Electronic metering of active electrical energy
United States Patent [191 Milkovic ELECTRONIC METERING OF ACTIVE ELECTRICAL ENERGY [75] Inventor: Miran Milkovie, Scotia, NY.  
 [73] Assignee: General Electric Company [22] Filed: May 17, 1973 [21] Appl. No.: 361,030  
 [52] U.S. Cl. 324/142 [5 1] Int. Cl. G0lr 21/00, GOlr 11/32 [58] Field of Search 324/142, 107  
 [56] References Cited UNITED STATES PATENTS 3,343,084 9/1967 Gambale et a1 324/142 3,718,860 2/1973 Kwast et al. 324/142 OTHER PUBLICATIONS Evans, Elect. Rev., 18 Sept. 1970, pp. 403404.  
 Primary E.\&#39;aminerStanley T. Krawczewicz Attorney, Agent, or Firm-Cushman, Darby &amp; Cushman Apr. 1, 1975 [57] ABSTRACT Metering kWh in an electrical system involves producing analog signals from line currents and voltages. Pairs of analog signals, representing current and voltage variables, are processed in four-quadrant timedivision multiplier networks which, in effect, multiply said variables and produce series of width-andamplitude modulated pulse signals, each representing instantaneous partial power. Pulse signals from the different multiplier networks are summed to provide another series of pulse signals, each representing instantaneous total power. The series of pulse signals representing intantaneous total power are processed through a low-pass filter which produces another signal representative of average total power in the system. Subsequently, the signal representing average total power is processed in an analog to pulse-rate converter which produces a series of output pulse signals, each representing a constant, or quantized, amount of electrical energy. A stepping switch and register perform conventional accumulation, storage and display functions in response to said series of output pulse signals delivered thereto.  
 40 Claims, 36 Drawing Figures Lulu.  
 SHE? L2 11 time (6) time (t) time (a) L time (6) ELECTRONIC METERING OF ACTIVE ELECTRIC AL ENERGY CROSS-REFERENCES TO RELATED PATENT APPLICATIONS Employed to advantage in connection with the invention hereinafter disclosed are some of the principles disclosed in the following US. Pat. applications earlierfiled in behalf of Miran Milkovic, the same inventor in whose behalf this patent application is filed: Ser. No. 365,429, filed May 31, 1973 and titled CURRENT TRANSFORMER WITH ACTIVE LOAD TERMINA- TION said application Ser. No. 365,429 being a continuation of the now-abandoned application,&#39;, and, Ser. No. 346,412, filed Mar. 30, 1973 and titled CURRENT TRANSFORMER WITH ACTIVE LOAD TERMINA- TION FOR PROVIDING, INTER ALIA, PHASE ANGLE ALTERATION.  
  The entire right, title and interest in and to the inventions described in the aforesaid patent applications, as well as in and to the aforementioned patent applications, and the entire right, title and interest in and to the invention herein disclosed, as well as in and to the patent application of which this specification is a part, are assigned to the same assignee.  
 SUMMARY OF THE INVENTION The subject invention pertains, in general, to a method and apparatus for metering active (average) electrical energy (e.g., kWh) in electrical systems, and, in particular to converting analog signals representing measured currents and voltages to a series of output signals wherein the signal repetition rate, or frequency, represents average system power and each output signal represents a constant amount of system energy.  
  Electrical energy (kilowatt-hours, or kWh) has been, and continues to be, metered with the ubiquitous rotating disc type of meter which is disclosed in, among other sources, the Electrical Metermens Handbook,&#34; Chapter 7, Seventh Edition, published 1965 by Edison Electric Institute. The invention hereinafter disclosed represents a substantial departure from the methodology and apparatus exemplified by the rotating disc type of meter.  
  In addition, those who are familiar with the instrumentation and metering arts, respecting electrical power and energy, know of proposed systems including apparatus employing electronic and solid state devices for measuring power and energy. In such apparatus the electronic and solid state devices replace the conventional rotating disc. For example, the following patents disclose systems including electronic and solid state devices for measuring electrical energy: Canadian Pat. No. 801,200; US. Pat. No. 3,602,843; and Swiss Pat. No. 472,677. The invention hereinafter disclosed represents a departure from the methodology and apparatus disclosed in the aforesaid patents.  
  One object of the invention is the provision of a method of, and apparatus for, metering active (average) electrical energy in electrical systems.  
  Another object of the invention is the provision of a meter for metering active electrical energy; said meter comprising solid state circuitry which may be fabricated in the form of monolithic integrated structures.  
  Another object of the invention is the provision of a method of, and apparatus for, metering active electrical energy; said method and apparatus employing analog-to-modulated pulse conversions as well as analogto-pulse rate conversions in computing active electrical energy.  
  In accordance with the invention, active electrical energy metering in, for example, a three-phase, threeline, f hertz system is accomplished by producing analog signals representing different line currents and line voltages. If the methodology of blondel&#39;s theorem is employed, two different line currents and two different line voltages may be represented by four different analog signals produced from measurements being made of said currents and voltages. Pairs of said analog signals, representing a current and a voltage, are, in effect, sampled and multiplied to produce from each pair a series of signals at a signal repetition rate f;, where f f so that k f /f T /T and in the time period T, there are first through kth consecutive signals in said series with each signal representing instantaneous partial power. Corresponding first through kth signals of the same ordinal number in the different series are summed to produce another series of first through kth consecutive signals, each representing instantaneous total power in the system. Subsequently, the series of signals representing instantaneous total system power is integrated and averaged over a relatively long time period T T l /f, to produce a relatively steady state signal representative of average total system power. Thereafter, the aforesaid steady state signal is converted to another series of equally quantized signals wherein said series has a varying repetition rate representative of average total power and each quantized signal represents a constant amount of electrical energy.  
  Although the invention is hereinafter disclosed as applicable for metering kWh in a three-phase, three-wire f hertz (e.g., hz.) electrical system having a balanced delta-connected load coupled thereto, it is to be understood that such disclosure is made for the purpose of giving one example of the method, and metering apparatus, provided by the invention for kWh metering. The invention may be employed, as well, for metering active electrical energy in electrical systems such as the following: polyphase systems, generally, i.e., systems having two, three, or more phases; three-phase systems having more than three wires or lines; combinations of polyphase systems; systems having electrical loads which are balanced or unbalanced; systems having electrical loads which may include reactive impedances; systems having sources, as well as loads, may be delta-connected, mesh-connected, Wye-connected, or star-connected; systems having a system frequency 11 which may be 60 hertz as well as less than, or more than, 60 hertz; systems wherein the various currents and voltages selected for measurement, initially, may be selected according to Blondel&#39;s theorem, or not. Furthermore, according to the invention, kWh metering may be performed as a real-time operation, or it may be performed as an off-line operation.  
  Other objects, as well as the various features of the invention, appear hereinafter wherein a method of, as well as apparatus for, metering active electrical energy is disclosed for the purpose of illustrating the invention; said disclosure including accompanying drawing figures.  
 DRAWINGS FIG. 1 is a block diagram and schematic illustration 3 showing, inter alia, various components comprising apparatus for metering active electrical energy in a threephase, three-wire, 60 hertz electrical system to which a three-phase, delta-connected electrical load is coupled.  
  FIG. 2 is a phasor diagram showing various current and voltage phasors, and their relative angular displacements, for the delta-connected load shown at FIG. 3.  
  W FIG. 3 shows the delta-connected electrical load of FIG. 1 and indicates the various line and phase currents and voltages thereof.  
  4 is a sinusoidal waveform of one line-to-line voltage v showing the instantaneous voltage amplitude thereof, as a function of time t, between two lines, lines 1 and 2, of the three-phase, f hertz, three-wire, electrical system illustrated at FIG. 1.  
  FIG. 5 is a sinusoidal waveform of one line current 1&#39;, showing the instantaneous current amplitude thereof as a function of time; the current i being the current in one of the lines, line I, of the ac. electrical system of FIG. I.  
  FIG. 6 is a sinusoidal waveform of another line-toline voltage .v showing the instantaneous voltage amplitude thereof as a function of time between lines 3 and 2 of the electrical system illustrated at FIG. 1.  
  FIG. 7 is a sinusoidal waveform of another line current i showing the instantaneous current amplitude thereof as a function of time; the current i being the current in one of the lines, line 3, of the electrical systern of FIG. 1&#39;.  
  FIG. 8 is a graphical representation showing instantaneous power p in the whole system as a function of time.  
  FIG. 9 is another graphical representation showing active average power P, in the whole system, as a function of time 1; Le,  
  FIG. 10 is another graphical representation showing a sawtooth waveform representing energy it f Pdt,  
 as a function of time t.  
  FIG. 11 is another graphical representation showing quantized output pulses as a function of time, each output pulse representing a quantized, or constant amount of, energy W, said quantized output pulses being delivered as output signals from an analog to pulse-rate (A/PR) converter employed in the system shown at FIG. I. I  
  FIG. 12 is a block diagram for illustrating the basic operating principle of the four-quadrant timedivision PWA multiplier network employed to convert pairs of signed analog signals to a series of width-and-amplitude modulated pulses, each representing instantaneous power.  
  FIG. 13 is a graphical representation showing a waveform of one output pulse signal developed by a PWA multiplier; e.g., the PWA multiplier shown in FIG. 12.  
 FIG. 14 is another diagram showing in more detail.  
 the multiplier network of FIG. 12.  
  FIG. 15 is a sinusoidal waveform representing a signal voltage V delivered to an input of the PWA multiplier network of FIG. 14.  
  FIG. 16 is a bipolar periodic pulse waveform of a signal voltage V developed at the output of a comparator unit included in the PWA multipliers employed in the meter of the invention.  
  FIG. 17 is a bipolar periodic pulse waveform of the signal voltage V in its pulse-width-modulated form, after being width modulated.  
  FIG. 18 shows sinusoidal waveform representations of signal voltages +Vy and Vy in phase displacement.  
  FIG. 19 shows a waveform of a width-and-amplitude modulated signal voltage V which is delivered at the output of a PWA multiplier; V, being proportional to the instantaneous product of the signals V X and Vy.  
  FIG. 20 is a diagram showing, inter alia, the combination of a four-quadrant multiplier, an [IV converter, inverter and LP filter.  
  FIG. 21 is a graphical representation showing active system power P as a function of time.  
  FIG. 22 is a graphical representation showing the variation of the output voltage signal V delivered at the output of the aforesaid LP filter.  
  FIG. 23 is a graphical representation showing the sawtooth output signal variation as a function of time in the integrator section of the A/PR converter.  
  FIG. 24 is a graphical representation showing corresponding quantized output pulses, as a function of time, produced by the A/PR converter.  
  FIG. 25 is another graphical representation showing corresponding output pulses, as a function of time, delivered at a divided frequency rate by the A/PR converter.  
  FIG. 26 is a graphical representation showing a triangular waveform representing a signal voltage V delivered at an integrator section in the A/PR converter.  
  FIG. 27 is a block diagram of an A/PR converter employed in the meter of the subject invention for providing a trail, or series, of quantized output signal pulses, each representing a predetermined, constant quantity of energy W,,.  
  FIG. 28 is a simplified block diagram of a low cut-off pulse filter unit employed in the subject meter.  
  FIG. 29 is a graphical representation showing the pulse, rate, or frequency, of the output pulses delivered by the A/PR as a function of load power P; the minimum and maximum pulse rateand power ranges being indicated.  
 FIG. 30 is a more detailed block diagram, including schematic details, of the low cut off pulse filter of FIG. 28.  
  FIG. Slis a schematic diagram of a solid state demand switch network employed in the energy meter of the subject invention.  
  FIG. 32 is another schematic diagram showing, inter alia, a solid state output pulse amplifier unit employed in the meter of the subject invention.  
  FIG. 33 is a diagram indicating how FIGS. 34A and 34B, hereinafter identified, are to be matched side-byside to form a complete electrical diagram of the subject metering apparatus according to the invention.  
  FIGS. 34A and 348, when matched side-by-side as indicated inFIG. 33, form a complete electrical diagram, of the electrical&#39;energy metering apparatus in ac-i cordance withone illustrative embodiment of the invention.  
 DESCRIPTION OF THE ILLUSTRATIVE EMBODIMENT In the simplified diagram at FIG. 1 the three power lines 1, 2 and 3 of a three-phase, 60 Hz electrical system conduct instantaneous line currents I, i, and to a delta-connected polyphase electrical load. Across the three branches of the electrical load three instantaneous line-to-line voltages v v and v are impressed. Two instrument current-transformers CT, and CT, as well as two instrument potential-transformers PT and PT are electrically coupled with the transmission lines 1, 2 and 3 as shown in FIG. 1. The aforesaid instrument transformers are coupled with the transmission lines according to the teachings of the wellknown Blondel theorem. Thus, line 2 has been arbitrarily selected as the common point, or line, for carrying out power and energy metering in accordance with the aforesaid theorem. The current transformer CT provides an output analog signal representative of the instantaneous line current The, current transformer CT provides an output analog signal representative of the instantaneous line current i The potential transformer PT provides an output analog signal representative of the instantaneous line voltage v The potential transformer PT provides an output analog signal representative of the instantaneous line voltage v The analog signals representing i, and v are delivered to the input of a multiplier M Similarly, the analog signals representing i and v are delivered to the input of another multiplier M The multiplier M in effect, multiplies the signals representing i, and v. and produces at the output of said multiplier a signal v which is proportional to the product p =1, v The multiplier M in effect, multiplies the signals representing i and v and produces at the output of said multiplier another signal v which is proportional to the product p =1; v As indicated at FIG. 1, the output signals v and v which represent instantaneous partial powers p and p respectively, are summed at a SUMMING POINT 40 to provide another signal representing the total instantaneous system power p,  
 where P l 12 a a:  
  The metering principle employed in the illustrative example (FIGS. 1, 34A and 34B) is based on the use of the Blondel theorem which enables power measurement in, for example, a three-phase electrical system, but uses only two multiplying channels. According to the theorem the power in a system of N lines may be measured by (N-l) wattmeter elements so arranged that each of the (N-l) lines contains one current measuring element with a corresponding potential measuring element being connected between each of the lines and a common point. In the event that the common point happens to be one of the lines (e.g., line 2 in FIG. 1) power can be measured by (N-l) elements. Thus, in the three-wire system of FIG. 1 (and FIGS. 34A and 34B) the total instantaneous power p delivered to the load is:  
  P 12 i2 za za ai ai 4 Fit; and V31: V32+V2| 4.1.2)  
 . 6 Thus. P =3 iz m za ss a n an a: A150, P 12 t&#39;s ar) s: a1&#34; 2s)- q- Since, I1=i 2 in In I31 and s s: s: 31 n q- 4.1.4) the total instantaneous power p from the foregoing equations is equal to:  
  P l rz s 32 P12 +Paz where v and v are instantaneous line voltages and i and i. are instantaneous line currents. Also 2,, and p are instantaneous partial powers.  
  In FIG. 1 the signals v, and v representing the aforesaid partial powers p12 and Pan. are combined at the SUMMING POINT 40 and delivered to an input of a summing low-pass filter 42. The filter 42 sums, or integrates, and averages the aforesaid signals representing the partial powers p and p to produce at the output of said filter a signal V,- proportional to the active average total system power P. In effect, the filter 42 performs integrating and averaging operations in accordance with the following relationship:  
 2-1 iv dt+1 iv (it (e .4.1.6  
  T or P I 1 p dt: 1 p dt:  
  T o 12 1&#39; 32 wherein, P I 1 p dt, and  
 P 1 p dt Therefore, P P P (eq. 4.1.7)  
 where P and P are average partial powers and P is average total power. Also, from the phasor diagram shown in FIG. 2,  
  12 12 1 01 12 $51 a: s: a C05 l&#39;as s) (eq. 4.1.9)  
 P V I (cosllr cos ,9. sinlli sin 9,) (eq.  
 Pa, V [3 (coslbag. C05 9 SIIIIIJH. SI 9;) (eq.  
 where V and I represent the rms values of voltage and current, respectively, 6 is the load impedance phase angle, and II: is the angle between phase current and line current.  
  In the case of a balanced load: 1b., tb 30; 6 9 =9 =9;V ,=V;I =I =I From equations (4.1.10) and 4.1.11) the active, average pol phase power P can be shown to be:  
 where V represents rms line voltage and 1 represents rms line current; P representing the true active average power in a polyphase load; and 0 lieing is the phase angle as shown in FIG. 2.  
  The output signal V; at the output of the filter 42 is delivered, as indicated at FIG. 1, to the input of an ana- 7 log to pulse-rate converter 44, or A/PR converter. which functions to convert the signal V (which is proportional to P) to system energy W according to the relationship:  
  &#39;r w- [Pdt However, if the time duration T T, (i.e., the indi-.  
 cated integration occurring in the A/PR converter 44 for a finite time duration T.,) then each time the energy W accumulates to a quantity W, in said converter according to the relationship q Pdt (eq. 4.1.13 q o An output signal pulse V representing a predetermined quantity of electrical energy W.,, is delivered at the output of the A/PR converter 44. For example, in the specific embodiment illustrated each output signal pulse V,,- is representative of the quantized electrical energy W, l.2 Watt-hours (Wh). Thus, the A/PR converter 44 delivers a series, or train, of pulses V,,, at its output; the accumulated number of output pulses V N representing the total electrical energy W of the system. The aforesaid series of pulses V has a variable pulse repetition rate f which is proportional to the total average system power P. As indicated at FIG. I, the output pulses V are delivered to the input of a pulse amplifier 46, the amplified output of which drives a stepping motor SM. The stepping motor SM, in turn, operates an electromechanical kW-hour display register 48 which displays, in decimal digits, the accumulated energy in kilowatt-hours (kW-hours). While a conventional stepping motor SM and electromechanical register 48 are illustrated at FIG. 1, it is to be understood that the stepping motor SM and register 48, are indicated by way of example only. The electrical energy meter according to the present invention may employ, instead of the aforesaid stepping motor and electromechanical register, a liquid crystal or LED display suitably coupled with a non-volatile electronic memory element and driven by logic circuitry.  
  Referring, again, to the operation of the A/PR converter 44, the average power P in equation (4.l.l3) is constant, as shown in the graphical representation at FIG. 9, and  
  W, PT, constant fit; where W, represents the constant quantized energy of each of the output signal pulses VN and W, is designated as the Watt-hour constant. That is, W., is constant and independent of the product PTq T,  
 is inversely proportional to P due to the operation of the A/PR converter 44 and the output pulse rate f of the A/ PR converter44 is:  
 f= l/T, P/W.,= P/Watt-hour constant (eq. 4.1.15)  
  Hence, the frequency f or output pulse rate of the A/PR converter 44 is proportional to the active average power P in the polyphase load.  
  The time interval T,,, in seconds, between output pulses V from equation 4.l.l4 is:  
 T, W,/3600P (seconds) 4 le i where T, is in seconds, W is in Watt-hours and P is in watts.  
  Also, the time interval T, of equation (4.1.14) can be expressed as:  
 expressed as:  
 V, K P  
 where K is a multiplication factor of the multipliers in amp and P is the power in watts in the load.  
  By combining equations (4.l.l4), (4.1.17) and (4.l.l8) the watt-hour constant W becomes:  
  W KC/KM (eq. 4.1.19 Thus, the watt-hour constant W, is a quantity determined solely by circuit and system parameters. Therefore, the energy meter provided by the invention is one wherein K and K depend only on the values of resistors, reference voltages, and transistors V BE ratios, rather than on absolute values of voltage.  
  Each multiplier M and M is a fourquadrant timedivision multiplier; i.e., the pulse-width-amplitude, or PWA, type. Such multipliers are known to those in the art. See, for example, the article A Transistorized Four-Quadrant Time-Division Multiplier with an Accuracy of 0.] Percent&#34; by Hermann Schmid, IRE Transactions on Electronic Computers, March 1958. See, also, the article A High-Accuracy Time-Division Multiplier by Edwin A. Goldberg, RCA Review, September 1952. FIGS. 12 and 13 illustrate the basic operating principle of a PWA multiplier. As shown in FIG. 12, a basic PWA multiplier employs a PULSE-WIDTH MODULATOR and an ANALOG SWITCH. Thei SWITCH and MODULATOR of FIG. 12 function to multiply the input signal voltages V V X (which, in the present case, are proportional to an instantaneous line current i and instantaneous line voltage v, respectively) so as to produce an output signal voltage V, which is; proportional to the product of the input signal voltages V and V As is described in more detail hereinafter, with reference to FIGS. 14-20 the incoming analog signal voltage V; (FIG. 15) is combined with a constant reference voltage V (of selectable polarity or at the sampling frequency of f HTS, which sampling frequency is the frequency of the signal voltage V having the triangular waveform indicated in FIGS. 12, 14 and 20. In the illustrative embodiment f kHz 50 which is very much greater than the line frequency f Hz. As indicated at FIG. 12, the MODULATOR, or PWM, produces an output signal voltage V In effect, the signal V X (FIG. is converted to the pulse-widthmodulated signal V (FIGS. 16 and 17 Subsequently,  
 55 the signal V shown at FIGS. 16 and 17, drives the AN- ALOG SWITCH which, in effect, passes, or gates, the incoming signal voltage V (FIG. 18) through said switch for a duration of time T proportional to the time ratio T /T where (eq. 7.2.1) In other words, the output signal voltage V,, illustrated at FIGS. 13 and 19, has a waveform whose amplitude is proportional to the variable signal voltage:  
  (proportional to instantaneous line current 1&#39;) and whose width ratio or time duration ratio T IT is proportional to the variable signal voltage V (proportional to the instantaneous line voltage 0). Where the signal V consists of symmetrical pulses, the ANALOG SWITCH passes, or switches, VY  
  9 and V,- (FIG. 18) to the output of said switch such that V 0. If the signal V consists of nonsymmetrical pulses the value of the V is greater than zero. Expressed mathematically,  
  2 VI (ZTA/TS (eq. 7.2.  
 and, combining equations (7.2.1) and (7.2.2.) results 7.2.3) where R R (see FIG. 14)  
  Thus the average value of V as indicated in FIG. 13 is proportional to the product of V and Vy as well as inversely proportional to V FIG. 14 shows one four-quadrant time-division multiplier M in more detail. The multiplier M is similar and it functions in a similar way. The waveforms of FIGS. 15-19 serve to illustrate the operation of the multipliers. In FIG. 14 an analog voltage V,, proportional to the line voltage V is delivered to a summing point, or node, 50 formed at the junction of two equal-valued resistors R1 and R6. The summing point 50 is connected to the inverting input terminal of an operational amplifier Al, the non-inverting input terminal of the amplifier being connected as indicated to a signal ground or reference point. A capacitor C1 is connected between the summing point 50 and the output terminal of the amplifier Al. The non-inverting input terminal of another operational amplifier A2 is connected to the output terminal of the amplifier Al; the amplifier A2 functioning as a comparator while amplifier Al and capacitor C 1 function as an integrator. A triangular signal V having a sampling frequncy f 10 kilohertz delivered via a resistance element to the inverting input terminal of the amplifier A2 serves to sample the analog signal V (representing v It times during the period I/f TL. SInCef andf 60, approximately. As indicated in FIG. 14 the output terminal of the operational amplifier A2 is coupled with two analog switches S1 and S2. Analog switches S1 and S2 are illustrated as single-pole double-throw switches. However, they are electronic switches which are switched at very high speeds by the signal V The analog switch S1 switches the reference voltages +V as well as the reference voltage V,, to the summing point 50 via the resistance element R6. The analog switch S2 switches the analog signals +V and -Vy. Advantageously, the analog switches S1 and S2 may be comprised of complementary MOS devices. As indicated in FIG. 14 an inverter 52 is provided for the purpose of inverting the +Vy analog signal to the V,; analog signalras shown at FIG. 18.  
  The multiplier M shown at FIG. 14 employs a feedback type up-down integration principle. The triangular signal V having the sampling frequency f much greater than f is delivered to the amplifier A2 (comparator). When the analog signal V is zero the output signal V from the amplifier A2 consists of a series of symmetrical pulses, shown at FIG. 16, having a frequency of about kilohertz. This pulse series V drives the analog switch S1 and alternately switches the resistor R6 to +V and V reference voltages thereby feeding equal amplitude currents V /R6 into the summing point 50 during the positive and negative portions of V Thus, capacitor C1 is charged and discharged by the equal amplitude currents so that the average value of V at the output terminal of the operational amplifier A1 equals zero. When V is greater than zero, the aforesaid balance is changed inasmuch as capacitor C] is not charged and discharged with equal amplitude currents. Consequently, V is no longer equal to zero. Due to the non-symmetry of the charging and discharging currents in C1 and because of the presence of the 5 FEEDBACK LOOP, the signal V no longer consists of symmetrcal pulses required to maintin the summing point 50 at virtually zero potential. Hence, the duty cycle, or time ratio activity T /T of the output voltage V is defined by the equation (7.2.1) for the condition 10 RI R6. In effect, the analog signal V produces a signal V which is pulse-width modulated. By applying the signal V to control the analog switch S2 there results, in effect, an amplitude modulations. If the signal V, consists of symmetrical pulses (FIG. 16) the analog switch S2 switches V and -V (FIG. 18) to the output of analog switch S2 such that V; 0. If however, V consists of non-symmetrical pulses V 2 becomes greater than zero. Mathematically V may be defined by the equations (7.2.2) and (7.2.3). Accordingly, where R1 20 R6 and V is a constant reference voltage the output voltage V; from multiplier M is directly proportional to the product of V and V In FIG. 19, the output signal V is shown as a series of pulses which are both width modulated and amplitude modulated. The FIGS.  
  15-19 illustrate the situation where the width of the 10 kilohertz (f sampling frequency pulses are modulated by the signal V which is proportional to the line voltage v and the amplitude is modulated by the 180 out-of-phase signals +V and -V which are proportional to the line current i The output signal V shown in FIG. 19 is proportional to the instantaneous product of V and Vy.  
  With the multiplier shown in FIG. l4,f 10,000 and f 60 so that k =f,lb and approximately k 167 samplings and multiplications of instantaneous line voltage and line current are accomplished. Inasmuch as the multiplier M 32 is similar to that of multiplier M shown in FIG. 14, the multiplier M samples and multiplies the instantaneous line voltage v and instantaneous line current i approximately k, or 167, times.  
 Multiplier M (hereinbefore discussed with reference to FIGS. 14-19) is shown again within the dotted line box in FIG. 20 as being in combination with the inverter 52, and UV converter 54, CT,, PT and the lowpass filter 42. The combination of CT, with converter 54 and inverter 52 is disclosed in the patent application Ser. No. 262,643 hereinbefore identified in more de tail. Converter 54 is comprised of operational amplifier 01 which has the feedback resistor R2 and impedence F1 connected therewith as shown. The impedence F 1 serves as a phase compensation or phase correction e1- ement. See patent applicaiton Ser. No. 346,412 hereinbefore identified in more detail. The secondary winding of the current transformer CT, is connected across the inverting and non-inverting input terminals of the operational amplifier 01 and in effect is terminated in a virtual short circuit condition. At the output of the operational amplifier 01 there is produced an analog signal 60 voltage which is proportional to the current i in the secondary winding of CT,. The aforesaid analog voltage is delivered via resistance R3 to inverter 52 which is a transreslstance amplifier comprised of the operational amplifier 02 and the feedback resistance R5.  
 55 Although the signal V proportional to v is described hereinbefore (and shown in FIGS. 13 and 14, among other places) as being used to convert V to a pulse-width modulated signal, it is to be understood that the signal V proportional to i,, could be used instead. In other words, in FIG. 13 the signal V could have been amplitude modulated by signal V, and width modulated by signal V rather than (as shown) amplitude modulated by signal V, and width modulated by signal V Thus, multiplier M can be adapted to perform the aforesaid modulations and ultimately perform the required multiplication of i, and v Similarly, the multiplier M can be adapted to perform similar modulations and ultimately perform the required multiplication of u and i The multipier M is similarly combined with an I/V converter and another inverter. Also, the instrument transformers CT;, and PT are employed in a manner similar to that shown in FIG. for the multiplier M The output voltage V,;, from multiplier M is delivered via resistor R20 to a low pass filter 42. Similarly, another output voltage from the multiplier M is also delivered via resistor R19 to the low pass filter 42. As shown in FIG. 20 the ends of the resistors R19 and R20 are commonly connected to the inverting input terminal of an operational amplifier 07. The non-inverting input terminal of amplifier 07 is connected to signal ground. As shown in FIG. 20 a capacitor C and parallel feedback resistor R21 are connected between the output terminal and inverting input terminal of the operational amplifier 07. The combination of amplifier 07, resistor 21 and capacitor C4 form an active filter. The active filter 42 averages out the DC component from the summed output signals delivered at the summing point 40 delivered thereto from the multipliers M M In the embodiment shown in FIG. 20, R19 =Rl9. The values of R19, R20, R21 and C4 are determinative of the corner frequency or cutoff frequency of active filter 42. In the embodiment shown in FIG. 20 and FIGS. 34A and 34B the corner frequency may, for example, be 3.18 hertz. As indicated the output terminal of the operational amplifier 07 produces a voltage signal V; which is representative of the average power in the whole system. See FIGS. 9, 21 and 22.  
  The A/PR converter 44 is shown in detail in FIG. 27. The purpose of converter 44 is to convert the DC signal V,- produced by the active filter 42 to a series of quantized pulses, each representing a quantized, or constant amount, of active energy. As shown in FIG. 27 the converter 44 includes an operational amplifier 08 having inverting and non-inverting input terminals as well as an output terminal. The DC signal V,- is coupled via resistor R23 to the non-inverting input terminal of the operational amplifier 08. The non-inverting input terminal is coupled via resistor R24 to signal reference point, or ground. A capacitor C is coupled between the inverting input terminal and output terminal of amplifier 08. The output of operational amplifier 08 is coupled to a threshold (delay) flip-flop 56. A fixed-frequency (crystal) reference oscillator 58 and frequency divider unit 60 are also provided, as shown. In addition, a feedback pulse-height reference unit 62 is provided. As indicated, the reference unit 62 is driven by two inputs, a reference voltage V, and the voltage V The reference unit 62 delivers an output current pulse I R of pulse width or time duration T to the inverting input terminal of the operational amplifier 08. See FIG. 27.  
  FIGS. 21-27 serve to illustrate the operation of the converter 44 shown in FIG. 27. Each pulse in the series of pulses delivered at the output of the converter 44 represents a quantized, predetermined amount of active electrical energy of l.2 watt-hours, for example. During maximum power in the system, shown at FIG. 21, a quantized pulse representing 1.2 Wh appears at the output of the binary divider unit 78 every 2.078 seconds. Ultimately, each quantized pulse is employed for driving a stepping motor SM. Likewise, at minimum power in the system, a quantized pulse representing the same 1.2 Wh appears at the output of the binary divider unit 78 every 166.28 seconds. In view of the very long time periods involved, the pulse rate converter 44 is comprised of an integrating section (operational amplifier 08 and capacitor C and a pulse rate divider section comprising the units 58, 60, 56 and 62. By employing pulse rate division, the capacitor C need not be prohibitively large. Thus, by employing pulse rate division, the binary divider unit 78 does provide an output pulse rate of l/l66.28 seconds at the minimum power condition in the polyphase system. See FIGS. 21 and 22.  
  In FIG. 27 the summing point 64 is at virtually zero potential due to the large open loop gain of operational amplifier 08 and due to feedback action of C The input current I; is a function of the input voltage V, and resistor R23. When the voltage on capacitor C reaches a certain level, the delay flip-flop 56 is switched for a precise time interval T During the time interval T an analog switch in the feedback pulse height reference unit 62 is activated and causes a current I to be produced, discharging C Previously as shown in FIG. 26, the capacitor C, was charged by the input current I,- in accordance with the following relationship T F. IF clt (eq.7.4.1)  
 where Qp is the charge on capacitor C Similarly, the discharge of the capacitor C, follows the relationships:  
 Q (1 I a: (eq.7.4.2  
 Since Qr(t) Q (t) the pulse rate (or frequency) is, consequently Also,  
  ii: R&#34; (eqs. 7.4.5  
 The pulse rate from eq. (7.4.4) is consequently I, g v. Ru 1 i In. &#39;I&#39;..K.. K.  
 Where.  
  K is the analog conversion factor in volt sec. T is the crystal oscillator period (7&#34;,, l/f,,) K, is the oscillator divider factor (K =64) Also.  
  im rl u (eq. 7.4.7)  
 The output pulse rate in eq. (7.4.6) is directly proportional to the input voltage V,- (or current I,-). Because I and T as well as R and R are constant. an accurate analog conversion is achieved. The time reference T is produced by using a crystal-oscillator 58 which oscillates at. for example, 400 kHz. A 6 bit binary divider 60 converts the 400 kHz oscillator frequency down to f,; l/T =f /64 6250 Hz. T is the time reference and determines the down integration time of the A/PR converter 44. The pulse current 1,, is determined by a constant reference voltage V and value of resistor R This current is switched on and off by an accurate analog switch incorporated in the down integration loop of the A/PR-converter. FIGS. 23, 24 and 25 show the output signals occurring in various parts of the A/PR converter 44.  
  A more detailed description of the A/PR converter 44 of FIG. 27 appears hereinafter with reference to FIGS. 34A and 34B.  
  In FIG. 28 there is illustrated a simplified block diagram of a low cut-off pulse filter unit 66 employed in conjunction with the converter 44. The low cut-off pulse filter unit 66 is situated within the dotted lines in FIG. 28 and, as shown, is comprised of a pulse-rate-tovoltage converter 68 and a threshold detector and gate unit 70 as well as a NAND gate 72. The details of the low cut-off pulse filter unit 66 are shown in FIG. 30 and the fundamental operation thereof is illustrated graphcially in FIG. 29. The purpose of the low cut-off pulse filter unit 66 is to prevent pulses below a preselected minimum pulse rate, representative of a preselected minimum power level, in the load to be passed and ultimately registered in the display register 48. In FIG. 30, pulses from the converter 44 can pass into an I l-bit binary divider unit 78 (see FIGS. 34A, B) only if the gate G3 output is at logical l or if the collector of transistor T4 is at approximately zero volts. Such is the case when about 0.6 volt level is accumulated across the integrating capacitor C6 for activating transistor T4. The cutoff frequency of the unit 66 may be adjusted to the required preselected value by varying resistor R30 and C6. At too low a pulse-rate the voltage across C6 is too small to activate transistor T4 and as a result the input of gate G3 is at logical l and therefore the output of the gate G3 is at logical 0. Thus, no pulses can pass to the gate G2.  
  FIGS. 34A and 34B hereinafter discussed shows how the low cut off pulse filter unit 66 is incorporated with other circuits and networks comprising the electrical energy meter of the invention.  
  FIG. 31 is a schematic ofa solid state demand switch network 74 employed in conjunction with the metering apparatus provided by the invention for the purpose of enabling a demand metering function. That is. transferring quantized pulses from the A/PR converter 44 to a remote station so that signals representative of such pulses may be stored on any demand recorder device. such as a magnetic tape recorder for, inter alia. offline processing. The network shown in FIG. 31 is in effect a form (switch The network 74 is essentially com prised of two three-stage switching amplifying chan nels. Each time one of the two transistors T14 or T9 is conductive. or on, a capacitor in an external network at the remote metering station is charged rapidly to about 50 volts with transient current of about 200 mA. After the transient time duration interval, the current approaches a steady-state value of about 35 mA. When T14 or T9 switches to the non-conductive, or off condition. the voltage across the output terminals rises to approximately 50 volts. FIGS. 34A and 348 show how the demand switch network 74 is incorporated in the energy meter of the present invention.  
  FIG. 32 is a schematic diagram showing an output pulse amplifier 76 for driving the stepping motor SM. which in turn actuates display register 48. The pulse amplifier 76 delivers current pulses of about l20mA peak during msec to the stepping motor SM which drives the register 48. The amplifier 76 has, as shown, three amplifying stages and a reverse transient protection diode D16. The pulse amplifier 76 is also shown in FIGS. 34A and 34B.  
  FIGS. 34A and 348 which are intended to be matched according to the direction indicated in FIG. 33 form a complete electrical diagram of the electrical energy metering apparatus in accordance with one illustrative embodiment of the invention. In operation. current in line I and line 3 is measured with the instrument current transformers CT and CT;,. respectively. Also voltage between line 1 and line 2 is measured by the instrument potential transformer PT Similarly, the voltage between line 3 and line 2 is measured by the potential transformer PT The primary windings of both PT and PT have series connected resistors R therein, as shown in FIG. 34A, for providing phase correction or compensation. The aforesaid current transformers and potential transformers are coupled as shown in FIG. I with the power lines 1, 2 and 3 according to the Blondel otheorem, hereinbefore discussed. An I/V converter 54 which is comprised of operational amplifier OI, resistor R2, and phase correction or compensation impedence Fl provides at the output of the operational amplifier 01 a first analog signal voltage of frequency f, 60 Hz, responsive to and representative of the current measured by CT, in line I. As indicated the output terminal of the operational amplifier OI is directly connected as an input to the multiplier M Also a phase-inverted first analog signal voltage of frequency f, 60 Hz is developed by the inverter 52 which is comprised of operational amplifier O2 and feedback resistor R5. The aforesaid inverted first analog signal voltage is developed in response to the analog signal developed at the output terminal of the operational amplifier 01. The inverted output signal voltage from operational amplifier O2 is also delivered as an input to the multiplier M The converter 54 and inverter 52 are shown and described in FIG. 20, and described hereinbefore, as well as disclosed in the patent applications hereinbefore identified. Oppositely poled diodes DI and D2 and their purpose are also disclosed in the aforesaid patent applications. Similarly, oppositely poled diodes are used with the potential transformers as shown in FIG. 34A. A second analog signal voltage of frequencyf 60 H2 is developed by the potential transformer PT and is representative of the voltage between lines 1 and 2. As indicated one end of the secondary winding of the potential transformer PT is connected via resistor R1 to the multiplier M In addition, one end of the resistor R1 is connected to an end of each of the elements. resistor R6 and capacitor C,. A momentary reference to FIG. will show that the resistor R1 is the input resistor coupled to summing point 50 which is at the same potential as the inverting input terminal of the operational amplifier Al within the multiplier M The capacitor C, and resistor R6 which are shown as externally connected to the multiplier M in FIG. 34A are, nevertheless, part of the multiplier M as more clearly indicated in FIG. 20. Also connected to the multiplier M are the various voltage sources, such as +V,, V +VR and VR,.  
  Also shown in FIGS. 34A and 34B is a triangular volt age, V generator section for providing the sampling frequency f,- of, for example, 10 kHz. As indicated, the triangular voltage generating section is comprised of the amplifiers 05 and 06, resistors R15, R16, R17, R18, capacitor C and the five diodes D5, D6, D7, D3 and D4. The triangular output voltage V of frequency f, l0,000 Hz, is delivered from the output of the amplifier 06 to the multiplier M The current transformer CT, is instrumental in conjunction with an l/V converter comprising operational amplifier 03 in providing a third analog signal voltage of frequen y ft 60 HZ in response to, and representative of, the current measured in line 3 of the polyphase electrical system. Similarly, an inverter comprising the operational amplifier 04 is instrumental in conjunction with (T and the aforementioned l/V converter comprising amplifier 03 in providing a l80 phase-inverted third analog signal representative of the current measured in line 3. The aforesaid third analog voltage signal and inverted third analog signal are, as indicated, delivered to the multiplier M Also, a fourth analog signal voltage of frequency f, 60 Hz is developed by the potential transformer PT in response to, and representative of, the voltage between line 3 and line 2 of the polyphase electrical system shown in FIG. 1. The aforesaid fourth analog signal voltage is delivered by a resistor R8 to the multiplier M and to the junction of one end of the elements R13 and C The other inputs to the multiplier M are the voltages +V,, V +VR and VR,. In addition, the triangular voltage V at the sampling frequency f,- 10 kHz is also delivered as an input to the multiplier unit M Each of the multipliers M and M develops therein a signal comprising a series of pulses like that shown in FIG. 16. More particularly, as shown at FIG. 16 there is produced a series of bipolar pulse signals having con stant positive and negative signal amplitudes and a pulse rate of frequency f, 10 kHz, said series having a plurality k =f,-/f of such bipolar signals consecutively occupying the time period 7&#39;, l/f This series of hi polar pulse signals are conveniently designated as the first through the kth bipolar pulse signals. In each of the multipliers M and M the respective analog voltage signals representing the line-to-line voltages are used for the purpose of pulse-width modulating the aforesaid series of bipolar pulse signals shown at FIG. 16. The result is another series of bipolar pulse signals like that shown in FIG. 17. In FIG. 17 there is shown a modulated signal comprising a series of first through kth consecutive pulse-width-modulated bipolar pulse signals,  
 each having the period &#39;11, l/fl. Each pulse width modulated bipolar pulse signal has a positive signal portion with a time duration TA such that the ratio T /T for each pulse-width-modulated bipolar pulse signal is representative of a corresponding one of a consecutive first through kth sampled amplitudes of, for example, the second analog voltage signal representing the voltage between the lines 1 and 2. The multiplier M provides such a consecutive series of signals representative of a corresponding one of consecutive first through kth amplitudes of the fourth analog signal representing the voltage between lines 3 and 2. The sampling and production of the consecutive first through kth signals occurs during the time period T, l/fL as indicated in FIGS. 15 through 17. For the multiplier M the positive signal portions of each of the consecutive pulse modulated bipolar signals shown at FIG. 17 are employed for gating for the periods of their respective time durations T corresponding first through kth consecutive portions of the first analog voltage signal representing current in line 1. Also, the negative signal portions of the consecutive pulse-width-modulated bipolar pulse signals of FIG. 17 are employed for gating for the periods of their respective time durations (T T,,) corresponding first through kth consecutive portions of the inverted first analog signal voltage representing the phase inverted line current in line 1 to produce the signal shown at FIG. 19. The multiplier M performs the same time-division four-quadrant multiplication for analog signals representing the voltage between lines 3 and 2 and the analog signals representing current in line 3 and the l phase-inverted analog signal representing the current in line 3. The output from the multiplier M in a series of pulse-width and amplitude-modulated signals similar to that shown in FIG. 19.  
  Pulse width and amplitude modulated signals, like those shown in FIG. 19, are delivered to a summing point 40 via the resistors R20 and R19 from multiplier M and multiplier M At the summing point 40 the pulse width and amplitude modulated signals from the multipliers are summed so that in each series of first through kth modulated pulses corresponding pulses are added, algebraically. For example, the first pulse in the series delivered by the multiplier M is algebraically added with the first pulse in the series delivered by the multiplier M and the second pulse delivered by multiplier M is added to the second pulse delivered by the multiplier M etc. At the summing point 40, therefore, there appears a series of pulse width and amplitude modulated consecutive first through kth signals similar in appearance as that shown in FIG. 19, but, in fact, is the summation of the series output of both multipliers, whereby each pulse is representative of the instantaneous power in the whole system. The summing point 40 is directly connected to an input of an operational amplifier 07, which together with capacitor C4 and resistor R21 forms the summing low-pass filter 42.  
  The summing low pass filter 42, in effect, integrates and averages the pulse width and amplitude modulated series of signals received from the summing point 40. At the summing point 40 the series of pulse width and amplitude modulated signals (similar in waveform to those shown in FIG. 19) represents instantaneous power in the whole system. However, the summing low pass filter 42 at the output thereof produces a voltage V, which is a DC signal (See FIG. 9) representing the average power in the whole system. As shown, the DC signal V is coupled via resistor R23 to an input termi-