EM P 08 IOT Energy Systems Analysis Slides

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

[email protected]


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Energy Management

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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Energy Management


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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Energy Management


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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Energy Management


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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Energy Management


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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Energy Management


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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Energy Management


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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Energy Management


[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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Energy Management


[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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Energy Management


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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Energy Management


Solution Problem 03

E M t


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Energy Management


Solution Problem 03

E M t


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Energy Management


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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Energy Management


Solution Problem 04

Energy Management


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Energy Management

Cl #8P P IOT E S t M d li Slid 18 f 53

Solution Problem 04

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EM P 08 IOT Energy Systems Analysis Slides

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