WO2023152715A1

WO2023152715A1 - Energy measurement apparatus and methods for processing power factor, transmitted, received, dissipated, reserved, residual and reactive ac power

Info

Publication number: WO2023152715A1
Application number: PCT/IB2023/051277
Authority: WO
Inventors: Peter AKUON
Original assignee: Agwara Charles; Agwaro Paul
Current assignee: Agwara Charles; Agwaro Paul
Priority date: 2022-02-14
Filing date: 2023-02-13
Publication date: 2023-08-17
Anticipated expiration: 2024-08-14

Abstract

A simple energy meter apparatus for measuring amount of AC power in terms of power dissipated, power reserved at input, power consumed, power delivered at load, residual power at load, power reserved at load and phasor reactive power. The energy meter is accurate even in cases of harmonic distortion and resilient to varying frequencies, in single and multi-phase power systems and consists of a very fast processor for power. The invention is applicable in the power design for insulation, protection and billing industry for AC power systems, remote electricity meters, and electronics and for measurements in the hybrid vehicle industry and for measurements in the telecommunications sector. It is useful in measuring incoming power factor and outgoing power factor.

Description

ENERGY MEASUREMENT APPARATUS AND METHODS FOR PROCESSING POWER FACTOR, TRANSMITTED, RECEIVED, DISSIPATED, RESERVED, RESIDUAL AND REACTIVE AC POWER

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to measurement of a.c. power components and power factor measurements under all conditions of a.c. power load including harmonic distortion in a circuit. The circuit is coupled to an a.c. power source generating a.c. current and a.c. voltage. The invention is useful for application in power billing industry to determine more accurate prices, measurements and to aid in effective design of electrical systems such as insulation of conductors.

2. Description of the Related Art

Power factor helps in measuring the amount of apparent power required in order to maintain a similar value of current as if there were no reactive loads.

Several measurement methods have been introduced in the prior art. The techniques apply different approaches such as temperature changes, estimation of harmonic distortion in the case of non-linear loads and lowering processing complexity in measurements.

Nonlinear loads include: fluorescent and arc-discharge lighting; adjustable- speed motor drives; computers and computerized controls; and heating elements and temperature-controlled furnaces. Nonlinear loads, rather than using AC electric power directly, often convert AC power into direct current before it is used to accomplish their functions. A common element in nonlinear loads is some kind of rectifier to accomplish this AC to DC conversion. Some elements such as rectifiers do not draw sinusoidal currents.

For example, electrical meter of Nikola Tesla of patent USS 14974 of 1894 discloses a meter that utilizes predictive effect of gas particles on conductors.

Patent US 12197238 of 2011 discloses harmonic decomposition through P'ourier series. The patent US14471107 discloses a meter consisting of a processor that computes values in the frequency domain. Patent. US5072187 of 1991 discloses apparatus for accurately determining the total harmonic distortion and the power factor attributable only to a non-linear load circuit coupled to an a.c, power source when a.c. current input to the non-linear load circuit is substantially in phase with the a.c. voltage provided across the load circuit by the a.c. power source.

In the complexity approach, Patent CA2062914 of 1991 discloses a process that avoids computation of power law functions. In addition, Patent US20 180331551 of 2018 discloses a meter that produces a hybrid mix of alternating-current and direct-current power.

A recent analysis of total instantaneous power shows that the voltage and current values as measured are actually correlated components and the singularity of their effect in the total a.c. power can be estimated as described in the publication

Gaps a) Total amount of AC power consumed in the power network is hard to decide on. A constant charge rate is normally applied to estimate cost of total a.c. power based on power factor (PF). In fact, a.c. power is mainly treated as a two-component entity in literature. Some researchers have proposed that a.c. power is equivalent to a beer in a glass, where the active power is the liquid and the frothy foam being the apparent power. We show in the present invention that this analogy is an incomplete depiction of cyclic power flow. The analogy is true in the first cycle when the inductive load is turned on, but changes as soon as the inductor has magnetized. True analogy shows that two layers of residue should exist at the bottom of the glass as well as the top part. b) Accurate measurements are desired even in cases of harmonic distortion. c) The industrial art is sensitive to frequency changes which affect the limits of integration or number of samples required to compute true root- mean-square values when frequency fluctuates. A frequency insensitive energy meter is desired to develop standards under distortion. d) A less computationally complex algorithm is desired for the meter to save on depreciation of the processor, memory and power consumption.

Solution

It is a difficulty of the present invention to derive and distinguish a.c. power into the amount dissipated, reserved at input, reserved at load, amount received at load, residual power stored at load and the total amount transmitted and phasor reactive power. The components are shown in FIG. 1. These components of a.c. power can be used to effectively provide billing formula. The difficulty is in the fact that in conventional absorption coefficient of transmission lines, the absorbed power is treated as the difference between the input supply and the reflected energy.

Conventionally, the absorption coefficient p_A is given as,

where E_i refers to incident energy, E_r refers to reflected energy and E_t is the transmitted energy.

It is important to understand the nature of resistive and reactive power network so as to design the true absorption coefficient in an a.c. power circuit.

A principle of energy gradient analysis for AC power flow is used to derive the power components of the present invention. In the methodology, the present art of the invention introduces the amount dissipated, reserved at input, reserved at load, amount received at load, residual power stored at load and the total amount transmitted and phasor reactive power, redefine absorption coefficient and devise a less complex algorithm to estimate phasor values of a.c. power.

In the present invention, the absorption coefficient is the difference between power received at load and reserved amount. The key aspect of the present invention is the discovery that equal amount of the reflected power is returned back to the source and to the load in a cyclic manner and it is half the constant amount that is residual amount at the load. So the absorption coefficient in a.c. power network is substantially different from that of a transmission line. The coefficient p_AI of the present invention is expressed as,

TABLE I COSTS FOR A DOMESTIC CONSUMPTION FOR 45.73KWH

The true components of power are necessary in providing occupancy rates of the a.c. power channel and that is important in determining the pricing for power bills and for designing adequate insulation.

Description for pricing

In the present industry, the billing approach for a.c. power applies both constant rates and variable costs based on the amount of power dissipated and reactive power.

The rates per kWh are the consumption, fuel energy charge (FEC), Forex charge (FERFA) for foreign exchange rate fluctuation adjustment, inflation adjustment (IA), variable cost (WRA), Energy Regulatory Authority levy (e.g. ERA), REP charge, which is a percentage of base rate (e.g. 5%) and value-added tax (VAT) as a percentage of total cost less levies. An example of cost elements for domestic power use is in Table I with a base rate of 57.629% of total cost.

Power Factor (PF) techniques

There are several well-known methods for estimating power factor for reactive AC circuits. The methods in the prior art are mainly categorized as, i) displacement power factor (DPF), where the PF is a cosine of i9 as determined from the leading or lagging angle between the voltage the current waveforms, ii) effective power factor (EPF) as the ratio of active power and apparent power. Watt-meters are used in the prior art to estimate active power.

The average PF is derived from the average integral of the power waveform, (IPF) and the apparent power is computed from the product of the true root-mean-square (TRMS) values of current and voltage waveforms.

The integral power factor (IPF) is determined from the following function,

However, memory limits the number of samples in digital TRMS converters. Furthermore, the two methods hardly give similar results in the cases of harmonic distortion. For example, harmonics have no particular phase angle and tend to average out rather than add up in the network. In addition, there are hardly any standards for PF for harmonic distortion. It is therefore difficult to present accurate PF information to be used in billing systems for AC power. In addition, the industrial technique of the integral technique is very sensitive to frequency fluctuations. It becomes less accurate when the frequency in the line is unknown.

Power equation with harmonica The following is an example for power waveforms where both voltage and current waveforms undergo harmonic distortion due to higher frequency components.

In the case of the harmonics, the instantaneous power is expressed as,

The power factor equation in the cases of harmonic distortion is well-known and is given as

where, THD refers to total harmonic distortion which is computed as

However, this technique does provide a harmonic distortion and power factor measurement for non-linear load circuits when the current and voltage waveforms are in phase.

In the case given in the example,

However, the THD for both current and voltage, which have the same phase, is given as

The total power factor under harmonic distortion is computed as

However, when the phase difference is substantially different, the relations for harmonic distortion are not very accurate.

The present invention discloses a simple energy meter that is able to measure accurate PF even in cases of harmonic distortion from non-linear loads and under frequency variations. The approach used in the present invention is based on the coefficient of the amount of power dissipated and the amount of power reserved at reactive load beyond the residue. This new technical solution is called absorption coefficient PF (APF) or simply as absorption PF.

Theory of Energy Gradient in Power Equation

In order to underpin the technical nature of the present disclosure, a theory of energy gradient is now presented in more details. Power flow analysis is presented based on energy gradient. When a reactive load is switched on in an AC network, several processes take place that lead to a reflection of power from the load towards the supply side and eventually stabilize the components of reactive power at supply and load such that only the active power flows as shown in FIG. 2. In terms of instantaneous power,

1) Initially, an apparent power is supplied towards the load: = VI to cater for the demand of active power and the instantaneous

reactive part

, To determine the PF, the reactive component Q is determined and the true RMS values of V and I.

Step 1 culminates into apparent power towards the load.

2) Since Q¹ is stored in the magnetic field of the reactive load, the energy gradient will reduce and the new demand from the supply will be equal to the active load, P. The second supply from source will be based on the previous demand, and is given as . On average, the supply is

given as,

At this point the PF is calculated through estimation of P and the true RMS values of V and I.

Step 2 culminates into active power towards the load.

3) In the third step, the gradient from the load is given by the amount of reactive residual power stored at the load during the initial supply, i.e., . However, after returning half of this residual power i.e.

, the gradient becomes zero, so there will be a permanent residue that is twice the amount that is returned, thus,

Power exchanged and reserved at source,

Residual power stored while online, .

Step 3 culminates into reactive power reserved at the source.

4) In the fourth step, since

has been returned to source and now reserved, and is stored at the load, then the amount of the

next power demand that will be delivered to the load is given as, When received, the residual power at the

load goes back to

. At this step, the PF can be estimated directly from the peak value

.

Step 4 culminates into a fraction of the apparent power towards the load.

5) In the fifth step, the reactive component , will be forwarded to the load

in order to balance out the reserved at the source.

Step 5 culminates into reactive power reserved the load in addition to the residue

.

6) Finally, since

is reserved at the source,

is available at source, and

is available at the load, and since , the

only amount of power demand will be the dissipated load P = VI cos fl. Stability is achieved and the active power flows until the load is switched off. Step 6 culminates into a constant active power towards the load.

It is clearly seen that the power dissipated in the AC network is never returned to the supply source and the residual power stored is also not returned to the supply source as long as the reactive load is on.

In terms of pricing for the billing system, it is more accommodative to treat both as power consumed since they occupy the channel twice across

the six steps.

Then, the total power consumed from source or supply from source is given as,

In this process, the power dissipated is the difference between the total power consumed from source and the power reserved at load, i.e.

This is not the conventional theoretical form of calculating the absorbed component as a difference of the input and reflected component.

Concurrent instantaneous power equation

A more realistic form of AC power can be expressed in terms of five (5) concurrent instantaneous components that form the total power in a reactive circuit. In this way, it is easy to experimentally measure the role of each component on the changes that occur on the physical conducting medium. Considering a case where all a.c. power components of the present disclosure are flowing concurrently, then it is clear that the power waveform s_m oscillates between a maximum peak S⁺ and minimum peak S-. A value P_m is the positive peak,

of the power waveform s_m, while the residual power stored is the negative peak , of the power waveform.

Since the peak-to-peak apparent power is given as, , it can also

be expressed as, .

From this theory, which has been derived from an analysis of energy gradient, the following components are summed up to form the AC power equation:

( )

Let the power dissipated be

which means that the source will be supplying active power of 2P in order to be able to dissipate an amount of P.

Then, the instantaneous reactive power balance will be , where

Reactive power returned to source is given as as an equal amount,

is being concurrently supplied into the circuit.

In addition, for the load to return the amount of power of , a double

amount of power must be retained at the load so that the residual power is given as,

Subsequently, the overall concurrent instantaneous form of the power equation is given as

This concurrent instantaneous power equation can be used in different ways in determining the power bills. Relationship with phasor AC power equations

Since all the additive instantaneous power components are given in watts, a conversion into conventional units for reactive power in phasor form is performed as follows,

where k_IP is the constant of conversion from instantaneous to phasor power.

Note also that the computationally complex power functions of phasor form are avoided in the present disclosure.

Theoretical Concurrent Power Waveform

From FIG.l, the first four terms are sinusoidal waveforms while the residual power is a constant quantity and the waveform is conveniently placed on the positive side of the axes so that, in theory, the concurrent power equation can be written as,

Approximate Concurrent Power Waveform

Furthermore, an approximate equation for the concurrent power is written as,

The concurrent power waveform is plotted in FIG. 1 to depict the 5 concurrent instantaneous components of AC power.

Proposed Experimental Power Factor technique

Let the power waveform be in the form

Then, let

S⁺ be the maximum amplitude of the waveform on the positive side, S⁺ = max(+s_m) be the maximum amplitude of the waveform on the negative side,

Then the peak to peak amplitude is given as,

The power dissipated is given as (difference between input power and power residue stored at the load),

Note also that, as defined before and in FIG. 1.

Then, the coefficient of power dissipated/ absorbed, is given as

The PF technique of the present disclosure is advantageous since it involves a simple task of measurements of the peaks of the power waveform.

There is no need for measurement of phasor reactive component of power as it is calculated from the measurements of the peak and the knowledge of APF.

Also, the technique is resilient to current and voltage harmonics since both upper and lower peaks are equally affected by the distortions and are therefore reciprocating after tuning. Furthermore, frequency fluctuations result in reciprocating effects on these peak values, so the present invention leads to a resilient technique against these fluctuations as the load changes in the network.

The integral tuner of the present invention estimates the integral average and determines its distortion from the real power absorption value i.e. P_d, thus the integral tuned power factor is given as,

The power factor can be tuned to cater for harmonic distortion based on the normalized total power function. The tuning is performed based on recent theory of total instantaneous power (i.e. cos[theta]+sin[theta]), where T_η = 1 for pure sinusoid. In the case of harmonic distortion, the tuned power factor is given as,

where T_η denotes the 77th root of the normalized total power function and T) > 3.

Theoretical validation through concurrent power waveform

In the case of sinusoidal power, the absorption coefficient can be derived from the concurrent power equation as well from the following set of equations,

SUMMARY OF INVENTION

Accordingly, it is an object of the present invention to provide a method and apparatus for determining absorption coefficient power factor (APF) of a load coupled to an a.c. power source that generates and supplies a.c. current and a.c. voltage to the load, wherein power waveform (s_m) is produced as a product of a.c current and a.c voltage to be used in billing.

It is another object of the present invention to provide a method and apparatus for providing a determination of the absorption coefficient power factor (APF) of a load coupled to an a.c. power source that generates and supplies a.c. current and a.c. voltage to the load, wherein power waveform (s_m) is produced as a product of a.c current and a.c voltage to be used in billing.

Additional objects and advantages of the present invention will become apparent from the description which follows.

In accordance with the invention, as embodied and broadly described herein, the invention provides an apparatus for determining absorption coefficient power factor (APF) of a load coupled to an a.c. power source that generates and supplies a.c. current and a.c. voltage to the load, wherein power waveform (s_m) is produced as a product of a.c current and a.c voltage to be used in billing, comprising: first means for measuring the maximum amplitude (S⁺) of power waveform; second means for measuring the minimum amplitude (S-) of power waveform; third means coupled to the first means and the second means, for calculating apparent power (5) to the load as a function of both S⁺ and S-; fourth means coupled to the first means, the second means and the third for calculating active power dissipated (P) at the load as a function of S⁺, S- and 5; fifth means for measuring the instantaneous reactive power (Q^I) component sent to the load; sixth means for measuring the instantaneous residual reactive power

component stored at the load; seventh means for measuring the instantaneous exchanged reactive power (QBF) component circulating back and forth between the power source and the load; eighth means coupled to the third means and the fourth means, for calculating the absorption coefficient power factor (APF) of the load; ninth means coupled to the eighth means, for calculating the power factor angle (PF angle) of the load; tenth means coupled to fifth means and the ninth means, for calculating the phasor reactive power (Q) component as a function of both Q^I and PF angle; and eleventh means for calculating tuned power factor and cost of power bills (C_P) based on the power components.

The invention also provides a method for determining the absorption coefficient power factor (APF) of a load coupled to an a.c. power source that generates and supplies a.c. current and a.c. voltage to the load, wherein power waveform (s_m) is produced as a product of a.c current and a.c voltage, the method comprising the steps of: measuring the maximum amplitude (S⁺) of power waveform; measuring the minimum amplitude (S-) of power waveform; calculating active power dissipated (P) at the load; and operating a computational unit in accordance with a predetermined relationship which takes into account S⁺, S- and P to determine the absorption coefficient power factor (APF) of the load as a function of S⁺, S- and P.

DESCRIPTION OF DRAWINGS

The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate presently preferred embodiments and methods of carrying out the invention and, together with the general description above and the detailed description of the preferred embodiments and methods given below, serve to explain the objects, advantages and principles of the invention. Of the drawings:

PIG. 1 is a waveform diagram for concurrent instantaneous power waveform. FIG. 2 is an illustration of a stabilized concurrent instantaneous power flow. FIG. 3 is a waveform diagram of the purely sinusoidal voltage, current and power waveforms at the input of the load.

FIG. 4 is a waveform diagram of the voltage, current and power waveforms at the input of the load with two harmonic components.

FIG. 5 is a diagram of the variation of instantaneous power components with phase angle.

FIG. 6 is a diagram of an apparatus for determining absorption coefficient power factor (APF) as constructed in accordance with the present invention.

DETAILED DESCRIPTION

In accordance with the invention, a method and an apparatus are provided for determining the absorption coefficient power factor (APF) of a load coupled to an a.c. power source that generates and supplies a.c. current and a.c. voltage to the load, wherein power waveform (s_m) is produced as a product of a.c current and a.c voltage to be used in billing.

FIG. 1 is a waveform diagram for concurrent instantaneous power waveform. It illustrates the five components of instantaneous a.c. power that are taken to be concurrently occupying the channel for the power delivery to the load. It is observed that a.c. power delivery consists of a continuous cycle of instantaneous power flow for reactive power towards the load, the active power flowing towards the load as another active power is dissipated, reactive power being returned to source and residual reactive power at the load that maintains the energy gradient to push half of its power back to source. The overall sum of the five components of power results in the peak to peak apparent power in the circuit. FIG. 1 depicts the case where the concurrent power flow is plotted where the voltage waveform leads current waveform through 45°. FIG. 2 depicts the power flow analysis.

FIG. 3 is a waveform diagram of purely sinusoidal voltage, current and power waveforms at the input of the load. The concurrent power flow is plotted where the voltage waveform leads current waveform by 20°.

The voltage and current waveforms are purely sinusoidal and it is observed that the PF angle computed from the experimental instantaneous concurrent waveform s_exp of the present invention and that of the theoretical concurrent waveform s_conc; are very close to the ideal value of 20°.

FIG. 4 is a waveform diagram of the voltage, current and power waveforms at the input of the load with two harmonic components. The concurrent power flow is plotted where the voltage waveform leads current waveform by 30°.

The voltage and current waveforms are not purely sinusoidal and it is observed that the PF angle computed from the experimental instantaneous concurrent waveform s_exp(31.55°) of the present invention and that of the theoretical concurrent waveform s_conc(32.4°) are very close to the ideal value of 30°.

Comparisons for Measurement Results

We note that the power waveform for s_m is obtained experimentally as a product of the voltage and current waveforms. The concurrent waveform is an analytical form of In order to ascertain the theory of concurrent power, a power factor metric is devised and used to compare the results as obtained from the two scenarios. The PF methods in the prior art and the APF are used in the following section to compare measurement results that are obtained from known lagging power angles and results are given in Table II.

In the experiments, the displacement power factor (DPF) is determined from the lagging angle between the voltage and current waveform. The set up for single- factor harmonics is such that the second harmonic has amplitude which is 2% of the fundamental value for both current and voltage waveforms.

TABLE II MEASUREMENT RESULTS FOR POWER FACTOR

From Table II, it is evident that the displacement power factor is unable to predict the true power factor in the case of harmonic distortion of two parts. In fact, two different values of displacement occur between the voltage and current waveforms. In addition, the industrial PF calculation through the integrator with TRMS for voltage and current values also works only in the case of purely sinusoidal waveforms, where there are no harmonic distortions.

In all the three cases, the absorption technique, as disclosed in the present invention, presents a better accuracy compared to the displacement approach of the prior art.

Other prior arts involve complicated steps such as Fourier transforms that are not simple algorithms and they were not compared to the present invention. Further advantages of the present invention are now demonstrated through an analysis of PF under varying power line frequencies. Power line frequency is tested over 50Hz, 55Hz and 60Hz variations. It is assumed that the meter is initially set for 50Hz and further frequency measurements are not undertaken for calculating PF.

Another important result is that the theory of concurrent instantaneous waveform has been confirmed as it is observed that the predictions of the PF are accurate. The AC power waveform consists of five power elements that are useful in determining billing rates for AC power consumption.

TABLE III POWER FACTOR UNDER FREQUENCY FLUCTUATION

From Table III, it is evident that the APF of the present disclosure is more accurate compared to the industrial prior art over all values of the frequency fluctuations. The experiment is performed at PF angle of .

Additional competitive advantage

The other attractive attribute for absorption coefficient technique is the simple addition and division processes that are involved in computing AC power components. The computational complexity of the energy meter will be low hence leading to long life of its power system.

PIG. 5 is a diagram of the variation of concurrent instantaneous power components with phase angle. The concurrent instantaneous power of the present invention is quite useful in prediction of true billing costs based on the electrical activity in the conductor of electricity. The present invention classifies power in terms of the forward flow reserve at load, backward flow reserve at source, power received at load, dissipation, phasor reactive and residual power at the load. Furthermore, it is easy to derive the phasor reactive power as a fraction of the instantaneous residual power, rather than the conventional phase-shift operation in estimating the reactive power. This process results in a simple computational operation in the present invention. From FIG. 5, it is observed that one of the ways to specify the contribution of the consumed power to billing costs is to add power dissipated to that which circulates back and forth in the a.c. power circuit, as this accounts for occupancy of electricity in the conductor. This is the reserved power at the source and at the load.

FIG. 6 is a diagram of an apparatus for determining absorption coefficient power factor (APF) as constructed in accordance with the present invention. It illustrates the apparatus for the energy meter. The energy meter consists of several parts: controller 1, input/ output ports 2, sampler 3, computational unit 4, memory 5 and display unit 6. The component 1 is a programmable unit that holds the operating system for the energy meter. It also enables periodic installation of firmware for the hardware drivers of the energy meter. The component 1 is responsible for recording input and output information at 2. The 3 is enabled by 1 to sense a.c. current and a.c. voltage from 2, which transforms input signal, senses a.c. current and a.c. voltage rectifies power and regulates voltage levels. The power regulated by 3 can be optionally used to power the controller 1. The component 2 provides a means for connecting a.c. load to the energy meter e.g. load terminal and input power terminal. The controller 1 instructs 3 to send the a.c. current and a.c. voltage values to 5. 4 consists of a programmable processor that operates through calculations on values stored in 5 according to the instructions programmed into it e.g. the five a.c. power components and cost of billing. The calculations are performed according to the relationships as disclosed in the present invention. A communications module is optionally implemented in 1 through 2 to provide remote connectivity for exchanging information contained in 5. The output values are displayed onto 6 according to instructions from 1.

Claims

1. An apparatus for determining accurate power factor for a.c. power system, which is affected by harmonic distortion of a load coupled to an a.c. power source that generates and supplies a.c. current and a.c. voltage to the load, wherein power waveform (s_m) is produced as a product of a.c current and a.c voltage to be used in billing, comprising: a first means for measuring maximum amplitude (S⁺) of power waveform; a second means for measuring minimum amplitude (S-) of power waveform; a third means coupled to the first means and the second means, for calculating apparent power (5) to the load as a function of both S⁺ and S-; a fourth means coupled to the first means and the second means for calculating active power dissipated (P) at the load as a function of S⁺, S-; a fifth means for measuring the instantaneous power received at load (S^I) component; a sixth means for measuring the instantaneous residual reactive power

component stored at the load; a seventh means for measuring the instantaneous reserved reactive power

component circulating back and forth between the power source and the load; an eighth means coupled to the third means and the fourth means, for calculating absorption coefficient power factor (APF) of the load; a ninth means coupled to the eighth means, for calculating the power factor angle (PF angle) of the load; a tenth means coupled to sixth means and the ninth means, for calculating the phasor reactive power (Q) component as a function of both and PF angle;

an eleventh means of calculating tuned power factor and a twelfth means for calculating cost of power bills (C_F) based on the power components.

2. The apparatus according to claim 1, wherein the means for calculating the apparent power includes means for determining the apparent power according to the relationship: 5 = 0.5 * [S⁺ + S-]

3. The apparatus according to claim 1, wherein the means for calculating the active power dissipated includes means for determining the active power dissipated according to the relationship:

P = 0.5 * [S⁺ — S-]

4. The apparatus according to claim 1, wherein the means for calculating the absorption coefficient power factor includes means for determining the absorption coefficient power factor according to the relationship:

5. An apparatus according to claim 1, wherein the first means for measuring S⁺ comprises a signal sampler and detector for detecting maximum value.

6. An apparatus according to claim 1, wherein the second means for measuring S- comprises a signal sampler and detector for detecting minimum value.

7. An apparatus according to claim 1, wherein the means for calculating the absorption coefficient power factor comprises a computational unit.

8. An apparatus according to claim 1, wherein the means for calculating the absorption coefficient power factor includes a programmable processor.

9. The apparatus according to claim 1, wherein the means for calculating the instantaneous reactive power to the load includes means for determining the instantaneous power received at load according to the relationship:

10. The apparatus according to claim 1, wherein the means for calculating the instantaneous residual reactive power stored at the load includes means

for determining the instantaneous residual reactive power stored at the load according to the relationship:

11. The apparatus according to claim 1, wherein the means for calculating the instantaneous exchange reactive power

circulating back and forth between the power source and the load includes means for determining the instantaneous returned reactive power circulating back and forth between

the power source and the load according to the relationship:

12. The apparatus according to claim 1, wherein the means for calculating the phasor reactive power (Q) includes means for determining the phasor reactive power according to the relationship:

13. The apparatus according to claim 1, wherein the means for calculating the tuned power factor includes means for determining the tuned power factor according to the relationship:

14. The apparatus according to claim 1, wherein the means for calculating the cost of power bills includes means for determining the cost of power bills (C_P) according to the relationship:

15. An apparatus according to claim 1, further comprising a display connected to the means for calculating the absorption coefficient power factor for displaying the absorption coefficient power factor.

16. An apparatus according to claim 1, wherein each of the means is provided in a single piece of programmable electrical equipment.

17. A method of determining accurate power factor for a.c. power system which is affected by harmonic distortion of a load coupled to an a.c. power source that generates and supplies a.c. current and a.c. voltage to the load, wherein power waveform (s_m) is produced as a product of a.c current and a.c voltage to be used in billing, the method comprising the steps of: measuring maximum amplitude (S⁺) of power waveform; measuring minimum amplitude (S-) of power waveform; calculating active power dissipated (P) at the load; and operating a computational unit in accordance with a predetermined relationship which takes into account S⁺, S- and P to determine the absorption coefficient power factor (APF) of the load as a function of S⁺, S- and P ;

18. A method according to claim 17, wherein the operating step includes the step of calculating the absorption coefficient power factor according to the relationship:

19. A method according to claim 17, wherein the means for calculating the tuned power factor includes means for determining the tuned power factor according to the relationship:

20. A method according to claim 1 and claim 17, further comprising the step of remote access and display of the calculated absorption coefficient power factor, apparent power, active power dissipated, instantaneous reserved reactive power, instantaneous reactive power, instantaneous power received at load, phasor reactive power and instantaneous residual reactive power components and power bills.