Markov Jump Linear System Analysis of a Microgrid Operating in Islanded
and Grid Tied Modes
The analysis of power system dynamics is usually conducted using
traditional models based on the standard nonlinear differential
algebraic equations (DAEs). In general, solutions to these equations can
be obtained using numerical methods such as the Monte Carlo simulations.
The use of methods based on the Stochastic Hybrid System (SHS) framework
for power systems subject to stochastic behavior is relatively new.
These methods have been successfully applied to power systems subjected
stochastic inputs. This study discusses a class of SHSs referred to as
Markov Jump Linear Systems (MJLSs), in which the entire dynamic system
is jumping between distinct operating points, with different local
small-signal dynamics. The numerical application is based on the
analysis of the IEEE 37-bus power system switching between grid-tied and
standalone operating modes. The Ordinary Differential Equations (ODEs)
representing the evolution of the conditional moments are derived and a
matrix representation of the system is developed. Results are compared
to the averaged Monte Carlo simulation. The MJLS approach was found to
have a key advantage of being far less computational expensive.