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A new control algorithm for a three-phase three-wire series active power filter is proposed. With the proposed control algorithm, the series active power filter compensates for the harmonics and reactive power that are generated by non-linear loads, such as diodes or thyristor rectifiers. The proposed control algorithm is based on the generalised p-q theory. It may be applied to both harmonic voltage sources and harmonic current sources. In this algorithm, the compensation voltage references are extracted directly. Therefore, the calculation of the compensation voltage reference will be much simpler than for other control algorithms. In addition, the difficulty of finding the voltage reference gain disappears. The compensation principle of the proposed control algorithm is presented in detail. To verify the effectiveness of the proposed algorithm, a prototype of a three-phase three-wire series active power filter has been manufactured and some experiments carried out.