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L02 / Course & power-system overview

Power-System Evolution and Symbolic Representation

Trace the physical power system, construct a one-line diagram, and reconcile real and reactive power.

Available33 slides
Equipment, one-lines, and power accounting

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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Slide text
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Figures and page order follow the student PDF for this lecture.

A load requires 80 MW and 30 Mvar. Can the generator supply only 80 MW when equipment has losses? Predict which quantity shunt capacitors change.
  • Explain generators, transformers, lines, buses, loads, and shunt compensation.
  • Distinguish MW, Mvar, and MVA and reconcile power with a declared sign convention.
  • Declare data, reference directions, and assumptions before interpreting a result.
Course introduction & power-system overview: concept and calculation route
Course-authored concept route; the numerical experiment follows below.

From equipment to a one-line

Generators supply energy, transformers connect voltage levels, lines connect buses, loads consume power, and shunts inject or absorb reactive power. A one-line preserves equipment endpoints and roles while representing a three-phase network.

Three power quantities

S=P+jQ,\qquad |S|=\sqrt{P^2+Q^2}

P describes average energy conversion, Q reactive exchange, and |S| voltage–current loading. Equipment MVA ratings and real MW are not interchangeable.

Declare accounting signs

P_G=P_L+P_{line}+P_{tx},\quad Q_G=Q_L-Q_c+Q_{line}+Q_{tx}

Here load P and Q are positive consumption and capacitor Qc is positive injection. Add equipment real loss and reactive absorption to the source requirement. Check the receiving bus before the complete system.

Baseline example: check each step

  1. Receiving bus: Qnet = 30 − 10 = 20 Mvar.
  2. Line sending end: P = 83 MW and Q = 25 Mvar.
  3. Generator: P = 84 MW and Q = 27 Mvar.
  4. Using 138 kV line voltage and sending-end |S| gives balanced current ≈ 362.657 A.
Original slide headings for this lecture30
  1. 1Two views of the same power system
  2. 3From local service to interconnection
  3. 4National grid
  4. 5Network reliability
  5. 6Smart-grid layers
  6. 7Traditional and evolving grids
  7. 8Generation mix
  8. 9Resource geography
  9. 10Variable generation and net load
  10. 12Starting problem
  11. 13Physical path
  12. 14Generator
  13. 15Bus
  14. 16Transformer
  15. 17Transmission line
  16. 18Load
  17. 19Shunt
  18. 20Six symbols
  19. 21Three-phase system, one drawn path
  20. 22Plant to campus
  21. 23Define voltage zones
  22. 24Preserve endpoints and roles
  23. 25Complete the one-line
  24. 26Given data and sign convention
  25. 27Real-power balance at Bus 3
  26. 28Reactive power at Bus 3
  27. 29Line sending-end power
  28. 30Generator output
  29. 31System reconciliation
  30. 32System-data record
Cross-check the original slides

02 / EXPLORE

Change one input and explain the response

Compare current at 69 and 138 kV. Explain why physical I²R losses require a line-impedance model.

Advanced parameters / test readings

Preparing the model.

Generator P—
Generator Q—
Net receiving Q—
Transmission current—

Power at the declared boundaries

Current intermediate values and numerical checks
This account uses prescribed equipment losses and a balanced three-phase current estimate. Voltage changes the estimated current; loss values remain input data.
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
Load 80 MW/30 Mvar; capacitor 10 Mvar; line loss 3 MW/absorption 5 Mvar; transformer loss 1 MW/absorption 2 Mvar.
Practice uses fixed baseline inputs independently of the controls. Each field displays its tolerance.
±0.05 MW
±0.05 Mvar
±0.05 Mvar
  
What happens when capacitor injection increases from 10 to 20 Mvar with prescribed losses unchanged?
Finally, explain in your own words
  1. What are the inputs, references, and main assumptions?
  2. Compare current at 69 and 138 kV. Explain why physical I²R losses require a line-impedance model.
  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.”