The probabilistic study of voltage problems in distribution network with small dispersed generation

Fulfilling voltage limits produces the bottleneck of sending the whole dispersed generation to the MV network. The voltage regulation at a dispersed power station and the HV/MV transformer on-load tap changer can be simultaneously used for voltage control. To achieve proper results, the randomness of active and reactive node loads should be taken into consideration. The rectangular probability distribution of node loads may be assumed as a pessimistic one. So the node loads are described by Ey, the expected value, and My, the covariance matrix. To find the value of node voltages and reactive node generation, load flow equations can be linearized. Rectangular components of node voltages are treated as the linear transformation of uniformly distributed node loads. All non-linear functions of rectangular components of node voltages can be linearized as well. It means that the node voltage magnitudes and reactive generations are random variables subjected to the normal probability distribution. All considerations are illustrated with an example MV power network with two parallel small CHP generators.