2021-22 Sem 2 Project 4: Power Factor Correction

Project duration: 2 weeks practical work + 1 week video production

Project type: group (3 per group)

In this project, you will work in teams to solve a very practical electrical engineering problem using the theory and tools we have been learning about for the last couple of weeks (e.g. phasors, impedance, MATLAB/Octave, LTspice). This project is designed to force you to do independent research on the topic of power in AC circuits and especially power factor correction.

The problem you need to solve is described below. Begin by discussing the problem description with your team and identifying knowledge gaps you need to fill. Then go and learn whatever you need to learn to solve the problem. Finally, present your solution in a group video presentation that will be uploaded to YouTube. We will screen all the videos together in class in the final lab session of the project.

Problem Description

On an island far from the mainland, a small power station (i.e. a voltage source) supplies 50 Hz AC power to a remote water pumping station via a long single-phase (i.e. 2 conductor) overhead power line. The power line cable is solid aluminium with a circular cross section. The pumping station can be modeled as a resistance in series with an inductance. The inductance and capacitance of the power line can be ignored, as can skin effect. However, the resistance of the power line will be significant, so it must be taken into account. Your first task is to analyse the power factor of the load (the pumping station) and calculate the losses in the power line. Your second task is to design a power factor correction solution for the pumping station and calculate the reduction in power line losses. Finally, you will present your work in a group video presentation.

The following information will be provided to your team (different values for each team):

• V_S : the r.m.s. voltage supplied by the power station
• R_load : equivalent resistance of the pumping station
• L_load : equivalent inductance of the pumping station
• d : distance from the power station to the pumping station
• D : diameter of the aluminium power line cable

Once your lab instructor assigns a number to your team, select your values from the list below.

Derek / Ted’s teams:

• Team 1: V_S =400 V r.m.s., R_load = 7.12 Ω, L_load = 12.9 mH, d = 2.5 km, D = 8.0 mm
• Team 2: V_S =380 V r.m.s., R_load = 7.42 Ω, L_load = 13.9 mH, d = 2.4 km, D = 7.0 mm
• Team 3: V_S =400 V r.m.s., R_load = 7.62 Ω, L_load = 12.9 mH, d = 2.6 km, D = 7.2 mm
• Team 4: V_S =380 V r.m.s., R_load = 7.02 Ω, L_load = 13.9 mH, d = 2.5 km, D = 7.8 mm

Kevin’s teams:

• Team 5: V_S =400 V r.m.s., R_load = 7.52 Ω, L_load = 13.9 mH, d = 2.6 km, D = 8.0 mm
• Team 6: V_S =380 V r.m.s., R_load = 7.22 Ω, L_load = 12.9 mH, d = 2.5 km, D = 7.0 mm
• Team 7: V_S =400 V r.m.s., R_load = 7.02 Ω, L_load = 13.9 mH, d = 2.4 km, D = 7.2 mm
• Team 8: V_S =380 V r.m.s., R_load = 7.32 Ω, L_load = 12.9 mH, d = 2.6 km, D = 7.8 mm

Suggested calculations

You will find it useful to calculate the values listed below. You may need to carry out some independent research to learn what some of these are.

• Power factor of the RL load, cos(ϕ),
• Load voltage phasor V_load and load current phasor I_load,
• Complex, active, reactive and apparent power in the load (S, P, Q, and |S| respectively) before and after power factor correction,
• The active power dissipated in the power line (P_line).

The following page summarises a lot of relevant background information:

https://voltageandcurrent.wordpress.com/ac-circuits/

Video Presentation

Specification:

• One video per team.
• Your video must be publicly visible on YouTube.
• Minimum duration: 3 minutes.
• Maximum duration: 5 minutes.
• All team members must be clearly identified at the start of the video.
• Every team member must present part of the video.

Content:

• Show your analysis of the circuit (power station, power line, pumping station).
• Show your calculation of the power factor in the load and the losses in the power line.
• Show how your power factor correction solution reduces losses in the system and quantify those savings.
• Prove that your solution works by including LTspice simulations of the system before and after power factor correction. Explain whatever you show.

Video assessment – marks will be awarded for:

• Technical correctness and clarity.
• Quality of spoken presentation.
• Quality of visual presentation.
• Complying with the specification and prescribed content listed above.
• Individual contribution to the solution presented in the video.