Optimal control theory approach for power grid EMP protection
A high altitude electromagnetic pulse (HEMP) or solar-geomagnetic disturbance (GMD) can introduce geomagnetically-induced currents (GICs) flowing through grounded power transformers that have the potential to severely impact the operation of large-scale electric power grids. A top-down mitigation design strategy considers grid-wide dynamic behavior during an HEMP/GMD event and uses optimal control theory to determine the compensation signals required to protect critical grid assets. As examples, the approach is applied to both a standalone transformer system, small power 3- and 4-bus systems, and large-power 20-bus system.
1 . An electric power grid, comprising:
at least one transformer comprising a transformer core and a transformer neutral, wherein a low frequency current pulse generates a magnetizing flux in the transformer core;
a blocking device comprising a voltage source providing a neutral-path control signal between the transformer neutral and ground; and
a flux-blocking device comprising a current source providing a magnetizing-path control signal to the transformer core;
wherein the neutral-path control signal and the magnetizing-path control signal are optimized to keep the magnetizing flux below a saturation limit in response to the low frequency current pulse.
2 . The electric power grid of claim 1 , wherein the transformer core is characterized by a nonlinear magnetizing inductance.
3 . The electric power grid of claim 1 , wherein the low frequency current pulse comprises a geomagnetically-induced current.
4 . The electric power grid of claim 1 , wherein the low frequency current pulse has a frequency of less than 1 Hz.
5 . The electric power grid of claim 1 , wherein the blocking device comprises a linear quadratic regulator or an optimized controller based on the saturation limit.
6 . The electric power grid of claim 1 , wherein the blocking device comprises a blocking capacitor.
7 . The electric power grid of claim 1 , wherein the at least one of the neutral-path and magnetizing-path control signals is optimized by minimizing an objective function, J, according to
min
x
(
t
)
,
u
(
t
)
J
=
∫
t
0
t
f
F
(
x
(
t
)
,
u
(
t
)
,
t
)
dt
such that,
x
˙
(
t
)
=
f
(
x
(
t
)
,
u
(
t
)
)
lb
≤
g
(
x
(
t
)
,
u
(
t
)
)
≤
u
b
where F is a cost function, {dot over (x)}=f(⋅) is a system dynamic equation, u(t) is the control signal, t f is a pulse interval, g(⋅) is the magnetizing flux lm, lb is a negative saturation limit, and ub is a positive saturation limit.
8 . The electric power grid of claim 1 , wherein the at least one transformer comprises a generator transformer and at least one load transformer, and wherein a low-frequency electromagnetic pulse is coupled to a transmission line connecting the generator transformer to the at least one load transformer.
9 . The electric power grid of claim 8 , wherein the at least one load transformer comprises two or more load transformers in parallel and wherein each of the load transformers has a separate blocking device and/or flux-blocking device providing a separate neutral-path control signal and/or magnetizing-path control signal for each of the load transformers.
10 . The electric power grid of claim 8 , wherein the at least one load transformer comprises two or more load transformers in parallel and wherein the neutral-path control signal and/or the magnetizing-path control signal from one of the load transformers is optimized to minimize transformer saturation at a system-level.