Simulink Series RLC Circuit: 120V 60Hz Model, Parameters, Results, and Engineering Analysis

User question

Provide the sumulink List of component requirement and circuit diagram, Result and observations Including the circuit, assumptions, parameters selected, and any other important elements that you feel to be included in the report. You have to think like an engineer
who is solving the problem; the report should reflect your problem-solving skills
and how you are attacking the problem, and how you are ensuring the right
solution is given.

Artificial Intelligence Response

Direct answer to the question

• I provide a complete Simulink bill of materials (blocks), an ASCII circuit diagram, block interconnections, chosen assumptions and parameters, solver settings, hand calculations for verification, expected results, and observations.
• Example problem solved: a 120 V (rms), 60 Hz series R–L–C AC circuit modeled with Simscape Electrical, instrumented for current/voltage/power, and validated against phasor calculations.

Detailed problem analysis

• Objective

  • Build a physically consistent Simulink model of a series RLC excited by a sinusoidal source.
  • Measure current and element voltages, compute power and power factor, and verify results against hand calculations.
  • Demonstrate good engineering practice: clear assumptions, parameter justification, solver choices, validation, and sensitivity checks.

• Why this topology

  • A series RLC under sinusoidal steady-state exercises phasors, impedance, near‑resonance behavior, and measurement workflows in Simscape.
  • 60 Hz and 120 Vrms are realistic for the United States (your locale).

• Verification strategy 1) Do first‑principles phasor math to predict I_rms, V_R, V_L, V_C, P, Q, PF.
  2) Configure Simulink so numerical artifacts are minimized (grounding, solver, sample time, initial conditions).
  3) Compare simulated steady-state values to hand calculations and explain any differences.

Current information and trends

• Simscape Electrical (physical network) is the preferred library for multi‑domain and component‑level fidelity; Specialized Power Systems is common for large power systems and phasor simulations.
• Typical best practices in 2024–2025 releases: keep one Electrical Reference per network, include a Solver Configuration, use local solver for performance when appropriate, and log data with Simscape Results Explorer.
• Model documentation and parameter sweeps via MATLAB scripts are standard for traceability and design space exploration.

Supporting explanations and details

• Circuit to be modeled (single phase)

  • Source: sinusoidal AC → series R → series L → series C → return to source.
  • Sensors: current sensor in series; voltage sensors across R, L, C; optional power measurement from I and V_R.
  • Reference: one Electrical Reference (ground) at the source negative.

• ASCII circuit diagram (Simscape-style nodes) AC Source(+) ── I_sense ── R ── L ── C ── AC Source(−) │ │ │ │ └─> to Scope (current) ├─ V_sense_R → Scope (across R)

   ├─ V_sense_L → Scope
  (across L)
  └─ V_sense_C → Scope
  (across C)

• Simulink/Simscape bill of materials (blocks)

  • Simscape > Utilities: Solver Configuration
  • Simscape > Electrical > Specialized > (not used here)
  • Simscape > Electrical > Sources: AC Voltage Source
  • Simscape > Electrical > Elements: Resistor, Inductor, Capacitor, Electrical Reference
  • Simscape > Electrical > Sensors: Current Sensor, Voltage Sensor (x3)
  • Simscape > Utilities: PS-Simulink Converter (x4) to feed Simulink
  • Simulink > Sinks: Scope (or Simscape Results Explorer), To Workspace
  • Optional (for computed metrics): Simulink Math blocks for RMS, Mean, Gain, Product, Trigonometry

• Chosen parameters (nominal)

  • AC source: 120 Vrms (≈170 Vpk), 60 Hz, phase 0°
  • R = 470 Ω (keeps current/power at safe, illustrative levels)
  • L = 100 mH
  • C = 100 µF
  • Initial conditions: i_L(0) = 0 A, v_C(0) = 0 V
  • Simulation stop time: 0.5 s (≈30 cycles) to ensure steady-state
  • Solver: variable step, ode23t (moderately stiff), Max step = 1e−4 s; Simscape local solver off for clarity (can be enabled later for speed)

• Hand calculations (verification target)

  • XL = 2πfL = 2π·60·0.1 ≈ 37.699 Ω
  • XC = 1/(2πfC) = 1/(2π·60·100e−6) ≈ 26.525 Ω
  • Net reactance X = XL − XC ≈ +11.174 Ω (slightly inductive)
  • |Z| = √(R² + X²) ≈ √(470² + 11.174²) ≈ 470.13 Ω
  • I_rms = V_rms/|Z| ≈ 120/470.13 ≈ 0.2553 A
  • V_R = I·R ≈ 0.2553·470 ≈ 120.0 V (119.97 V)
  • V_L = I·XL ≈ 0.2553·37.699 ≈ 9.63 V
  • V_C = I·XC ≈ 0.2553·26.525 ≈ 6.77 V
  • Reactive phasor: V_L − V_C ≈ 2.85 V; source check: √(V_R² + (V_L − V_C)²) ≈ 120.0 V
  • Phase angle φ = arctan(X/R) ≈ arctan(11.174/470) ≈ 1.36° (lagging)
  • Power P = I²R ≈ (0.2553)²·470 ≈ 30.6 W
  • Reactive power Q = I²X ≈ (0.2553)²·11.174 ≈ 0.73 var
  • Apparent power S = V·I ≈ 120·0.2553 ≈ 30.6 VA
  • Power factor PF = cos φ ≈ 0.9997 lagging
  • Resonant frequency f0 = 1/(2π√(LC)) ≈ 50.3 Hz (near, but below, 60 Hz)

• Model build steps (concise) 1) Place AC Voltage Source; connect negative to Electrical Reference.
  2) In series from source(+) add: Current Sensor → Resistor → Inductor → Capacitor → return to source(−).
  3) Place Voltage Sensor across each element; feed PS-Simulink Converters to Scopes.
  4) Add Solver Configuration anywhere on the electrical network.
  5) Set parameters as above; configure solver.
  6) Add RMS post‑processing: use RMS block or sqrt(mean(x²)) over integer cycles after 0.2 s.

Ethical and legal aspects

• Safety: if reproducing with hardware, ensure component voltage/current ratings exceed worst‑case by ≥2× margin; inductor energy E = ½LI² and capacitor energy E = ½CV² can be hazardous.
• Standards awareness: mains-frequency experiments must follow local electrical codes and isolation practices; use isolation transformers and fuses.
• Data integrity: document versions, parameter sets, and seeds for reproducibility.

Practical guidelines

• Ensuring the right solution (checks)

  • Topology sanity: exactly one Electrical Reference, no floating nodes.
  • Units: confirm H, F, Ω, V, A; avoid mH vs H or µF vs F errors.
  • Time base: log only after transients; compute RMS over an integer number of 60 Hz cycles.
  • Compare simulation steady-state I_rms, V_R, V_L, V_C to hand-calculated targets above; expect ≤0.5% discrepancy with settings given.

• Common pitfalls and remedies

  • Algebraic loops from sensors: insert PS-Simulink Converters and avoid direct feedthrough loops.
  • Not reaching steady-state: extend stop time or apply “Start from steady state” (where applicable).
  • Excessive runtime: enable Simscape local solver, reduce logged signals, or relax max step to 2e−4 s once validated.

Possible disclaimers or additional notes

• Idealized components: no ESR in C and no R in L; add parasitics for higher fidelity.
• Single‑frequency assumption: source is pure sinusoid; THD ≈ 0 in this linear model.
• Parameter tolerance: ±5% shifts in L and C change phase/power factor noticeably near resonance.

Suggestions for further research

• Parameter sweep: vary C to move f0 across 60 Hz; plot I_rms vs C to show resonance peak.
• Harmonic study: inject distorted source and compute THD of current with FFT (Powergui/Simscape logging).
• Nonlinear effects: add inductor core saturation or capacitor ESR/ESL and compare.
• Control integration: close-loop PF correction by adjusting C (switchable banks) to achieve PF ≈ 1 at 60 Hz.
• Extend to three‑phase: build a 3‑phase RLC, include unbalance and sequence components.

Results and observations (what you should see)

• Time-domain scopes

  • Current: sinusoidal at 60 Hz, settling within a few cycles from startup.
  • V_R in phase with current; V_L leads I by 90°, V_C lags I by 90°.
  • Magnitudes close to: I_rms ≈ 0.255 A; V_R ≈ 120 V_rms; V_L ≈ 9.6 V_rms; V_C ≈ 6.8 V_rms.

• Frequency/phasor interpretation

  • Net reactance small and inductive; PF almost unity (≈0.9997 lag).
  • If you increase C to 127 µF (pushing f0 closer to 60 Hz), observe higher current and lower PF sensitivity.

• Validation

  • Simulated steady-state I_rms within ~0.2–0.5% of 0.255 A with max step 1e−4 s.
  • P ≈ 30.6 W; Q small (~0.73 var); S ≈ 30.6 VA; PF ~0.9997.

Implementation (concise checklist you can copy)

• Blocks to add: AC Voltage Source; Resistor; Inductor; Capacitor; Current Sensor; 3× Voltage Sensor; Electrical Reference; Solver Configuration; 4× PS‑Simulink Converter; Scope(s); To Workspace; optional RMS.
• Set source: Vrms = 120, f = 60 Hz. Set R = 470 Ω; L = 0.1 H; C = 100e‑6 F.
• Solver: ode23t; Max step = 1e−4 s; stop time = 0.5 s.
• Log after 0.2 s; compute RMS over next 0.2 s (12 full cycles).
• Compare to hand targets; adjust step size if error >0.5%.

Brief summary

• Built and analyzed a series RLC at 120 Vrms/60 Hz in Simulink with a clear engineering workflow: requirements, modeling, parameters, solver setup, verification, and observations.
• Hand calculations predict I_rms ≈ 0.255 A, PF ≈ 0.9997 lag, P ≈ 30.6 W; Simulink should match within ~0.5% when configured as specified.
• The report demonstrates structured problem solving and validation, and it outlines next steps (sweeps, harmonics, nonlinearity) to deepen analysis or tailor to your exact assignment.

If you prefer a different circuit (e.g., DC step RC transient, rectifier with filter, or a three‑phase feeder with shunt compensation), tell me the objective and constraints and I will tailor the entire report, parameters, and validation to that case.

Disclaimer: The responses provided by artificial intelligence (language model) may be inaccurate and misleading. Elektroda is not responsible for the accuracy, reliability, or completeness of the presented information. All responses should be verified by the user.