DE19539547A1 - Electronic meter for measuring electric work as power consumed by electric unit - Google Patents

Abstract

The electronic meter has an analogue-digital converter to give a digitised measurement of the working current and voltage. For the real time operation, the digital amplitude of the values of U and I are multiplied by a digital multiplier. The resulting positive and negative parts are both integrated by a summation building of each half wave. This leads to the effective work, which is indicated in a meter reading. The additional steps required for the effective value formation and the consideration of reactive components, required using alternating values. Also the further computing of the electrical values for the result, can be dispensed with. Because the reading of the measured electric work can be realised, by the mathematical physical use of the theory of electron flow (ES) and ion flow (IS).

Description

A large number of devices are known which use electrical energy measure electronic counting devices.

A wide variety of electronic counters are used, which are Principle, or count on an analog and digital basis. A the book provides a good and detailed description of this: "Electrical energy, electronically measured "[0].

In general, the illustrated and other electronic counting devices have such a type Properties on that they are not yet able to seriously reduce the induction counter replace.

Because it is becoming more and more necessary, besides measuring the energy at the same time Device reference variables of any electrical parameters z. B. for the purpose of The induction meter will be able to supply energy control or regulation in the future Not meet requirements. This also includes data exchange for billing and Tariff management variables, because this should be easily created using modular solutions be.

Of course, with the current state of the art, these requirements are no longer a hurdle also with the conventional induction counter. Solutions are known that allow pulses to be taken from the rotating disk of the counter and processed accordingly. These impulses can be with the electronic Prepare data processing in any form so that all requirements are met can, as listed above. However, these claims require one equipment expenditure, which the manufacturers obviously cannot afford because an all-electronic measured value acquisition is to be expected in the foreseeable future that the Place the described solution immediately in the area of an outdated technology. With my explanations it should be achieved that with reasonable means a device can be produced, which with pure digital electronic means the described and a number of other claims.

It is currently evident that the digital measuring instruments for current and voltage are different prevailed over conventional measuring devices with mechanical pointer deflection to have. Despite the existence of all technical requirements for a digital Electrical energy metering device (ELT metering), this device is not yet on the market broad base available.  

The problem that the electronic solution does not yet have the necessary scope among other causes lies in the current interpretation of the measured values Current I and voltage U. More specifically, U and I z. B. by the crest factor in the case of sine variables, a value of

ξ _S = (1)

[1 p. 23], processed for further calculation. The crest factor is one Ratio, formed from the quotient of the maximum or peak value and the RMS value of the respective amplitude, which is measured over a half-wave. In the context of electronic data processing technology, there are rich, inexpensive and space-saving hardware and software solutions that are able to handle them correctly, with few resources the product of U × I × time required for the energy to form and interpret it as a usable digital value, or for the most diverse To make representations available.

E = UIt (2)

Eq. 2 is the energy resulting from the output values of direct current and direct voltage results. If it is alternating current and alternating voltage, Eq. 2nd known to be in the following form, with the phase shift = 0 first should be present.

e = u · i · t (2.1)

Of the applicable input values for the Elt count, namely u and i, it is advantageously not necessary to use the effective value, but can be dispensed with on the basis of the solution according to the invention. The effective value is anyway only a mathematical statement with a physical background, which emerged from the history of the emergence of electrical measurement technology as an obvious finding. The electrodynamic measuring mechanism and the induction counter are only supplied with the pure sine variables of u and i in their measuring task and it cannot be assumed that their mode of operation will result in processes which are equivalent to the formation of an effective value. A few more comments on the arithmetic or algebraic mean. According to [2 p. 137] this arithmetic mean is simply defined as half of their sum for two quantities a and b. With n sizes a₁, a₂,. . .a _n the value is calculated according to the known relationship

However, the result is not used in electrical engineering using Eq. 3 found, but it will certain integral solved as follows

As is known, this result can be converted into an area by the following calculation Amplitude size

To some readers, this derivation will appear somewhat erratic, so that here too Representation according to [1 p. 18] with the output equation of the current

i = I _{max or vertex} sin α

should be done.

Half the period is π. The algebraic mean thus results in

This result 0.637 is thus an average amplitude, which corresponds to the side length of the rectangle, which has the same area as the calculated area of the integral according to Eq. (4) was determined. It is the integral amplitude or it is the calculated amplitude value from the equivalent area according to Eq. 2.1 in relation to the direct current values according to Eq. 2. The formula symbol for these integral amplitude values should be for the current I _⌀ and for the voltage U _⌀ . If the reader deals with these relationships, we will be able to reach the following agreement for the definition of nominal alternating current and voltage.

U _n = 0.637U _apex = U _⌀ (4.1)

I _n = 0.637I _crest = I _⌀ (4.2)

Why the integral amplitudes I _⌀ and U _{⌀ should be used} as input variables for the power and energy is to be derived from the physical relationships of the mechanism of the electrons in the electrical conductor.

So that the reader can understand this electron theory briefly a few explanations. It originated from a topic that I had in the context of my diploma thesis in 1975 edited. In the 20 years of hard work, I have a number of patents written, but found no response. From this the electron theory can be read, [3 pt. 2.1.1.] Unpublished works, however, can affect the image for the attentive reader first round off.

What should be taken from the scriptures? The electrical voltage is a SI unit and is measured in V (volts) and as Potential difference shown.  

It is defined verbally in [4 S 17] as follows. "1 V equal to the electrical voltage between two points of a conductor in which the power 1 W at a current of 1 A is implemented ".

Thus, the voltage is considered a static value. The energy created by one There is nothing static about determining the counter. This energy comes from the movement e.g. B. the turbine as the drive unit of the Elt generator. So it’s obvious that for this energy also the corresponding input variable in the form of a movement variable must be used.

That the energy is something dynamic can also be deduced from the SI unit work where the following is defined in [4 p. 15].

1 electron volt (eV) is defined as the kinetic energy that an electron passes through a potential difference of 1 V in a vacuum.

In order to convert the tension from the static state into a dynamic state known with two options.

• 1. from the electrical power according to the relationship
• 2. from the kinetic energy of translation according to the relationship

According to Eq. 5, the dynamic voltage is calculated from the following output variables:

I got the dynamic voltage from the conditions of the physics ion current (IS) called. IS is calculated according to Eq. 5 thus too

IS from option 2 is calculated using the following initial values:
The mass or rest mass of the electron is m = 9.11 · 10 ^-31 kg.
With a volt potential difference, this electron receives an energy of 1 electron volt. Specifically, an eV = 1.602 · 10 ^-19 Nm [4 p. 15] is assigned.
The second value thus results in

The fact that the two values differ from one another can have many causes. Maybe it turns out once out that such quantities as the electron mass, the defined energy of eV or the other input variable are changed by tiny orders of magnitude. That could be too approximation of the two values.

How does IS appear in contrast to voltage U? Compare Figure 2.

Figure 2a shows the well-known sine wave of the voltage, as can be made visible in the oscillograph.

Figure 2b shows the dynamic voltage IS, which occurs as the electron velocity. In contrast to Figure 2a, because it is a speed, there are no negative values. This fact can be shown mathematically, as it is already written down in Figures 2a and b. The known initial equation for the calculation of the instantaneous values according to Figure 2a is.

u = U _vertex sin ϕ (8a)

The following applies to the velocity-time diagram of the electrons in the form of the instantaneous values following equation.

is = IS _max (1 - sin ϕ) (8b)

In the comparison of the images 2a and 2b is seen that a maximum voltage (it occurs in the image 2a and 2b at the time of 5 ms and 15 ms on) an ion-speed IS = causing 0th If the voltage passes the 0 point in Figures 2a and 2b at 10 ms, IS will reach its maximum speed.

From the point of view of the elementary processes in the leader, the times 5 and 10 ms describe as follows.

At the time g is 5 ms. U = max = 1 and IS = 0, i.e. H. the IS electron is on Reversal point and has a maximum distance to the origin atom. This The turning point also seems to be the point in terms of place and time at which a mutual influence of the IS electron with the ES electron in the form of the largest Probability takes place. The mechanism of energy transport using ES The reader can read about electrons in [3 and 6]. One can say that in this Influencing the origin of the heat of electricity or the amount of heat is caused by exposure is produced by current and voltage. The term should be better for electricity heating Power conversion or the like can be used because heat does not arise from electricity alone. At any generation or dissipation of heat caused by electricity is U and I. involved.

At the time 10 ms, with U = 0 and IS = max or 1, the IS electron is the smallest distance from the nucleus of the origin. Since it has maximum kinetic energy, and at the same time it is highly likely that this kinetic energy is supported by the electric field of the magnet wheel, the IS electron moves to the reversal point 15 ms. This can be seen in Figure 2c.

The velocity-time diagram was created by placing the origin of the coordinate at ν _max = 1 and furthermore, no coordinates with negative sign had to be created in the diagram.

Why should the integral amplitudes U _⌀ and I _⌀ be used for the power or energy determination instead of the RMS values of U and I?

The following example of a voltage measurement is the most meaningful. Let there be a sinusoidal 50 Hz voltage

• 1. the peak value 1 V
• 2. the peak value 2 V

available.

An oscillograph, a moving coil and a moving iron instrument are used for the measurement. How do the different measuring devices now perform the individual measuring tasks?

To 1

As is known, the moving coil measuring device shows the value 0. The oscillograph realizes a display according to Figure 3a. The measuring device with the moving iron measuring device adjusts itself to a value which results as follows. The curve in Figure 3b is to be used, in which the peak value of the amplitude is also 1 V. Curve 3b is known as the i² curve, or it can be measured in the oscillograph in real-time mode by multiplying u and i in real-time mode and simultaneously outputting it as a 50 Hz curve according to Figure 3b. How is the RMS value to be calculated from the 50 Hz curve, but when interpreting this curve one should not assume a representation with double frequency, since after the definition of the oscillation there is no double frequency. The RMS value of an alternating current or voltage is defined as follows according to [0 p. 188].

"The rms value of an alternating current is defined by the direct current value at the same amount of heat is generated in the same times in an ohmic resistor like through the alternating current ".

The definition includes the concern for a defined electrical constant Equivalent change size to show what can be achieved by means of the effective value believes. You will no longer be able to do justice to this concern in the future, because with the current numerical value of the effective value an incorrect value applied becomes.  

In order to take a closer look at the numerical value, the one in the effective value definition should first be considered exposed term amount of heat are illuminated in more detail.

The heat quantity has the formula symbol Q according to [5 pt. 5.7] and is determined by the SI unit (J) Joule reported. In [4 p. 15] you can also read that

1 J = 1 Ws

corresponds.

It can be seen from this that the heat of electricity is therefore the amount of heat of one Energy, which is based on the proportions. GL. 2 composed. The averaging results from this situation as follows:

Analogous to Eq. 4 is again the size of an area, that is to say an amplitude value of the AC power analogous to I _⌀ and U _⌀ of

Analogous to Eq. 4.1 and 4.2, the nominal power of alternating current and voltage define as follows.

P _n = 0.5P _peak = P _⌀ (9.1)

With the determination of the value according to Eq. (9 or 9.1) the averaging is complete. An additional step of averaging from the mathematical calculation of the quadratic mean is not appropriate because the application of this method is wrong Result produced.

A comparison should clarify this state of affairs.

The effective value deviates from the integral power amplitude by 41%. The problem lies furthermore in the fact that the effective value formation is based on a performance, that is performs a quadratic sine function. The application and further use, however is tailored to the current and voltage of an elementary sine function. Here the values 0.5 and 0.637 are compared, which corresponds to an error of 27%.

How do the displays look like example 2 with U _peak = 2V. The moving coil instrument again shows the value 0. However, circuits are known which allow a measured value display by means of rectifier diodes. Because of the behavior of the threshold voltage in rectifier diodes for measuring small voltages according to [7 S 35f] half-bridges, if necessary also with additional electronic amplifiers.

A rectifier circuit would result in a measured value of 2 × 0.637 = 1.274 V. A figure according to Figure 3c would be visible on the oscillograph.

From the point of view of dynamic tension, there is a real value analogous to Figures 2a and 2b, which corresponds to the complex of equations. 4, 7 and 8 can be represented as follows.

IS _⌀ = IS _n = 0.637IS _max = U _⌀ = 1.274 V (10)

At this point it should be remembered again that the electron at the location IS _max has come closest to the original atom. If IS _{crest is} reached, then the speed = 0 and the electron or electrons are at the point of reversal. With these few explanations, I hope to have made it clear that the originally arithmetic value, but now shown as an integral current or voltage amplitude, should be used for any further calculation. This statement does not mean that electronic data processing must be followed in accordance with such a scheme to determine energy consumption.

What does the moving iron measuring device show? According to picture 3d, P _peak = 4W. According to Eq. 9.1 is P _⌀ = 2W. The scale of the measuring device calibrated to a voltage must therefore have a scale value of 1.274 V at this point. Since there is the possibility, as already stated, of using a moving coil instrument or digital measuring mechanisms, such a calibration can be dispensed with.

Using the effective value would result in a display value of 4 × 0.707 = 2.828 V out. Due to the calibration, however, the calculation is 2 × 0.707 = 1.414 V to make. Nevertheless, the error is 1.414 / 1.274 = 10.9%. For the actual display value 2 W, the error is 1.414 / 2 = -29.3%. The interesting question is why the moving iron instrument has a square display makes. It is more correct to assume that there is not a square display, but a performance indicator. How does this happen. It is known that a current measurement is realized by converting the real current value into an analog voltage becomes. This can be achieved using the transformer principle (current transformer), or by means of a voltage tap via a defined resistance (shunt). The characteristic of the iron in the moving iron measuring mechanism has one in an electromagnetic field Property that for the pointer deflection in addition to the IS- offered by the voltage Electrons the additional same quantum of ES electrons from the energy source requests. It therefore has a behavior, as is known in hot wire instruments, which also need energy (heat generation from electrical energy).  

The oscillograph performs a pure voltage evaluation. In the vacuum chamber of the Braun tube, only IS electrons emerge from the electrode due to emission. The degree of deflection, caused by the action of the baffle plates, indicates the level of tension. With such a measuring method, no ES electron is required, so that a pure voltage measurement can be assumed, the exact value of which can be most easily determined by measuring IS _⌀ and ES _⌀ using the Braun tube. For the implementation of this project, a measurement is made on the basis of a comparison or a comparator similar to Figure 5, only the comparison method is not based on heat.

First, alternating current with direct current and alternating voltage with direct voltage be compared with each other oscillographically. This is with a two-beam oscilloscope to realize advantageous. To determine the equivalent measurement of both channels To prove it, a channel change can be made to check the truth after the Take measurement. When comparing energies of direct and alternating quantities, that is To activate the pair of measuring plates of the oscillograph by means of a multiplier, which is supplied with current and voltage at the input and supplies the output "power" which as already mentioned serves as an input variable for the oscillograph. With this circuit visible that the amount of work of changing quantities according to the definition [14] 1/4 the work resulting from equals (see also end of this section).

To Eq. 8a and 8b cf. see Figures 2a and 2b in the form

u = 1sin ϕ = sin ϕ (11a)

is = 1 (1 - sin ϕ) = 1 - sin ϕ (11b)

there is still from the point of view of classical physics according to the law of conservation and Conversion of energy [8 p. 12f] interpretation options.

According to [9 p. 108] this law reads:
"In a closed mechanical system, the sum of the mechanical energy (potential and kinetic energy including the rotational energy) remains constant".

It is used by the following equation (for an explanation of the indices see table of the Formula symbols) described.

E _p + E _k + E _r = E _tot = constant (12)

First of all, it can be assumed that E _r , the rotational energy 0 = is assumed. The rotational energy would have to be applied to ES, however further explanations in this regard are not to be made here. This reduces Eq. 12 on

E _p + E _k = E _tot = constant. (12a)

Now equations 11a and 11b and 12a are to be connected. To following introduction.

The equivalent relationships from mechanical to electrical energy show that Equations 7 and 8. Because the electron has a mass, as already mentioned, can be as is known from the velocity associated with the mass according to Eq. 6 the corresponding Allocate energy. I take the view that Eq. 6 regarding the determination of the Energy content is applicable. In contrast, we know the relationship of the moving Dimensions [10 p. 97]

which says that with speed the energy, and therefore the mass of a body grows. This statement does not apply to the electron movement, which will be confirmed if the example described in [6 pp. 10-13] is demonstrated in the form of an experiment. [6 p. 10 Eq. 2] shows that an electrical voltage of 510 V at accordingly existing short-circuit power of the voltage or energy source are suitable, the To give electron a speed greater than the speed of light. Because of this fact is not Eq. 13 but, as already stated, Eq. 6 applicable.

In analogy to mechanics, the function corresponds to Eq. 11a the course of the potential energy, and the function according to Eq. 11b the course of the kinetic energy. According to the energy conservation law

u + is = sin ϕ + (1 - sin ϕ) = 1 = constant. (14)

To round off what is shown, the following should be written down for the effective value. The effective value is a good term, but its definition is not correct. The definition is incorrect because the physical quantities of current and power are mixed together, which leads to errors. This should be based on the following definition taken from [11 p. 201]:
"The RMS value in AC technology is the value of the current that produces the same thermal effect in an ohmic resistor as a DC current" can be shown again from the following point of view.

The current is according to Ohm's law

So in addition to the voltage U and the resistance R only one factor that is responsible for the heat effect, that is the power conversion. A definition of current = heat effect is not possible for the reasons mentioned and also because the comparison of the heat effect with only one electrical component of three leads to a false statement according to logical rules. With regard to the calculated value, reference should again be made to all equations 4 and 9. It can be seen that with all equations 4 in the evaluation of the current or voltage _sine wave the integral amplitudes I _⌀ or U _{⌀ are} meaningful and correct.

The meaning of the rms values of alternating current I and alternating voltage U must also in following consideration can be seen. If U and I are multiplied, the result is achieves a performance that works as z. B. in the 50 Hz system expressed a lot or one Embodies the amount that is 25% compared to working with direct current and direct voltage is.

Here it becomes necessary to generally point out some things about the electrical quantities. Because it It is often difficult to define sinusoidal or sin²-shaped quantities find out whether it is the respective elongation, determined by the phase position, which in the Argument is defined, i.e. a current amplitude, or whether it is the corresponding surface of the curve or the inclusion of the curve, or whether it is simply the representation of the course of the curve goes. So it is z. B. in AC power after DIN 40 110 [14] defines the performance over the area of a period. There is only one poor demarcation from electrical work, what to do with all electrical Sizes very difficult. This is very noticeable in this elaboration, so that actually a lot of things orally, so clarified with explanation and counter-explanation would have to be to then take the next step. Unfortunately this is not the case at the moment possible. My suggestion would be to use the elongation only, so timelessly define. The timeless definition is only possible through the formation of the effective value, because this is to be determined over a half-wave, that is, the time unit over a half-wave. Just there should be a time reference for this within the scope of the service. The effective value then is one pure amplitude size and can therefore be treated timelessly.

The time reference should only be made for the electrical work. That in the theoretical derivation of some things a time reference always has to be taken for granted, however this can be shown accordingly. With this statement regarding treatment time Power and energy I refer to the SI units [4 p. 15 u. 16]. There is the following known representation included.

Energy W = I U t and power P = U I or P = W / t  

Mathematical description of the electrical quantities for the count 1. Active consumption in the presence of a cos ϕ

When counting of active consumption occur by the condition cos φ = 1 ratios, as illustrated by Figure 3a and 3b. Current and voltage are in phase, so that the curve in Figure 3b can be formed as shown in Figure 4 with the representation of the active energy wave in the 50 Hz network in the form of individual steps. In order to correspond to the conditions of the energy, the coordinate designation of the abscissa axis is now carried out over time in Figure 4, ie with a 50 Hz network, as in the figure and the table, the sampling points can be seen in steps of 0.33333 ms, which corresponds to an angular step of 6 °, i.e. a radian of.

In the case of radians, the sampling point 7.1 (see Table 1, Figures 4a and 4b) in the current and voltage curve Figure 4a is connected by means of the line g for a better overview of the sampling point 7.1 of the power. Point 7.1 was also recorded outside the 0.33333 ms steps because the 45 ° angle represents a striking value. The amplitudes of u and i are at and the amplitude value of the power p is 0.5. The known mathematics of these sample or amplitude values results from the instantaneous power of AC quantities according to the relationship

p = ui (15)

Because in figure 4 u and i were chosen with the sizes I _crest and U _crest = 1 for the sake of a simple representation, the performance arises mathematically with P _crest = 1.

The equivalent circuit diagram for this example is shown in Figure 6a.

To the energy consisting of alternating quantities (i.e. alternating current and alternating voltage) count, Eq. 2.1 are written as follows.

e = p · t (16)

To count the instantaneous values, Eq. 16 in the following form.

E _⌀ = P _⌀ · t (17)

Assuming the maximum amplitude values of 1 V and 1 A, as well as for t = 10 ms without phase shift (according to Figure 4 of a half-wave), we get according to Eq. 17 and Eq. 9

Eq. 18 therefore contains an area value, which is expressed by means of the indicated transformation into the time domain as an energy value of 5 mWs, and accordingly according to Eq. 9.1 developed an integral power _value P _⌀ of 0.5. A more detailed description of the transformation of an area value into an energy value can be found in [6 p. 23 see wave]. The formation of curve 3b using Eq. 2.1 was carried out as in the illustration of item 7.1 with items 1-15 Table 1, Figures 4a and 4b. The curve in Figure 3b is thus identical to the curve in Figure 4b.

In order to count the Elt energy, the curve according to Figure 4b must be integrated. According to Eq. To calculate 18 E _⌀ , the area of E was used. In the time axis it is π, ie 10 ms. In the ordinate it is 1, which in the example is carried out with 1 W, or fractions or a multiple value thereof can be included in the calculations. This well-known fact can be seen from Figure 4c-e. In the time of 0-10 ms, an energy of 5 mWs was taken from the energy wave using E _⌀ according to Figure 4d with the assumed input parameters, whereas under conditions of constant power the energy has a value of E = 10 mWs.

Corresponding to the time interval of 0.3 33 ms in which the respective individual acquisition for the Integration is carried out, the individual integrals are summed. After the expiry of the Total integration over half a period can be done in the size of 5 ms be issued.

Is there a curve shape deviating from Figure 4b z. B. in the form of harmonics, the sampling points change, which usually changes the integration value to larger or smaller sums. These changes or energy differences of the different half-waves are taken into account in the subsequent electronic counter modules due to the effect of the overflow or, more correctly, the transfer.

2. Active consumption at cos ϕ = 1 to 0, especially

In the following considerations, the terms power and energy seem a little to be treated incorrectly. It should be borne in mind that in the Colloquial, or in the opinion of electrical engineers in the context of the term Voltage and the current of various meanings, which are not always new z. B. as Instantaneous value, effective value, mean value, nominal value, course, leading, lagging, Peak value is defined. All of these terms can also be applied to performance, where the power according to the SI definition "1 W is the power of a uniform process in which the work is done in 1 s 1 year "[4 p. 16]. The time is included in the definition in the performance, but it is included in the considerations Current and voltage are always companions, although basically a timeless yet time-related amplitude value.

The phase shift should be 45 °, with, as in the previous example, U _peak and I _peak both being 1 V and 1A. The apparent power can be calculated

S _apex = U _apex · I _apex (19)

Eq. 19 is assigned concrete values by the equivalent circuit diagram (see Figure 6a). If you want the apparent power according to Eq. 19, you will find that the result leads to the statement in Figure 4b. To access the statement of the image 7b, initially applies the graphical representation of Figure 4a and 4b. The integral over the curve 4b gives the full picture of the content over the power content viewed over a half-wave. If the cos ϕ is taken into account, then Eq. 19 into the known form of determining the active power using the following equation.

P _peak = U _apex · I · cos φ _{the apex} (20)

For Eq. 20 is no longer applicable to Figure 4, but now the graphic representation in Figure 7 with the associated Table 2 and the equivalent circuit diagram in Figure 7b applies. However, the part of the active power from which the energy or power results over the time range of a half-wave cannot be seen from Figure 7b. But you can see the negative portion of the energy in the time range of 0-2.5 ms. During this time, IS and ES are opposed, there is reactive power or reactive energy. The positive energy wave in the time range 2.5-10 ms embodies the proportion of active energy according to Eq. 20 if the energy component is subtracted 0-2.5 ms.

With this way of looking at it is possible to do it within half or full period through the integration already described, the actual energy consumption as a numerical value with the unit Ws or the resulting part and multiple sizes.  

This mathematical-physical quantity can be transferred to the corresponding counting unit forward the overflow principle. In the next half wave or period, the repeats itself Process with constant or changed power, phase shift or frequency. These brief explanations are intended to make it clear that the possibility of enables simple electronic arithmetic unit for an Elt counting device because not the equation in the time domain of a half wave or period

according to [4 p. 16] must be used, but the task is with the mathematical Basic arithmetic subtraction accomplished.

In electrical engineering there are a number of mathematical aids for more convenient Calculate known, of which e.g. B. the transformation into the complex or imaginary level be called. In real-time operation of energy, however, simple subtraction can be used will.

It is possible because the calculation is also not based on the theory of rotating pointers, but with the electrical scalar quantity energy per half wave according to the following relationship is expected.

e _HW = pos _HW - neg _HW (22)

Mean in it

e _HW = active energy component of a half wave,
pos _HW = energy portion of the positive half wave, and
neg _HW = energy component of the negative half-wave.

If the reactive power of a half wave is determined, this is according to Eq. 23 as follows to make.

q _HW = 2 · neg _HW (23)

To Eq. 23 to be able to better assess the "blind component" in the statement of the energy component, the reader should research the statement on the wave at [6], especially pages 25 and 26.

Before the determination of the cos φ received, shall be provided to previously made statements of mathematical proof in hand of a discussion with the pictures 4b and 7b. The value is from Table 1 and Figure 4b

P _apex = 1 W (24)

read. The following statements are made from Table 2 and Figure 7b.

The numerical values can be found in table 2, points 3.1 and 18.1.

With the values Eq. 25 and 26 the following subtractions are now carried out.

pos _HW - neg _HW = 0.853573 - (-0.14643) = 1.000003 W (27)

The deviation with the 3 in the 6th position to 1 results from the inaccurately chosen Angular values in the context of the trigonometric function.

It can be seen that equations 24 and 27 are identical with 1 W each. This comparison proves the size of the apparent power according to Eq. 19. In order to calculate the active power, the reactive power must be determined. This can be done by determining the contents of the area 0-2.5 ms, i.e. neg _HW and 2.5-10 ms = pos _HW according to Figure 7b.

First, the energy content is to be determined, which is given by Eq. 24 or 27 is expressed. The relevant solution has already been described in the context of Eq. 9, and at Eq. 18th traced again in individual steps. However, the integration took place in the area what the result

led. When viewing Figure 4b, it says that the energy content of the half-wave is 0-10 ms, e _HW = pos _HW = 5 mWs. As a reminder once again on the images 4d and 4e made. In order to calculate neg _HW , the graphic display is first realized by setting the start of the curve to 2.5 ms (point 7.1, table 1). The later start of the recording is compensated for by adding the same time to 12.5 ms. By drawing the zero line at an amplitude = 0.5, Figure 8 is created. The curve obtained in this way has its appearance due to the conditions cos ϕ = 0, that is to say from the occurrence of pure reactive consumption. The representation of the right ordinate makes this clear once again. According to the course, this curve is a sin² curve, which, however, runs through an entire period within a period of 10 ms. This is a known mathematical fact given by the course of the curve

the goniometric function of the double angle.

In [6 p. 27] I commented that the given course of the curve is not so it should be interpreted that it is a double frequency.

Eq. 28 can be symbolically described using the given course of the curve.

In the general spelling, Eq. 29.1 over into the form

sin · sin + x = ± ASin 2x (29.2)

Taking into account the elongation in the positive and negative range, the information is The amplitude and argument (angle) for the energy can be found in Table 3. As an an example there is a phase shift with the amount or value of 45 °, which is indicated in line 45 Tab. 3 lets you read the following values. Peak value of positive amplitude = 0.8535533 W, Peak value of the negative amplitude = -0.1464467 W. The value range of the positive Half wave corresponds to 135 °, at 50 Hz this corresponds to a time of 12.5 ms. For the negative Half wave the values 45 ° and 2.5 ms can be determined.  

Figure 8 serves in addition to the clarification that the basic course of the sin² curve is retained even when the phase is shifted, secondly to the concrete energy content z. B. to determine in the unit mWs as an explanatory intermediate step, so that the energy share of neg _HW as a prerequisite for the quantification according to Eq. 23 can be proved mathematically. In particular, however, the proof is to be provided that the arithmetic treatment of the energy components as a mathematical starting point for the counting function of the electronics is correct, ie patent-relevant.

The reactive energy content E _B according to Eq. 29, shown in Figure 8, is calculated as follows, assuming U _crest = I _crest = 1.

In the negative range of the amplitude, i.e. the ordinate, the size of the Rectangle with the parameters

in order to

and the Abscissa

to Rectangular area

E _B results from Eq. 30.3-31

as a mathematical expression.

According to Eq. 18 can be the actual energy content by means of

determine in the form of pos _HW by the three-sentence.

According to Eq. 32 is

Now the project is to be realized to mathematically determine the active consumption according to Eq. 22 at a cos ϕ = 0.7071, starting with the area determination of neg _HW . The integration limits for this area are.

The same calculation method is used for the determination of pos _HW .

With the calculated values, sin can now be proven that with the basic calculation type subtraction in the mathematical level of the work the result according to Eq. 20 is achieved. Here are the Values of Eq. Subtract 35 from 38. 3.7770453-0.2415119 = 3.5355334 mWs. Now the calculation according to Eq. 20th

The deviation in the seventh digit can be more precisely Reduce input values.

3. Active consumption = 0 at

Figure 8 already shows conditions as they appear when the value cos (ϕ = 90 °) occurs. It is neglected, the line resistance, so that an ideal tuned circuit between generator (power supply) and consumer (X _C or X _L. See Figure 6c and 6d) forms. Pure reactive energy oscillates between the voltage source and the consumer, which is shown as a graphic representation in Figure 9 for better understanding. The reactive energy, or the graphic representation of the reactive energy wave, has the same appearance regardless of inductive or capacitive consumers. The wave is characterized by the fact that it swings in equal proportions around the zero point, so there is no active power that is implemented.

The amount of reactive energy that oscillates around the zero point in the form of ± neg _{HW can be} calculated from Eq. 28, according to the known scheme of Eq. Calculate 30-38.

The value Eq. 39.3 expresses itself physically in that only IS between producer and Consumer occurs. Such an arrangement becomes real by using R between producers and dummy switching element is made zero by means of superconductivity. The share of IS Electrons that the producer sends to the consumer is equal to the proportion that the consumer receives Get the blind element back. From this it can be seen that the actual carriers for the active power conversion are the IS electrons. You can do this describe. According to Kirchhoff's sentences, the current is in everyone in the series circuit Conductor section the same. The voltage or voltage drop is proportional to the resistance values of the consumer resistors. Thus, the known one reveals itself The fact that the loss of performance or revenue from the respective Voltage drop of the relevant resistance results. The IS electrons are at Presence of R slowed down because presence of R means that the ES- Electrons have a larger spatial structure within the conductor material. Incidentally, the Superconductivity is made possible by the spatial structure of the ES electrodes Falling below the jump temperature should be kept so low that the probability the mutual influence of ES and IS electrons goes towards 0.

The mathematical / data processing determination of the cos ϕ

[0 pt. 4.1-4.1.5] shows a detailed discussion of circuits for phase shifting in reactive load consumption measurement. In the current versions, there is no question of how a blind consumption measurement is set up or carried out. This question got the answer with the determination of negative _HW , because the reactive consumption measurement is according to the guideline Eq. 23, where a cos ϕ or sin ϕ is not required as a value for determining the reactive power. With the help of the statements Eq. 22 and 23 no longer the question of realizing a circuit for determining the phase shift in the conventional sense. In conventional technology, it is the bumblebee circuit that accomplishes this task. According to the state of the art, the electronics use a wide variety of filters for this. With the representation of the electrical quantity work in wave format or as a curve shape, the cos ϕ can be determined by the possibility of evaluating the zeros of the function course of the energy wave.

The energy function according to Figure 7b has 3 zeros. 2 zeros are immovable, ie the 1st and 3rd zeros always occur at 0 ° and 180 °. The second zero, which occurs at 45 ° as shown in Figure 7, is variable, ie dependent on cos ϕ. This can easily be determined with electronic logic, which will be carried out later. In table 3, the 2nd zero point through the column "negative half-wave, Wink-Dn" corresponds to the angular range on the abscissa in which neg _HW occurs. The range of 90-180 ° is not occupied because this phase shift only occurs with special parameters.

As shown in Figure 7b, the cos ϕ = 45 °, which corresponds to the 2nd zero. Compare table 3, line 45. The column - negative half-wave, time-Dn - also shows the time span of a 50 Hz oscillation in which neg _HW occurs. For the zeros, the amplitude value of the argument is 0. In order to identify the cos ϕ as a word using an electronic counter, it must internally carry out the corresponding time measurement between the two 0-digits in relation to the entire half-period.

The energy wave in a summarized mathematical view

The previous statements on the formulation of the energy wave were presented in two states. According to Eq. 17.1 in the first state the graphic function was interpreted according to Figure 4b with pure active power

e = p · sin²ϕ · t

The second state was with a phase shift of 90 ° and according to Eq. 28 with the function

shown with the statement of Figure 9. However, because in the practice of electrical counting, values of the most varied power factors have to be evaluated, it is necessary to formulate the energy function for all these values from the input values. In the literature, the addition theorems are often used here, but this does not lead to a useful result. In [15 p. 256] it is explained and explained with the help of examples that dealing with the addition theorems are angle sums and differences and not a multiplicative treatment of a trigonometric function. Because the respective amplitudes of the corresponding angle have to be multiplied in order to obtain an energy, the procedure must be different. With Eq. 29.2 the trend is pointed out, which calculation method is to be used (see also products of functions [2 p. 157]. A detailed procedure of the calculation method is for example for a phase shift of 45 ° the following:

The index values 1-n result from the respectively selected sampling time or they correspond the respective angle, at the value of which the corresponding amplitude multiplication is made. Table 2, column "sin × 45sin" shows for n = 0 to n = 30 how the energy function emerged as a table of values and is calculated. So you want for any phase shifts the respective energy function according to Eq. 40 determine, is Use table 2 for this, or use the arithmetic operations described Table values with greater accuracy and denser angle values, e.g. B. 0-90, too produce or the invoice is to be made with suitable computing technology.

Based on the energy function Eq. 40 the amount of energy can be according to the relationship

determine. For the real work count for Eq. 41 to choose the integral form.

The through Eq. 42 expressed integral form of energy quantity determination refers primarily on electronic integration. To what extent Eq. 42 can be solved mathematically, I am currently unable to assess. Eq. 42 can also be used as an energy collector Denote (accumulator) the single integrals over a half wave. The values dt are in in a later chapter for the C574C circuit with 40 µs, what the Collection of values per half-wave amounts to 200 current values. On the collection of the Amplitude values are referred to in the same later chapter.  

Purchase and delivery from the electronic meter

With the inner life on the basis of the mathematical treatment presented so far the construction of the meter should be such that it can be used as one device for all possible functions with regard to the creation or delivery of electrical parameters. It will consequently there are no separate designs of reactive and active power meters.

The extent to which different nominal current ranges are required as modules becomes important be determined by the practical result. The meter will be designed so that Depending on the upcoming energy level, the meters with low hysteresis values of reference can switch to delivery.

If the usage and delivery terms are transferred to a drinking water clock, then is on the clock shows an arrow direction from the drinking water producer to Drinking water consumer shows. According to § 18 AVBWasserV measurement is a measuring device among other things, the backflow preventer listed. One can therefore assume that the Installation of the meter the flow direction of the drinking water is technically determined, and this cannot be changed without technical and contractual changes, provided it these are not illegal activities.

With the many billions of electrical household meters, this arrow direction is on the Counter not included, but given by the counter installed by a specialist. Here the cos ϕ 1-0 is added internally as a counting criterion. But increasingly are in the context of agreements on this consumption metering system Introduced use cases in which the consumer temporarily or continuously as Energy supplier occurs (e.g. wind power or solar energy). In such cases and when Energy suppliers and producers have the result that the power circuit according to DIN 410 / 03.68 over 360 ° from the meter. Accordingly, in the reference arrow direction Active energy delivery are measured with leading IS or lagging IS. If the Customer as a supplier, then this active energy value becomes a negative value Reference arrow direction occur, again with the two possible components forward and lagging IS.

The electronic components of the meter

As already mentioned at the beginning, when developing a new product it is necessary with simple test objects to carry out the test in order to  Stage to produce verifiable results. This is used to measure whether the goal set achieved, or whether there is content in the considerations that the project in the Lead towards a negative result.

For this reason, a simple AC energy meter is built, in which the Problem of a potential-free current measurement does not have to be realized. Of the The reference point of the measurement can therefore be placed where the current and voltage path of the Meter are connected. The choice of the transmitter for the input parameters is not play a greater role in the selection in practical construction. For the The voltage input will be a tap from a resistor connected to the mains voltage. A transformer-type transmitter is used for the current input reach, since DC components of the current are initially not integrated into the task. Should If a requirement for the counting of equal shares arises, then the use of a shunt required.

The outputs of the transmitters are connected to the inputs of the analog-digital converter, it is also referred to as an analog-digital converter (ADC). When choosing the It is not absolutely necessary for ADC to use the flash type, but with the help of the An ADC is sufficient for parameters, in particular the conversion time Implementation process of successive approximation (or weighing process) works. The Outputs of the two ADC are provided with tristate output drivers and can therefore be used via the data bus can be connected to a microcomputer.

As an example, the AD conversion using a C 574 C circuit, equivalent to the AD 574 from Analog Devices [16 S 94], will now be described. The circuit is wired so that all 12 bits are output in parallel. With this data word width, the analog input signal can be converted into a discrete value of 2048 depending on the level of the input voltage. For this purpose, the inputs 12/8 must be connected to + 5V. Since the input variables are both alternating voltage and alternating current, the bipolar operation of the ADC can be established by connecting the input BO to the reference voltage source. The conversion time is specified according to the data sheet for the C 574 C with a t _c = 40 µs, so that at 50 Hz per period 400 values, i.e. 400 differential electrical voltage and current quantities with 2048 different and quantization levels to be implemented theoretically and practically as already explained downstream microcomputers are to be taken over.

An ADC is provided in the current and voltage path.  

The computer program, ie the software of the microcomputer, is to be set up in such a way that the Multiplication of the current and voltage differentials from the 12-bit word width of the ADC outputs first by subtracting a sign bit while maintaining the 12-bit Word width is created. The sign bit can be established by the data word in Dual number format 010000000000 is subtracted from each generated quantization level. If the result is data word 12 × 0, there is a zero crossing of the current or the tension. Because of the determination of the cos ϕ it is necessary that Arrange data word 12 × 0 as a symmetrical dual number word. Because it's a bipolar arrangement means symmetrical in this sense that the ADC is adjusted so that 2047 12-bit data words are used for practical evaluation. The division is with 1023 levels in the positive range, 1023 levels in the negative range and one level to Representation of the 0 made.

To determine the cos ϕ, the data word result is 12 × 0 in further processing return a single bit and set by means of single bit processing until the next zero crossing is completed. A distinction is made between the flank of the Zero crossing, d. H. the logic must evaluate whether the zero crossing from the positive range coming into the negative area. These respective edges are to be related by means of the time courses. The resulting ratio number makes it possible that the cos ϕ can be output as a numerical value.

Because Zeroflag always under the sampling condition from time to amplitude quantization is to be set precisely, the determination (see claims) is by means of Make transient storage.

This is followed by the multiplication of the two signed differential quantities to make. This creates a differential of an electrical power quantity with a Word length of 24 bits. Because this power value only from the parameters of the circuit data has arisen, it is necessary to multiply by an additional constant factor make the respective transmission ratio of the current and voltage path considered. It is also advantageous to add a factor that the Quantization error of digitization in ADC according to [17 p. 17f] eliminated accordingly, if one wants to do without the threshold values in the quantization device move. The third factor is the integration factor, which records the sampling time. The C 574 C has already been specified as 40 µS. However, these are 40 µs slightly due to the clock frequency emanating from the microcomputer to this working frequency changed.  

All three sub-factors can be combined into one factor, which is then combined with the Power quantity in the form of the 24-bit word is to be multiplied. Although was already from spoken differential quantities, but assumes that the differential from the point of view of Scan width is to be considered. After multiplying the 24-bit word by the factor k there is an energy differential, which can be expressed in parts of Ws. A The data word 000000000000 = 12 × 0 is an exception. If this Sample occurs, the product is correctly formed 0, because a product results in 0 if is a factor of zero.

Electronic filtering of the active energy per half wave

The equations form the basis for the electronic determination of the electrical active work 20, 22; 34 to 38 and 40 to 42. The electronic realization of this mathematical Relationships are determined by an up / down counter or by corresponding ones Subtraction and addition elements realized, the final sum after a half-wave in one Shift register, the accumulator, is forwarded. The flow of this process should go here are shown in more detail, also with a generally unbound Presentation method should be continued. The unbound representation is therefore chosen because with the electronic version of the meter there is also the possibility exists, the necessary operations with the special circuits, such as. B. Multipliers, counters, shift registers, etc. without necessarily Micro or one-chip computer comes into use. In the next few years high number of electric meters to be used, also optionally with convenient ones Tariff switching, it also makes sense to consider whether or not a specific one Circuit should be developed.

The up and down counter is controlled with a negative counting method if Current and voltage have different signs. As already described, it will Sign, which is also formed and processed by a separate flag register can be obtained by the subtraction shown. Current and voltage come in the area of the same sign, the area 12 × 0 has already been passed through and the Counter now works in the positive range. With a total blind consumer would be the end the half-wave the counting result of the up and down counting = 0. With cos cos-loaded Active consumption becomes the corresponding positive count amount, i.e. 12 × 0 in the next run, which corresponds to a half wave, pushed into the accumulator. At the same time is with this  Set the flag of the up and down counter back to 0 to the active energy content of the to determine the next half-wave.

The result of each half-wave is summed up in the accumulator and then arrives with one such value in the register preparing for the display, which, depending on the measuring range of the Meter is usually shown with 0.1 kWh steps.

How the function mechanism works is that from the 24-bit data word in the pre / Down counter a data word adapted to the conditions regarding the number of digits in the preparatory display register is done, will not be discussed in more detail here. The Computational processing of the higher-value bits in the accumulator to a meaningful, the clock cycle appropriate result is considered the state of the art in electronic Data processing required. The low-order bits are easily in the result introduced without influencing errors.

Difference to conventional electronic counters

The electronic meters tried and tested in practice have not reached the state that with them a continuous digital processing of the dual, gained from the ADC’s Measured values are carried out. So the devices that use the time division method, Evaluation using Hall sensors or the thermal power frequency Change work, electrical components such. B. capacitors that are not sufficient Have constant parameters with aging. However, a direct comparison can only be made with the Counter of the system of "sampling, analog-digital conversion with digital computational Multiplication "according to [0 p. 58]. The heart of this is the measuring principle of the digital Signal processor [0 p. 243]. The digital processing of measured values takes place with this counter due to clock frequencies also high frequency. However, these are test counters, which must therefore implement a power-frequency conversion, and thereby differ in this respect from a typical data processing.

The counter presented can advantageously dispense with this conversion and thus has a basic mode of operation, as is customary in the computer industry. Because no effective value determination is required for active energy energy metering using the described method of mathematical electron movement descriptions according to Figure 2 and equations 29.2 and 40, only simple electronic assemblies are required to solve the task.

The roll counter with electronic feedback as data storage, Data error control device and source for data processing typical remote meter reading transmission

The fully electronic counters according to [0 point 2.4.2] have the disadvantage that they are legible the meter reading in the event of a power failure without suitable or additional means is guaranteed. Furthermore, for the reproducibility of the counter reading Power failure special measures required by the following Proposed solution can be dropped. This affects the manufacture of a household meter cheap in terms of price, and electronic Remote meter reading transmission offers good prospects. The following solution is provided:

The register preparing for the display of the Elt consumption is in the carry (carry flag) to be designed in such a way that this is always triggered at the corresponding clock cycles, if 0.1 kWh is available for the normal metering process. The 0.1- kWh clock is passed to the relay or the step mechanism of the roller counter, so that this according to its decimal counter roll by the smallest unit = 1 is transported further.

However, due to suitable mechanical designs, there are dual ones on the counter roller to install optoelectronic feedbacks or to consider them as attached. With With the help of the optocouplers, the decimal number 0-9 of each single reel is converted into a 4-bit binary number to convert according to the dual number code. The roll counter is in the decimal range Executed in six digits, based on this initial situation 6 × 4-bit binary numbers are over To control optocouplers.

The bit pattern of the dual numbers is in the memory of the accumulator with the memory content compared, which had the value of the last carry flag = 0.1 kWh. So that's certainty achieved that the step pulse produced the correct decimal number. At The memory content of the electronic memory can be without voltage loss Consequences are lost, because the roller counter is, according to the statement, as one mechanical memory designed, the bit pattern at any time when voltage returns to the Electronics can be read. As already stated, this is done mechanically attached optocoupler. At the same time, the one provided by the counter can also be used Bit patterns are adopted from a port that e.g. B. the possibility of a serial electronic remote transmission of data via an interface. The query can ever  if required once or monthly 1 × via such a V.24 interface [17 pt. 3.2] be carried out without a continuous for the determination of the counter reading Registration of counts is necessary.

Explanations from the perspective of an application example

The essentials are to be explained here again in a summarized form. By multiplying the ADC input variables with cos ϕ, i.e. the instantaneous values of current and voltage, the energy function is obtained according to equations 40 shown with a cos ϕ = 0.707. Figure 7 shows this energy function in the form of the corresponding energy components pos _HW and neg _HW . The energy quantity is determined electronically using Eq. 42. With the help of the theory of ES and IS electrons and the mathematical options presented, the effective work of a counter according to Eq. 22

pos _HW - neg _HW = e _HW

by means of pure arithmetic subtraction. This arithmetic or accumulation of Individual values are carried out over a half-wave, the gear ratios of Current and voltage transformers must be included in the calculated value. Makes it need to calibrate the quantization error of the ADC, then the corresponding one Factor advantageously to be included at this point.

In detail, it is a question of integrating the curve neg _HW by means of a countdown. The counter practically sums the negative quantized partial areas from the product of the amplitudes n 1,. . . n₇ of the values shown in Table 2 times the respective quantized time unit. The zero flag is set in position 7.1. With the practical sine wave in the steep zero crossing, Zeroflag will rarely be able to be set by the ADC. However, the accuracy requires that zero = 0 is set at every zero transition. Therefore, the zero flag is to be determined using a transient loop using a linear function equation of the type y = mx going through the zero point.

Then, starting from point 8, figure 7 and table 2, the counting up takes place in the pos _HW area. After half a period, i.e. at Zeroflag item 30, the result is formed from the upward count minus the downward count and enter them in the accumulator and reset both counters to 0. Now the next half-wave is to be counted in the same way as already stated. If the current and / or voltage values have changed, this is taken into account by changing the output words of the ADC's.

It is known to the reader that there is no _HW at cos 1 = 1neg, so there is a curve according to Figure 4 and Table 1. In this example, the number of sampling points can be tracked up to 15. A zero flag only occurs with sampling 0 and 15. Current and voltage are never contradictory here.

For both representations or for any other cos ϕ value, the accumulator over the required number of overflow flags (overflow) until the Transfer flag (carry) of the size 0.1 kWh can be formed. Carry flag increases each time the decimal counter reading of the roller counter by 1, d. H. by 0.1 kWh each. Thus the electronic counter described, the today's Ferrari counter by larger Reliability, higher accuracy, longer service life with less self-consumption will be superior.

However, the electronic counter can still meet requirements that cannot be directly realized by the Ferrari counter. The evaluation of flags 0 between neg _HW and pos _HW and flag 0 after 180 ° enables the display of the cos ϕ. This is handled by a small computer program within the existing electronics. In conventional technology, a separate cos ϕ measuring device is required.

If you want to count the reactive energy, you can again add the neg _HW values according to Eq. 23, and dispense on the counter roll. With the Ferrari meter, this would have to be connected separately via a bumblebee circuit.

The problem of electronic feedback in the roller counter has its substance an application possibility with the electronic counter as well as with the Ferrari counter. At the latter, this additional effort will no longer make sense, since the additional electronics from The principle would be to reinstall in this. Because of the existing electronics (Power supply parts, etc.) the electronic meter can be used mechanical memory advantageously. The way it works is that a Paper tape in the roll behind the decimal number is optically scanned, then in the Electronics to be read in and evaluated. Comes a counter with high Tariff claims are used, so there is also the possibility of parallel scanning a Date roll. The date and meter reading can then be conveniently transmitted electronically.  

List of the formula symbols used

ζ _p

Crest factor
A area to be integrated
E Energy (electrical), output variable are direct current and direct voltage
E _total

Total energy = ΣE _p

+ E _k

+ E _r

E _k

kinetic energy
E _p

potential energy
E _r

Rotational energy
E _⌀

Alternating energy (as an amplitude value, which is calculated from the respective value of the surface area of the energy, that is to say integral alternating energy amplitude)
E _B

Reactive energy
e instantaneous value of energy (electrical); Output variables are instantaneous values of the alternating current and the alternating voltage
I RMS value of an alternating current
IS ion current or dynamic voltage
k Multiplication factor, consisting of gear ratio, sampling time and correction of the quantization error
I _⌀

Current (as amplitude value, which is calculated from the respective value of the area of the alternating current, i.e. integral current amplitude)
P power
P _⌀

Alternating power (as an amplitude value, which is calculated from the respective value of the area of the power, i.e. integral alternating power amplitude)
P instantaneous value of the power
Q reactive power
R electrical resistance, effective resistance, resistance
S Apparent power
s Instantaneous value of the apparent power
t time
Δt time difference
U RMS value of an AC voltage
U _⌀

Voltage (as an amplitude value, which is calculated from the respective value of the area of the AC voltage, that is to say integral voltage amplitude)
W energy electrical
X reactance
| Z | Impedance, amount of impedance

List of abbreviations

ES electron current. Is the physical representation of the current. The electrons bound to the atomic core of the conductor material are electrically excited, which is expressed by a modified or enlarged orbit around the atomic nucleus.
IS ion current, also dynamic voltage, can be seen in Figure 2b. Physically, these are electrons released from the atomic core of the conductor material, which move in the conductor according to their energy.
e _HW Share of active energy within a period that is expressed in the positive half-wave, but according to Eq. 22 is to be subtracted by the proportion of the negative half-wave.
pos _HW energy component of the positive half wave, consisting of active energy and 1/2 reactive energy
neg _HW energy component of the negative half-wave, represents half the reactive energy.

bibliography

[0] Kahmann, M., electrical energy, measured electronically: measuring instrument technology, test equipment, applications - Berlin; Offenbach: vde-Verlag, 1994
[1] Teuchert, H./Wahl, K., Fundamentals of Electrical Engineering, Vol. 2, AC Technology, Verlag Technik Berlin 1959
[2] Bronstein, IN / Semendjajew, KA, Taschenbuch der Mathematik, 10th edition, Teubner, Leipzig 1969
[3] Belle, P., published patent application DE 42 42 385 A1 D, "The direct conversion of the thermal energy of an artificial plasma and the conversion of the radiation energy of the sun into electrical energy by means of the Plasmaelt generator
[4] Fischer, R./Padelt, E./Schindler, H., Physical and technical units applied correctly, SI Verlag Technik Berlin 1975
[5] DIN 1304, general formula symbols, connection with international standards, April 1979
[6] Belle, P., 20 years of PeG (plasma generator), unpublished February 1995
[7] Böttle, P./Boy, G./Grothusmann, G. - Electrical measurement and control technology, Vogel Buchverlag Würzburg 1991
[8] Herneck, F., pioneer of the atomic age, great naturalist from Maxwell to Heisenberg - The Morning Berlin, 6th edition 1972
[9] Kuchling, H., Taschenbuch der Physik, 14th edition, Fachbv. - Leipzig; Cologne 1994
[10] Berger, C.-P., Technical Formulas, 4th Edition - Fachbv. Leipzig, 1962
[11] Kahnt, W., Der Brockhaus, in a volume from AZ, Mannheim: Brockhaus, 1990
[12] DIN 57 418 Part 1 / VDE 0418 Part 1, provisions for electricity meters
[13] Verification Act of August 12, 1988, Appendix 20: Measuring Devices for Electricity (BGBl. I p. 512)
[14] DIN 40 110 AC quantities, October 1975 and DIN 40 110 AC quantities, Part 1, March 1994
[15] Beweert, F., Mathematics for engineers and technical schools, Bd. II, Fachschulverlag Leipzig 1961
[16] Kühnel, C., AD and DA converter, military publisher of the GDR 1989
[17] Germer, H., Wefers, N., Meßelektronik Bd. 2, Digitale Signalverarbeitung, Mikrocomputer, Meßsysteme, 2nd edition, Hüthig, Heidelberg 1990

Table 1

Table 2

Table 3

Claims (4)

1. Electronic counter for measuring the electrical work that occurs as energy consumption of electrical devices operated, characterized by the following features:

• a) The output variables for measuring the work current and voltage are digitized using an analog-digital converter.
• b) The digital amplitude values of U and I are multiplied by a digital multiplier.
  • b₁) According to Figure 4a Table 1, this means in mathematical form:
    sin × sin = sin² (value 1 is 0.109, value 2 = 0.0432 etc.).
• c) The resulting product is characterized by the energy function.
• d) The product energy amplitude according to 1b and 1c in the form of a differential quantization stage is multiplied for the purpose of integration by the current-voltage conversion ratio and the time interval, that is to say the temporal sampling of the analog input signal.
  • d₁) According to Figure 4a Table 1, this means without taking into account the current-voltage conversion ratio in mathematical form:
    Time (ms) × sin² = pos _HW (value 1 is 0.00364, value 2 = 0.014407 etc.).
• e) The individual differentials according to 1d are integrated in ohmic consumers by means of electronic up-counters (addition elements) to determine the real work over a half-wave.
  • e₁) According to Figure 4b and Table 1, this means in mathematical form:
    Sum formation of pos _HW = 5.16643.
    According to Eq. 18, a mathematical value of 5 mWs has been calculated in accordance with the transformation into the time domain. pos _HW would have to be calculated in Table 1 with more precise angle values in order to come closer to the exact result.
• f) In the case of consumers with a cos ϕ der 1, the integration process of the individual differentials is carried out over a half period by means of up and down counters (addition and subtraction elements, more precisely with an arithmetic logic unit [ALU, the count shown in the half-wave problem is in this regard to consider]) realized. The reader can do the mathematical processing himself.
• g) The count amount over half a period embodies the real work and can be calculated according to Eq. 22
  e _HW = pos _HW - neg _HW
  determine.
• h) The down counter always comes into action by setting the corresponding flags, ie it counts when the current and voltage have different signs.
• i) The reactive energy is counted with the half-wave down counter, however the factor 2 according to Eq. 23 q _HW = 2 neg _HW must be taken into account.
• j) The half-wave count amounts in the up and down counter are collected or added up by means of up-counting in the accumulator. The corresponding zero flag causes the half-wave counters to be reset to 0.
• k) Because of the relatively low sampling rate in the time domain compared to that in the amplitude domain, the zero flag is rarely set directly by the ADC 12 × 0.
• l) To set the zero flag (zero flag) always and in the correct position in the amplitude and time range, and to make it available for the corresponding further calculations, the two quantization levels adjacent to 0 are 12 × by means of a transient loop in the area of the zero point transition in order to form the zero flag 0 record.
• m) The transient loop evaluates the zero flag in the area of a linear curve segment.
• n) The mathematical formation of the zero flag is carried out using the functional equation y = mx. The increase in the transition from zero to positive is calculated The increase in the transient process is negative to positive The time x can thus be calculated from the respective y values around the zero point.
• o) The accumulator is summed until the carry flag can usually be set to 0.1 kWh. Carry = 00.1 kWh can advantageously be entered on a roll counter. It is also happy to save this data in EEPROM's.

2. Electronic counter for displaying the electrical work that occurs as energy consumption of operated electrical devices, equipped with a roller counter and feedback in the event that the use of an EEPROM is not advantageous, characterized by the following features:

• a) A roller counter with digital feedback is used because in the event of a power failure, it is possible to read the meter reading without aids. There is no change in the meter reading in the event of a power failure.
  • a₁) There are no restrictions on the design of the counter roller. A stepping mechanism (stepper motor) can act as a drive element as well as a relay-controlled or similarly acting stepping mechanism.
• b) The digital feedback is a mechanical / optoelectronic memory.
• c) If the decimal number appears in the display field, the bit pattern of the decimal number is read simultaneously as a binary number using an optocoupler or other scanning method using a paper tape and evaluated in the memory.
• d) The bit pattern obtained in this way is suitable for remote data transmission of the meter reading at any time.
• e) No continuous transmission rate of information is required for the transmission of the counter reading by means of a bit pattern. As a rule, the data can be transmitted serially using the V24 interface. The connection to an IEC bus can also be carried out without any problems.
• f) The meter reading can be read by machine in any commercially available computer. As with other applications, a modem is required for remote data transmission.
• g) For special counting devices, it is also possible to use a date scroll mechanism, e.g. B. controlled by a radio clock to run with dual bit pattern.
• h) The generation of the bit pattern in the electronic counter is inexpensive because power supply and other electronic components are available anyway, which can also be used.

3. Electronic counter for measuring the electrical work that occurs as energy consumption of operated electrical devices, according to the mode of operation of the functional principle of the mathematically physical relationships of electron and ion current, characterized by the following features.

• a) Electron current (current) is characterized in that the electrons excited by the force remain bound to the respective atomic nucleus, but their path around the atomic nucleus has been made more energetic (larger ellipse).
• b) Ion current (voltage) is characterized in that the excitation of the electron emanates from an electromagnetic field. In the excited state, the excited IS electron leaves the atomic group of the original atom and moves in the conductor at a speed proportional to the magnitude of the voltage. Figure 2b shows the speed curve of the current IS.
• c) With the knowledge that energy transport takes place in the electrical conductor through kinetic energy of IS and ES electrons, the energy measurement is based on dynamic processes in the electrical conductor.
• e) The physical description processes of IS and It reproduce more precisely what is generally referred to as the current conduction in the electrical conductor by free electrons.
• f) With the electronic recording of the input variables and the further processing shown, it is not necessary for the realization of an Elt counter to form the effective value in order to carry out a further calculation.
• g) With the detection of neg _HW and pos _HW , the real work can be determined by means of simple arithmetic operations.
• h) At the level of energy quantities, simple arithmetic operations are effective, which is why the effective value determination and further calculation using the electrical equations P _Wirk = can be dispensed with, which greatly simplifies the computing operations and thus the hardware requirements and software for the calculation.
  • h₁) The basics of multiplying two phase-shifted sine functions, which can be phase-shifted in the angular range <0 ° and <90 °, are given by Eq. 40 for ϕ = 45 °, and that as amplitude values.
  • h₂) For energy quantity determination, i.e. amplitude values × time unit, Eq. 42 to.
• i) In order to approve a test meter for alternating energy, it should receive the approval if it has met the criteria according to the heat comparison method according to Figure 5.

4. Claim 3 is a main claim. Claims 1 and 2 arise as a result of Claim 3.