advertisement

ELEC 331 FUNDAMENTALS OF ELECTRICAL POWER ENGINEERING LABORATORY MANUAL EXPERIMENT 1 POWER MEASUREMENT IN THREE-PHASE CIRCUITS I. OBJECTIVES There are three objectives to this experiment: - To study the relationship between voltages and currents in three-phase circuits with delta and wye connections; - To measure power in three-phase circuits using the two-wattmeter method; - To become familiar with the principle of power factor correction. II. INTRODUCTION A three-phase circuit is usually connected in either delta or wye configuration. Power in a three-phase circuit is usually measured using two wattmeters – the dual wattmeter method. At power factors less than 0.5, one of the instruments has a negative reading. When a reading is negative, it is necessary to reverse the voltage or current connection in order 1 to obtain an upscale deflection (with the Lab-Volt dual three-phase wattmeter, the reversal is done with a toggle switch). Remember that all voltage and current quantities are line-toline and line quantities unless otherwise specified. Note that in Fig. 1-4 the voltage and current isolators E1 and I1 are combined to form a single wattmeter in a two wattmeter system. Similarly, E2 and I2 form the second wattmeter When the source and load are both balanced, expressions for the dual wattmeter readings are: P1 Vab I a cos(angle between Vab and I a ) or VL I L cos(30 ) P2 Vcb I c cos(angle between Vcb and I c ) or VL I L cos(30 ) where is the load angle and total power is the sum of P1 and P2. When the power factor is less than unity, a current that is greater than the minimum is required to transmit a given active power, resulting higher transmission losses and loading of transformers. There are means to minimize these losses. For inductive loads, for example, the most common solution is to install capacitor banks in parallel with the loads. Strategies that improve the power factor of electrical circuits are classed as power factor correction (PFC) techniques Three-phase ac circuits, transformers, ac machines and their per-phase equivalent circuits can be described by phasor diagrams. Figure 1-1 shows a wye-connected 3-phase source that is connected to a wye-connected load. In this case, the voltage sources and the load elements are assumed to be equal, hence the system is said to be balanced. The phase loadangle, , is the same for each load. 2 E3 To Osc. i I3 To Osc. Figure 1-2 shows the phasor diagram that corresponds to the 3-phase 1 2 3 system given in Fig. 250Vac 1-1. The per-phase equivalent circuit is also shown as it would appear on an oscilloscope display. Note that the voltage Van is taken as the reference for the single-phase equivalent A circuit. 5 0-208V Three-Phase Wye Connected Source Ia Three-Phase Wye Connected Load a 0-208V + Van Load a Vab 0o Van V Za n n o -240 Vcn Load b + + c To DAQ Vbn In -120o b Vbc Zc + Ib Zb Vca Load c L Ic Osc. Figure 1-1. A 3-phase wye connected source and load. D o 150 120o Vcn Vca Ic Ib -90o Ia 30o Van Ia Vbn Vab Van Vpk Ipk Vbc -120o 16.7ms t (ms) 8.33ms (b) Oscilloscope representation of 1-phase equivalent wye connected circuit (with lagging PF). (a) Phasor diagram of 3-phase wye system. Figure 1-2. Phasor diagram of 3-phase system and the voltage and current waveforms of a single phase (lagging PF, 60 Hz). 3 Ia Ia a a + Van Vab Vca Zbn b n Vab Zab Vca Zcn + Vbc Ib Vab Zan I ab + Ib Vbc Zca Zbc b Ic Ica + Vbc + Ic Vca + c Ibc c Figure 1-3. The wye and delta connected loads. Wye to Delta Transformation. The transformation of a load from the wye configuration (Y) to the delta connection (Δ) can be done on the basis of equal per-phase power capacity. Assume that the line-line voltages (Vab, Vbc, Vca) in Fig. 1-3 are the same for each circuit. Starting with the wye circuit the power in each phase is 𝑃∅𝑌 = 𝑉∅𝑌 ∙ 𝑉∅𝑌 𝑍∅𝑌 By equating the power-per-phase in each circuit, PϕY = Pϕ Δ , the equivalent impedance of the delta circuit can be found from 𝑍∅∆ = 𝑉∅∆ ∙ 𝑉∅∆ 𝑃∅𝛥 By comparing the values of the impedances, ZϕY and ZϕΔ, the transformation ratio can be found. Neutral Current in an Unbalanced Load. The three-phase circuits used in this laboratory are assumed to be balanced. However, in reality, three-phase sources and loads are often unbalanced (unequal). In the wye connected systems this imbalance can be measured by observing the neutral current, In. (Fig. 1-1, Fig. 1-4). The value of the In is given by 𝐼𝑛 = 𝐼∅𝑎 + 𝐼∅𝑏 + 𝐼∅𝑐 Where for a balanced system, 4 𝐼∅𝑎 = 𝐼 cos(−𝜃) + 𝑗 sin(−𝜃) 𝐼∅𝑏 = 𝐼 cos(−𝜃 − 120°) + 𝑗 sin(−𝜃 − 120°) 𝐼∅𝑐 = 𝐼 cos(−𝜃 − 240°) + 𝑗 sin(−𝜃 − 240°) Note that when the load impedance is resistive the phase angle is zero and an open circuit carries no current (I = 0). Refer to: 1) Chapman, Stephen J., Electric Machinery Fundamentals, 4th ed., New York, McGraw Hill, Appendix A. (Examples A-1 and A-2, pgs. 695 – 698). III. 1. PRE-LAB CALCULATIONS Calculate the power factor (cos), load angle (), wattmeter readings P1 and P2, total power from P1 and P2 readings (P1+P2) and total power using the direct method (Pphase = 1.73 VI cos) for the followings loads and operating conditions, with loads wyeconnected to a 208 V, three-phase line-to-line power supply. Sketch a 3-phase phasor diagram showing the current phasors for parts a,b and c. Indicate whether the currents are leading or lagging. Sketch the 3-phase phasor diagram indicating the angles between Vab and Ia, Vcb and Ic for part d. (a) Each resistive load element rated at 120 V, 0.4A; (b) Each capacitor load element rated at 120 V, 0.4A; (c) Each inductor load element rated at 120 V, 0.4A; (d) Each load element rated at 120 V, 0.4 A with 0.5 power factor lagging. 2. For the resistive load, compute the value of the resistance required in a delta connection, for the same power dissipation. Sketch the per-phase (single phase) phasor diagram. 3. For the 0.5 power factor load defined in 1(d), compute the values of R and L assuming R and L are in series. Sketch the per-phase (single phase) phasor diagram. 5 Warning: High voltages are present in this experiment! DO NOT make any connection while the power is on. IV. PROCEDURE The data to be collected for each step in this experiment is taken from the meters shown in each diagram. In Fig. 1-4, for example, the rectangular boxes with upper-case letters refer to voltmeters and ammeters located on the Lab-Volt Data Acquisition and Control Interface (LVDAC). Text boxes with lowercase letters refer to voltage and current isolators located on the Lab-Volt test-bench. These isolators are usually connected to the oscilloscope. Circular text icons refer to analog voltmeters and ammeters located on the test-bench. The label, DMM, refers to a digital multimeter. Normally all data can be recorded and transferred to the PC using the data table in the Lab-Volt software. From the Lab-Volt table the test results should be transferred immediately to an Excel spreadsheet for calculation and plotting of the results. If communication with the LVDAC is interrupted the Lab-Volt data table on the PC may freeze and the results can be lost. All the details of the bench operation are in the document, Undergraduate Lab Equipment and Procedures found on the Moodle course website and as Introduction to Lab Test Equipment on the technicians personal webpage: users.encs.concordia.ca/~joe/ . This manual should be consulted throughout the semester. The procedures in the document will be included in the lab exam. 1. Turn on the LVDAC, the oscilloscope, and the computer. On the PC open the LVDAC software and open the MS Excel software. Connect the circuit as shown in Fig. 1-4 with the resistive load unit in a wye configuration. Have your instructor check the circuit. The numbers 4,5,6 in Fig 1-4 correspond to the Lab-Volt voltage source 6 connections. Refer to the appendices or the Lab Equipment and Procedures document for instructions on how to set up the oscilloscope, PC and data acquisition software. If necessary, use E1 and E2 to verify the phase rotation of the voltage source. (To satisfy the 2-wattmeter method, the polarity of E2 must be the reversed as shown in Fig. 1-4, Vcb not Vbc). Set the resistance of each section to 300 . Turn on the power supply and observe the ammeter to make sure there is no short circuit. Slowly adjust the line voltage to 208 Vac as indicated by the voltmeter. Measure and record the all the measurements shown in Fig. 1-4 including the neutral current. The required data is indicated in the data-table found at the end of this document. Ia To DAQ a + 4 connections, 4, 6 are reversed in diagram. A I1 + 0-208V To DAQ b 0-208V c i W1 250Vac 1 I3 2 3 W2 6 5 4 Vab Ib To DAQ Vbc + Vca Ic 0 – 300 Ω Neutral To DAQ e To Osc. n Vcn Ic + b I2 E3 L O A D Van Vbn To DAQ E2 + Ia Ib + 6 a I3 V E1 5 To Osc. To DAQ 2.5Aac Note: W2 DMM A M + c I4 Figure 1-4 The Lab-Volt experimental circuit. 2. Measure and record the phase angle between the phase voltage (V), and the phase current (I), using the oscilloscope (model Fluke; refer to Appendix for setting the Oscilloscope). For the LeCroy oscilloscope refer to the Lab Equipment and Procedures document. Note that the phase angle can also be seen using the LVDAC phasoranalyzer on the PC. 3. Measure and record the meters shown in Fig. 1-4 using the Lab-Volt DAC and the data table as in step 1. Include the line voltages and currents, the phase-voltages and currents, the wattmeter readings and the powers, P, S and Q indicated on the PC (LVDAM). Return the voltage to zero and turn off the power supply. 4. Open the resistance of one section, phase C. Use an Ohmmeter to adjust the variable ballast resistance to 300 . Turn on the power supply and observe the ammeter to 7 make sure there is no short circuit. Slowly adjust the line voltage to 208 Vac as indicated by the voltmeter E1. Reduce the ballast resistor to 0 . Measure the neutral current on the DMM to record the imbalance. If the ammeter I4 is in the circuit record the value of the current in the Lab-Volt table. Turn the voltage down to zero and turn off the power supply. 5. Set the load on all 3 phases to 200 (parallel the 300 and 600 resistors). Turn on the power supply and observe the ammeter to make sure there is no short circuit. Slowly adjust the line voltage to 120 Vac as indicated by the voltmeter E1. Record all measurements as before (see data table). 6. Return the voltage to zero and turn off the power supply. 7. Replace the resistive load of Fig. 1-4 with the capacitor load. Set the capacitance of each section to 4.4 F and the line voltage to 208 Vac. Repeat the measurements of Steps 2 and 3. Return the voltage to zero and turn off the power supply. 8. Replace the resistive load of Fig. 1-4 with the inductor load. Set inductance of each section to 0.46 H (3.2 H || 1.6 H || 0.8 H) and the line voltage to 208 Vac. Repeat the measurements of Steps 2 and 3. Return the voltage to zero and turn off the power supply.. 9. Replace the resistive load of Fig. 1-4 with the resistive-inductive load composed of R = 300 and L = 0.46 H (3.2 H || 1.6 H || 0.8 H) connected in series, and the line voltage to 208 Vac. Repeat Steps 2 and 3. Print the waveforms that are observed on the oscilloscope. All the phase angles can also be seen using the LVDAM phasoranalyzer on the PC. Print these diagrams in phase related groups (E1 and I1, E2 and I2, E3 and I3). Return the voltage to zero and turn off the power supply. 10. Connect a capacitor of 4.4 F in parallel across each phase of the RL series-load as shown in Fig. 1-5, and repeat Steps 2 and 3. Print the waveforms that are observed on the oscilloscope. All the phase angles can also be seen using the LVDAM phasoranalyzer on the PC. Print these diagrams in phase related groups (E1 and I1, E2 and I2, E3 and I3). Return the voltage to zero and turn off the power supply. 8 To DAQ 4 a + connections, 4, 6 are reversed in diagram. A I1 4 + 0-208V V E1 To DAQ 5 To Osc. To DAQ 2.5Aac Note: W2 Ia a i I3 + Ia 250Vac b W1 1 2 3 W2 6 5 Van 4 To DAQ + To Osc. Vcn Vab Ib Vbc + Vca I2 + e n To DAQ 0-208V E2 c To DAQ Vbn Ib 6 E3 L O A D Ic b + c Ic Figure 1-5. The power-factor correction circuit. 11. Connect the circuit as shown in Fig. 1-6 with the resistive load unit connected in delta, and have your instructor check the circuit. Be sure to note the high and low sides of the load elements and the meters Depending on the orientations of the components, there is one correct set of results that 2.5Aac To DAQ + 4 A I1 + 0-208V To DAQ 5 0-208V 6 V E1 E2 W1 W2 4 5 6 1 2 3 250Vac To DAQ + Ib Vbc b Ibc + To Osc c + Vab Vca E3 e To DAQ To Osc I3 Zab Iab + Zbc Ic To DAQ + Use same phase current as line (phase) current in step 3 (300 To DAQ ,resistors). Zca Ica a Ia i I2 Figure 1-6. The Delta connected circuit. is relatively easy to explain. There are several other data sets that do not correspond to the normal conventions of describing 3-phase power circuits. These variations will have to be explained in your report. 12. Set the resistance of each section to 600 . Turn on the power supply and adjust the line voltage to obtain the same phase (and line) voltage as the line voltage in Step 2 where the load is connected in wye (The value of E3 in Fig. 1-6, should be the same as E1 in Fig. 1-4, Step 2, i.e. 120 Vac). Record the value of source voltage.Measure and record the values as before. 14. Return the voltage to zero and turn off the power supply. 9 V. Safety 1. Locate the poster that shows the security-procedures and emergency-contact information. Note the sections for fire and medical emergencies. 2. Locate the fire extinguisher in the lab. Consul the internet (or other source) and the label on the extinguisher to identify the classes of extinguisher, what types of fire they are used for and the type of extinguisher in the lab. VI. QUESTIONS 1. Derive the transformation that will change a wye-connected circuit to a deltaconnected circuit as shown in the introduction. Assume that each circuit has an equivalent power rating and a three-phase balanced load. Using this transformation (ratio), calculate the equivalent delta connected R, C, L, load-components for the wyeconnected circuits (and corresponding measurements) of Step 10 (i.e. transform Fig. 1-5 into a delta circuit similar to Fig. 1-6). Make sure all units (Ohms, Farads, and Henries) are indicated. Hint: do the initial calculation in terms of Ohms (XC and XL at 60 Hz). Include a hand-drawn (freehand) sketch of the 2 circuits in your report. In the drawings include the load-side voltage and current measurement devices shown in Figs. 1-5 and 1-6. 2. Calculate and tabulate the theoretical and experimental power and power factors (PF) for Step 10 (Fig. 1-5, Power-Factor Correction). How well (%) do the experimental readings from 1) the dual-wattmeters, 2) the 2-wattmeters readings (LabVolt DAQ), 3) the single-phase readings (LabVolt DAQ) and 4) the phasor analyzer (LabVolt DAQ), compare with a theoretical calculation of power and power factor based on the 2-wattmeter method? The theoretical power calculation is based on the four equations given in the introduction (page 1) of this experiment. Sketch the 3-phase phasor diagram that corresponds to the circuit of Step 10 (Fig. 1-5). A freehand drawing is acceptable. Indicate the angles of the phasors. If necessary, include a sample calculation to explain each table entry. 3. Does the value of the neutral current measured in Step 4 satisfy the equations given in the Introduction of this lab? 10 4. For Fig. 1-4 (Steps 1-9, R, C, L, RL loads), Calculate the theoretical value of the power and power factor for each circuit based on the specified phase voltage given in the procedure and the specified impedance. Re-calculate the power factor of each circuit using the observed values the load-angle taken from the oscilloscope and the LabVolt phasor analyzer. Include the print outs of the waveforms taken from the oscilloscope. For each of the 4 circuits put the three values of the power-factor in a table. For each circuit, which of the experimentally-derived values, oscilloscope or phasor, differs the most (percentage) from the theoretical value? Include a sample calculation for the RL load circuit and the oscilloscope trace for each entry. 5. Compare the power factor variation in Steps 9 and 10 (RL and RLC loads) and comment on the results. Which circuit transfers the most power for the least amount of current? Calculate the exact capacitor value that would yield unity power factor for the circuit of Fig. 1-5. Show your calculation. Why is unity power factor desirable? 6. Calculate the theoretical power in each phase (resitive load) and the total power consumed by the load for Step 12 (Fig.1-6). Do these values agree with your experimental data? Does the ratio of the loads in Step 5 and Step 12 (wye and delta circuits) support the derivation in Question 1? Is the assumption of an equal power dissipation per-phase valid? Sketch the phasor diagram of the 3-phase delta connected system. Show Vline, Iline, Vphase, Iphase and the associated angles and magnitudes. Indicate the phasors used in the 2-wattmeter method. Could the same phasors be used when applying the 2-wattmeter method to describe the wye-connected system? A freehand drawing is acceptable. Why are the phase angles of the oscilloscope and the Lab-Volt phasor analyzer different? 7. Where are the security-procedures and emergency-contact information posted? 8. Where is the fire extinguisher in the lab located? What type (class) of extinguisher is it? What types of fire are treated with each class of extinguisher? 9. What route should be taken to exit the lab and building in case of fire? 11 ELEC 331, Data Tables for Experiment 1 Table 1 Data for Wye Connected Load (* print-out of graphical display or oscilloscope trace is required) Vab Ia R XL XC W1 W2 Vph Iph Ineutral P3,Q ph Vcb c ph (V) (A) (V) (A) (A) 3,S3 LabOscilloVab, (V) (A) () () () (W) (W) (W, Volt scope Ia Var, Phasor (deg or ref VA) (deg rad) Vab or rad) 300 0 0 * 208 * Open 0 0 * 1 ph C 300|| 0 0 * 120 600 3-ph 0 0 600 * 208 0 300|| 0 * 600|| 1200 300 300|| 0 * * * 600|| 1200 300 300|| 600 * * 600|| 1200 12 Vcb, Ic ref Vab * * P1, S1 (W, VA) P2, S2 (W, VA) Table 2. Data for Delta Connected Load (* print-out of graphical display is required) P3, Q3, ph R XL XC W1 W2 Vph Iph e-Vab,i-Ia Vab Ia S3 (W, (A) Lab-Volt Oscillo- (V) (A) () () () (W) (W) (V) scope N.B Var, Phasor VA) (deg or See (deg or rad) Iph rad) I ph is same as 300 load above Vcb c P1, Vab, (V) (A) Vcb, S1 (W, Ia Ic VA) ref ref Vab Vab P2, S2 (W, VA) above 600 0 0 * * 120 * * E3, I3 are phase parameters. E1, I1, E2, I2 are the line (line-to-line) parameters: Vab, Ia, Vcb and Ic. E2 is oriented to support the 2Wattmeter method. All numerical data can be recorded in a LabVolt data table, copied to Notepad and printed. 13 14