(b) Turbine-governor: Turbine-governors provide the mechanical power for generators and are modelled in detail in the package.
To simulate the forced oscillations, mechanical power of a generator is modulated with a sinusoidal signal in [17].
Since the mechanical power of one generator equals its electromagnetic power in steady state, that is {P}_{mathrm{m} i}^{mathrm{S}}={P}_{mathrm{e} i}^{mathrm{S}}={displaystyle sum_{k=1}^m{P}_{mathrm{G} j,mathrm{L} k}^{mathrm{S}}}+{P}_{mathrm{G} j,mathrm{L}mathrm{oss}}^{mathrm{S}} (12).
Apply Laplace transformation to the swing equation and assume the mechanical power input of generator does not change, i.e. ΔP m = 0 [21]: left{ begin{array}{l} sDelta delta (s) = varOmega_{0} Delta omega (s) hfill sDelta omega (s) = frac{1}{M}( - K_{1} Delta delta - K_{2} Delta omega - DDelta omega ) hfill end{array} right.
On the basis of that, it can quantify the contribution of the mechanical power of the generators, the load power and the transmission losses for the frequency deviation.
The power system frequency influencing factors are then constructed and applied to find the reasons of frequency decline and to quantify the contributions of the mechanical power of the generators, the load power and the transmission losses for the frequency deviation.
The reason is that, without compensation, there is a larger unbalance between the slowly varying mechanical power driving the generators and the instantaneously changing electrical power, which gets drastically reduced in proportion to the voltage reduction at node C, until the short circuit is cleared.
The mechanical power for an electric generator is usually obtained from a rotating shaft and is equal to the shaft torque multiplied by the rotational, or angular, velocity.
As a result the power output of the DFIG stabilizes which helps in maintaining the equilibrium between the electrical and mechanical power of the nearby generators.
In particular, a linearized model of the system and an LMI-based control design method are used to achieve frequency and voltage regulation subject to small perturbations to mechanical power inputs to synchronous generators in the system.
