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L07 / Single-phase AC circuits

Single-Phase AC Circuits III

Determine target reactive power, shunt compensation, and capacitance for power-factor correction.

Available18 slides
Reactive compensation and power-factor correction

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.

At 120 V RMS and 10 A RMS, voltage leads current by 50°. Why is P not 1200 W? How does source current change when pf reaches 0.95?
  • Keep RMS, cosine reference, and current direction consistent.
  • Use the current conjugate to calculate P, Q, |S|, and power factor.
  • Calculate target Q, capacitor rating, and corrected source current.
Single-phase AC circuits: concept and calculation route
Course-authored concept route; the numerical experiment follows below.

Conjugate and signs

S=\mathbf V\mathbf I^*=VI(\cos\Delta\phi+j\sin\Delta\phi)

Current enters the positive load terminal, using the passive convention. Δφ = φV−φI; positive Δφ means lagging current and positive Q. Calculate S = V I* before reading P and Q.

Shunt correction

Q_c=Q-P\tan(\cos^{-1}pf_t),\quad C=\frac{Q_c}{\omega V^2}

Keep load P fixed. Target lagging Q is P tan(arccos target pf), and Qc = Qload−Qtarget. Add capacitance only to reduce inductive Q; this lab adds none when the target is already met or the load is capacitive.

Baseline example: check each step

  1. Δφ = 50° and |S| = 1200 VA.
  2. P ≈ 771.345 W, Q ≈ 919.253 var, pf ≈ 0.643 lagging.
  3. Target Q ≈ 253.529 var; capacitor rating ≈ 665.724 var.
  4. C ≈ 122.628 μF; load current remains 10 A while source current falls to ≈ 6.766 A.
Open the L05 waveform and phasor-addition lesson →
Original slide headings for this lecture15
  1. 1Lecture outline
  2. 2Load and generator sign conventions
  3. 3Capacitor power and power balance
  4. 4Shunt compensation
  5. 5Power-factor correction
  6. 6Step 1: Target reactive power
  7. 7Step 2: Required compensation
  8. 8Step 3: Capacitance
  9. 9Step 4: Verification
  10. 10Worked example: the L06 load
  11. 11Example: Step 1
  12. 12Example: Step 2
  13. 13Example: Step 3
  14. 14Example: Step 4
  15. 15Correction summary
Cross-check the original slides

02 / EXPLORE

Change one input and explain the response

Set Δφ to −30° and explain Q and the absence of added capacitance. Edit the Python phase and check P²+Q²=|S|².

Advanced parameters / test readings

Preparing the model.

Real P—
Reactive Q—
Load pf—
Correction capacitance—
Capacitor rating—
Corrected pf—
Corrected source current—

Voltage/current phase comparison

Instantaneous and average power

Current intermediate values and numerical checks
The model assumes single-frequency sinusoidal steady state, fixed voltage, and fixed load power. Correction changes source Q and current; normalized curves compare phase only.
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
V=120 V RMS, I=10 A RMS, voltage leads current by 50°, ω=377 rad/s, target pf=0.95 lagging.
Practice uses fixed baseline inputs independently of the controls. Each field displays its tolerance.
±0.05 W
±0.05 var
±0.05 μF
  
Which operation gives load complex power under the passive convention?
Finally, explain in your own words
  1. What are the inputs, references, and main assumptions?
  2. Set Δφ to −30° and explain Q and the absence of added capacitance. Edit the Python phase and check P²+Q²=|S|².
  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.”