# Time Domain Simulations of Power Systems

From Open Electrical

In time domain simulations of power systems, a dynamic model is defined as any model that can be described by a set of differential-algebraic equations (DAE), commonly presented in the following form:

- [math] \dot{\boldsymbol{x}} = \boldsymbol{f}(\boldsymbol{x},\boldsymbol{y},\boldsymbol{p},t) \,[/math]

- [math] \boldsymbol{0} = \boldsymbol{g}(\boldsymbol{x},\boldsymbol{y},\boldsymbol{p},t) \,[/math]

where [math]\boldsymbol{x} \,[/math] is a vector of state variables

- [math]\boldsymbol{y} \,[/math] is a vector of algebraic variables
- [math]\boldsymbol{p} \,[/math] is a vector of constant or controllable parameters
- [math]t \,[/math] is time (an independent variable)
- [math]\boldsymbol{f}(.) \,[/math] are the differential equations
- [math]\boldsymbol{g}(.) \,[/math] are the algebraic equations