Page 49 - Renewable Energy Devices and System with Simulations in MATLAB and ANSYS

36 Renewable Energy Devices and Systems with Simulations in MATLAB and ANSYS ®
®

The rate of change of rotational speed is dependent on torque balance of any spinning mass and
yields from

dω
T m − T e = I (2.7)
dt
where T and T are the mechanical and electrical torques, respectively. The stored kinetic energy
e
m
is often indicated as a proportional to its power rating (S rated ) and is called the inertia constant H(s)
as described by
1 Iω 2
H = 2 (2.8)
S rated
Consequently, the rate of speed/frequency change is given by

2
dω = ω ( T m − ) (2.9)
T e
dt 2 HS rated
and is expressed in per-unit as

dω ( P m − ) (2.10)
P e
=
dt 2 HS rated
in which P and P are the mechanical and electrical torques (in per-unit), respectively.
e
m
The equilibrium of a synchronous machine can therefore be perturbed if the mechanical or elec-
trical power is changed. For instance, in CSPs and due to the intermittent nature of solar energy
higher than the inertia constant, the mechanical and electrical outputs may fluctuate and conse-
quently affect the synchronous machine’s equilibrium. The higher the inertia constant, the higher the
system’s resistance is to abrupt changes [44].
2.4.4.2 Electrical Power
The electrical output of the single-machine infinite-bus model is given by (2.11), where the maxi-
mum electrical power (P max ) depends on the reactance (X ) of the transmission line interfacing the
eq
generator to the grid, the machine’s voltage (E), and the grid voltage (V). Hence, any change in one
of these parameters affects the system’s transient stability since the accelerative power described in
(2.10) becomes nonzero [42, 43]:

EV
P e = sinδ = P max sinδ (2.11)
X eq
where
P is the electrical torque in per-unit
e
X is the equivalent line reactance in per-unit
eq
E and V are the machine’s and grid voltage, respectively, in per-unit
P max and δ are the maximum electrical power and rotor angle, respectively, in per-unit
2.4.4.3 Mechanical Power
The mechanical power in a steam-based CSP plant is based on the pressure that drives the turbine.
The governor controller regulates the mechanical torque applied to the shaft of the generator by