Laboratory #3: AC Power and Transformer Circuits ... · PDF filePower Factor (PF) The cosine...

Laboratory #3: AC Power and Transformer Circuits Electrical and Computer Engineering EE 204.3 University of Saskatchewan

Denard Lynch of 15 Oct 7, 2013

Authors:

Denard Lynch

Date:

Sep 22, 2012 Oct 2&7, 2013: revisions-djl Description:

This laboratory explores the power in AC circuits, and transformers The student will measure parameters to verify real, reactive and apparent power in AC circuits, and the effect of Power Factor correction. In addition, the student will the operation of an AC transformer for voltage/current and impedance transformation.

Learning Objectives:

In this laboratory, the student will: • Calculate real, reactive and apparent power based on AC circuit measurements, • Correct the Power Factor in an AC circuit. • Determine transformer parameters like transformation ratio, a (or turns ration, n)

from observed circuit behavior • Verify impedance transformation of restive and complex impedance loads

Safety Considerations:

In addition to general electrical safety considerations, the student should also be aware of the following considerations specific to this laboratory exercise:

• Resistors carrying current will generate heat energy and can be overheated in AC circuits. Power is based on RMS voltages and currents. In all other respects, the same considerations as in DC circuits apply.

• Unlike DC circuits, capacitors and inductors under AC excitation will conduct current and can have potentials across them even in steady-state (not only transient) conditions. The reactance (opposition to flow), current and voltage present are also a function of the frequency of the excitation source. Always consider these parameters when anticipating potential safety hazards and the required ratings of components.

• Measurement of AC circuit parameters requires suitable test gear or the selection of the appropriate scale and range. Use of DC instruments or incorrect scales can result in equipment damage or safety risks.

Background and Preparation:

In this lab you will again measure phase differences using the time scale on your ADM as well as circuit voltages and currents (using the voltage across a resistor).



Please refer to the class notes on AC circuits. A summary of key points is provided in Appendix A at the end of this procedure.

Terms:

Complex Power A representation of Apparent (S), Reactive (Q) and Active (Real) power (P) in AC circuits that can be derived using phasors and impedances.

Power Triangle A graphical representation of the components of complex power consisting of P, Q, the complex vector, S, and its angle

Power Factor (PF) The cosine of the angle, θ, of the complex power, S. It is a number between 0 and 1 and represents the fraction of the Apparent power, S, that is Real or Active pawer, P. It is specified as either lagging if the load is primarily inductive, and leading if the load is primarily capacitive. It is Unity or 1, if the load is entirely resistive.

transformer An electromagnetic device consisting of 2 or more mutually inductive coils, which can be used to transform (raise or lower) the voltage or current of an AC waveform

n Turns ratio: NS/NP ; n=1/a; a = transformation ratio. Can also use the basic transformer relationships:

VP

VS=

NP

NS;

IP

IS=

NS

NP;

ZP

ZS=

NP

NS

⎛

⎝⎜⎞

⎠⎟

2

Excitation current Small amount of current required to establish the flux in a transformer’s core so that voltage transformation can take place

Procedure:

A: The first procedure will involve constructing several different circuits with combinations of resistance, capacitance and inductance and determining the real, reactive and apparent power in the circuit by using your Analog Discovery Module (ADM) to measure the voltage and current in various elements as well as the phase difference between the voltage and current. You will use these measured parameters to verify your theoretical values. On a select circuit, you will add a reactive element and determine the improvement in Power Factor by, again, measuring circuit parameters. B: The second part of this laboratory will involve wiring a transformer in different configurations and determining the transformer characteristics by again measuring circuit parameters like voltage, current and phase angle. You will also verify the impedance matching ability of a transformer by measuring parameters to determine input and load impedances.



Modeling- (determining what you would expect to see)

This will involve using AC circuit and transformer theory to predict the circuit parameters for each circuit. The required parameters are described in the detailed procedure below. Please read the entire procedure over carefully before the lab and calculate the expected values of the various parameters using AC circuit and transformer theory. Note that you are again using a “practical inductor”, which has some internal resistance. The transformer you will be using is also an inductive device and the windings will also have an internal resistance. You should account for this fact in your theoretical calculations, and adjust your observable expectations accordingly.

Measurements- I. Determining Power and Correcting the Power Factor

In this part of the procedure, you should measure the phasor voltage and current across the R-L load. Then, after adding a Power Factor Correction capacitor to balance some of the inductive VARs, measure the new total current supplied from the source. Observe the change in current and phase angle in the circuit and determine how much the source current is reduced as a result of correcting the PF. Use your solderless breadboard and set up the circuit shown in Figure 1. A good first step is to examine the circuit, make a list of the parts you will need, obtain the necessary parts and construct the circuit. You may also need to measure the actual value of your components (e.g. using the RLC Tester in 2C80 or equivalent) versus their nominal value. For example:

Component Nominal Value Measured Value 1/4W resistor 1000Ω 986Ω

Capacitor 100WVDC 0.1µF 0.092µF Etc.

Your lab instructor will indicate where to obtain the necessary parts if they are not already in your parts kit, and how to measure their actual value. You can use your Analog Discovery Module (ADM) as the AC source for these procedures. (Note: there is a very limited amount of current available from the ADM’s WaveGen (Arbitrary Waveform Generator); ~8 mA maximum, depending on the USB port capability. Check your theoretical calculations, and observe the sinusoidal waveforms to make sure there is no obvious signal distortion and the supply isn’t overloaded whenever you use it.) Using the circuit shown in Figure 1, without the Power Factor correcting capacitor, CPF, you can determine the real, reactive and apparent power dissipated in this circuit before correction. You will then add a corrective element (reactor), and measure the effect on the total current draw and net reactive and apparent power.



Since the current in the series R – L circuit is common to both elements, we can just measure the voltage across each element to determine the magnitude of the real power, P in the resistor, and the reactive power, Q in the inductor. (Remember: there will be some real power dissipated in the inductor because of its internal resistance – you can estimate the total real power by adding Rint to the external resistance. On the ‘Z-diagram’, at right, this resistive component is shown along the real axis. ) In this case, it is advisable to use the 10Ω sense resistor to measure current, as it will allow you to monitor the phase and magnitude of the load current, IL, both before and after the addition of a corrective element in parallel with the load. Remember, the smaller the sense resistor, the less effect it will have on your circuit. You have already measured the voltage across the same R-L combination in a previous lab. A quick measure will verify the information required (VLoad. ILoad) to determine the magnitude of the apparent power, S (=VI*). You have also measured the differential phase angle between the voltage and current in this circuit, which is the angular argument of the complex impedance, Z, and also the angular argument for the complex apparent power, S (voltage leading current is a positive angle, indicative of an inductive load. A capacitive load would have a negative angle.).

Figure 1: Power and PF Correction

Procedure Summary: 1. measure the RMS current with the ADM and a 10Ω sense resistor 2. measure the voltage across the R-L load (V+ : V-) using the ADM 3. measure the phase angle between VLoad and ILoad. 4. calculate S, P and Q in the circuit using these measurements 5. calculate the element required to correct the P.F. to Unity (1) 6. insert an available reactive element (your 47nF) to improve the P.F. 7. measure the new phase angle for the load and determine the new P.F.

Digilent ADM WaveGen (W1) Amplitude: 5V Offset: 0V Symmetry: 50% f = 5 kHz

ZR

ZL-real ZX



Details: Use one input channel of your ADM to measure the voltage across the sense resistor so you can calculate the current through the load. Use the other input channel to measure the voltage across the whole (R-L) load. Measure the time differences between the voltage and the current and calculate the phase shift. How does it compare to your theoretical expectation? You can use these measurements to calculate the real and reactive power being consumed in this circuit. What is the Power Factor of this R-L combination prior to any correction? Recall that to correct (improve) the Power Factor, we want to “add” VARs of the opposite sign. Since this is originally an inductive circuit, the VARs consumed will be “positive”, and you will want to add negative VARs to compensate; this will require the addition of a capacitor. (There are, in theory, situations where the opposite will be the case, but in practice most correction situations are for predominantly inductive loads and require the addition of a capacitor.) The best place to add this corrective element is as shown in Figure 1, as it will have a minimal effect of the voltage available, and thus the power, to the load. (Note: this is effectively across the source side of the “load” (the R-L). The current sense resistor is considered part of the source in this case, and the source voltage across the load is as measured between V+ and V-.) You should calculate the size of capacitor needed to correct the PF to Unity (1) based on your measurements of Q above, but use a capacitor value that is available, say 0.047µF (the slightly smaller, brown capacitor in your parts kit), and also calculate the expected improvement using this value. What is the Power Factor of the corrected load? How does this compare to your theoretical expectations? Optionally, you can also measure the current through the corrective element by using another sense resistor and the ADM ‘scope, or an ammeter. If you use a sense resistor, you can observe the phase of the current compared to the “load” current, and then plot both on a current phasor diagram to prove to yourself that ISource = ILoad + IC-PF. Record relevant values, such as those suggested in Table 1 and any others you may need in your lab notebook. Show that the values you observed are substantially what you would expect form your theoretical predictions.



Table 1

Pre-Correction

Post-Correction

Comments

IRMS Common to L & R series elements

Vload, φload QXL I2XL, or VLIL. can use Vr to

determine IL

PR+Rint Must stay the same |S| VLoadILoad φS PF = cos(φ)

QC-PF E2/XC new Q

New PF

II. Transformation of Voltages, Currents and Impedances

In this part of the procedure, you will want to measure voltages to verify the transformer operation (step up or step down). Voltage current measurements will also allow you to verify the impedance transformation and the preservation of the phase angle of the load. As discussed in the background, transformers are very common and useful pieces of electrical gear. In this part of the lab, you will predict and then measure voltage and current transformation in step-up and step-down configurations. A practical transformer, like a practical inductor, has some resistance in its windings. You should measure the resistance of the winding(s) you are using in each circuit below (the nominal values are also in the data sheet for these transformers, posted with this lab n the Class Web site). The simple model shown in Figure 2 will help provide accurate prediction of the circuit’s behaviour. Note the dots by pins 1 and 4.

Figure 2: Simple Transformer Model

a) Step-down configuration:

Set up your ADM WaveGen for a 5V sinusoidal output at ~5 kHz. Use the Tamura TTC-108 transformer supplied in your parts kit, measure the internal resistance of



the windings you will be using in this part (Primary: 1-3; Secondary: 4-5). (There is a data sheet for the TTC-108 transformer posted on the class web site on the Labs page.) R1 and R2 represent the nominal values of the internal winding resistances of your priomary and secondary respectively. Connect as shown in Figure 3 with a 220Ω resistor (R3) as a load.

Figure 3: Step-down Transformer Circuit

Procedure Summary: 1. With the load disconnected (i.e. open circuit secondary), measure the

primary current using a 10Ω sense resistor and one input channel of your ADM. This is the “excitation current” and will be quite small.

2. measure the primary voltage using the second channel of your ADM, observe the phase angle between the current and voltage.

3. measure the phase angle between the primary voltage and current. With no load, the transformer primary will look like an inductor.

4. measure the secondary open-circuit voltage; determine a turns ratio. 5. connect the 220Ω load and measure the primary and secondary currents.

Also use these to determine a turns ratio. Which should be more accurate?

Details: The ADM may be less accurate for measuring small voltages, so you could use a DMM to find the primary current, but you will need to use the ADM to obtain the phase relationship with the voltage. Observe the “dot notation” on the transformer, and connect your leads so that the phases are consistent (as suggested in Figure 3). Remember, there is an “excitation current” required to establish the magnetic flux in the transformer core, which is basically an inductor, even without any load. The initial measurements will identify this current. Note the phase angle with the voltage. Is it what you would expect from an inductor? (Note: If your partner also has an ADM, you can use a second one to simultaneously measure the secondary parameters. Plug the second ADM into another USB port and start another instance of the Waveforms software. The main Waveforms window will be identified as “Digilent Waveforms 2”) With the exception of the excitation current, there should be little voltage variation between what you measure at the terminals and the “true” primary and secondary voltages, as there should be little, if any, voltage distortion across the internal resistances of the windings (very low current). This should give a reasonably accurate estimate of the turns ratio. How does this compare to the turns ratio




estimated by using the secondary and primary currents when there is a load? Can you explain the similarity or difference? The load resistor should “appear” at the primary being multiplied by n2. You can verify this by using the measured voltages and currents to determine the apparent primary and secondary impedances. You would expect the primary voltage and current to be in phase, as they are in the secondary, but there may be a slight distortion due to the inductive impedance of the primary and the excitation current. How close is the primary impedance to a true reflection of the secondary load resistance? Can you explain any variation”?

Table 2

Measurement Comments Primary I No load, use Rsense Primary V

φ

secondary V

n Turns ratio Secondary I Load connected

n Using current ratio

b) Step-up configuration: This is almost identical to the previous procedure. The circuit is shown in Figure 4. Note the higher load resistance for this configuration due to the higher output voltage.

Figure 4: Step-up Configuration Procedure Summary:

1. With the load disconnected, measure the primary current using a 10Ω sense resistor and one input channel of your ADM

2. measure the primary voltage using the second channel of your ADM 3. measure the secondary open-circuit voltage; determine n 4. connect the 2200Ω load and measure the secondary current ( use V across

the load resistor)




5. calculate the turns ratio, n, using the primary and secondary current measurements

Details: Again, note and measure the excitation current with no load connected. Does it differ from what you measured for the step-down case? Remember you are using approximately ½ of the available primary turns in this circuit; that means the inductance will be approximately ¼ that of the step down case ( L ∝ n2 ). Along with the lower internal resistance, this means a lower impedance presented to the same source voltage, so we would expect a higher current. Whether you use the voltage or current ratios to estimate the turns ration, the internal resistance of the windings will affect your result. The voltage drop across the internal R will leave less “true” voltage across the coil, and less current because of the higher total R. You can improve the estimate by taking this internal resistance into account, but remember this is a simple model; don’t expect a high degree of accuracy. Note from your measurements of primary and secondary voltage and current how the load impedance if affected as it is “transferred” through the transformer. After compensating for the internal resistance and excitation current, you should notice a reasonable comparison.

Table 3

Measurement Comments Primary I No load, use Rsense Primary V

secondary V

n Turns ratio Secondary I Load connected

n Using current ratio

c) Complex Impedance Transformation: The impedance transformation of a simple resistance is fairly straight forward to understand, but a slight modification of the circuit in Figure 4 will allow you to find out how a complex impedance is “reflected” back on the primary side. When the voltage and current are in phase, there is no real concern about what happens with the “angle” through the transformer, but when there is a phase difference, the result may not be intuitively obvious. The objective in this part is to determine how the phase angle of a complex impedance “behaves” when reflected through a transformer.



Figure 5: Complex Impedance Load

Modify the load in your circuit as shown in Figure 5. If your partner has a parts kit, use a second .047µF capacitor in series to obtain the .023µF value. If not, ask your instructor for an additional .047µF or a single ~.02µF capacitor. Procedure Summary:

1. use open circuit excitation current and voltage phase information from last part

2. measure load voltage and current (you can use the voltage across the 1000Ω resistor to calculate the current)

3. measure the voltage and current from the primary side, and use to determine the apparent impedance (magnitude and angle)

Details Measuring the voltage, current and phase angle on the primary and on the load side will allow calculation of the complex impedance as seen by the source and the actual load. Since the voltage and current are transformed by the turns ratio (or transformation ratio, a, if you prefer), the magnitude of the impedance (V/I) is also transformed in a predictable fashion. Since these are both transformed directly by the transformer, it follows that the phase difference between them is unaffected!. When comparing the phase angle on the primary side, don’t forget to consider the initial “lag” of the excitation current. If we consider a “parallel” model (i.e. the transformed load impedance appears in parallel to the transformer primary), the phasor addition of the currents gives a little better correspondence to the phase angle on the load side.

Table 4

Measurement Comments secondary I secondary V

ZS

Primary I Primary V

ZP n Apparent turns ratios using Zs




Optional: Power Conservation Verification

Use the voltage and current measurements you have taken above for either configuration and verify that the power coming from the source is equal to the power lost in the transformer (or other circuit losses) plus the power delivered to the load. (This should be true for P and Q in your circuit.)



Reporting- Use your lab notebook (logbook) to document

• the key objectives of this laboratory, • your theoretical calculations • Parts List: your equipment and circuit components used • any measured values of components • your measurements verifying your theoretical expectations (you can paste in

screen shots from your ADM where appropriate), • use Power Triangles and Phasor Diagrams to help illustrate results (e.g. the

relationship between voltages or currents or powers). • your observations and comments about how closely your observations matched

your expectations, • related comments on practical limitations for your observations and comments on

possible sources of error



APPENDIX A: Background & Preparation Information

Recall some of the characteristics of the basic circuit elements (R, L, C) in AC circuits. “Opposition to flow” in AC circuits is a scalar value measured in Ohms (Ω) and called reactance, X, for capacitors and inductors. Resistance is generally the same value in AC and DC circuits (RAC = RDC), but the reactance of capacitors and inductors is given by:

, (C in Farads) , (L in Henrys),

where Phasor quantities (which are represented as complex-valued numbers), are used to represent voltage and current in AC circuits, and the “opposition to flow” in the Phasor domain is called the impedance, Z, and is also measured in Ohms and is defined as:

, or , where we use the standard units of measure (Ohms,

Volts, Amperes). In rectangular form, the complex impedance can be written in terms of the scalar resistance and reactances:

, and can be shown graphically on a phasor diagram.

Power in AC circuits has special considerations too. While we can consider the power in individual elements as scalar values, the overall power is again more usefully represented as a complex-valued number and determined using phasor values. To differentiate between the power in different elements and under different circumstances, the units vary too. The “complex power” in an AC circuit is given by:

, where S is the “Apparent Power” measured in Volt-Amperes (VA), V is the phasor voltage and I* is the complex conjugate of the phasor current. Again, this can be represented in terms of its scalar components in a rectangular form:

, where P is the real power, that which does actual

work or is converted to heat ( ) and is measured in Watts (W) as in the DC

case, and Q is the reactive power ( ) and is measured in volts-amperes-

reactive (VARs). Note that the reactive power is considered positive for inductors and negative for capacitors (the reactive powers, as all powers in an AC circuit, vary sinusoidally, and are 1800 out of phase with each other, so one “subtracts” from the other). It does not do any “real” work, and alternately transfers from the capacitance to the inductance, and vice versa, at twice the excitation frequency.

Finally, the Power Factor is a unit-less number that gives an indication of how much real work is being done by the current that is flowing. A Power Factor of 1 (or Unity; 100%) means the voltage and current are completely in phase. A power Factor of 0 (zero) means the voltage and the current are 900 out of phase. It is the cosine of the

XC = 1ωC

Ω XL =ωLΩ

ω = 2π ⋅ frequency(Radians second)

phasor _ voltagephasor _ current

Z =VI

Z = R + j XL − XC( )

S =VI *

S= P + jQInd , or P − jQCap

P =

V 2

R= I 2R

Q =

V 2

X= I 2X



phase angle between the voltage and current in an AC circuit. An equivalent expression is:

where θ is both the angular part of the complex power value, S (in polar form), and also the phase angle between the voltage and the current (it can be shown that they are mathematically related), and the phase angle of the complex impedance of the load, ZL. Since cosine is ambiguous for positive and negative angles, it must be specified whether the Power Factor is leading (for capacitive loads) or lagging (for inductive loads); i.e. whether the current is lagging or leading the voltage, respectively. In order to improve the power-delivering efficiency of an AC system, the Power Factor is “corrected” by “adding VARs” with a reactive element (capacitor or inductor) that will reduce the net VARs in the circuit, thus reducing the phase angle of the load impedance (and the phase angle between the voltage and current), thus making sure more of the current that is delivered is used for actual, real work (power). As a quick summery, the steps typically involved in determining the corrective element are:

1. determine the Power Triangle components for the load prior to correction (at least the P and the “old Q”)

2. determine the “new Q” required so that the new Power Factor is as desired while maintaining the same P (QNew = tan cos

−1 newPF( )( )P ) 3. determine the amount and type of Q that must be “Added” to the circuit

(ΔQ=QNew – QOld; +ve = inductive, -ve = capacitive)

4. calculate the value of the element ( X = ESource2

ΔQ; C = 1

ωXC

or L = XL

ω)

Transformers are very useful devices in AC circuits. They operate based on the principle, described by Faraday’s Law, of magnetic induction. In simple terms, a magnetic field produced by a current can induce a voltage in another coil of wire “coupled” by the same flux. The magnitude of the induced voltage of proportional to the number of turns of wire. By designing the number of turns in each coil appropriately, the device can be used to efficiently increase (step-up) or decrease (step down) the voltage for different purposes (e.g. step up to transmit energy over long distances with reduced loss, or step down to obtain a voltage suitable for powering small electronic devices or charging a battery). Transformers are also used to provide electrical isolation (i.e. no conducting, metallic contact between one circuit and another) and impedance matching to help maximize power transfer. The key characteristic of a transformer is the ratio of the number of turns in the input (primary) coil to the output (secondary) coil. This dictates, with some practical limitations, the voltage and impedance levels that are obtained. A summary of the relationships between the number of turns and resultant voltages, currents and impedances are given in Table 5 below.

Power Factor, FP =

P

S= cos θ( )



Table 5: Ideal Transformer Equations

Voltage

Current

Impedance

Notes: Turns ration, .

Transformation ratio,

Theoretical calculations of various circuit parameters should be performed as part of the lab preparation (i.e. prior to your lab period). Calculating the expected currents and voltages will also allow you to determine the required ratings for your components (i.e. how much power they must dissipate, how much voltage they must withstand etc.) Please refer to the Class Notes for background theory on impedance, reactance and complex power and transformers.

References:

EE204 Course Notes

Es = nEp Ep = Es

n

Is = Ipn

Ip = nIs

Rs = n2Rp Rp = Rs

n2

Ep−max = 2π fNpΦmax

n= Ns

Np

a=Np

Ns

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