Solution of DC power flow for nongrounded traction systems using chain-rule reduction of ladder circuit Jacobian matrices

The power networks of nongrounded DC traction systems are generically longitude ladder-like circuits. The solution of DC power flow for such circuits using nodal analysis requires manipulation of large conductance matrix and Jacobian matrix. We present an approach that decomposes the whole network into individual ladder circuits and employs the chain rule to reduce the Jacobian matrices into the product of a sequence of derivatives. Thus we can solve the DC power flow iteratively without dealing with large matrices, making it simple and efficient for either manual or computer calculation.