. MEASEMENT OF OE CONSMTION OF THE NONBALANCED THEE-HASE LOAD Task of the measurement. Measure the active power and the reactive power of the nonsymmetrical -phase load in Y-connection. Do not connect the common node of the load to the common point of wattmeters voltage coils. Measure the active power: a) using three wattmeters; b) using two wattmeters; verify by three measurements the Blondel theorem. Measure the reactive power using three wattmeters. Make correction of the error of the method where appropriate. Estimate the expanded uncertainty of measurement in all measurements (k = ).. Verify the function of the three-phase electronic (static) watt-hour meter and compare the reading of the h-meter with results gained by other measuring instruments. Schematic diagram Connection for measurement of the active power is shown in Figs. 7a. and 7a.. Connection for the measurement of the reactive power is shown in Fig. 7a. and connection for verification of the h-meter function in shown in Fig. 7a.. I A L L ELECTONIC L h-mete L I A V L L L I A Fig. Connection for measurement of the active power of the three-phase load using three wattmeters, and for verification of functions of electronic h-meter. I A L I V L A L I A Fig. Example of connection for measurement of active power using two wattmeters - Aaron connection
I A L I V L A I L A Fig. Connection for measurement of reactive power of the non-symmetrical three-phase load using three wattmeters Notes to the measurement: a) Check correct connection (with respect to the phase sequence) of power supply and the load. b) The 0 V voltage system is used in delta connection. c) Take care in all measurement of the correct connection of beginnings of current and voltage coils of wattmeters and of the electronic watt-hour-meter. d) Do not let the load connected to the power line source for more than 5 minutes. Load might be damaged if connected to power line for longer time. e) Do not disconnect the electronic h-meter, let it connected in all measurements, even if it is not shown in the schematic diagrams. List of the equipment used A - iron-vane ammeter, accuracy class, measurement range used: ; A - iron-vane ammeter, accuracy class, measurement range used: ; A - iron-vane ammeter, accuracy class, measurement range used: ; - electrodynamic wattmeter, accuracy class, voltage measurement range used: V, current measurement range used: A, voltage coil resistance:... ; - electrodynamic wattmeter, accuracy class, voltage measurement range used: V, current measurement range used: A, voltage coil resistance:... - electrodynamic wattmeter, accuracy class, voltage measurement range used: V, current measurement range used: A, voltage coil resistance:... ;, L, L - power line AC source 0 V; L - the measured load; electronic H-meter EM 0, ZA Trutnov, Czech epublic.
Theoretical background Measurement of the active power using three wattmeters Connection in Fig. 7a. will be used for measurement of active phase powers,,, consumed by load in phases, L, L. If not only the total three-phase load active power should be measured but also the individual phase active powers should be measured, then (since the measurement here takes place in three-wire system without neutral wire) wattmeters with identical voltage coil resistances should be chosen. In this case the common point of the ends of wattcmeters voltage coils in Fig.7a. is the power line neutral point (socalled artificial neutral ), and voltages across voltage coil on every wattmeter is the same and equal to power-line phase voltage. There is an ammeter in series with the current coil of every wattmeter. According to the readings of these ammeters the current measurement ranges of the corresponding wattmeters should be selected. The total measured active power Cm consumed by the load is given by the sum of the active powers of individual phases: K K K () () Cm where K to K are wattmeter constants (/division), to are wattmeter deflections (divisions). The methodical error (error of the method) is here caused by power consumption of voltage coils of individual wattcmeters n p n n n () () where p is the phase voltage, voltage across the wattmeter voltage coil (V), n is resistance of the wattmeter voltage coil (more exactly wattmeter voltage circuit, since it includes the series resistor setting the voltage range); in this measurement voltage coil resistances are in all tree wattmeters identical (. Error of the method shall be corrected by subtraction of the total power consumption of all three voltage coils: C Cm p () () Standard uncertainty of the reading by measurement of the active power using three wattmeters is n u u u u () (4) The term expressing correction of the methodical error in expression (7a.), that is the term ( p / n ) is disregarded in standard uncertainty estimation, since it is much lower than the total measured power Cm. If three identical wattmeters (identical type and measurement ranges) are used for measurement of total active power, then the standard uncertainty of each wattmeter reading is
where AC is accuracy class of the wattmeter, is wattmeter measuring rang (). M u AC M u u u () (5) 00 Expanded uncertainty of the C for the coverage factor k = is then c u () (6) The result of measurement of the total active power shall be expressed in the () (7) C c Measurement of active power using two wattmeters According to Blondel theorem, (n - ) wattmeters are necessary for measurement of active power in n-wire system. One of possible connections for the case of the -wire net is shown in Fig. 7a. (the so-called Aaron connection). This scheme can be applied subsequently to all three combinations of two wattmeters connection. The total active power measured by two wattmeters is after correction of the methodical error (caused by power consumption of two wattmeter voltage coils with resistances n and n ) given as C K K () (8) where n and n are resistances of voltage coils of the used wattmeters ( ), and are line voltages in the three-phase voltage system used (V). Since voltage coil resistances of all wattmeters are identical here and identical are also the line voltages in the 0 V power line net, there is C n K K () (9) and if both wattmeters are identical and using the same measuring ranges, the expanded measurement uncertainty can be estimated (for k = ) as n n u () (0) C where u is given by the equation (5). The term correcting in the relation (9) the methodical error ( / n ) is not taken into account by estimating uncertainty of measurement since it is much smaller than the sum K + K. esult of measurement using two wattmeters should be again expressed in the form () () C C Measurement of reactive power using three wattmeters Connection for measurement of the reactive power is shown in Fig.. Voltage coils of the wattmeters are connected to line voltage lagged (delayed) by / with respect to the phase voltage of the phase where is connected the current coil of the corresponding wattmeter. 4
Deflection of each wattmeter is proportional to the reactive power of the corresponding phase multiplies by, since magnitude of the line voltage connected to its voltage coil is - times larger than the phase voltage (the voltage system is symmetrical). The reading of each wattmeter must be therefore divided by, and the total reactive power is therefore given by the expression N N N K K K Q C Q Q Q (VAr), () where N, N and N are readings of wattmeters and other symbols have the same meaning as in relation (7a.). Standard uncertainties of individual wattmeter readings can be estimated (as in (7a.5)) as u N AC M (VAr), () 00 where AC is accuracy class of the used wattmeter (%), M is measurement range of the used wattmeter (VAr), is uncertainty of the wattmeter reading (VAr). u N ncertainty of the reactive power measured by each wattmeter can be using () estimated as un uq (VAr) (4) The expanded uncertainty (k = ) of the total measured reactive power Q C is given as Q C uq uq uq (VAr) (5) If all three wattmeters are identical (both type and range), the expanded uncertainty Qc (for k=) can be expressed as QC u N un (VAr) (6) and the result of measurement of reactive power shall be expressed in the form Q Q (7) C Q C hase shifts of phase voltages with respect to phase currents can be found for all three phases from the equation Qi i arctg ( ), i =,, (8) Note: For wattmeters with voltage and current coils connected according to Fig. 7a. positive wattmeter deflections correspond to positive reactive powers. If some of the wattmeters read negatively (deflection tends to be out of scale in negative direction) it is necessary to commutate the polarity of the voltage coil and take the wattmeter reading as negative. Quadrant in which lies the phasor of current I i, respectively to it corresponding phase shift i can be found according to the signs of both i and Q i. i 5
Demonstration of the three-phase static (electronic) watt-hour meter EM 0, manufacturer ZA cz Trutnov, Czech epublic According to Fig. 7a., part of the measuring circuit is also a three-phase electronic (socalled static ) watt-hour meter. This watt-hour meter allows measurement of large number of parameters in the three phase net. The h-meter is for common energy consumer programmed usually so that the readings of the active energy rotate in each 0 s in individual (in altogether 4) tariffs. The watt-hour meters EM 0 used in this task were free of charge supplied to our department by the company ZA cz Trutnov (www.zpa.cz). h-meters were programmed so that after switching on they show the total energy consumed in all phases (kh). After repeated pushbutton switching there are in sequence displayed following readings, demonstrating broad measurement ability of the meter: Total reactive energy (kvarh), Total apparent energy (kvah), Instantaneous active power in all phases (,,) (k), Instantaneous active power in phase (k), Instantaneous active power in phase (k), Instantaneous active power in phase (k), Instantaneous reactive power in all phases (,,) (kvar), Instantaneous reactive power in phase (VAr), Instantaneous reactive power in phase (VAr), Instantaneous reactive power in phase (VAr), Instantaneous apparent power in all phases (,,) (kva), Instantaneous apparent power in phase (VA), Instantaneous apparent power in phase (VA), Instantaneous apparent power in phase (VA), hase voltage of phase (V), hase voltage of phase (V), hase voltage of phase (V), Line voltage - (V), Line voltage - (V), Line voltage - (V), Current in phase (A), Current in phase (A), Current in phase (A), cos in phase, cos in phase, cos in phase. 6