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L17 / Exam 1 practice & review

Exam 1 Review

Review the first course block and connect circuit calculations with design checks.

Available44 slides
Exam-1 review and diagnostics

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.

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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 lecture38
  1. 1Review outline
  2. 2Starting problem
  3. 3RMS phasors
  4. 4Time domain to RMS phasors
  5. 5Complex-number forms
  6. 6Complex power uses the current conjugate
  7. 7Impedance power check
  8. 8Power-factor correction
  9. 9Positive-sequence set
  10. 10Wye line voltage
  11. 11Delta line current
  12. 12Three-phase power
  13. 13Example: feeder data
  14. 14Example: solution route
  15. 15Example: voltage reference
  16. 16Example: delta equivalent
  17. 17Example: line current
  18. 18Example: sending voltage
  19. 19Example: total load power
  20. 20Example: feeder loss
  21. 21Transformer quantities
  22. 22Practical transformer model
  23. 23Example: short-circuit test
  24. 24Example: test solution
  25. 25Single-phase per-unit bases
  26. 26Practice: referral and base
  27. 27Practice: referral answer
  28. 28Review error checks
  29. 29Core review summary
  30. 30Demand, energy, capacity
  31. 31Load-duration curve
  32. 32Screening curves
  33. 33Renewable shares
  34. 34Feasible generation mix
  35. 35Planning extension: data
  36. 36Planning: installed capacity
  37. 37Planning: peak adequacy
  38. 38Planning: result summary
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.”