三相功率计算

概述

三相电力是全球交流发电、输电和配电的标准方法。与单相系统相比，三相提供恒定的瞬时功率（无零点），相同功率传输所需的导体材料更少，并支持自启动电机。它是工业、商业和公用事业规模电气系统的骨干。

三相系统使用三个相隔 120° 的电压波形。它们可以连接为星形（Y）或三角形配置，每种配置都有不同的电压和电流关系。

关键公式

有功功率

平衡三相系统提供的总有功功率：

$P = \sqrt{3}\; V_{L}\; I_{L}\; \cos\phi$

其中 $V_L$ 和 $I_L$ 分别为线间电压和线电流，$\phi$ 为电压与电流之间的相位角。

视在功率

$S = \sqrt{3}\; V_{L}\; I_{L}$

无功功率

$Q = \sqrt{3}\; V_{L}\; I_{L}\; \sin\phi$

功率因数关系

$\cos\phi = \frac{P}{S}$

每相等效

对于星形（Y）连接的负载：

$P_{phase} = V_{phase}\; I_{phase}\; \cos\phi$

其中 $V_L = \sqrt{3}\; V_{phase}$，$I_L = I_{phase}$。

由已知功率计算电流

$I_L = \frac{P}{\sqrt{3}\; V_L\; \cos\phi}$

变量

星形与三角形连接

常见系统电压

典型功率因数值

计算器 — 三相有功功率

计算器 — 由功率计算线电流

制动马力

电机轴输出通常以制动马力表示。在与机械输出比较之前，必须对电输入功率进行功率因数和电机效率修正。

还原的原始源表

以下表格还原自原始来源页面，以保留完整的参考数据。

Three-Phase Power Factors

工程要点

• Constant power transfer: Unlike single-phase, three-phase delivers non-pulsating instantaneous power, reducing vibration in motors and allowing smaller flywheel masses.
• Balanced loads matter: The formulas above assume balanced conditions (equal impedance in all three phases). Unbalanced systems require symmetrical component analysis.
• Power factor correction: Utilities often penalize low power factor. Capacitor banks at the load or distribution panel can raise the plant power factor toward unity, reducing current draw and losses.
• Neutral conductor sizing: In star-connected systems with non-linear loads (e.g., switching power supplies), third-harmonic currents add in the neutral. The neutral conductor may need to be rated at or above the phase conductor capacity.
• Motor starting current: Induction motors draw 5–8× rated current during direct-on-line starting. Soft starters or variable-frequency drives limit this inrush and also allow power factor optimization at partial loads.
• Wire sizing and derating: Always apply applicable NEC/IEC standards for conductor sizing, ambient temperature derating, and short-circuit protection when designing three-phase circuits.

参考资料

• Original Source — Engineering ToolBox: Three-Phase Power