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L16 / Exam 1 practice & review

Exam 1 Practice

Practice the first-exam topics with the current lecture's worked problem sequence.

Available42 slides
Exam-1 integrated practice

01 / UNDERSTAND & PREDICT

Understand the model, then predict the result

Finalized lecture slides

Open / download original PDF ↗

Follow the original explanations, diagrams, derivations, and examples in slide order, then use the companion experiment below.

L16 original slide 1 of 42
L16 · 1 / 42
Slide text
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Figures and page order follow the student PDF for this lecture.

Review requires more than final numbers. Predict the sign of load Q when voltage is −20° and current +10°, then connect the method to a delta load, base changes, and capacity planning.
  • Write given data, references, and unknowns before choosing the method.
  • Check physical units, sequence, power sign, and transformer side.
  • Reproduce intermediate values in Python, then submit independent fixed-case answers.
Exam 1 practice & review: concept and calculation route
Course-authored concept route; the numerical experiment follows below.

Phasors and conjugation

S=\mathbf V\mathbf I^*

L16 example 1: V=180∠−20° V, I=12∠+10° A with current entering the positive terminal. Δφ=−30° means leading current and negative load Q.

Delta-load reference

L16 example 2 uses ZΔ=8+j6 Ω, VAB=208∠0° V and abc. Set source VAN to −30° before deriving branch and line currents. This differs from other examples using VAN=0°.

Single-phase transformer bases

L16 example 5A uses Sb=30 kVA, Vb,H=1500 V, Vb,L=150 V and ZH=1.50+j3.4369 Ω. Single-phase Ib=Sb/Vb and Zb=Vb²/Sb. Referral to LV must retain zpu.

Capacity and economics

L16 example 6 uses GT fixed/variable costs 75000 and 85, and CC 195000 and 45. A separate capacity case has 160 MW peak, 15% reserve, and full capacity credit.

Stepwise checks

Check RMS versus peak, line versus branch, single- versus three-phase bases, and source versus receiving end. Then use recovery, power accounting, or equivalent transforms. Return to the relevant module after an error.

Baseline example: check each step

  1. Example 1: P≈1870.615 W, Q=−1080 var, pf≈0.866 leading.
  2. Example 2: IAB=20.8∠−36.870° A and IA≈36.027∠−66.870° A.
  3. Example 2: P=10383.36 W and Q=7787.52 var; ZY=(8+j6)/3 Ω checks equivalence.
  4. Example 5A: Ib,H=20 A, Ib,L=200 A, zpu≈0.020000+j0.045825 on both sides.
  5. Example 6: crossover 3000 h/year; at 2000 h GT=245000 and CC=285000 $/MW-year; required capacity=184 MW.
Original slide headings for this lecture35
  1. 1Exam 1 format and timing
  2. 2Exam materials and conduct
  3. 3Answer format and grading
  4. 4Practice topics
  5. 5RMS phasors and complex power
  6. 6Example 1: sinusoidal voltage and current
  7. 7Solution 1: phasors and power
  8. 8Balanced three-phase circuits
  9. 9Example 2: balanced delta load
  10. 10Solution 2: branch and line currents
  11. 11Solution 2: power and equivalent Y
  12. 12Power-factor correction: the L07 method
  13. 13Example 3A: single-phase correction
  14. 14Solution 3A: target power and capacitor rating
  15. 15Solution 3A: capacitance and current check
  16. 16Parallel loads: combine powers first
  17. 17Example 3B: combine parallel loads
  18. 18Solution 3B: combined power and compensation
  19. 19Ideal transformer ratios
  20. 20Transformer tests and referral
  21. 21Example 4A: SC test and referral
  22. 22Solution 4A: impedance on both sides
  23. 23Open-circuit test
  24. 24Example 4B: open-circuit measurements
  25. 25Solution 4B: excitation parameters
  26. 26Per-unit bases
  27. 27Example 5A: transformer on rated bases
  28. 28Solution 5A: current and impedance bases
  29. 29Solution 5A: normalized impedance
  30. 30Changing the per-unit base
  31. 31Example 5B: changing the power base
  32. 32Solution 5B: new base and physical check
  33. 33Planning: screening cost and capacity
  34. 34Example 6: cost and required capacity
  35. 35Solution 6: screening and capacity
Cross-check the original slides

02 / EXPLORE

Change one input and explain the response

Complete the seven numbers, then use a base scan to check physical invariance. Classify errors as phasor, three-phase, equipment, or planning and revisit that module.

Advanced parameters / test readings

Preparing the model.

Example 1 P—
Example 1 Q—
Example 2 line current—
Example 5A Re(Zpu)—
Example 5A Im(Zpu)—
Example 6 reserve capacity—
Example 6 crossover—

Switch review plots by topic

Current intermediate values and numerical checks
Fixed practice uses original L16 examples 1, 2, 5A, and 6 separately from variable experiments. Three-phase bank connections are extensions and are not added to this Exam-1 check.
03 / EDIT & COMPUTE
Edit code to reproduce the model independently
Reproduce the baseline, then modify the parameter scan. The source contains reusable independent model functions; edit the current function and inspect numerical checks.
case is a snapshot of the controls when you press Run. Call solve(case) and assign the final solution to result to plot it.
 
Download teaching models
The first run needs internet access to download Python. Computation stays in your browser; the solver uses only the standard library.
Ready to run.
Output appears here.
Inspect and edit the model source (advanced)
Edit this module's function and run again. case.module selects the module; solve(case) returns values, plots, and checks. The parameter experiment keeps the original JavaScript reference for comparison.
04 / CHECK & EXPLAIN
Companion experiment practice and feedback
Fixed practice inputs
Use the fixed original L16 data above: V=180∠−20°, I=12∠10°; Δ branch 8+j6 Ω, VAB=208∠0°; single-phase Sb=30 kVA, VH=1500 V, ZH=1.5+j3.4369 Ω; planning peak 160 MW, PRM 15%.
Practice uses fixed baseline inputs independently of the controls. Each field displays its tolerance.
±0.05 W
±0.05 var
±0.05 A
±0.0005 pu
±0.0005 pu
±0.05 MW
±0.5 h/year
  
If zpu differs between corresponding transformer bases, what should you check first?
Finally, explain in your own words
  1. What are the inputs, references, and main assumptions?
  2. Complete the seven numbers, then use a base scan to check physical invariance. Classify errors as phasor, three-phase, equipment, or planning and revisit that module.
  3. Did your code edit change physical parameters, the method, or representation bases? Which check helps identify that?
Passing numerical and understanding checks records this lecture’s companion practice as “practice checks passed.”