Leistungsberechnung Wechselstrom

🔄 Alternating Current (AC) Calculations

Alternating Current (AC) is the standard power supply in households and industry. The calculations consider not only voltage and current but also the power factor (cos φ) and phase shift – essential for precise results.

Available Calculations:

Apparent Power: S = U × I

Calculate apparent power in AC systems

Active Power: P = U × I × cos φ

Effective power considering the power factor

Reactive Power: Q = U × I × sin φ

Calculate non-usable reactive power

Power Factor: cos φ = P / S

Ratio of active to apparent power

Reactive Factor: sin φ = Q / S

Ratio of reactive to apparent power

Specifics of Alternating Current

In alternating current, the current direction changes periodically, typically at 50 Hz in Europe. A distinction is made between apparent power (S), active power (P), and reactive power (Q). The power factor cos φ describes the ratio between active and apparent power and is crucial for the efficiency of electrical systems.

AC Apparent Power
S = U × I

Calculate the apparent power, voltage or current.

S = U × I

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 230 Volt single-phase AC motor has a rated current of 30 Ampere. What apparent power results from these values?
S = U × I
S = 230 V × 30 A
S = 6.9 kVA

Units of Measurement:
Apparent Power S = Kilovolt-Ampere [kVA]
Voltage U = Volt [V]
Current I = Ampere [A]

AC Active Power
P = U × I × cos φ

Calculate the active power, voltage, current or power factor.

P = U × I × cos φ

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A single-phase 230 V AC motor has a rated current of 3.506 Ampere and a cos φ of 0.93. What electrical power results from these values?
P = U × I × cos φ
P = 230 V × 3.506 A × 0.93
P = 0.75 kW

Units of Measurement:
Active Power P = Kilowatt [kW]
Voltage U = Volt [V]
Current I = Ampere [A]
cos φ = unitless

AC Reactive Power
Q = U × I × sin φ

Calculate the reactive power, voltage, current or sin φ.

Q = U × I × sin φ

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 230 Volt single-phase AC motor has a rated current of 8.56 Ampere and a sin φ of 0.92. What reactive power results from these values?
Q = U × I × sin φ
Q = 230 V × 8.56 A × 0.92
Q = 1.811 kVAr

Units of Measurement:
Reactive Power Q = Kilovolt-Ampere Reactive [kVAr]
Voltage U = Volt [V]
Current I = Ampere [A]
sin φ = unitless

AC Power Factor
cos φ = P / S

Calculate cos φ, active power or apparent power.

cos φ = P / S

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
A 4.0 kW three-phase motor (or 400V electric motor) has a cos phi of 0.85. What apparent power results from these values?
cos φ = P / S
S = P / cos φ
S = 4.0 kW / 0.85
S = 4.706 kVA

Units of Measurement:
Active Power P = Kilowatt [kW]
Apparent Power S = Kilovolt-Ampere [kVA]
cos φ = unitless

AC Reactive Factor
sin φ = Q / S

Calculate sin φ, reactive power or apparent power.

sin φ = Q / S

💡 Enter the known values – leave the field you want to calculate empty.

✅ Result:

Example Calculation:
An AC motor with apparent power of 3.2 kVA has a sin phi of 0.234. What reactive power results from these values?
sin φ = Q / S
Q = S × sin φ
Q = 3.2 kVA × 0.234
Q = 0.749 kVAr

Units of Measurement:
Reactive Power Q = Kilovolt-Ampere Reactive [kVAr]
Apparent Power S = Kilovolt-Ampere [kVA]
sin φ = unitless

Formeln für Wechselstrom

  • Wirkleistung: P = U × I × cos φ
  • Scheinleistung: S = U × I
  • Blindleistung: Q = U × I × sin φ
  • Wirkleistungsfaktor: cos φ = P / S
  • Blindleistungsfaktor: sin φ = Q / S

Besonderheiten bei Wechselstrom

Bei Wechselstrom wechselt die Stromrichtung periodisch, in Europa typischerweise mit 50 Hz. Man unterscheidet Scheinleistung (S), Wirkleistung (P) und Blindleistung (Q). Der Leistungsfaktor cos φ beschreibt das Verhältnis von Wirk- zu Scheinleistung; er steht auf dem Typenschild des Motors.

Rechenbeispiel Scheinleistung

Ein 230-V-Einphasen-Wechselstrommotor hat einen Nennstrom von 30 A.

S = U × I
S = 230 V × 30 A
S = 6,9 kVA