Application of continuation power flow method in radial distribution systems

The paper presents a set of equations (SOE) comprising voltage magnitude and nodal real/reactive power balance equations to model a radial distribution system (RDS). The voltage equations in the SOE have dual roots. Then a Newton–Raphson (NR) method is presented to solve the SOE to determine the voltage solution of an RDS. This NR method is extended using the continuation technique to trace the P–V curves and to determine the maximum loading point of an RDS. Implementation of the proposed method on some common RDS and a 5002-bus RDS is demonstrated. An interesting characteristic of the path traced by the minimum singular value of the system Jacobian during the application of the continuation method for a system with shunt capacitors is reported. An analysis of a simple 4-bus system with and without a capacitor demonstrates that the presence of capacitive load creates multiple positive regions of σ_min. One positive region exists when the system is healthy (before collapse). The second region exists in between collapse point and the point where an increase in the load creates reactive power flow reversal on the source line.