Generator Parallel Operation Calculator

ANA›Life Services Authority›National Calculator Authority›Generator Parallel Operation Calculator

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Generator Parallel Operation Calculator

Calculate load sharing, circulating current, and power distribution for two generators operating in parallel.

### Generator 1

Rated kVA (kVA)

Power Factor

Terminal Voltage (V)

Synchronous Impedance Zs1 (Ω)

EMF E1 (V)

### Generator 2

Rated kVA (kVA)

Power Factor

Terminal Voltage (V)

Synchronous Impedance Zs2 (Ω)

EMF E2 (V)

### System Load

Total Load (kW)

Load Power Factor

System Phases

3-Phase 1-Phase

Calculate

function genCalc() { var kva1 = parseFloat(document.getElementById('gen-kva1').value); var pf1 = parseFloat(document.getElementById('gen-pf1').value); var v1 = parseFloat(document.getElementById('gen-v1').value); var zs1 = parseFloat(document.getElementById('gen-zs1').value); var emf1 = parseFloat(document.getElementById('gen-emf1').value); var kva2 = parseFloat(document.getElementById('gen-kva2').value); var pf2 = parseFloat(document.getElementById('gen-pf2').value); var v2 = parseFloat(document.getElementById('gen-v2').value); var zs2 = parseFloat(document.getElementById('gen-zs2').value); var emf2 = parseFloat(document.getElementById('gen-emf2').value); var totalLoad = parseFloat(document.getElementById('gen-totalload').value); var loadPF = parseFloat(document.getElementById('gen-loadpf').value); var phases = parseInt(document.getElementById('gen-phases').value);

var errors = []; if (isNaN(kva1) || kva1 0."); if (isNaN(pf1) || pf1 1) errors.push("Generator 1 power factor must be 0.1–1."); if (isNaN(v1) || v1 0."); if (isNaN(zs1) || zs1 0."); if (isNaN(emf1) || emf1 0."); if (isNaN(kva2) || kva2 0."); if (isNaN(pf2) || pf2 1) errors.push("Generator 2 power factor must be 0.1–1."); if (isNaN(v2) || v2 0."); if (isNaN(zs2) || zs2 0."); if (isNaN(emf2) || emf2 0."); if (isNaN(totalLoad) || totalLoad 1) errors.push("Load power factor must be 0.1–1.");

var res = document.getElementById('gen-result'); if (errors.length > 0) { res.innerHTML = '' + errors.join('') + '

'; return; }

// ── Proportional kVA load sharing ────────────────────────────────────────── // Each generator shares load in proportion to its rated kVA var totalKVA = kva1 + kva2; var totalKW = totalLoad; var totalKVAr = totalKW * Math.tan(Math.acos(loadPF));

var share1 = kva1 / totalKVA; // fraction var share2 = kva2 / totalKVA;

var kw1 = totalKW * share1; var kw2 = totalKW * share2; var kvar1 = totalKVAr * share1; var kvar2 = totalKVAr * share2; var kvaLoad1 = Math.sqrt(kw1 * kw1 + kvar1 * kvar1); var kvaLoad2 = Math.sqrt(kw2 * kw2 + kvar2 * kvar2); var pf1actual = (kvaLoad1 > 0) ? kw1 / kvaLoad1 : 0; var pf2actual = (kvaLoad2 > 0) ? kw2 / kvaLoad2 : 0;

// ── Per-unit loading ──────────────────────────────────────────────────────── var pu1 = kvaLoad1 / kva1 * 100; var pu2 = kvaLoad2 / kva2 * 100;

// ── Rated currents ────────────────────────────────────────────────────────── // I_rated = kVA × 1000 / (√3 × V) for 3-phase // I_rated = kVA × 1000 / V for 1-phase var vFactor = (phases === 3) ? (Math.sqrt(3) * v1) : v1; var vFactor2 = (phases === 3) ? (Math.sqrt(3) * v2) : v2; var iRated1 = (kva1 * 1000) / vFactor; var iRated2 = (kva2 * 1000) / vFactor2;

// Actual load currents (proportional share) var iLoad1 = iRated1 * (kvaLoad1 / kva1); var iLoad2 = iRated2 * (kvaLoad2 / kva2);

// ── Circulating current (no-load, due to EMF difference) ─────────────────── // Ic = (E1 - E2) / (Zs1 + Zs2) [phasor magnitude, assuming same angle] var deltaE = Math.abs(emf1 - emf2); var ic = deltaE / (zs1 + zs2);

// ── Voltage regulation ────────────────────────────────────────────────────── // VR = (E - V) / V × 100% var vr1 = ((emf1 - v1) / v1) * 100; var vr2 = ((emf2 - v2) / v2) * 100;

// ── Short-circuit current capacity ───────────────────────────────────────── // Isc = E / Zs var isc1 = emf1 / zs1; var isc2 = emf2 / zs2;

// ── Efficiency estimate (simple copper-loss model) ────────────────────────── // η = P_out / (P_out + P_loss), P_loss ≈ I²×R (assume R ≈ 0.8×Zs typical) var r1 = 0.8 * zs1; var r2 = 0.8 * zs2; var ploss1 = (iLoad1 * iLoad1 * r1) / 1000; // kW var ploss2 = (iLoad2 * iLoad2 * r2) / 1000; var eff1 = (kw1 > 0) ? (kw1 / (kw1 + ploss1)) * 100 : 0; var eff2 = (kw2 > 0) ? (kw2 / (kw2 + ploss2)) * 100 : 0;

// ── Synchronising power coefficient ──────────────────────────────────────── // Psync = (E1 × E2) / (Zs1 + Zs2) [per-phase, approximate] var psync = (emf1 * emf2) / (zs1 + zs2);

// ── Warnings ─────────────────────────────────────────────────────────────── var warnings = []; if (pu1 > 100) warnings.push("⚠️ Generator 1 is overloaded (" + pu1.toFixed(1) + "% of rated kVA)."); if (pu2 > 100) warnings.push("⚠️ Generator 2 is overloaded (" + pu2.toFixed(1) + "% of rated kVA)."); if (ic > 0.1 * Math.min(iRated1, iRated2)) warnings.push("⚠️ Circulating current (" + ic.toFixed(2) + " A) exceeds 10% of smaller generator's rated current — check voltage matching."); if (Math.abs(v1 - v2) > 0.02 * Math.max(v1, v2)) warnings.push("⚠️ Terminal voltages differ by more than 2% — synchronisation may be difficult.");

var warnHTML = warnings.length > 0
? '' + warnings.join('') + ''
'';

res.innerHTML = warnHTML + '' + 'ParameterGenerator 1Generator 2Combined' + '' + 'Rated kVA' + kva1.toFixed(1) + ' kVA' + kva2.toFixed(1) + ' kVA' + totalKVA.toFixed(1) + ' kVA' + 'Load Share (kW)' + kw1.toFixed(2) + ' kW' + kw2.toFixed(2) + ' kW' + totalKW.toFixed(2) + ' kW' + 'Load Share (kVAr)' + kvar1.toFixed(2) + ' kVAr' + kvar2.toFixed(2) + ' kVAr' + totalKVAr.toFixed(2) + ' kVAr' + 'Apparent Load (kVA)' + kvaLoad1.toFixed(2) + ' kVA' + kvaLoad2.toFixed(2) + ' kVA' + (kvaLoad1+kvaLoad2).toFixed(2) + ' kVA' + '% Loading' + pu1.toFixed(1) + '%' + pu2.toFixed(1) + '%—' + 'Actual Power Factor' + pf1actual.toFixed(4) + '' + pf2actual.toFixed(4) + '' + loadPF.toFixed(4) + '' + 'Rated Current' + iRated1.toFixed(2) + ' A' + iRated2.toFixed(2) + ' A—' + 'Load Current' + iLoad1.toFixed(2) + ' A' + iLoad2.toFixed(2) + ' A—' + 'Voltage Regulation' + vr1.toFixed(2) + '%' + vr2.toFixed(2) + '%—' + 'Short-Circuit Current' + isc1.toFixed(2) + ' A' + isc2.toFixed(2) + ' A—' + 'Copper Losses (est.)' + ploss1.toFixed(3) + ' kW' + ploss2.toFixed(3) + ' kW' + (ploss1+ploss2).toFixed(3) + ' kW' + 'Efficiency (est.)' + eff1.toFixed(2) + '%' + eff2.toFixed(2) + '%—' + 'Circulating Current (Ic)' + ic.toFixed(4) + ' A (ΔE = ' + deltaE.toFixed(2) + ' V)' + 'Synchronising Power Coeff.' + psync.toFixed(2) + ' W/rad (per-phase approx.)' + ''; }

#### Formulas Used

Proportional kVA Load Sharing: Share₁ = kVA₁ / (kVA₁ + kVA₂) kW₁ = P_total × Share₁  |  kVAr₁ = Q_total × Share₁ kVA_load₁ = √(kW₁² + kVAr₁²)

Rated Current (3-phase): I_rated = (kVA × 1000) / (√3 × V)

Circulating Current: I_c = |E₁ − E₂| / (Z_s1 + Z_s2)

Voltage Regulation: VR = (E − V) / V × 100%

Short-Circuit Current: I_sc = E / Z_s

Synchronising Power Coefficient (approx.): P_sync = (E₁ × E₂) / (Z_s1 + Z_s2)

Copper Loss Estimate: P_loss = I_load² × R   (R ≈ 0.8 × Z_s assumed)

Efficiency Estimate: η = P_out / (P_out + P_loss) × 100%

#### Assumptions & References

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References

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