Optimizing sizing of grid-scale batteries for frequency regulation services
Systems and methods for optimal sizing of one or more grid-scale batteries for frequency regulation service, including determining a desired battery output power for the one or more batteries for a particular period of time. A battery size is optimized for the one or more batteries for the particular period of time, and the optimizing is repeated using different time periods to generate a set of optimal battery sizes based on at least one of generated operational constraints or quality criteria constraints for the one or more batteries. A most optimal battery is selected from the set of optimal battery sizes.
1. A method implemented by a computer for optimal sizing of one or more grid-scale batteries for frequency regulation service, the method comprising:
by the computer iteratively repeating:
receiving frequency regulation signals at intervals of at least 4-seconds;
adjusting the received frequency regulation signals based upon a ±10 mHZ deadband such that any deviation less than ±10 mHZ is considered zero, wherein said adjusted signal is indicated by f reg (t);
determining for each 15 minute interval a desired battery output power for the one or more batteries for the at least 4-second time interval according to the following:
P desired 4sec ( t )=−5×8×( f reg ( t ));
wherein
P desired 4sec (t)>0=discharging signal, and if
P desired 4sec (t)<0=charging signal;
determining, for each 15-minute interval, P desired 15 min (t) a desired battery output power, from the separate averages of both the charging and discharging signals;
iteratively determining a minimum battery size for the one or more batteries according to an optimization of the following:
Min{size batt }:
subject to:
P
batt
(
t
)
=
P
regulation
(
t
)
-
P
deviation
(
t
)
soc
(
t
+
1
)
=
soc
(
t
)
-
P
batt
(
t
)
×
Δ
t
soc
min
%
×
size
batt
≤
soc
(
t
)
≤
soc
max
%
×
size
batt
}
,
representing operational constraints;
P
regulation
(
t
)
P
regulation
(
t
)
×
P
deviation
(
t
)
≤
0.4
×
P
regulation
(
t
)
Sign
(
P
deviation
(
t
)
)
=
(
Sign
P
regulation
(
t
)
)
Sign
(
P
batt
(
t
)
)
=
(
Sign
P
regulation
(
t
)
)
}
≡
P
batt
(
t
)
≥
0.6
×
P
regulation
(
t
)
,
representing quality criteria of active power change; and
P
regulation
(
t
)
-
0.8
≤
P
batt
(
t
)
-
P
50
Hz
≤
P
regulation
(
t
)
+
0.8
P
50
Hz
=
average
15
minutes
(
P
batt
)
-
average
15
minutes
(
P
regulation
)
}
,
representing quality criteria of the required active power;
wherein
P batt represents battery output power;
P regulation represents desired power to regulate frequency;
P deviation represents deviation of battery power from desired power;
soc represents state of charge;
size ban represents the battery size and
sign is the sign of the function;
and
generating based on the interative optimization a set of grid scale batteries that meet the determined minimal size; and
selecting a battery from the set of grid scale batteries that meet a most optimal battery size for a particular period of time.