2.4. Initialisation
Dynamic systems that are solved by numerical methods need to be initialised. The initial conditions act as a starting point for the simulation, from which the trajectory of the dynamic system is then calculated. In power systems, the initial conditions are typically based on a steady-state power flow solution. The key assumption is that prior to the start of the simulation, the system is operating at a steady-state equilibrium and all derivatives are zero.
Given the power flow results (voltages, currents and powers at each bus) and the assumption that all derivatives are zero, then all state variables can be initialised. For example, consider a 4th order machine model. The initial generator terminal voltage and current injections are taken directly from the power flow results. These values are used to compute the initial rotor angle and subsequently the generator voltage and current in the dq reference frame (Vd, Vq, Id and Iq). The state variables (d-axis and q-axis transient emfs) can then be calculated directly from the machine equations based on the assumption that all derivatives are zero, i.e.
The following models need to be initialised:
- Machines and sources, e.g. generators, grids, motors, etc
- Controllers, e.g. AVRs, governors, etc
All machine and source models have built-in equations for the initialisation of state and algebraic variables based on the initial power flow results. The initialisation equations are generally derived by re-arranging the machine equations with derivatives set to zero.
For the actual initialisation equations used in the machine models, please refer to the Machine Models reference page.
Controllers such as AVRs and governors need to be initialised by user-defined equations in the controller (*.dyn) file. There is a special section for setting the initialisation equations of state and signal variables (refer to the Controller page for more detail).
The order in which the initialisation routines are performed is important and is generally run as follows:
- Network equations (i.e. from power flow)
- Machines and sources
- Controllers