This paper proposes a model of the total-quadrant security region for distribution systems(TQ-DSSR)with distributed generators(DGs). The topological characteristics of TQ-DSSR for urban distribution network are observed and analyzed. First

the constraints of normal operation and N-1 security for the active distribution network are discussed

and the TQ-DSSR is modeled. Second

the two-dimensional sections of TQ-DSSR are observed. Compared with the traditional DSSR

it is most obvious that the region is transformed from a single-quadrant region to a total-quadrant region. For the urban distribution system with power supply as the main function

such as the urban grids in China

other topological characteristics include: 1)the shapes of TQ-DSSR are the same as DSSR

which are triangle

pentagon

trapezoid and rectangle

but the angle towards the region between bevel edge and coordinate axis is not always 45°

but also 135°; 2)the most secure operating point in TQ-DSSR is the one at which DG output reaches the peak value and the power of load is zero

which differs from the original point in traditional DSSR; 3)the security property in the state space of TQ-DSSR meets the generalized monotonic decrease

that is

the security will decrease or remain unchanged with an increase in the payload of the cut-set. The model of TQ-DSSR reflects the basic characteristics of reverse power flow both in branches and buses for active distribution network

laying the foundation for subsequent consideration of energy storage

micro-grid

and demand response based integral DSSR.