2.1. Program Structure and Flow

The aim of a transient stability program is to solve a system of differential-algebraic equations (DAE) involving the electrical network (which is assumed to be algebraic for the time-scales involved in stability runs) and dynamic elements interfaced to the network (e.g. machines, controllers, non-linear loads, etc).

The approach adopted by PYPOWER-Dynamics is to solve the DAE system using a partitioned solution approach and a current injection model to form the algebraic network equations:

• Partitioned solution approach: in this approach, the differential equations and algebraic equations are solved separately (i.e. partitioned) and are interfaced within a single time step. The order in which the equations are solved is somewhat arbitrary and in PYPOWER-Dynamics, the differential equations are solved first.

• Current injection model: in this model, the current injections at each network bus [I] are known (i.e. calculated) and the bus voltages [V] are solved algebraically at each time step using the bus admittance [Ybus] matrix, i.e. [V] = [Ybus]^(-1) * [I].

TBA