FCLTY F ENGNEERNG LB SHEET EEL1196 nstrumentation & Measurement Techniques TRMESTER 2 2017-2018 M2: Power Measurement sing Two Wattmeter Method *Note: Students will have to tabulate the theoretical values of the power measurement for each circuit in Table 2.1 BEFRE THE LB SESSN. These values will be checked by the instructor prior to the commencement of the lab session. n-the-spot evaluation will be carried out during or at the end of the experiment. Therefore, students MST read through this lab sheet before the experiment. Your performance, teamwork, effort and attitude will count towards the marks.
bjective: To examine the methods of power measurement using wattmeter in a DC circuit and three-phase circuits. pparatus required: Multi-range wattmeter: 3 V, 10 V, 30 V, 100 V, 300 V, 500 V 0.1, 0.3, 1, 3, 10 mmeters: a.c.0-5, d.c. 0-1. Voltmeter: a.c. 0-500 V, d.c. 0-10 V. Resistors: 1 box-unit containing three 1800 Ω, 150 W resistors. Capacitors: 1 box-unit containing three capacitors of 4.2 µf each. D.C. Power supply: 0-240 V,.C.Power supply: Three phase and single phase, 50 Hz supply 1.Theory: 1.1 Power Power in an electrical system is the product of the voltage v and current i. n S-units, v is in volts, i is in amperes and the power P is in watts. n d.c. circuits, v and i do not vary with time and are normally represented as upper-case letters V and. The power P is also constant in d.c. circuits. We can write: P = V. (1.0) n a.c. circuits, we have an instantaneous power, p and an average power, P. These are given by: p = v.i (1.1) T 1 P = v.i.dt (1.2) T f v and i vary sinusoidally with time as the instantaneous power is o v = 2 V cos ω t (1.3a) i = 2 cos (ω t - ϕ ), (1.3b) p = v.i = 2 V cos ω t. cos (ω t - ϕ) (1.4) where V and are the effective (R.M.S.) values of the voltage and current.
n equations (1.3 b) and (1.4), a + sign denotes a capacitive load (current leading the voltage) and a sign denotes an inductive load (current lagging behind the voltage). The average power is T 1 P = v.i.dt = V.. cos ϕ (1.5) T o n an a.c. circuit, the voltage and current are represented by phasors. The term cosϕ is called power factor. f v and i are of different frequencies, the value of the integral in equation (1.5) will be zero. P = V is the apparent power and P = V.. cosϕ is the active power of the load. 1.2 Wattmeter terminals: wattmeter is an indicating instrument, which takes v and i, and performs the multiplication, integration and averaging indicated in equation (1.2). The average power, P (also called true power) is shown on the instrument by a pointer-position (or digitally). For connection to the circuit, a wattmeter has four terminals - two current terminals and two potential terminals as shown in figure 1.1. The connections are made such that, the current-element of the wattmeter is connected in series with the load circuit. The load current is sent into the current-element of the instrument in a specified direction. This direction is usually marked on the wattmeter. n the same way, the direction of voltage-drop to be applied to the potential terminals is also given on the instrument. f the reference current direction and voltage drop are properly taken into account, the meter will give positive reading in a load that consumes power. Wattmeter.C. Source ZL Load Figure 1.1 Connecting a Wattmeter in a circuit.
1.3 Three phase power measurement 1.3.1 Voltage and Currents in Star- and Delta-Connected Loads: three-phase ac system consisting of three voltage sources that supply power to loads connected to the supply lines, which can be connected in either delta ( ) or star (Y) configurations, are as shown in the figure 1.2. Figure 1.2 Load configurations. n balanced three-phase systems, the voltages differ by a phase of 120, and their frequency and amplitudes are equal. f the three-phase loads are balanced (each having equal impedances), the analysis of such a circuit can be simplified on a per-phase basis. The voltage and current relationships in three-phase ac circuits (in a balanced three-phase system) can be simplified as shown in Table 1-1. Table 1-1. Voltage and current relationships in three-phase circuits. Star-Connected Balanced Load Phase current: 1p = 1L, 2p = 2L, 3p = 3L Line current: L = 1L = 2L = 3L Delta-Connected Balanced Load Phase current: = Line current: L = 1L = 2L = 3L and p = 12p = 23p = 31p P L 3 VL Phase voltage: V P = 3 Line voltage: V L = V 12 = V 23 = V 31 Phase voltage: V 12 = V 12p, V 23 = V 23p, V 31 = V 31p Line voltage: V L = V 12 = V 23 = V 31 and V p = V 1p = V 2p = V 3p
1.3.2 Three Phase Power Measurement using Two Wattmeter Figure 1.3 shows the two wattmeter connection may be used to determine the power in a threephase three-wire circuit (balanced or unbalanced). W 1 W 1 = B - C V B Z 1 V B B Z 1 Z2 C B Z 2 Z 3 B = CB - B Z 3 CB V CB V CB C C = C - CB W 2 W 2 Figure 1.3 Measurement of 3φ power using two wattmeter. Star connection: Power indicated by W 1 : P 1 = V B cosφ B- (1.6) φ B- is the phase difference between V B and. V B = V N - V BN (Potential drop across W 1 ) Power indicated by W 2 : P 2 = V CB C cosφ CB-C (1.7) φ CB-C is the phase difference between V CB and C. V CB = V CN - V BN (Potential drop across W 2 ) Sum of the powers measured by the two wattmeters W 1 and W 2 would equal: P T = P 1 + P 2 (1.8) The total power measured (P 1 +P 2 ) is the sum of real power consumed in the three phases. 1.3.3 nalysis in the Balanced Star Connection The voltage, V B = V N V BN and is indicated by the phasor diagram in Fig. 1.4. Phase difference between V B and V N is 30. f the load is assumed to be inductive, the current is lagging behind their respective phase voltage by φ, the phase difference between and V B is = (30 +φ).
V B φ V -V B 30 o V BC C N VC B V B V C Figure 1.4 Phasor diagram for balanced case. For a balanced supply and three-phase load system, the magnitudes V B = V CB = V L (line voltage: voltage between any pair of terminals, eg. V B ). Power indicated by wattmeter W 1 : P 1 = V B cosφ B- = V L. L.cos(φ +30 o ) (1.9) where V L is the magnitude of the line voltage and L is that of the line current. Power indicated by wattmeter W 2 : P 2 = V CB C cosφ CB-C = V L. L.cos(φ -30 o ) (1.10) The sum of the two wattmeter readings: P 1 + P 2 = V L. L.cos(φ +30 o ) + V L. L.cos(φ -30 o ) = V L. L.[cos(φ +30 o ) + cos(φ -30 o )] = 3 V L L cos φ (1.11) This is the total power P T consumed by the load. Hence, the sum of the readings of the two meters gives the total power P T consumed by the load. n this method, the reading of the wattmeter W 1 can become negative if φ is greater than 60 0 (refer equation 1.9). For a balanced three-phase system, the reactive power: Q = 3 V L L sin φ (1.12)
Caution: HGH VLTGE!!!. Please make sure that all the connections are correct before switching on the power supply. You are required to get the permission from the instructor to switch on the power supply. 2 Experimental Procedure: 2.1 Power Measurement in a DC Circuit a) Establish the connections for power measurement in DC circuit according to the circuit diagram shown in Fig. 2.1 and select the ranges on the wattmeter as indicated. b) djust the source voltage to 10V such that the current through the circuit is 0.1. djust the resistor such that the resistance is 100Ω. Write down the reading of the wattmeter, taking into account its multiplication factor. Wattmeter (10V, 1.0 ) 1 10Vd.c. V V 1 100Ω Figure 2.1 Connection of a wattmeter in a d.c. circuit Wattmeter reading = W. Calculate the theoretical average power and compare with the measured value. Record the values in Table 2.1.
2.2 Power Measurement in Three-Phase Circuits sing Two Wattmeter 2.2.1: Resistive Load in Star Connection Symmetrical a) Establish the connection for power measurements in a three-phase star connection load according to the circuit diagram shown in Fig. 2.2(a). (Note that in this circuit arrangement, a three-phase balanced supply is feeding a balanced three-phase load.) b) djust each of the resistances to 470 Ω and connect them in star. (The load consists of three equal resistances.) c) se wattmeter, W 1 and W 2, to measure the power between line and line B, and between line B and line C, respectively. The current circuit of W 1 is connected in series with line, and that of W 2 is connected in series with line C of the three-phase circuit. The potential circuit of W 1 gets the voltage V B applied across it. The potential circuit of W 2 has the voltage V CB across it. d) djust the three phase supply voltage to be 250 V line-to-line. Read the corresponding measured values: of the ammeter, V of the voltmeter and P 1 and P 2 of the wattmeters, which are W 1 and W 2 respectively. Record the measured values in Table 2.1. Calculate the total power P consumed by the load using the formula:- P T = P 1 + P 2 e) Repeat step (d) by adjusting the three phase supply voltage to 150 V and 100 V. Record the measured values in table 2.1. 1 W 1 (300V, 1, PF) 415V 3φ B V V 1 470Ω per phase C W 2 (300V, 1, PF) Figure 2.2(a) Resistive load in Star - Symmetrical. 2.2.2: Resistive Load in Delta Connection - Symmetrical a) Establish the connection for power measurements in a three-phase delta connected load according to the diagram shown in Fig 2.2(b). b) djust the three phase supply voltage to be 150 V line-to-line.
c) Read the corresponding measured values: of the ammeter, V of the voltmeter and P 1 and P 2 of wattmeter, W 1 and W 2, respectively. Record the measured values in Table 2.1. 1 W 1 (300V, 1, PF) 415V 3φ B V V 1 470 Ω per phase C W 2 (300V, 1, PF) Figure 2.2(b) Resistive load in Delta Symmetrical. 2.2.3: Capacitive Load in Delta Connection - Symmetrical a) Connect three capacitors of equal value of approximately 3.7 µf each in delta as shown in Fig. 2.2(c). b) djust the three phase supply voltage to be 150 V line-to-line. c) Read the corresponding measured values: of the ammeter, V of the voltmeter and P 1 and P 2 of wattmeter, W 1 and W 2, respectively. Record the measured values in Table 2.1. (NTE: ne of the wattmeter will show a negative reading as the pointer will show a value less than zero.) d) Modify the connection of the wattmeter showing the negative reading to obtain a positive reading. 1 W 1 (300V, 1, PF) 415V 3φ B V V 1 C W 2 (300V, 1, PF) Figure 2.2(c) Capacitors in Delta Symmetrical.
* mportant note: Compute the theoretical values of total power for the different types of circuits/loads in Table 2.1 below before the lab session. This column must be filled up before being allowed to proceed with the experiment. TBLE 2-1: EXPERMENTL RESLTS N. NTRE F LD 1 (mps) V 1 (Volts) P 1 (Watts) P 2 (Watts) TTL PWER P = P 1 +P 2 (W) (only for 3-phase circuits) Experimental Theoretical % Error 1. Resistive load in a DC circuit R = 100Ω V = 10V Resistive load in 2. star (symmetrical) R = 470 Ω /ph V = 250 V Resistive load in 3. star (symmetrical) R = 470 Ω /ph V = 150 V Resistive load in 4. star (symmetrical) R = 470 Ω /ph V = 100 V Resistive load in 5. (symm.) R ph = 470 Ω/ph V = 150 V Capacitive load in 6. (Symmetrical) C = 4.2 µf/ph V = 150 V 10 250 150 100 150 150 3. nswer the following questions: a) For the case covered by section 2.2.1, based on the phasor diagram given in the theory section showing all the voltages and currents, draw the phasor of V CB (in star connection). Find the phase angle between the voltage and current associated with each wattmeter and hence, calculate the readings of P 1 and P 2. b) What is the power factor at which the reading of one of the wattmeters would be zero? c) nder what load conditions do the two wattmeters indicate readings of equal magnitude (a) with the same sign, (b) with opposite sign?
d) Design a balanced three-phase star connected load (resistive load) with a supply voltage of 150 V line-to-line and with the total power consumed by the load equal to the total power measured in the three-phase delta connection load as shown in Fig 2.2(b). 4. Laboratory Report The report should contain the following: a) bjective. b) Schematic diagrams and theory. c) Summary of the experimental procedure. d) Tabulation of measured and computed data. e) nswers to the exercise questions. f) Your own results and conclusions. mportant: You are given one week to prepare, write and submit your lab report to the same laboratory. ll reports must be neatly handwritten. Typewritten reports will not be accepted under any circumstances. Neatness and carefulness in preparing report are taken into account when awarding marks. Write your own report and use your own findings and results, similar reports won t be given marks for both the original and the copied ones (strictly no plagiarism, references should be properly cited). Late submission of lab report will be penalized through deduction of marks.