Abstract: The volume of security region, as an important index of the distribution system security region (DSSR), describes the size of the DSSR. In this paper, the definition and the new algorithm of the total quadrant security region volume for the active distribution networks satisfying the N−0 (DSSR0) and the N−1 security criteria are proposed. First, the volume for the active distribution networks is defined as the n-fold integral in the state space, which is different from the volume of the traditional DSSR in the following aspects: 1) The integral variables are different: the traditional volume takes the feeder load, while the volume for the active distribution networks uses the node's net power; 2) The quadrants of the state space are different: the traditional DSSR is located in the first quadrant, while the security region of active distribution networks occupies the whole quadrant. Second, a new volume algorithm based on the Quasi Monte Carlo is proposed, which is suitable for the volume calculations of the active and the traditional distribution networks. Compared to the existing Monte Carlo algorithm, it is better in accuracy and speed and more applicable to the security region models of the DC and the AC power flows. Finally, the definition and algorithm of this paper are verified by the distribution network cases. The variation rules and reasons of the DSSR0 and the DSSR volumes on the location and penetration of the distributed generation are obtained.