Lab 4 Power Factor Correction Last Name: First Name: Student Number: Lab Section: Monday Tuesday Wednesday Thursday Friday TA Signature: Lab objectives o Introduction to Power Factor o Introduction to Maximum Power Transfer o eactive Power Compensation Equipment o Measurement tool (Oscilloscope), o AC voltage source, o ange of resistances, capacitors, and inductors. Pre Lab Mark: /2 Lab Mark: /8 Total: /10 o Page 1 of 7 v1. Fall 2018
Pre-Lab: 1. Power Factor (PF) Power Factor in an electric circuit is defined as the ratio of real or average power being delivered to a load to its apparent or reactive power. PF can also be calculated by measuring the phase shift between voltage and current waveforms of an electric component. Figure 1 illustrates these two methods for calculating PF of component a as follows. cos(θ V θ I ) = cos(θ) = PF = P S = P P 2 + Q 2 Where P is the real or active power in watts (W), Q is reactive power in reactive volt-amperes (VA), and S is apparent or complex power in volt-amperes (VA). The PF itself has no units and it is a number between zero and one. Figure 1 Depending on the load characteristic, we might end up with three different types of PF. When the load is a pure resistive one, there will be no reactive power transmission in the circuit. This would make S to be equal to P and as a result a PF equal to 1. This is when the voltage and current of an element have the same phase angle. A PF of one or as they call it unity power factor is the main goal of any electric utility company for an optimized operation. A PF below one means excessive supply of current to an electric user for a specific amount of power utilization, which would increase the cost of power delivery for utilities. The second type of PF is a lagging one when the load consumes a positive amount of reactive power. This means that the load is more inductive than capacitive. As a result, the load current will be lagging its voltage. It is while for the third type of PF, the load has a capacitive characteristic and is generating reactive power than consuming it. This would result in a leading current with respect to the load voltage. Therefore, having the load phase angle, one can calculate the PF as well. Page 2 of 7 v1. Fall 2018
2. Maximum Power Transfer AC electric network can be modeled as an ac voltage source representing power generation units connected to a series L circuit representing transmission lines and power transformers and then delivering power to an electric load as in Figure 2. As it can be seen, some amount of apparent or complex power being generated in the electric network will be dissipated through the transmission process. Therefore, if we have such an option as designing the load, then we can do it in a way that maximum generated real power be transferred to the load so that the power utilities can charge their customers efficiently for delivered electric energy. First step in designing the load for a maximum real power transfer can be considering the combination of voltage source and transmission line as the Thevenin s equivalent circuit being seen by the load. Based on Thevenin s theorem, when the load resistance is equal to the Thevenin s equivalent resistance ( th ), maximum power will be transferred to the load. On the other hand, as we introduced the term power factor, we learned that a unity PF is desired in all networks. Considering these two concepts, one can design the load for maximum real power transfer. Design the load based on the values of, L, ω in a way that the maximum real power transfer to the load would be achieved. Assume that the voltage source is applying V s sin(ωt) to the transmission line with the impedance of Z T = + jωl. What should be the load impedance Z L? In this case, how much power is being supplied by the source and what portion of that power will be delivered to the load? What is the efficiency of the circuit? Hint: All the answers in this page will be parametric except the term efficiency! Electric Network Model V S L Load Transmission Line Figure 2 Page 3 of 7 v1. Fall 2018
3. eactive Power Compensation As previously mentioned, a high power factor close to unity is generally desirable in power systems to minimize the power losses. It can also regulate the voltage level at load side due to reduction in reactive power consumption. Industrial facilities mostly have an inductive impedance due to a high number of electric induction motors, which would result in a lagging power factor. This in turn would increase their apparent power demand from supply system. Therefore, electric power transmission utility applies extra charges on industries with a low power factor to make them install PF correction equipment to prevent extra losses and inefficient power delivery. Installing capacitive banks at the load terminals can be considered as a general approach for increasing power factor when the load is an inductive one as in Figure 3. This is what they call power factor correction in power systems. jωl V S sin(ωt+θ V ) I S sin(ωt+θ I ) Load Capacitive Compensation Figure 3 At the last part of the Pre-lab we will try to calculate the power factor of a series LC circuit based on what we learned here. If we have a series LC as an electric load being connected to an ac source, what would be the load power factor based on values, L, C, and ω? Hint: First, try to find the equivalent impedance and then try to calculate the load phase angle! L C V S sin(ωt+θ V ) I S sin(ωt+θ I ) Figure 4 Page 4 of 7 v1. Fall 2018
Lab work 1. Simulation of an AC circuit under steady state Simulate the circuit of figure 1 in MultiSim with the following values. L = 10 mh = 10 Ω C = 100μF f = 159.16 Hz V S = 5.0 V(Maximum possible voltage) V in + _ jωl I S sin(ωt+θ I ) -j ωc V S sin(ωt+θ V ) + 1Ω V out _ Figure 1 Measure the input voltage and current waveforms and try to find the system power factor. Build the same system on breadboard and using oscilloscope try to find the phase difference between input voltage and current waveforms. To measure the current try to add a 1 Ω resistor as shown and measure its voltage which is proportional to the system current. Also, try to calculate the PF and show your calculations below. Multisim esults Phase difference = [ ] Power Factor = [leading/lagging] Setup esults Phase difference = [ ] Power Factor = [leading/lagging] Calculation esults Phase difference = [ ] Power Factor = [leading/lagging] Show the results to the TA and ask for signature. Page 5 of 7 v1. Fall 2018
Using the Oscilloscope Math Function find the input power based on time. Overlay this with the input voltage and current waveforms and draw all of them in Figure 2. Figure 2 Volt/Div (with unit) = ---------------- Time/Div (with unit) = ---------------- What are the measured and calculated average power waveform and its frequency? Comment on your observation and what you have learned about instantaneous power. Multisim esults Average Power = [W] Frequency = [Hz] Setup esults Average Power = [W] Frequency = [Hz] Calculation esults Average Power = [W] Frequency = [Hz] Show the results to the TA and ask for signature. Page 6 of 7 v1. Fall 2018
2. Maximum Power Transfer and Efficiency Consider the following circuit as shown below. If L = 10 mh, = 5 Ω, f = 159.16 Hz, and V S = 5.0 V (or Maximum possible voltage) then try to answer following questions. jωl V S sin(ωt+θ V ) I S sin(ωt+θ I ) Load Figure 3 Design the load such that maximum real power is transferred to the load. What would be the load impedance in this case? How much power is being delivered to the whole circuit by the voltage source? What portion of the whole power will be received by the load? What is the circuit efficiency in this case? *Please put your answers in the following table. Zload =. [ ], inductive/capacitive P(source) = [W] P(load) =. [W] Efficiency =.. [%] Show your calculations here. Build the circuit and measure the power supplied by the source and received by the load and then try to compare the results with calculated values. P(source) = [W] P(load) =... [W] Efficiency = [%] Based on the system efficiency, is the system loading an acceptable one? Show the results to the TA and ask for signature. Page 7 of 7 v1. Fall 2018