em p 08 iot energy systems analysis slides
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8/9/2019 EM P 08 IOT Energy Systems Analysis Slides
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Energy Management :: 2008/2009
Class # 8P
Process IOT - Energy Systems Modeling
João Parente
joao.parente@dem.ist.utl.pt
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Class # 8P :: Process IOT -Energy Systems Modeling Slide 2 of 53
Energy Systems Analysis using IOT (“ standard” formulation)
The specific consumption of each sub-product can be determined by:
c4 = cST + SST ⋅ c3 c4 = cST + SST⋅(f ST_1 ⋅ c1 + f ST_2 ⋅ c2 + f ST_3 ⋅ c3 + f ST_4 ⋅ c4 );
c3 = cSE + SSE ⋅ c2 c3 = cSE + SSE⋅(f SE_1 ⋅ c1 + f SE_2 ⋅ c2 + f SE_3 ⋅ c3 + f SE_4 ⋅ c4 );
c2 = cOV + SOV ⋅ c1 c2 = cOV + SOV⋅(f OV_1 ⋅ c1 + f OV_2 ⋅ c2 + f OV_3 ⋅ c3 + f OV_4⋅ c4 );
c1 = cRM+ 0 c1 = cRM + SRM⋅(f RM_1⋅ c1 + f RM_2 ⋅ c2 + f RM_3 ⋅ c3 + f RM_4⋅ c4 );
Thedimensionof [k] ismxm!!!!
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Class # 8P :: Process IOT -Energy Systems Modeling Slide 3 of 53
Energy Systems Analysis using IOT (“ standard” formulation)
In the specific case of our example:
(2) (3)
Losses Losses
(4) Final Product
Boundary
OVen SElection STorageRM(1)
Without recycling, every position in the matrix
diagonal and bellow is equal to 0 no backflow!
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Class # 8P :: Process IOT -Energy Systems Modeling Slide 5 of 53
PIO - Basic concepts
EXAMPLE: Simple energy system with 3 process and 3 products
By definition:
A14 = A24 = A34 = 0 (no product consumption in the energy process)*, and
A11 = A22 =A33 = A44 = 1 (if the final products of process A, B, and C are 1, 2, and 3),
Outputs are “positive” and inputs “negative” (in theactivitymatrix).
* Insome particular cases thisconditionmight not betrue!!!
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Class # 8P :: Process IOT -Energy Systems Modeling Slide 6 of 53
PIO – Mathematical formulation
EXAMPLE: Simple energy system with 3 process and 3 products
So, to determine the activity level required at each process to fulfill a specific final production:
[A]-1 ⋅ [Δa] = [ΔT]
If we wish to determine the activity level required to produce one unit of product 3:
[Δa] = [ 0 0 1 0]T
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Class # 8P :: Process IOT -Energy Systems Modeling Slide 7 of 53
IOT
PROBLEM 01
Consider the first company from last class, which produces aluminum profiles. The production process had the
following sequence:
In these conditions, indicate how you could determine the specific consumption of the painted profile, using theinput-output model (standard formulation) applied to processes. Clearly present the coefficients of the k matrix.
Extrusion
2
Reheat
Painting Treatment
REcycling
1
3
4
8
9
5
6
7
CE4=CEP +SPCE3+SPTCE7
CE7=CETCE3=CER+SRCE2
CE2=CEE+SE(f 1CE1+f 9CE9)
CE9=CERECE1=2 * CERE
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Class # 8P :: Process IOT -Energy Systems Modeling Slide 8 of 53
CPROD = CPROC + [K] 1 2 3 4 7 5 6 8 9 x CPROD
1 RM RM 1
2 E E 2
3 R R 3
4 P P 4
7 T T 7
5 RE'5
RE'5
5
6 RE'6
RE'6
6
8 RE'8
RE'8
8
9 RE RE 9
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Class # 8P :: Process IOT -Energy Systems Modeling Slide 9 of 53
CPROD = CPROC + [K] 1 2 3 4 7 5 6 8 9 x CPROD
1 RM RM 1
2 E E 2
3 R R 3
4 P P 4
7 T T 7
5 RE'5
RE'5
5
6 RE'6
RE'6
6
8 RE'8
RE'8
8
9 RE RE 9
CPROD
= CPROC
+ [K] 1 2 3 4 7 5 6 8 9 x CPROD
1 RM RM 0 0 0 0 0 0 0 0 0 1
2 E E f 1E
SE
0 0 0 0 0 0 0 f 9E
SE
2
3 R R 0 f 2RSR 0 0 0 0 0 0 0 3
4 P P 0 0 f 3P
SP
0 f t7P
StPT
0 0 0 0 4
7 T T 0 0 0 0 0 0 0 0 0 7
5 RE'5
RE'5
0 0 0 0 0 0 0 0 0 5
6 RE'6
RE'6
0 0 0 0 0 0 0 0 0 6
8 RE'8
RE'8
0 0 0 0 0 0 0 0 0 8
9 RE RE 0 0 0 0 0 f 5RE
SRE
f 6RE
SRE
f 7RE
SRE
0 9
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Class # 8P :: Process IOT -Energy Systems Modeling Slide 11 of 53
[K] 1 2 3 4 5 6 7 8 9 10 11RM
DC
CUP
CUT
RW
EW
F
PT
T
R'
R
CPROD = CPROC +* C
PROD
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Class # 8P :: Process IOT -Energy Systems Modeling Slide 12 of 53
[K] 1 2 3 4 5 6 7 8 9 10 11RM
DC
CUP
CUT
RW
EW
F
PT
T
R'
R
CPROD = CPROC +* C
PROD
[K] 1 2 3 4 5 6 7 8 9 10 11
RM 0 0 0 0 0 0 0 0 0 0 0
DC f 1DC
SDC
0 0 0 0 0 0 0 0 0 0
CUP 0 f 2CUP
SCUP
0 0 0 0 0 0 0 0 0
CUT f 1CUTSCUT 0 0 0 0 0 0 0 0 0 0
RW 0 0 0 f 4RW
SRW
0 0 0 0 0 0 0
EW 0 0 f 3EW
SEW
0 f5EW
SEW
0 0 0 0 0 f 11EW
SEW
F 0 0 0 0 0 f 6F
SF
0 0 0 0 0
PT 0 0 0 0 0 0 f 7PT
SPT
0 f t9PT
StPT
0 0
T 0 0 0 0 0 0 0 0 0 0 0R' 0 0 0 0 0 0 0 0 0 0 0
R 0 0 0 0 0 0 0 0 0 f 10R
SR
0
CPROD = CPROC + * CPROD
E M
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Class # 8P :: Process IOT -Energy Systems Modeling Slide 13 of 53
IOT
PROBLEM 03
Consider the first company from last class, which produces aluminum profiles. The production process had the
following sequence:
In these conditions, indicate how you could determine the specific consumption of the painted profile, using theprocess input-output model. Clearly present the coefficients of the activity matrix (A).
Extrusion
2
Reheat
Painting Treatment
REcycling
1
3
4
8
9
5
6
7
CE4=CEP +SPCE3+SPTCE7
CE7=CETCE3=CER+SRCE2
CE2=CEE+SE(f 1CE1+f 9CE9)
CE9=CERECE1=2 * CERE
E M t
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Class # 8P :: Process IOT -Energy Systems Modeling Slide 14 of 53
Solution Problem 03
E M t
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Class # 8P :: Process IOT -Energy Systems Modeling Slide 15 of 53
Solution Problem 03
E M t
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Class # 8P :: Process IOT -Energy Systems Modeling Slide 16 of 53
IOT
PROBLEM 04
Consider the second company from last class, which produces steel bottles to store gasses. The production
processhad thefollowingsequence:
In these conditions, indicate howyoucould determine thespecific consumption of the painted profile, using the
process input-output model. Clearlypresent thecoefficients of theactivity matrix (A).
RM
DC CUT
CUP RW
EW
F
PT T
R
Final product
1
2 4
3 5
6
7
8
9
10
11
CE8=CEPT+SPTCE7+SPT_TCEt9
CE7=CEF+SFCE6
CE6=CEEW+SEW(f 5CE5+f 3CE3+f 11CE11)
CE5=CERW+SRWCE4
CE4=CECUT+SCUTCE1
CE3=CECUP+SCUPCE2
CE2=CEDC+SDCCE1
CEt9=CEtT
CE11=CER=0
CE10=0
Energy Management
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Class # 8P :: Process IOT -Energy Systems Modeling Slide 17 of 53
Solution Problem 04
Energy Management
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Cl #8P P IOT E S t M d li Slid 18 f 53
Solution Problem 04
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