Fundamental current
825 A
Calculadora de Harmónicos e Filtro Desafinado (PFC)
Dimensionar uma bateria de condensadores de correção do fator de potência com um reator de desafinação em série — kvar de compensação, verificação da frequência de ressonância e a configuração do filtro.
Resultado
Insira sua carga → obtenha um projeto completo e BOM em segundos
Saída de exemploRequired compensation
277 kvar
400 kW · PF 0.7 → 0.95 · THDi 30% · 7% reactor
Harmonic current
247 A
Resonance freq
189 Hz
Cap voltage
430 V
Calculation
| Quantity | Value |
|---|---|
| Reactive power Qc | P × (tanφ₁ − tanφ₂) = 400 × (1.020 − 0.329) = 276.6 kvar |
| Fundamental current I₁ | P ÷ (√3·V·PF) = 400 kW ÷ (√3 × 400 V × 0.7) = 824.8 A |
| Harmonic current Ih | I₁ × THDi = 824.8 × 30% = 247.4 A |
| LC resonance frequency | f₁ ÷ √(p) = 50 ÷ √(0.070) = 189 Hz |
| Dominant harmonic | 5ᵗʰ = 250 Hz → above resonance (filter is inductive) — Detuned — safe from resonance ✓ |
| Capacitor voltage | V ÷ (1 − p) = 400 ÷ 0.93 = 430 V |
| Reactor rating | 7% × 277 = 19.4 kvar |
Filter configuration
277 kvar capacitor bank + 7% detuning reactor (19.4 kvar)
Detuned at 189 Hz, below the 5ᵗʰ harmonic (250 Hz) — the branch stays inductive at the dominant harmonic, preventing resonance amplification.
Bill of materials
| Equipment | Spec | Qty | Subtotal |
|---|---|---|---|
| Power factor correction capacitor bank | 277 kvar · 400 V · detuned | 1 | POA |
| Series detuning reactor (7%) | 19.4 kvar · 189 Hz tuning | 1 | POA |
| Total equipment | POA |
Para engenheiros que projetam correção do fator de potência e filtros de harmónicos desafinados em redes com variadores de velocidade e outras cargas não lineares.
Utilizar a calculadora
Exemplo prático
Um exemplo de referência pré-calculado (rastreável — não requer JavaScript). Introduza os seus próprios parâmetros acima para um resultado em tempo real.
Exemplo resolvido — 400 kW, PF 0,70→0,95, THDi 30%, reator de 7%
Required compensation
277 kvar
400 kW · PF 0.7 → 0.95 · THDi 30% · 7% reactor
Fundamental current
825 A
Harmonic current
247 A
Resonance freq
189 Hz
Cap voltage
430 V
Calculation
| Quantity | Value |
|---|---|
| Reactive power Qc | P × (tanφ₁ − tanφ₂) = 400 × (1.020 − 0.329) = 276.6 kvar |
| Fundamental current I₁ | P ÷ (√3·V·PF) = 400 kW ÷ (√3 × 400 V × 0.7) = 824.8 A |
| Harmonic current Ih | I₁ × THDi = 824.8 × 30% = 247.4 A |
| LC resonance frequency | f₁ ÷ √(p) = 50 ÷ √(0.070) = 189 Hz |
| Dominant harmonic | 5ᵗʰ = 250 Hz → above resonance (filter is inductive) — Detuned — safe from resonance ✓ |
| Capacitor voltage | V ÷ (1 − p) = 400 ÷ 0.93 = 430 V |
| Reactor rating | 7% × 277 = 19.4 kvar |
Filter configuration
277 kvar capacitor bank + 7% detuning reactor (19.4 kvar)
Detuned at 189 Hz, below the 5ᵗʰ harmonic (250 Hz) — the branch stays inductive at the dominant harmonic, preventing resonance amplification.
Bill of materials
| Equipment | Spec | Qty | Subtotal |
|---|---|---|---|
| Power factor correction capacitor bank | 277 kvar · 400 V · detuned | 1 | POA |
| Series detuning reactor (7%) | 19.4 kvar · 189 Hz tuning | 1 | POA |
| Total equipment | POA |
Exemplo resolvido — 800 kW, PF 0,75→0,98, THDi 25%, reator de 6%
Required compensation
543 kvar
800 kW · PF 0.75 → 0.98 · THDi 25% · 6% reactor
Fundamental current
1540 A
Harmonic current
385 A
Resonance freq
204 Hz
Cap voltage
426 V
Calculation
| Quantity | Value |
|---|---|
| Reactive power Qc | P × (tanφ₁ − tanφ₂) = 800 × (0.882 − 0.203) = 543.1 kvar |
| Fundamental current I₁ | P ÷ (√3·V·PF) = 800 kW ÷ (√3 × 400 V × 0.75) = 1539.6 A |
| Harmonic current Ih | I₁ × THDi = 1539.6 × 25% = 384.9 A |
| LC resonance frequency | f₁ ÷ √(p) = 50 ÷ √(0.060) = 204 Hz |
| Dominant harmonic | 7ᵗʰ = 350 Hz → above resonance (filter is inductive) — Detuned — safe from resonance ✓ |
| Capacitor voltage | V ÷ (1 − p) = 400 ÷ 0.94 = 426 V |
| Reactor rating | 6% × 543 = 32.6 kvar |
Filter configuration
543 kvar capacitor bank + 6% detuning reactor (32.6 kvar)
Detuned at 204 Hz, below the 7ᵗʰ harmonic (350 Hz) — the branch stays inductive at the dominant harmonic, preventing resonance amplification.
Bill of materials
| Equipment | Spec | Qty | Subtotal |
|---|---|---|---|
| Power factor correction capacitor bank | 543 kvar · 400 V · detuned | 1 | POA |
| Series detuning reactor (6%) | 32.6 kvar · 204 Hz tuning | 1 | POA |
| Total equipment | POA |
Como foi calculado
- · Potência reativa: Qc = P × (tanφ₁ − tanφ₂).
- · Corrente harmónica: Ih = I₁ × THDi%.
- · Frequência de ressonância LC: f_res = f₁ ÷ √(p), onde p é o fator de desafinação (6% → ≈204 Hz, 7% → ≈189 Hz, 12.5% → ≈141 Hz).
- · Verificação de desafinação: o ramal é indutivo (sem amplificação) quando o harmónico dominante está acima de f_res.
- · Tensão do condensador com reator: Vc = V ÷ (1 − p).
Normas referenciadas
| Standard | Scope |
|---|---|
| GB/T 14549 | Qualidade do fornecimento de energia elétrica — harmónicos na rede pública de abastecimento |
| IEC 61000-3-2 | Limites para emissões de corrente harmónica (equipamentos ≤ 16 A) |
| IEC 61642 | Redes industriais de corrente alternada afetadas por harmónicos |
| IEEE 519 | Prática recomendada para o controlo de harmónicos em sistemas de energia elétrica |
Perguntas frequentes
What harmonic limits does IEEE 519 impose?
IEEE 519 limits total demand distortion (TDD) at the point of common coupling, typically 5% for systems below 69 kV, with individual harmonic limits (e.g. 5th/7th capped around 4%). Stricter limits apply where the short-circuit ratio is low. The calculator sizes filtering to meet these limits.
What is the difference between a passive and active harmonic filter?
A passive filter is a tuned LC circuit (often a detuned capacitor bank) that traps a specific harmonic; cheap but fixed. An active harmonic filter (APF) injects a cancelling current dynamically, handling multiple and varying Harmonics at 2-4x the cost. The calculator recommends detuned banks for steady harmonics and APF for dynamic loads.
Why do VFDs cause harmonics?
VFD rectifiers draw current in pulses rather than a sine wave, generating 5th, 7th, 11th and 13th harmonics (6-pulse drives). A 6-pulse VFD can produce 30-40% THDi at the drive terminals; 12- or 18-pulse and active-front-end drives reduce it. The calculator models the harmonic source share.
What detuning factor protects a capacitor bank from resonance?
A 7% series Reactor detunes the capacitor bank below the 5th harmonic so the bank never resonates with the network at 250 Hz. A 6% reactor is used when only the 5th harmonic is significant; 7% is the default for networks with 5th and higher harmonics. The calculator applies the detuning factor.
How do I estimate the harmonic filter kVAR needed?
The filter kVAR is based on the non-linear load share and the required distortion reduction. As a rule of thumb, size detuned capacitors to 25-35% of the VFD load, and an APF to 15-25% of the harmonic-producing load. The calculator estimates the compensation and filter rating from the load mix.
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