Project 2 Assignment Computer Simulation of Transient Voltages 1 Abstract- This document describes the second of two computer-based projects assigned to students. In this project the software packages LTspice and

Matlab are used. Part A of the project deals with lumped parameter circuits and Part B deals with distributed parameter transmission line circuits. Part C describes briefly the written report. Appendixes have been written to clarify details. Associated with this assignment is a rubric that should be consulted. Part A - Lumped Parameter Circuits Preface to Part A - For Part A several circuits will be simulated with an array of parameters. Objectives are to 1) explore under damped, over damped and critically damped series and parallel RLC circuits and 2) explore transient recover voltage (TRV) circuits. Procedures for Part A SERIES RLC CIRCUITS The series RLC circuits being simulated are described in Figure 1 and Table 1. L ros t=0 Vo T C '2₁ (+) m Figure 1. Series RLC circuit. Circuit Name "Over" "Under" "Critical" Vo(V) 7.32 x 10³ 7.32 x 10³ 7.32 x 10³ Table 1. Parameters for three different series RLC circuits. C(F) 7.32 x 10-6 7.32 x 10-6 7.32 x 10-6 Undamped Natural + Frequency: 1 fo= 27/LC (Hz) 2+√LC 7.32 x 10³ 7.32 x 10³ x 10³ V₂ PARALLEL RLC CIRCUITS The parallel RLC circuits being simulated are described in Figure 2 and Table 2. vi (t) t=0 L = 1 (2πfo)²C (H) Use LTspice to simulate the three series RLC circuits with the parameters shown in Table 1. Use your undergraduate text to obtain the analytical expressions for the current i₁(t) that you expect to flow in the three series RLC circuits named "over", "under" and "critical". export your LTspice data for i₁(t) to Matlab and compare the LTspice results with the analytical equations. Plot the Matlab-generated results from your equations as a solid line and plot the LTspice results as data points (show a legend on your Matlab plot so that the reader is clear about how you are presenting LTspice data compared to data generated from your analytical expressions.) Students should obtain quite good agreement (say 3% or better) between LTspice and the analytical equations. Save Matlab and LTspice plots and screen captures for your report (Part C). Include in your report Table 1 containing numerical values for all of your parameters. -To Calculate Calculate Calculate Calculate Calculate Calculate w Figure 2. Parallel RLC circuit. Characteristic Impedance: Zo = √√12 R R(Q) 5(2Z0) (2Zo)/5 (2Zo) Circuit Name "Over" "Under" "Critical" Vo(V) 7.32 x 10³ 7.32 x 10³ 7.32 x 10³ Table 2. Parameters for three different parallel RLC circuits. Undamped Natural C(F) 7.32 x 10-6 7.32x 10-6 7.32 x 10-6 Frequency: 1 fo = 2mLdHz) 2π√LC R 7.32 x 10³ 7.32 x 10³ 7.32 x 10³ roos L •Vmain (wt) с L = 1 (2πfo)²C (H) vi Calculate Calculate Calculate Use LTspice to simulate the three parallel RLC circuits with the parameters shown in Table 2. For this part there will be no detailed comparison to theory thus there is no requirement that you use Matlab. Capture for your report (Part C) LTspice plots of v₁(t) for the circuits in Table 2 named "Over", "Under" and "Critical". Include in your report Table 2 containing numerical values for all of your parameters. TRANSIENT RECOVERY VOLTAGE (TRV) CIRCUITS The TRV circuits being simulated are described in Figure 3 and Table3. t=t₂ Joon Characteristic Impedance: Zo = √√/2 Figure 3. TRV circuit. Calculate Calculate Calculate 5₁ R Ω (Zo/2)/5 5(Zo/2) (Zo/2) Circuit Name "Large X/R" "Small X/R" Table 3. Parameters for two different TRV circuits. See the three notes below the table. Vm(V) 7.32 x 10³ 7.32 x 10³ @ (rad/sec) 2π60 2+60 C(F) [Note 1] 7.32 x 10-⁹ 7.32 x 10-⁹ L(H) 7.32 10 X 3 7.32 x 10-3 TRV Undamped Natural Frequency: 1 fo=27(Hz) Calculate Calculate X R || 5 @ L R 15 5 R(Q) Calculate t₁ (s) [Note 2] Calculate [Note 2] t₂ (s) [Note 3] [Note 3] Note 1: When S₁ closes at t = t₁, the energy stored in C will discharge into the shorted path consisting of S₁ and S₂ in series with C, resulting in very large high frequency oscillations if the "loop" inductance is not handled properly. The instructor solved this (high current at high frequency) issue by inserting series resistance and series inductance into the model for C. See Figure 4 for an example of how the instructor modeled C in LTspice. Note 2: Use t₁ values that give symmetrical fault current (no DC offset current). Establish t₁ via trial-and-error or best via phasor analysis. Note 3: Use t₂ values that provide switch opening at the current zero closest to one 60-Hz period after the fault is applied. When a breaker clears at a non-current-zero time then the phenomenon is called "current chopping" and we are not studying that presently thus it is important to have t₂ equal to the time at which the natural current zero appears. Establish t₂ via trial-and-error or best via phasor analysis (making t₂ equal to "t₁ plus the 60-Hz period" is the correct approach, assuming that your t accurately gave a symmetrical fault current.) Use LTspice to simulate the two circuits with the parameters shown in Table 3. For this part there will be no detailed comparison to theory thus there is no requirement that you use Matlab. For the two sets of circuit parameters in Table 3, capture for your report (Part C) LTspice plots of 1) generator voltage; 2) switch S₁ current; 3) TRV voltage v₁(t); and 4) an expanded time scale showing the current as it approaches extinction and a few cycles of the TRV voltage (as the instructor shows below in Figure 8.) Include in your report Table 3 containing numerical values for all of your parameters. Describe in your report how you established t₁ and t₂./nAbstract- This document describes the second of two computer-based projects assigned to students. In this project the software packages LTspice and Matlab are used. Part A of the project deals with lumped parameter circuits and Part B deals with distributed parameter transmission line circuits. Part C describes briefly the written report. Appendixes have been written to clarify details. Associated with this assignment is a rubric that should be consulted.