% to experience the light from the bulb flickering. Flicker problems arise primarily in areas with markedly heavy industry (ironworks and paper mills, etc.) but can also occur in areas with weak electricity grids and in the vicinity of wind power plants.

In the event of an unclean electricity network including flicker, it is interesting to know where the source of interference is. An electricity producer wants to show that it is a consumer who is cleaning up the electricity grid and can in such fail ask the consumer to pay a penalty or rectify the problem. Of course, a consumer wants to show that it is not he who is causing the impurity. In addition, the consumer wants value for money and thus wants to demonstrate that it is the electricity producer who supplies unclean electricity.

Addressing the problem of flicker is often an expensive operation where all or part of the grid may need to be rebuilt in such a way as to reduce the internal impedance of the electricity grid, e.g. through new and coarser cables. Another way to fix the problem is to install countermeasures to the current malfunction. Such countermeasures are normally very costly. Examples of countermeasures are Static Var Compensator (SVC) ”which dynamically controls changes in the system.

There are methods to determine the level of voltage flicker, as described in the standard IEC-61000-4-15. Measuring instruments that record voltage flicker in accordance with this standard demonstrate the presence of voltage flicker by calculating and presenting the parameters Ifl, Pst and Pit. However, there is nothing in the standard or in existing measuring instruments that shows the direction of the source of disturbance in relation to the measuring point.

EP 1072897 discloses a measurement method for determining the direction of a source of disturbance in a low current network where an induced error signal is generated in a conductor due to an external electromagnetic source of noise. The method includes the steps of measuring current and voltage in the conductor and then calculating the total power as ·· ·

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.j obtains a character value depending on the polarity of the measuring device. The method of EP 1072897 cannot be applied to a power network comprising low frequency amplitude variations (flicker) since induced signals are added (superposed) to an already existing signal and do not give rise to low frequency amplitude variations. Should the method be used in a normal state, the method would always indicate where the generator is located since the carrier frequency in the power grid is dominant and thus the method would not give any information about where the flicker source is.

CN 1195775 discloses a method for determining the direction of a fault in the form of a short circuit in a high current network. The method includes the steps of measuring current and voltage when the fault occurred, and then calculating the total power that receives a character value depending on where in the network the fault is. The method of CN 1195775 cannot be applied to a power grid comprising low frequency amplitude variations (flicker) since such error as referred to in CN 1195775 does not give rise to low frequency amplitude variations. Should the method be used in a normal state, the method would always indicate where the generator is located since the carrier frequency in the power grid is dominant and thus the method would not give any information about where the flicker source is.

US 4251766 discloses a method of determining the direction of a fault in the form of a short circuit in a high current network. The method includes the steps of measuring current and voltage in a normal state and in a state when an error has occurred. Then the total effect is calculated in both cases and a comparison is made. The method of US 4251766 cannot be applied to a power grid comprising low frequency amplitude variations (flicker) since such error as referred to in US 4251766 does not give rise to low frequency amplitude variations. Should the method be used in a normal state, the method would always indicate where the generator is located since the carrier frequency in the power grid is dominant and the method would thus not give any information about where the flicker source is located, and that the effects calculated on the two occasions would be equal and no difference would exist.

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US 4352137 discloses a method for determining the direction of a fault in the form of a short circuit in a high current network. The method includes the steps of measuring current and voltage in a normal state and in a state when an error has occurred. Then the total effect is calculated in both cases and a comparison is made. The method of US 4352137 cannot be applied to a power grid comprising low frequency amplitude variations (flicker) since such error as referred to in US 4352137 does not give rise to low frequency amplitude variations. Should the method be used in a normal state, the method would always indicate where the generator is located since the carrier frequency in the power grid is dominant and the method would thus not give any information about where the flicker source is located, and that the effects calculated on the two occasions would be equal and no difference would exist.

Thus, there is a great desire for a method and apparatus that can determine the direction of propagation of flicker. The direction of propagation of the flicker indicates whether the source of interference is above or below a measurement point and can thus be of great benefit when the source of interference is to be traced.

DISCLOSURE OF THE INVENTION

The present invention relates to solving the problems set forth above in low frequency interruptions which cause periodic fluctuations in the effective value of the voltage. Such periodic fluctuations will hereinafter be referred to as low-frequency variations or flickering.

The problems are solved by a method for determining the direction of a disturbance source in relation to a measuring point in an alternating current electricity grid with a mains frequency f_cwith low-frequency amplitude variations from the noise source. The method is characterized by recording an amplitude-modulated current signal and an amplitude-modulated voltage signal. Both the amplitude modulated current signal and the amplitude modulated voltage signal are signal processed in such a way that the low frequency

.. j The amplitude variations in both current and voltage are separated from the carrier in the form of a disturbance contribution for current and a disturbance contribution for voltage. The disturbance contribution for current is then multiplied by the disturbance contribution for voltage in such a way that a product is formed. The product is processed in such a way that a flicker effect Π is obtained with a sign value indicating in which direction a source of interference is in relation to the measuring point.

According to one embodiment of the invention, the sign value of the flicker effect in the measuring point is negative when the source of interference is below the measuring point and positive when the source of noise is above the measuring point.

The method has two important advantages:

1st The flicker effect in the measuring point is determined. Thus, the source of interference (flicker source) can be traced.

2nd The method is also accurate when the measurement is carried out via voltage and current transformers installed in the network. Frequency spectrum of a signal with flicker consists of carrier (eg 50 or 60 Hz) and on both sides of the carrier sidebands with frequency spacing to the carrier corresponding to the flicker frequencies. The frequency spectrum of the entire signal package (carrier and the low-frequency signals) is thus in a narrow frequency band around the carrier, which means that measurement via existing current and voltage transformers can be utilized since these are designed for the highest accuracy around the network frequency.

The invention can be carried out by a number of methods described below.

In a first method (method 1) according to one embodiment of the invention, the method is characterized by the steps;

receiving an amplitude modulated current signal in (n) comprising signals derived from the network frequency f_c and the low frequency amplitude variations in the current signal in (n);

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• ·· · ·· ·» ·· ·· · .

• ·· ······♦· ··_· ·· ··· · · · · · ·· · · · • · · ···· · · · ··· · · · ··· · • * · ·· · · · ·· « · ·· ·· ·· ·· ·

recording an amplitude-modulated voltage signal u (n) comprising signals derived from the network frequency f_c and the low-frequency amplitude variations in the voltage signal u (n);

signal processing of the current signal in (n) in such a way that only the low frequency amplitude variations remain in the form of a disturbance contribution for the current signal in (n);

signal processing of the voltage signal (u (n)) in such a way that only the low frequency amplitude variations remain in the form of a disturbance contribution for the voltage signal u (n);

-creating a product by multiplying the power interrupt and the power interrupt,

-processing the product in such a way that a flicker effect Π is obtained with a sign value indicating in which direction the source of interference is in relation to the measuring point.

An advantage of the first method is that it does not require any large computing capacity, but can be easily implemented in a suitable device.

According to another embodiment of method 1, the method comprises:

- the signal processing of the current signal in (n) comprises the steps;

- forming a first demodulated signal by demodulating the current signal in (n);

filtering of the signals originating from the network frequency f_c in the first demodulated signal in such a way that only the low frequency variations remain in the form of the power interference contribution;

- the signal processing of the voltage signal u (n) comprises the steps;

forming a second demodulated signal by demodulating the voltage signal;

filtering of the signals originating from the network frequency f_c in the second, the signal is demodulated in such a way that alone

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The low-frequency variations remain in the form of: the interference contribution for voltage.

In another embodiment of method 1, the method comprises the steps;

-deletion of the signals derived from the network frequency f_c in the first demodulated signal in such a way that only the low frequency variations regarding the disturbance contribution for current remain in the form of a disturbance signal 1_LF (n) for current;

filtering out the signals originating from the network frequency of the second demodulated signal in such a way that the low frequency variations of the voltage interference contribution remain in the form of a disturbance signal U_LF (n) for voltage;

-the product forms an instantaneous power signal Π (η) by multiplying the interference signal li_F (n) for current and the interference signal Ulfm for voltage;

-that the product is processed by averaging the instantaneous power signal Π (η), whereby the flicker effect Π is formed by the character value.

According to yet another embodiment of method 1, the method comprises: -the first demodulated signal is formed by square demodulation of the current signal;

-the other demodulated signal is formed by square demodulation of the voltage signal.

According to one embodiment of method 1, the filtering is performed with a bandpass filter with a lower limit of 0.1 Hz and an upper limit of 35 Hz. However, a preferred upper limit is 25 Hz.

In a second method (method 2) according to one embodiment of the invention, the method is characterized by the steps;

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*· · ·· • · · · • · » · · • ···· · · · • · · · • · ·· ·· ··· ·« ·· ·· · • · · ·· · » · · · · · • ·«· · • · · ·· ·· ·

receiving an amplitude modulated current signal in (n) comprising signals derived from the network frequency f_c and the low frequency amplitude variations in the current signal in (n);

recording an amplitude-modulated voltage signal u (n) comprising signals derived from the network frequency f_c and the low-frequency amplitude variations in the voltage signal u (n);

-frequency analysis of the waveform of the voltage signal u (n) by a by-point DFT (Discrete Fourier Transformation) analysis, which gives rise to a voltage vector U containing frequency spectrum of the voltage signal u (n) in the form of N p complex voltages;

frequency analysis of the waveform of the current signal in (n) by a N-point DFT (Discrete Fourier Transformation) analysis, which gives rise to a current vector I containing frequency spectrum of the current signal in (n) in the form of N complex currents;

forming a power vector P by elemental multiplication of the voltage vector U and the current vector I;

multiplying the power vector P by a weight vector W which eliminates power contributions derived from the grid frequency, the power vector P comprising sub-effects P_k regarding power contribution from the source of interference,

-creating a flicker effect Π with a character value by summing the partial effects P_k, och;

analysis of the character value, the character value indicating the direction in which the source of interference is from the measurement point.

In the second method, the voltage signal u (n) and the current signal in (n) are processed by the frequency analysis described above. The product specified in method 1 corresponds in method 2 of the formation of the effect vector P. The disturbance contributions for current and voltage in method 1 do not have their direct equivalent in method 2, but the disturbance contributions arise in the form of power contribution P_k with respect to power contribution from the source of power after the power vector P has been multiplied elementally by the weight vector W comprising ·· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ··· · · · ·· ·· · elements w_k. The processing specified in method 1 corresponds to method 2 in that the partial effects P_k summed.

According to one embodiment of method 2, the flicker effect Π is formed by the following steps;

-summary of the partial effects P_k by the formula:

N n = £ Re &lt;

An advantage of this method is that no demodulation residues are generated.

In another embodiment of method 2, the flicker effect Π is formed by the following steps;

-quared demodulation x² of the voltage signal u (n);

-quared demodulation x² of the current signal in (n);

-calculation of the frequency spectrum of the square demodulated voltage signal by an N-point DFT (Discrete Fourier Transformation) analysis which gives rise to the voltage vector (U);

-calculation of the frequency spectrum of the square demodulated current signal by an N-point DFT (Discrete Fourier Transformation) analysis which gives rise to the current vector (I);

-creating the flicker effect Π by summing the sub-effects P_k contributing to the flicker phenomenon by the formula:

n = £ Re * = 1

-W2_k-r_k ·· · • · • · · · • · ···· where the elements w1_k and w2_k replaces W_k and eliminates power contributions derived from the grid frequency and emphasizes the correct amplitudes of the frequency component Ur and l_k according to - for l &lt;k &lt;in U_c for k&gt; i - for \ &lt;k &lt;i 0 for k&gt; i where it is assumed that the low frequency interferences are in a frequency band up to and including tones in (0 &lt;&lt;i).

As shown above, both method 1 and method 2 give rise to the flicker effect according to the invention Π with a sign value indicating in which direction a source of disturbance is in relation to a measuring point. Thus, it is possible to signal the current and voltage signals in both the schedule and the frequency plane to obtain the desired flicker effect Π.

The invention also relates to a device comprising means for carrying out the above methods.

According to one embodiment of the invention, the device comprises means for determining direction of disturbance source in relation to a measuring point in an alternating current electrical network having a mains frequency f_c with low-frequency amplitude variations from the source of interference. The device is characterized in that it also comprises; means for receiving an amplitude modulated current signal in (n) comprising signals originating from the network frequency f_c and the low frequency amplitude variations in the current signal in (n);

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······ ······ ··· · · · ··· • · · • · · · • ···· · ·

means for receiving an amplitude-modulated voltage signal u (n) comprising signals derived from the network frequency f_c and the low-frequency amplitude variations in the voltage signal u (n);

means for processing the current signal in (n) in such a way that only the low frequency amplitude variations remain in the form of a disturbance contribution for the current signal in (n);

means for processing the voltage signal u (n) in such a way that only the low frequency amplitude variations remain in the form of a disturbance contribution for the voltage signal u (n);

means to form a product by multiplying the power interference premium and the voltage interference premium,

means to process the product in such a way that a flicker effect Π is obtained with a sign value indicating in which direction the source of interference is in relation to the measuring point.

According to another embodiment of the invention;

- the signal processing means of the current signal (i (n));

means for forming a first demodulated signal by demodulating the current signal (i (n));

means for filtering out the signals originating from the network frequency (f_c) in the first demodulated signal in such a way that only the low frequency variations remain in the form of the power interference contribution;

- the means for the signal processing of the current signal {i (n)) the voltage signal (u (n));

means for forming a second demodulated signal by demodulating the voltage signal;

means for filtering away the signals originating from the network frequency in the second demodulated signal in such a way that only the low frequency variations remain in the form of the voltage interference contribution;

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According to another embodiment of the invention, the device comprises;

means for frequency analysis of the waveform of the voltage signal (u (n)) by a N-point DFT (Discrete Fourier Transformation) analysis, which gives rise to a voltage vector (U) containing frequency spectrum of the voltage signal (u (n)) in the form of N complex stresses;

means for frequency analysis of the waveform of the current signal (i (n)) by an N-point DFT (Discrete Fourier Transformation) analysis, which gives a current vector I containing frequency spectrum of the current signal (i (n)) in the form of N complex streams;

means for forming a power vector (P) by elemental multiplication of the voltage vector (U) and the current vector (I);

means for multiplying the power vector (P) by a weight vector (W) that eliminates power contributions derived from the grid frequency, the power vector (P) comprising sub-effects (P_k) with respect to power contribution from the source of interference, means for generating a flicker effect (Π) with a character value by summing the sub-effects (Pk), and;

means for analyzing the character value, the character value indicating in which direction the source of interference is from the measurement point.

DESCRIPTION

The invention will be described below in a number of embodiments with reference to a number of figures therein.

Fig. 1 shows an equivalent two pole for an electrical grid according to the invention;

Fig. 2a shows variations in the voltage effective value U1;

Fig. 2b shows variations in the current efficiency value 1_L;

Fig. 3 shows a frequency spectrum for an amplitude modulated voltage signal with only one low frequency component;

·· • · « • · · • · • · ·· ··.:··.: : ^Μ.ί · «· · · · · · · · · · · · · · · · · · · · · · · · ···

Fig. 4 shows a signal flow diagram for a measurement method according to an embodiment of the invention;

Fig. 5 shows a signal flow diagram for a measurement method according to another embodiment of the invention;

Fig. 6 shows a signal flow diagram for a measurement method according to a further embodiment of the invention;

Fig. 7 shows an amplitude characteristic of a bandpass filter used in the embodiment described in connection with Fig. 6;

Fig. 8 is a block diagram of a device which can be used in the methods described in the various embodiments;

Figure 9 shows schematically a network comprising a noise source F1, a load L1, an alternator G for generating AC voltage, and;

Fig. 10 is a schematic diagram of the flicker effect Π for a number of sampling points n.

PREFERRED EMBODIMENTS

Below, both general theory and a number of embodiments will be described. The general theory is necessary for understanding the embodiments described below. In the equations described, a point between two letters of an equation indicates an elemental multiplication of vectors.

As mentioned above, the invention aims to provide a method for determining in which direction a source of interference is in relation to a measuring point. In directional determination of low frequency variations such as flicker, the waveform of voltage and current must be recorded in the phase or phases where the direction is to be determined. Thereafter, the recorded information should be processed according to any of the embodiments described in the signal flow diagrams below. The result of the signal processing is a flicker effect Π with a character value. The sign value indicates the direction in which the source of interference is in relation to a measuring point.

Figure 1 shows an equivalent two-pole for an electrical grid according to the prior art. The power grid can be schematically divided into three parts, which are usually called generator 1, transmission line 2 and load 3. When a load 3 is connected, a current I will flow in the circuit. This causes a voltage drop Uzt to occur over the internal impedance Zt whereby the voltage U_L over load drops. If the load is switched on and off periodically (cyclically), the current I will also increase and decrease cyclically, whereby the voltage U_L decreases and increases cyclically (provided the generator voltage Ug is kept constant).

In Figure 1, a measuring point 17 and a point 18 are shown which indicate a point above, ie upstream, the measuring point 17 and a point 19 which marks a point below, ie downstream, the measuring point 17. The terms above and below the measuring point 17 are essential when it is to be stated. in which direction the source of interference is in relation to the measuring point.

In accordance with the invention, at the measuring point, an amplitude modulated current signal (s) is received, including signals originating from a network frequency._c and low-frequency amplitude variations in the current signal in (n). The low-frequency amplitude variations originate from the source of interference. In addition, an amplitude modulated voltage signal u (n) including signals originating from the mains frequency f_c and the low-frequency amplitude variations in the voltage signal u (n). Here, too, the low-frequency amplitude variations originate from the source of interference

Figures 2a and 2b show principle diagrams of variations in the voltage effective value Urms for the voltage U_L and the stream's effective value Irms for the stream I. According to the invention, the changes in the effective values ​​of

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• · «· ·· ·· ·· current and voltage U_RMs and l_RMS the instantaneous changes in voltage and current resulting from the low-frequency amplitude variations from the source of interference. Figures 2a and 2b do not show signals derived from the network frequency. However, it is known that the low-frequency amplitude variations modulate the network frequency f_c. Any changes that occur in current and voltage and that result from the mains frequency are negligible. The effect value changes Urms and I_Rms thus reflects the instantaneous changes in current and voltage that can be derived from the low frequency variations. Therefore, in Figures 2a and 2b it is only interesting from the point of view of the invention to show the variations in the effective value of the voltage Urms and the effective value of the current I_Rms · The variations in the voltage effective value U_Rms and the current effective value Irms is, according to the method of the invention described below, depending on whether the source of interference is above or below the measurement point 17.

Figure 2a shows the situation when the flicker effect propagates from load to generator, with the changes in the effective values ​​for current I_Rms and voltage U_Rms occurs instantaneously and in a counter phase. As the load increases, the current I increases, whereby the voltage drop across Uzt increases, which causes Ul to decrease momentarily.

Figure 2b shows the situation when the flicker effect propagates from generator to load, with the changes in the effective values ​​of current I_Rms and voltage U_Rms occurs instantaneously and in phase. An increase in Ug gives an instantaneous increase in current I, which gives an instantaneous increase in U_L, thus providing a simultaneous change of current and voltage.

In a theoretical consideration of flicker, it is appropriate to let the current and voltage signals u (t), i (t)) be described as an amplitude modulation. The mathematical expression for such signals is given by [1] and [2] according to:

u (t) = cos (fiV + Ä) Jcos (ö&gt;_er + J3_C) [1] ·· · ·· ·· ·· • · · · · · · • · · ····· • ···· · · · ··· · · • · · · ·· ·· ·· ··

<img file="SE525331C2_D0013.tif" />

[2]

The signals consist partly of a carrier U_ccos (o_ct) resp. IN_ccos (coct) and the low frequency flicker signals U_mkcos (oct) resp. IN_mi &lt;cos (&lt;±&gt; kt. Index c refers to the contribution of the carrier and index m refers to the contribution of the low frequency variation. Index k indicates the index for a summation of k = 1 values ​​to N values.

Figure 3 shows a frequency spectrum for an amplitude-modulated voltage signal with only a low-frequency component (singular modulation). The low frequency component here refers to a low frequency tone which gives rise to the variations in amplitude of both current and voltage. By low frequency tone is here meant a low frequency signal.

Figure 3 shows the frequency bands that cause the low frequency variation. In Figure 3, f_c the carrier frequency and f_m frequency of the low-frequency variation. The frequency components of the singular modulation are found at the frequencies f_c, f_c-fm and f_c+ f_m.

Figure 3 also shows the amplitude U_c for the voltage of the carrier frequency f_c as well as the amplitude U_m/ 2 for the voltage contribution from the low frequency variation f_c.

Figure 3 shows that a frequency spectrum of the modulating tone forms an upper sideband f_c+ f_m and a lower sideband f_c-f_m with half the origin amplitude U_m in each sideband and located at a frequency distance from the carrier frequency f_c corresponding to the modulating frequency f_m. Low frequencies such as the low frequency interference give rise to sidebands near the carrier frequency. The higher the frequency of the disturbance, the greater the frequency distance of the modulating frequency from the carrier frequency.

in

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<img file="SE525331C2_D0015.tif" />

jit = {orthogonal}}

The flicker effect, Π, is the effect that originates in the modulating tones and can be drawn «γ *

Σ^σ«* ^cos^ + Ä) IΣ⁷^ ⁺«*) * = IA * = i * = 1 ² * = l 4 [31

The formula [3] shows that the individual low-frequency tones in current and voltage form, after multiplication and integration, the flicker effect. To determine this effect, the low-frequency signals in voltage and current must be known for amplitude and phase and can be extracted from signal packets [1] and [2]. This can be done in a few different ways leading to the same result. Examples of various methods are described below as various embodiments of the invention.

Below, two embodiments will be described which are based on the frequency spectrum of the sampled waveforms u [n] and i [n] being determined by performing an N-point DFT (DFT = Discrete Fourier Transform) analysis. In the practical case, a FFT (Fast Fourier Transform) analysis can be used, which is a calculation algorithm that provides the same information as the Fourier transform). Output from the analysis will be two complex voltage voltages and current vectors U and I, which contain frequency spectrum for u [n] and i [n] in the form of k = N p complex voltages U_k and streams l_k. The frequency resolution obtained depends on the selected sampling frequency (f_s) and the number of samples N included in the calculation according to the relation Äf = f₈ / N.

Mathematically, the vectors U and I are drawn:

[4]

<img file="SE525331C2_D0016.tif" />

·· ·· • * · · · · «· · · · ··· · · ·· / - [/ j, /₂ 513) ·· N »]“] ί®]

The complex effect, S, is created from the vectors U and I and contains the effect quantities P (average power) and Q (reactive power) per ton according to

- [5,,5₂,53,..-5_ν,] 4 | υ₂µ &amp; · | /₂| Ζ-α₂.] Ϊ́₃\ Ζ-α ± \ υ_Ν\ Ζβ_Ν · \ Ϊ́_Ν\ Ζ-α_Ν

1 | ί /, | · | /, | ζ ^ i | i / 2 | -i / 2 | z ^, l | t /₃| - | AKP₃, .... l ^ | - | ^ K ^.

⁺ jQ \&gt; Pi ⁺/]] [θ]

The active power P1 is obtained as the real part of Si, according to:

P₁= Re {5₁} = Re {P₁₊yö_l} [7]

Vectors U, I and S contain frequency spectrum from the angular frequency f = 0 Hz to f = f_s Hz. Often you want to fold the information and / or reset certain frequencies. A simple and effective way to do this is to introduce the weighting vector W according to:

W = [8]

The weighting vector W contains elements, w_k, which contains constants that are elementally multiplied by U, I and S. If the voltage vector U is to be reset to frequencies above half the sampling frequency, the following operation is performed (the point notation in [9] refers to elemental multiplication):

[9]

V, '- J ·· ··· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·

N for 1 &lt;k &lt;-

N for - &lt;k &lt;N. 2

Umoci is the modified voltage vector containing frequency spectrum up to half the sampling frequency. In addition, the elements of the voltage vector are zero.

Weighting element, w_k, can be selected so that the desired result is achieved. For example, filter characteristics can be achieved by selecting appropriate values ​​for the elements w_k. Furthermore, different weighting vectors for U, I and S can be introduced in order to achieve the desired result.

The flicker effect, Π, is obtained by summing the effects, P_k, which contribute to the flicker phenomenon. Namely

[10]

Figure 4 shows a signal flow diagram for a measurement method according to an embodiment of the invention for a first measurement method. The flicker effect ff is calculated by frequency analysis of the waveform of voltage and current.

The input signals to the signal flow diagram in Figure 4 consist of the two input vectors, u [n] and i [n], which contain the sampled waveforms for voltage and current. The distance in time between two indices (n and n + 1) in the input vectors corresponds to 1 / f_s, where f_s refers to sampling frequency.

·· ··· · · ·· · ·· ·· ·· ·· · ···· · ·· · · · · ······· ·· · · * · · · ···· · · · ··· · · · ··· · • · ♦ · · ·· ·· ·· ·· ·

By using the previously described theory on the signal flow diagram described in Figure 4, the flicker effect can be calculated. In Figure 4, two blocks are designated DFT which represent a transformation of the current and voltage signals in (n) and u (n) through a so-called Discrete Fourier Transform. The signal coming out of the DFT of the voltage signal u (n) is called U and comprises the components ΙΛΖβκ which refer to a number of values ​​for different angles, where index k indicates which point is referred to in the DFT. The signal coming out of the DFT of the current signal in (n) is designated I and comprises the components 1_kZ &lt;p_k which refers to a number of values ​​for different angles &lt;p_k, where index k indicates which point is referred to in the DFT. Figure 4 shows a multiplier 3 where the vectors U, i and W are multiplied. The signal from the multiplier is called P and refers to a power vector comprising components sub-effects P_k describing the active power of [7] as the real part of the complex power S of [6] and [7],

P_k = Re {0.5 w_k· | U_k | Ζβ «· | l_k | Ζ-φκ} [1 Oa]

Figure 4 also shows a summation point Σ which indicates the formation of the flicker effect Π by summing the active effects P_k according to [10a], where;

^π = Σ Re {0.5 w_k· | U_k | Ζβ_κ· I l_k In Z- &lt;p_k} * = 1 [10b]

Frequency spectrum of the waveforms u [n] and i [n] is calculated using an Npoint DFT analysis. Then, the flicker effect Π is calculated using [10]. The content of the weighting vector W is decisive for the final result. The elements in W must be selected so that the power in the carrier is reset and that only the tones that emanate from flicker are included. This can be done in three ways. Either you use the information from 1) the upper sideband, 2) the lower

<img file="SE525331C2_D0017.tif" />

the sideband or 3) by frequency summarizes the information in the two sidebands and then calculates the effect by utilizing [10].

To exemplify how the calculations proceed, we assume that the carrier signal is in element M of vectors U and I. We further assume that the low-frequency flicker tones in vectors U and I are in elements k with the indices:

Mi &lt;k &lt;M and M &lt;k &lt;M + i

The number of flicker tones is given by the constant i. If you choose to use the information in the lower sideband when calculating the flicker effect, the elements w_k in the weighting vector W according to for i &lt;k &lt;Mi '2 for M-i &lt;k &lt;M&gt;

for M &lt;k &lt;N

The flicker effect is then created using formula [10].

If one chooses to use the information in the upper sideband when calculating the flicker effect, the elements w_k in the weighting vector W is selected according to for &lt;k &lt;M 2 for M &lt;k &lt;, M + i 0 for M + i &lt;k &lt;N

The flicker effect is then created using formula [10].

<img file="SE525331C2_D0018.tif" />

·· · ·· ·· ·· ·· • · ········ • · ···· · · · ··· · · · ··· • · · · ·· ··

If one chooses to utilize the information in both sidebands to calculate the flicker effect, the elements Wk in the weighting vector W should be selected according to for &lt;&lt;k &lt;Mi '1 for Mi &lt;k &lt;M and M &lt;k &lt;M + i&gt; 0 for k = M

The flicker effect Π is then created by the formula il n = £ Re &lt;* «o (M-i + k) ⁺ + «- *)) [10c]

Figure 5 shows a signal flow diagram of a second measurement method according to another embodiment of the invention, in which the calculation of the flicker effect is done by square demodulation of voltage and current, after which a DFT analysis of the low frequency signals is performed.

The method is similar to the first measurement method described in connection with Figure 4, with the difference that before the frequency spectrum is calculated, the signals are square demodulated, which in Figure 5 is called X². Thus, the low-frequency signals are separated from the carrier as follows:

· - {l + cos (2ö?_ci + 2 /?_c)) = ' 7 «² (0 = \ uc + Συη, cos (öV + got) cos² (G) ct + Ä) =

U_c²+ 2 U_c- ^ U_mk cosfat + f_k) + cos (åV + Ä)

<img file="SE525331C2_D0019.tif" />

<img file="SE525331C2_D0020.tif" />

-z- + τ · 2 · U_c · ^ U_ak cos (t_kt + fi_k) + - · ^ U_mk cos ((o_kt + β

2 2 t_i

<img file="SE525331C2_D0021.tif" />

[11]

Square demodulation means that two frequency-separated signal packets are created. One signal packet consists of an equal component, the modulating frequencies and the modulating signals in square. The latter is an undesirable blend product. The second signal packet contains the same terms fixed in frequency centered around the double carrier frequency. When calculating the flicker effect, only the terms marked with double underline are included in [11]. One term contains the low frequency flicker tones multiplied by the carrier amplitude and the other term is the modulated signal in square. In terms of size, the first term is much larger than the second, which means that the squared term affects the result very little. Corresponding expression is obtained when squaring the current signal in (t).

The input signals to the signal flow diagram in Figure 5 consist of the two input vectors, u [n] and i [n], which contain the sampled waveforms for voltage and current. The distance in time between two indices (n and n + 1) in the input vectors corresponds to 1 / f_s. IX² each element is squared into the input vectors and constitutes input to the N-point discrete Fourier transform DFT. The output of the respective DFT are complex value vectors U and I containing frequency spectrum for u [n] and i [n] (both ·· ··· · • · · · · · · · ·· · · · · ···· * ···· · · · ··· · · · ··· • · · · ·· ·· · ♦ ·· amplitude and phase information) with a frequency resolution of Af = fs / N. the contents of U and I are drawn:

u = h, t /₂,£/₃.- ^,] = DCZ, | Za. | U₂kA, | c /, | zA .-, | Ka.]

The complex effect, S, is calculated by;

S = | h1, £ / w2₍·/· [12]

The desired flicker effect Π is then obtained by the formula n = ÉRe * »1 wl. -IF · w2_t ·/?

[13]

The elements w1k and w2k reset the frequency components that do not cause flickering and emphasize the correct amplitudes of the frequency components U_k and lk according to wl, - for \. &lt;k &lt;i ^Uc for k&gt; i [14] for \ &lt;k &lt;i for k&gt; i

<img file="SE525331C2_D0022.tif" />

»2, [15]

*. .·

In [13], [14] and [15], it is assumed that flickering tones are in a frequency band up to and including tones in (0 &lt;ffiimmer i) · The correct value of the weighting factors can be identified by studying [11]. The method is not limited to the weighting factors given above, but other constants in the weight vector can be used to obtain the desired filter effect.

Figure 6 shows a signal flow diagram according to a further embodiment of the invention for a third measurement method, where the flicker effect is calculated by square demodulation of voltage u (n) and current in (n) where the low frequency tones are filtered out using bandpass filters 2A and 2B, respectively.

Instead of utilizing DFT analysis and weight vectors described in the two previous embodiments described in connection with Figures 4 and 5, in this measurement method bandpass filters 2A, 2B are used to filter out the low frequency flicker tones.

The input vectors u [n] and i [n] contain the sampled waveforms for voltage and current. Components 1A and 1B are separated, like the measurement method described in connection with Figure 5, carrier (signal from mains frequency) and the low frequency flicker tones by squaring each sample. Only the low frequency flicker tones are allowed to pass the bandpass filters 2A and 2B. Thus, as input to the multiplier 4, only the low frequency flicker tones are in voltage Ui_F [n] and current Ιυ [η]. The output of the multiplier 4 is the instantaneous flicker effect Π [η] = u_Lp [n] xi_LU.N]. The flicker effect Π is obtained by the integrator 5 averaging the instantaneous effect IT (n). This can be done with a digital filter in the form of e.g. a low pass filter.

The bandpass filters 2A and 2B are dimensioned to obtain a lower limit frequency of 0.1 Hz and an upper limit frequency of 25 Hz. Alternatively, · · · · ♦ · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ·

· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ··· ·· ··· ·· use the bandpass filters that are defined standard IEC 61000-4-15 which describes a flicker algorithm.

The transfer function of the filter in the IEC standard is plotted ka&gt;_} ss² + 2ÅS + O)² + J / island?₂ (s + l / &lt;y₃) (. s + l / &lt;y₄) [16]

The coefficients in [16] must have values ​​according to the table below.

<td>k = 1.748 02</td><td>λ = 2π ·· 4.059 81</td>

<td>ω₁= 2π · 9,154 94</td><td>ω₃= 2π · 1.225 35</td>

<td>ω₂= 2π · 2.279 79</td><td>θ4 = 2π · 21.9</td>

Table 1.

Figure 7 shows the amplitude characteristics of the bandpass filter with transfer function according to [16] and coefficients according to Table 1.

It is also possible to select bandpass filters with characteristics other than those described in [16]. For example, you can choose a M order of the Butterworth or Chebyshev filter.

Figure 8 shows a block diagram of the hardware of the instrument. The instrument is built around a signal processor 7 which administers the measurement information, performs the necessary calculations according to the measurement methods described in Figures 4-6 and 9. The signal processor 7 also controls the sampling process in the conversion of analog signals into digital signals (the A / D conversion). The recorded signals, ie. The waveform of current and voltage is obtained either from current and voltage transformers in the network or from measuring transducers available in ·· * ·· · · · · · · · · · · ····· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · »· ·· ·· · instrument. The signal processor may be a computer or a logic circuit, or some other suitable device for controlling devices and for processing signals.

Figure 8 shows a signal conditioning device 8 for the recorded voltage signal. The measured voltage is signal matched by a resistive voltage split, whereby the correct input signal level is obtained to the subsequent step, which is an Anti-alias filter 11.

Figure 8 also shows a signal conditioning device 9 for the received current signal. The signal level of the current channel is adjusted to the instrument either via low-ohm shunting, whereby the voltage drop across the shunt is amplified and becomes the input level to the subsequent step which is an Anti-alias filter.

10th Alternatively, the current signals may be obtained from current pliers connected to the instrument.

The task of anti-alias filters 10, 11 is to prevent folding distortion, which occurs if the received signal has a frequency content exceeding half the sampling frequency (see the theory of the sampling theorem). The anti-alias filters can be implemented in the form of an analog Sallen-Key low pass filter according to Fig. 7 and have a limit frequency corresponding to half the sampling frequency.

The level-matched and filtered signals are sampled in sampling devices 12, 13 with a sampling frequency, e.g. 6400 Hz. The digital raw data in the form of sampled amplitude values ​​is stored in a measurement memory 14 and then constitutes input to the measurement methods mentioned above.

The software that controls the signal processor 7 is in a program memory 15. The final result, ie the flicker effect with character value and the internal impedance, can be displayed both numerically and graphically in a presentation device 16. The presentation device can be any of the ·· ··· · · ·· · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · ··· «· · ·« ··········································································································································· I Preferably known device for numeric and graphical presentation, e.g. a monitor.

V *. ·

Figure 9 shows schematically a network comprising a source of interference F1, a load L1, a generator G for alternating voltage generation. In Figure 9, the current direction of the current I is shown with an arrow in the connection lines. The current goes from generator G to interference source F1 and load L1. Figure 9 also shows a first measuring point M1. In connection with M1 there is marked a point above 18 and a point below 19 measuring point M1. Figure 9 also shows a second measuring point M2. In connection with M2 there is marked a point above 18 and a point below 19 measuring point M2. The source of interference F1 in the network emits a low-frequency amplitude variation that propagates in the direction of a solid arrow 20 shown in Figure 9.

Using the inventive method described above, the sign of the flicker effect anger indicates the direction in which the source of the disturbance is in relation to a measuring point. According to one embodiment of the invention, the sign value of the flicker effect is negative when the source of interference is below 19 measurement point and positive when the source of interference is above 18 measurement point.

Thus, in the first measuring point M1, a negative sign of the flicker effect Π is obtained, since the source of interference F1 is below 19 the first measuring point. This is because the low-frequency variations in current and voltage are in the opposite phase in the first measuring point M1.

In the second measuring point M2, on the other hand, a positive sign of the flicker effect Π is obtained, since the source of interference F1 is above 18 the second measuring point M2. This is because the low-frequency variations in current and voltage are in phase in the second measuring point M2.

• · • · • ·&lt;

In Fig. 10, a diagram of the flicker effect Π for a number of sampling points n is shown schematically during a certain time interval when recordings were made of the modulated current and voltage signals in (n), u (n).

In Figure 10, a first curve K1 is shown on the negative lower part of the diagram. In addition, a second curve K2 is shown in the diagram on the upper part of the diagram. The first curve K1 corresponds to a power signal which, after averaging, gives rise to a flicker effect Π with a negative value and is thus corresponding to the flicker effect Π obtained at the first measurement point M1 in Figure 9. The second curve K2 corresponds to a power signal which, after averaging, gives rise to a flicker effect Π with a positive value and thus corresponds to the flicker effect Π obtained at the second measurement point M2 in Figure 9.

In Fig. 10 it is also shown that K1 mirrored over the sampling axis n corresponds to K2. This has proven to be a good match in experiments and has its explanation that the flicker effect Π exchanges signs as the spread of the low frequency disturbance changes from going towards the root direction of the tone to going with the root tone direction, or vice versa. It is thus necessary to know in which direction the generator and the load are in relation to the measuring point in order to be able to interpret the sign value correctly. The part of the diagram showing the period between zero and when K1 and K2 respectively starts, shows a time period when the source of interference F1 is not connected.

• · · • · « • ··· · 4