Optimal energy management of a microgrid system using multi-objective optimization
View Patent ↗Systems and methods are disclosed to improve energy efficiency of a farm with livestock wastes by generating a cooling, heating, and power (CCHP) microgrid model; performing on a computer a multi-objective optimization to improve system efficiency of energy utilization and reduce environmental problems caused by animal wastes; and displaying results of the optimization for review.
1. A method to manage energy efficiency of a microgrid, comprising:
generating a comprehensive cooling, heating, and power (CCHP) microgrid model;
generating a model for converting organic waste to energy;
performing on a computer multi-objective optimization to manage system efficiency of energy utilization and reduce environmental problems caused by organic wastes and to optimize microgrid operation;
displaying results of the optimization for review;
modeling distributed energy resources and grid connections; and
modeling energy storage systems (ESS) as follows:
e
ess
,
t
=
(
1
-
φ
ess
)
e
ess
,
t
-
1
+
τ
(
p
ess
,
t
chg
η
ess
chg
-
p
ess
,
t
dch
η
ess
dch
)
,
where e ess,t , φ ess , and τ represent energy storage level at time t, energy loss, and the time interval in hours, respectively and p ess,t chg , η ess chg , p ess,t dch , and η ess dch represent charging and discharging power and efficiencies of the ESS, respectively;
wherein modeling operational and maintenance costs of ESS includes its degradation costs is assumed to be proportional to the number of charging and discharging cycles, as follows:
C ess,t =C ess dg ½( v ess,t chg +v ess,t dch )+τ C ess om Ē ess,t ,
where C ess om denotes constant maintenance costs and C ess dg represents degradation costs of the ESS per cycle which can be calculated based on the total number of charging and discharging cycles of the ESS from manufacturer data and its replacement costs, v ess,t chg and v ess,t dch represent start up flags for the charging and discharging modes, respectively, defined as follows:
v ess,t chg ≧u ess,t chg −u ess,t−1 chg ,
v ess,t dch ≧u ess,t dch −u ess,t−1 dch ,
where v ess,t chg and v ess,t dch represent start up flaps for the charging and discharging modes, respectively.
2. The method of claim 1 , comprising modeling stored energy within the ESS as limited by minimum and maximum State Of Charge, SOC and SOC , respectively, as follows:
SOC ess Ē ess ≦e ess,t ≦ SOC ess Ē ess ,
where Ē ess,t denotes maximum capacity of the ESS.
3. The method of claim 1 , comprising
modeling constraints where P ess,t chg and p ess,t dch are less than maximum charging and discharging power ratings of the ESS:
0≦ p ess,t chg ≦u ess,t chg P ess
0≦ p ess,t dch ≦u ess,t dch P ess
where, u ess,t chg and u ess,t dch are binary variables representing charging and discharging operation modes of the ESS.
4. The method of claim 1 , wherein the ESS is inoperative in charging and discharging modes simultaneously as follows:
u ses,t chg +u ses,t dch ≦1.
5. The method of claim 1 , comprising modeling one or more Internal Combustion Engines (ICEs).
6. The method of claim 1 , comprising modeling minimum and maximum power and heat output characteristics of Internal Combustion Engine (ICE) units are modeled as follows:
P i u i,t <p i,t < P i u i,t ,
H i u i,t <h i,t < H i u i,t ,
where p i,t , h i,t , and u i,t denote power and heat generation and On/Off state of ICE i at time t, respectively, P i and P i , and H i and H i represent upper and lower bounds of ICE's power and heat generation, respectively, wherein an operational region of the CHP units is limited by minimum and maximum Power to Hear Ratio (PHR), which is formulated as follows:
PHR i h i,t <p i,t < PHR i h i,t .
7. The method of claim 1 , comprising modeling minimum up-time and down-time characteristics of ICEs are formulated with constraints:
v i,t −w i,t =u i,t −u i,t−1 , ∀t ε [2 ,T]
v i,t +w i,t ≦1 , ∀t ε[ 2 ,T]
Σ s=t−UP i +1 t v i,s ≦u i,t , ∀t ε[UP i +1 ,T]
Σ s=t−DN i +1 t w i,s ≦1 −u g,t , ∀t ε[DN i +1 ,T]
where v i,t and w i,t are binary variables indicating start-up and shutdown of ICEs, respectively, UP i is the minimum up time of device g in hours, and DN i is the minimum down time of device i in hours.
8. The method of claim 1 , comprising modeling ramp up and ramp down characteristics of ICEs, which limit their power output change between two consecutive time intervals with constraints:
p i,t −p i,t−1 ≦ R i u i,t−1 +R i SU (1 −u i,t−1 ), ∀ t ε[ 2 ,T]
p i,t−1 −p i,t ≦ R i u i,t +R i SD (1 −u i,t ), ∀ t ε[ 2 ,T]
where R i and R i denote ramp up and ramp down limits of ICEs, respectively, and R i SU and R i SD denote these limits during start up and shutdown times.
9. The method of claim 1 , comprising modeling load sharing of a plurality of Internal Combustion Engines (ICEs).
10. The method of claim 1 , comprising modeling load in proportion to rated power with following constraints:
p
i
,
t
P
_
i
≤
r
+
(
1
-
u
i
,
t
)
M
,
∀
i
,
t
P
i
,
t
P
_
i
≥
r
+
(
u
i
,
t
-
1
)
M
,
∀
i
,
t
where r represents the per unit ratio of load sharing among the operating units, and M denotes a large positive number.
11. The method of claim 1 , comprising modeling operational and maintenance costs model of ICEs.
12. The method of claim 1 , comprising modeling Operational costs of ICEs at each time interval are approximated as a linear expression including fixed costs, fuel consumption costs considering a constant efficiency coefficient, and start up and shut down costs, as follows:
c
i
,
t
=
τ
(
A
i
+
B
i
p
i
,
t
+
h
i
,
t
η
i
+
C
i
om
p
p
,
t
)
+
v
i
,
t
C
i
SU
+
w
i
,
t
C
i
SD
where A i and B i denote the fuel cost coefficients, η i and C i m indicate overall efficiency and maintenance costs, and C i SU and C i SD represent start up and shut down costs of ICE units, respectively.
13. The method of claim 1 , comprising modeling micro turbines (MTs) operational costs as follows:
c
m
,
t
=
τ
(
A
m
+
B
m
p
m
,
t
+
h
m
,
t
η
m
+
C
m
com
P
_
m
)
+
v
m
,
t
C
m
SU
where m is the index representing MTs.
14. The method of claim 1 , comprising modeling Fuel Cells (FCs) operational costs as a linear expression including fuel consumption costs, startup costs and maintenance costs:
C
f
,
t
=
τ
(
B
f
p
f
,
t
+
h
f
,
t
η
f
+
C
f
om
P
_
f
)
+
v
f
,
t
C
f
SU
+
w
f
,
t
C
f
SD
,
where η f , C f SU , C f SD , and C f m denote overall efficiency, startup costs, shut down costs, and maintenance costs of FC f, respectively.
15. The method of claim 1 , comprising modeling thermal energy storage (TESs) including Heat Energy Storage (HES) and Cold Energy Storage (CES) is given as follows:
e
tes
,
t
=
(
1
-
φ
tes
)
e
tes
,
t
-
1
+
τ
(
h
tes
,
t
in
η
tes
in
-
h
tes
,
t
out
η
tes
out
)
where h tes,t in and h tes,t out denote amount of thermal energy injected to or extracted from the TES, respectively, lower and upper bunds on thermal energy exchange of TES are modeled as follows:
H tes u tes,t out <h tes,t out < H tes u tes,t out ,
H tes u tes,t in <h tes,t in < H tes u tes,t in ,
u tes,t in +u tes,t out ≦1,
TE tes <e tes,t < TE tes ,
where H tes , H tes , TE tes , and TE tes denote upper and lower limits of heat exchange rate and thermal energy capacity of the TES, respectively.
16. The method of claim 1 , comprising modeling Gas Boiler (GB) and Absorption Chiller for Cooling (ACC) efficiency using a Coefficient of Performance (COP) defined as follows:
COP
i
=
h
i
out
h
i
in
where h i out represents amount of desired output thermal energy (heat or cold for i=GB or i=ACC, respectively) and h i in denotes input energy and wherein minimum and maximum heat output characteristics of the DER units are modeled as follows:
H i u i,t <h i,t out < H i u i,t ,
and operational costs of the DER units are modeled using the following equation:
c
i
,
t
=
τ
(
B
i
h
i
,
t
out
COP
i
+
C
i
om
H
_
i
)
+
v
i
,
t
C
i
SU
+
w
i
,
t
C
i
SD
.
17. The method of claim 1 , comprising modeling Heat Exchangers (HE) and absorption refrigerator (AR).
18. The method of claim 1 , comprising modeling converters as follows:
p inv,t AC =η inv p inv,t DC
p con,t DC =η con p con,t AC
P inv u inv,t <p inv,t AC < P inv u inv,t ,
P con u con,t <p con,t AC < P con u con,t ,
where η inv and η con denote the conversion efficiency in inventor and converter modes, respectively, u inv,t and u con,t are binary variables denoting inverter (DC/AC) and converter (AC/DC) modes of operation, respectively, the converter should not operate in DC/AC and AC/DC modes simultaneously, which is modeled as follows:
u inv,t +u con,t ≦1.
19. The method of claim 1 , comprising modeling minimization of GHG emissions of a microgrid as follows:
min
∑
t
=
1
T
τ
[
∑
i
=
1
N
ICE
ɛ
i
GHG
p
i
,
t
η
i
+
∑
m
=
1
N
MT
ɛ
m
GHG
p
m
,
t
+
h
m
,
t
η
m
+
∑
f
=
1
N
FC
ɛ
f
GHG
p
f
,
t
+
h
f
,
t
η
f
+
∑
i
=
1
N
GB
ɛ
i
GHG
h
i
,
t
out
COP
i
+
∑
j
=
1
N
ACC
ɛ
i
GHG
h
j
,
t
out
COP
j
+
ɛ
Gr
,
t
GHG
p
Gr
,
t
]
min
∑
t
=
1
T
τ
[
∑
i
=
1
N
ICE
ɛ
i
GHG
p
i
,
t
η
i
+
∑
m
=
1
N
MT
ɛ
m
GHG
p
m
,
t
+
h
m
,
t
η
m
+
∑
f
=
1
N
FC
ɛ
f
GHG
p
f
,
t
+
h
f
,
t
η
f
+
∑
i
=
1
N
GB
ɛ
i
GHG
h
i
,
t
out
COP
i
+
∑
j
=
1
N
ACC
ɛ
i
GHG
h
j
,
t
out
COP
j
+
ɛ
Gr
,
t
GHG
p
Gr
,
t
]
where ε i GHG and ε Gr,t GHG denote GHG emissions rate of DER i and marginal GHG emissions of the grid at time t, respectively.