AnOptimizationModelin SupportofBiomassCoFiringin ... Regional Confer… · AnOptimizationModelin...

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An Optimization Model in Support of Biomass CoFiring in Coal Fired Power Plants Sandra D. Eksioglu, Hadi Karimi Industrial Engineering Department Clemson University Sun Grant Conference Feb. 2015 Auburn, AL

Transcript of AnOptimizationModelin SupportofBiomassCoFiringin ... Regional Confer… · AnOptimizationModelin...

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An  Optimization  Model  in  Support  of  Biomass  Co-­‐Firing  in  Coal  Fired  Power  Plants  

Sandra  D.  Eksioglu,  Hadi  Karimi    Industrial  Engineering  Department  Clemson  University  

Sun  Grant  Conference  Feb.  2015  Auburn,  AL  

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Outline  

I.  Motivations    II. Research  objectives  III.   Problem  description  

IV.   Optimization  model  formulation  V.   A  case  study  

VI.   Conclusions  and  future  research  

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Motivation  Co-­‐Ciring  biomass  is  an  attractive  renewable  energy  option:    

Ø  Increases  renewable  energy  without  major  capital  investments  and  investments  in  the  infrastructure  

Ø  Low  risk  option      

Ø   Reduces  emissions  of  CO2,  SO2  and  NO2  emissions  Ø  5%  (15%)  co-­‐Ciring  would  reduce  CO2  emissions  by  5.4%  (18.2%)    

Ø  Minimizes  waste  -­‐  such  as,  wood  waste,  agricultural  waste  -­‐  and  the  environmental  problem  associated  with  waste  disposal  

Ø  It  is  a  near  term  market  solution  for  biomass  

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Motivation  Renewable  electricity  generation  is  expected  to  increase  due  to  the  following  reasons  (EIA):    

Ø  Increasing  demand  for  electricity  Ø  Programs  encouraging  renewable  energy  use  (e.g.  PTC,  RPS  etc.)  

Ø  PTC:  An  income  tax  credit  of  2.3  cents/kilowa;-­‐hour  Ø  The  implementation  of  new  environmental  rules  dampens  future  

coal  use  (e.g.  Cross-­‐State  Air  Pollution  Rule  of  EPA)  

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20.00 40.00 60.00 80.00

100.00 120.00 140.00

2008 2012 2016 2020 2024 2028 2032 2036 2040

Gen

erat

ed E

lect

. (B

ill. K

wh)

Year

Renewable  electricity  generation  by  biomass    (Billion  kilowatt-­‐hours),  EIA,  2012  

Renewable electircity generated by biomass (Billion kilowatthours)

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Literature  review  Ø Currently,  40  of  560  coal-­‐Cired  power  plants  in  USA  co-­‐Cire  biomass.    

Ø Two  major  barriers  for  adopting  co-­‐Ciring  are:  o  Additional  plant  investment    costs  o  High  cost  of  biomass  transportation  and  inventory  holding              

Ø  The  literature  is  mainly  focused  on  analyzing  its  technological  and  economical  feasibility.  

Ø  There  are  no  studies  which  integrate  logistics  and  investment  decisions  in  coal-­‐Cired  power  plants.    

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Research  Objectives  Ø Develop  an  optimization  model  in  support  of  biomass  co-­‐Ciring  decisions  in  coal-­‐Cired  power  plants.    

 The  model  captures  the:  o  Additional  costs  and  savings  o  Loss  of  process  efCiciencies    due  to  co-­‐Ciring    

Ø Evaluate  the  impact  of  Production  Tax  Credit  (PTC)  on  renewable  electricity  production.        

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Decision  variables  o  𝑿↓𝒊𝒋   the  amount  of  biomass  (in  tons/year)  delivered  to  coal  plant  j  

from  supplier  i  Amount  of  biomass  needed  at  plant  j  is:  ∑𝑖∈𝑆↑▒𝑋↓𝑖𝑗      

o  𝑩↓𝒋   the  percentage  of  coal  displaced  in  plant  j  

o  𝒀↓𝒋     binary  variable  which  takes  the  value  1  if  𝐵↓𝑗   ≤4%  and  takes  

the  value  0  otherwise  

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A  Non-­‐Linear  Optimization  Model  

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Model  Formulation  Modeling  of  plant  efCiciency  loss  due  to  co-­‐Ciring  [1].      

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Coal  Pant  j:  𝑻𝑪↓𝒋   capacity      𝒇↓𝒋       plant  utilization    𝝆↓𝒋↑         efKiciency  

Heat  input   Electricity  output  

𝑸↓𝒋↑ = 𝑻𝑪↓𝒋 ∗𝒇↓𝒋 /𝝆↓𝒋↑    

𝑴↓𝒋↑𝒄𝒐𝒂𝒍 = 𝑸↓𝒋↑ ∗𝑶𝑯↓𝒋 ∗𝑪↑𝒘𝒃 /𝑳𝑯𝑽↓𝒋↑𝒄𝒐𝒂𝒍    

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Model  Formulation  cont.  Biomass  has  a  lower  heating  value  than  coal.    Let  ∆𝑴↓𝒋↑𝒄𝒐𝒂𝒍   be  the  amount  of    coal  displaced.    

 Energy  balance  equation:  𝑳𝑯𝑽↓𝒋↑𝒃𝒎 ∗∑𝐢∈𝑺↑▒𝑿↓𝒊𝒋  = 𝑳𝑯𝑽↓𝒋↑𝒄𝒐𝒂𝒍 ∗∆𝑴↓𝒋↑𝒄𝒐𝒂𝒍  The  amount  of  biomass  required  is:    

∑𝑖∈𝑆↑▒𝑋↓𝑖𝑗  =  ∆𝑴↓𝒋↑𝒄𝒐𝒂𝒍 𝑳𝑯𝑽↓𝒋↑𝒄𝒐𝒂𝒍 /𝑳𝑯𝑽↓𝒋↑𝒃𝒎    

The  efCiciency  loss  of  boilers  when  biomass  is  used  (Tillman  2000):      

𝑬𝑳↓𝒋   =  0.0044*𝐵↓𝑗↑2 +  0.0055 ∑𝑖∈𝑆↑▒𝑋↓𝑖𝑗  =∆𝑴↓𝒋↑𝒄𝒐𝒂𝒍 ∗𝑳𝑯𝑽↓𝒋↑𝒄𝒐𝒂𝒍 /𝑳𝑯𝑽↓𝒋↑𝒃𝒎  ∗𝝆↓𝒋↑𝒃 /𝝆↓𝒋↑𝒃 − 𝑬𝑳↓𝒋    

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Problem  Description  Plant  investment  costs  Ø  If  the  percentage  of  coal  displaced  is  𝐵↓𝑗   ≤4%,  capital  investment    $50/KWbm    (Caputo  et  al.  2005):  

𝐼↓𝑗↑𝐶𝐴𝑃 =50,000∗𝑀↓𝑗↑𝑏𝑚 /𝑀↓𝑗↑𝑐𝑜𝑎𝑙 −∆𝑀↓𝑗↑𝑐𝑜𝑎𝑙  𝑇𝐶↓𝑗 ∗𝑓↓𝑗 ∗𝐿𝐻𝑉↓𝑗↑𝑏𝑚 /𝐿𝐻𝑉↓𝑗↑𝑐𝑜𝑎𝑙  =  50,000∗ 𝑇𝐶↓𝑗 ∗𝑓↓𝑗 ∗𝐿𝐻𝑉↓𝑗↑𝑏𝑚 /𝐿𝐻𝑉↓𝑗↑𝑐𝑜𝑎𝑙  ∗𝐵↓𝑗   /1− 𝐵↓𝑗      =   𝑰↓𝒋↑𝒄𝒂𝒑 (𝑩↓𝒋   /𝟏− 𝑩↓𝒋    

)  

Ø  If   𝐵↓𝑗 >4%,  new  investments  required:  Biomass  storage:   𝐼↓𝑗↑𝑆 =136578∗(𝑇𝐶↓𝑗 ∗𝑓↓𝑗 ∗𝐿𝐻𝑉↓𝑗↑𝑏𝑚 /𝐿𝐻𝑉↓𝑗↑𝑐𝑜𝑎𝑙  ∗𝐵↓𝑗   /1− 𝐵↓𝑗    )↑0.5575 =   𝑰↓𝒋↑𝒔 ∗(𝑩↓𝒋   /𝟏− 𝑩↓𝒋    )↑𝟎.𝟓𝟓𝟕𝟓   Biomass  handling:   𝐼↓𝑗↑𝐻 =55780∗(𝑇𝐶↓𝑗 ∗𝑓↓𝑗 ∗𝐿𝐻𝑉↓𝑗↑𝑏𝑚 /𝐿𝐻𝑉↓𝑗↑𝑐𝑜𝑎𝑙  ∗𝐵↓𝑗   /1− 𝐵↓𝑗    )↑0.9554 =   𝑰↓𝒋↑𝒉 ∗(𝑩↓𝒋   /𝟏− 𝑩↓𝒋    )↑𝟎.𝟗𝟓𝟓𝟒   Compressors  and  driers:  𝐼↓𝑗↑𝐶𝐷 =13646∗(𝑇𝐶↓𝑗 ∗𝑓↓𝑗 ∗𝐿𝐻𝑉↓𝑗↑𝑏𝑚 /𝐿𝐻𝑉↓𝑗↑𝑐𝑜𝑎𝑙  ∗𝐵↓𝑗   /1− 𝐵↓𝑗    )↑0.5575 =𝑰↓𝒋↑𝑪𝑫 ∗(𝑩↓𝒋   /𝟏− 𝑩↓𝒋    )↑𝟎.𝟓𝟓𝟕𝟓   

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Problem  Description  Ø Operating  costs  

o  Biomass  purchase  cost:  ∑𝑖∈𝑆↑▒𝑐↓𝑖↑𝑏𝑚  𝑋↓𝑖𝑗↑     

o  Transportation  cost:  ∑𝑖∈𝑆↑▒𝑐↓𝑖𝑗↑  𝑋↓𝑖𝑗↑   

Ø Savings  o Coal  displacement  

  𝑆↓𝑗↑𝑝 = 𝑐↓𝑗↑𝑐𝑜𝑎𝑙 ∗∆𝑀↓𝑗↑𝑐𝑜𝑎𝑙 =  𝜎↓𝑗↑𝑝 *  ∑𝑖∈𝑆↑▒𝑋↓𝑖𝑗↑        

o Production  Tax  Credit  (PTC):  2.3  cents/KWhbm     𝑆↓𝑗↑𝑡𝑎𝑥 =23∗𝐿𝐻𝑉↓𝑗↑𝑏𝑚 /𝐶↑𝑤𝑏  ∗𝑀↓𝑗↑𝑏𝑚 =  𝜎↓𝑗↑𝑡 ∗  ∑𝑖∈𝑆↑▒𝑋↓𝑖𝑗↑      

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Biomass  market  price  $/ton  

Unit  transporting  cost  from  supplier  i  to  plant  j  

Coal  market  price  $/ton  

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Objective  function  •  𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒:𝑍=  ∑𝑗∈𝐶↑▒█■    ((  𝜎↓𝑗↑𝑝 + 𝜎↓𝑗↑𝑡 )  ∑𝑖∈𝑆↑▒𝑋↓𝑖𝑗  )                                                            −  ∑𝑖∈𝑆,𝑗∈𝐶↑▒(𝑐↓𝑖𝑗↑𝑡 + 𝑐↓𝑖↑𝑏𝑚 ) 𝑋↓𝑖𝑗    •                                                   −∑𝑗∈𝐶↑▒(𝐼↓𝑗↑𝑠 +   𝐼↓𝑗↑𝑐𝑑 )(1− 𝑌↓𝑗 )(𝐵↓𝑗   /1− 𝐵↓𝑗    )↑0.5575    

•                                                   −  ∑𝑗∈𝐶↑▒𝐼↓𝑗↑ℎ (1− 𝑌↓𝑗 )(𝐵↓𝑗   /1− 𝐵↓𝑗    )↑0.9554    •                                                   −  ∑𝑗∈𝐶↑▒█■𝐼↓𝑗↑𝑐𝑎𝑝 (𝐵↓𝑗   /1− 𝐵↓𝑗    )𝑌↓𝑗       

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Savings due to coal displacement and PTC

Biomass procurement and transportation costs

Storage and compressor- drier costs for Bj >4

Handling costs for Bj >4

Capital investments costs for Bj ≤4

A  Non-­‐Linear  Optimization  Model  

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A  Non-­‐Linear  Optimization  Model  Constraints   •  Subject  to:  

•                           ∑𝑗∈𝐶↑▒𝑋↓𝑖𝑗  ≤ 𝑠↓𝑖                                           for  all    𝑖∈𝑆    (1)  

•                           ∑𝑖∈𝑆↑▒𝑋↓𝑖𝑗  ≤     (𝑄↓𝑗↑0 ∗𝑂𝐻↓𝑗 ∗𝐶↑𝑤𝑏 ∗𝜌↓𝑗↑𝑏 )/ 𝐿𝐻𝑉↓𝑗↑𝑐𝑜𝑎𝑙 /(   1∕𝐵↓𝑗  − 𝛼↓𝑗 )∗(𝜌↓𝑗↑𝑏 −0.0044𝐵↓𝑗↑2   −  0.0055)               for  all    𝑗∈𝐶    (2)  

•                           𝐵↓𝑗 −0.04  ≤𝑀(1−   𝑌↓𝑗 )                                                              for  all    𝑗∈𝐶    (3)  

                                   0.04− 𝐵↓𝑗 <𝑀𝑌↓𝑗                                                                                             for  all    𝑗∈𝐶    (4)  

•                           𝑋↓𝑖𝑗   ∈   𝑅↑+                                                                         for  all    𝑖∈𝑆,  𝑗∈𝐶            (5)  

•                         𝐵↓𝑗   ∈[0,  1]                          for  all    𝑗∈𝐶                              (6)  •                          𝑌↓𝑗   ∈{0,  1}                for  all    𝑗∈𝐶    (7)  

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A  Linear  Optimization  Model  

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Consider  plant  j  could  displace  coal  (by  mass)  either  at  a  rate  of  Bj  =  1%,  or  2%,  or  3%,  etc.      

Let  l  =  1,  .  .  .  ,  |L|  index  the  set  of  all  potential  values  that  Bj  can  take.    Ll  denote  the  l−the  element  of  this  set      

Decision  variables:    𝒀↓𝑙𝒋     binary  variable  which  takes  the  value  1  if  facility  j  displaces   𝐿↓𝑙 = 𝐵↓𝑗 %  coal,  and  takes  the  value  0  otherwise      

𝑿↓𝒊𝒋   the  amount  of  biomass  (in  tons/year)  delivered  to  coal  plant  j  from  supplier  i    

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A  Linear  Optimization  Model  

15  

For  a  Cixed  value  of  Bj  :      𝑀↓𝑙𝑗↑𝑏𝑚   =  (𝑄↓𝑗↑0 ∗𝑂𝐻↓𝑗 ∗𝐶↑𝑤𝑏 ∗𝜌↓𝑗↑𝑏 )/ 𝐿𝐻𝑉↓𝑗↑𝑐𝑜𝑎𝑙 /(   1∕𝐵↓𝑗  − 𝛼↓𝑗 )∗(𝜌↓𝑗↑𝑏 −0.0044𝐵↓𝑗↑2   −  0.0055)         is  a  constant.      

∑𝑖∈𝑆↑▒𝑋↓𝑖𝑗  ≤     (𝑄↓𝑗↑0 ∗𝑂𝐻↓𝑗 ∗𝐶↑𝑤𝑏 ∗𝜌↓𝑗↑𝑏 )/ 𝐿𝐻𝑉↓𝑗↑𝑐𝑜𝑎𝑙 /(   1∕𝐵↓𝑗  − 𝛼↓𝑗 )∗(𝜌↓𝑗↑𝑏 −0.0044𝐵↓𝑗↑2   −  0.0055)         (2)    

∑𝑖∈𝑆↑▒𝑋↓𝑖𝑗  ≤∑𝑙∈𝐿↑▒𝑀↓𝑙𝑗↑𝑏𝑚 𝑌↓𝑙𝑗              for  all    𝑗∈𝐶      (2*)  

 

𝐼↓𝑙𝑗↑ = 𝑰↓𝒋↑𝒄𝒂𝒑 (𝑩↓𝒋   /𝟏− 𝑩↓𝒋    )      is  a  constant.  

∑𝑗∈𝐶↑▒∑𝑙∈𝐿↑▒𝐼↓𝑙𝑗↑ 𝑌↓𝑙𝑗↑       

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   •  𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒:𝑍=  ∑𝑗∈𝐶↑▒█■    ((  𝜎↓𝑗↑𝑝 + 𝜎↓𝑗↑𝑡 )  ∑𝑖∈𝑆↑▒𝑋↓𝑖𝑗  )                                                            −  ∑𝑖∈𝑆,𝑗∈𝐶↑▒(𝑐↓𝑖𝑗↑𝑡 + 𝑐↓𝑖↑𝑏𝑚 ) 𝑋↓𝑖𝑗    •                                                   −∑𝑗∈𝐶↑▒∑𝑙∈𝐿↑▒𝐼↓𝑙𝑗↑ 𝑌↓𝑙𝑗↑       

16  

Savings due to coal displacement and PTC

Biomass procurement and transportation costs

Investment costs

A  Linear  Optimization  Model  

Subject  to:                            ∑𝑗∈𝐶↑▒𝑋↓𝑖𝑗  ≤ 𝑠↓𝑖                                         for  all    𝑖∈𝑆        (1)                            ∑𝑖∈𝑆↑▒𝑋↓𝑖𝑗  ≤∑𝑙∈𝐿↑▒𝑀↓𝑙𝑗↑𝑏𝑚 𝑌↓𝑙𝑗      for  all    𝑗∈𝐶      

 (2*)              ∑𝑙∈𝐿↑▒𝑌↓𝑙𝑗  ≤1          for  all    𝑗∈𝐶        (8)                            𝑋↓𝑖𝑗   ∈   𝑅↑+                                     for  all    𝑖∈𝑆,  𝑗∈𝐶              (5)                             𝑌↓𝑙𝑗   ∈{0,  1}                for  all    𝑙∈𝐿,𝑗∈𝐶    (9)  

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A  Case  Study  

17  

Biomass  supply  in  the  state  of  Mississippi  [4]:  •  Knowledge  Discovery  Framework  (KDF)  •  Woody  biomass;  available  for  different  price  targets    

   

Truck  transportation  [5]:    •  Distance  Cixed  cost  (DFC):  $3.01/(tons)  •  Distance  variable  cost  (DVC):  $0.112/(tons  mile)    •  𝑐↓𝑖𝑗↑𝑡 =𝐷𝐹𝐶+𝐷𝑉∗𝑑↓𝑖𝑗   

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A  Case  Study  

18  

Coal  plants  data  [6]:  •  National  Energy  Technology  Laboratory  •  Power  plants  of  capacity  greater  than  1MW  

Plant  Name   Primary  Fuel   Fuel  Type   Nameplate  

Capacity  (MW)  Capacity  Factor  

Red  Hills   COAL   Lignite  coal   514    0.7213  

Henderson   COAL   Bituminous  coal   59    0.1078  

R  D  Morrow   COAL   Bituminous  coal   400    0.7281  

Victor  J  Daniel  Jr   COAL   Bituminous  coal   2,229    0.4986  

Jack  Watson   COAL   Bituminous  coal   1,216    0.3544  

Product   LHV  (BTU/Ton)  

Woody  biomass   16,811,000  

Bituminous  coal   22,460,600  

Lignite  coal   19,536,300  

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Solved  using  GAMS  and  BONMIN,  CPLEX  on  a  personal  computer.    Ø It  took  a  few  seconds  to  solve  all  the    problem  instances.  

     Ø Increasing  the  size  of  |L|  impacts  the  quality  of  the  solutions  found  from  LP  formulation.      

Numerical  Results  

19  

Relationship  between  the  size  of  set  |L|  and  the  quality  of  solutions  of  LP  formulation.  

0.00  

0.50  

1.00  

1.50  

2.00  

2.50  

3.00  

3.50  

0   10   20   30   40   50  

Gap    

|L|  

Relative  gap  between  NLP  and  LP  solutions    

$80/ton  

$100/ton  

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Ø Increasing  the  target  price  of  biomass  for  a  Cixed  PTC  of  2.3cents  /kwh  :  o  Market  price  ≤  $120/ton:    

o  ProKits  increase  since  savings  from  PTC  are  greater  than  the  additional  costs  from  investment  and  transportation  

o  Renewable  electricity  production  increases.    o  Market  price  >  $120/ton:    

o  Renewable  electricity  production  remains  constant.  

 

Numerical  Results  

20  

Relationship  between  biomass  price,  investment  costs,  logistics  costs,  proCits,  biomass  use.  

0.0  0.5  1.0  1.5  2.0  2.5  3.0  3.5  4.0  4.5  

0  20  40  60  80  100  120  140  160  180  

40   70   100   130   160   190  

Biom

ass  used  (1,000,000  tons)  

Prfots/Costs  ($1,000,000)  

Price  of  Biomass  ($/ton)  

Total  ProCits  

Investment  Costs  

Logsitic  Costs  

Biomass  Used  

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21  

0  

500  

1000  

1500  

2000  

2500  

3000  

3500  

4000  

-­‐100  

0  

100  

200  

300  

400  

500  

600  

700  

0   0.5   1   1.5   2   2.5   3   3.5   4  

Biom

ass  Usage  (1000  Tons)  

Total  ProKit  (M

illion  $)  

Tax  credit  (cents/kwh)  

Obj.  Fun.  Val  Tax  Saving  Logsitics  Costs    Used  Biomass  

The  impact  of  tax  credits  on  proCits  and  biomass  usage  for  biomass  target  price  of  $100/ton  

Ø  In  Mississippi:  CoCiring  not  proCitable    for  PTC  ≤𝟎.𝟕  cents/kwh  Ø  For  PTC  ≥  2.2  

o  Renewable  electricity  production  does  not  increase    o  ProCits  continue  increasing      

           

Numerical  Results  

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22  

The  impact  of  tax  credits  on  proCits  and  biomass  usage  for  biomass  target  price  of  $100/ton  

Ø  South  Carolina:  CoCiring  not  proCitable    for  PTC  ≤𝟐.𝟏  cents/kwh  Ø  For  PTC  ≥  2.6  

o  Renewable  electricity  production  does  not  increase    o  ProCits  continue  increasing      

Numerical  Results  

0  

500  

1000  

1500  

2000  

2500  

3000  

3500  

4000  

-­‐600  

-­‐400  

-­‐200  

0  

200  

400  

600  

800  

0   0.2   0.4   0.6   0.8   1   1.2   1.4   1.6   1.8   2   2.2   2.4   2.6   2.8   3   3.2   3.4  

Bio

mas

s use

d (1

000

Ton)

Tota

l pro

fit ($

1000

00)

Tax credit (¢/kwh)

Total  Profit  

Tax  Saving  

LogsiQcs  Costs    

Biomass  Used    

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Summary  of  Cindings  Ø  Tax  credits  necessary  to  increase  the  production  of  the  renewable  energy.    

 

Ø  Tax  credit  should  not  be  “one  size  Cits  all”.  PTC  could  be  a  function  of  the  amount  of  renewable  electricity  produced.    

 

Ø  Biomass  availability  in  the  USA  differs  by  region.  To  optimize  renewable  energy  production,  the  tax  rate  

should  be  customized  by  region.  

 

23  

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 Develop solution algorithms to solve the LP approximation model:  •  𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒:𝑍=  ∑𝑗∈𝐶↑▒█■    ((  𝜎↓𝑗↑𝑝 + 𝜎↓𝑗↑𝑡 )  ∑𝑖∈𝑆↑▒𝑋↓𝑖𝑗  )  −  ∑𝑖∈𝑆,𝑗∈𝐶↑▒(𝑐↓𝑖𝑗↑𝑡 + 𝑐↓𝑖↑𝑏𝑚 ) 𝑋↓𝑖𝑗   

•                                                   −∑𝑗∈𝐶↑▒∑𝑙∈𝐿↑▒𝐼↓𝑙𝑗↑ 𝑌↓𝑙𝑗↑       

24  

Current  Research  

Subject  to:                            ∑𝑗∈𝐶↑▒𝑋↓𝑖𝑗  ≤ 𝑠↓𝑖                                         for  all    𝑖∈𝑆        (1)                            ∑𝑖∈𝑆↑▒𝑋↓𝑖𝑗  ≤∑𝑙∈𝐿↑▒𝑀↓𝑙𝑗↑𝑏𝑚 𝑌↓𝑙𝑗      for  all    𝑗∈𝐶      

 (2*)              ∑𝑙∈𝐿↑▒𝑌↓𝑙𝑗  ≤1          for  all    𝑗∈𝐶        (8)                            𝑋↓𝑖𝑗   ∈   𝑅↑+                                     for  all    𝑖∈𝑆,  𝑗∈𝐶              (5)                             𝑌↓𝑙𝑗   ∈{0,  1}                for  all    𝑙∈𝐿,𝑗∈𝐶    (9)  

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Current  Research  Ø  Investigate  the  impact  of  tax  schemes  on  

renewable  electricity  production:  o  Tax  rate  as  a  function  of  biomass  usage  

o  Tax  rate  as  a  function  of  plant  capacity  

o  Tax  rate  as  a  function  of  biomass  available  in  the  region  

   

Ø  Initial  results:  

 

 25  

Tax rate

X

X

Tax Savings ($)

2.3 (cents/kwh) α

γ 2γ 3γ

nα ….

15  20  25  30  35  40  

0.4   0.5   0.6   0.7   0.8   0.9   1   1.1   1.2  

Biom

ass  used  x  

100,000  

Value  of  α    

Biomass  Used    (γ  =  250,000)  

The  unit  PTC  is    smaller  than  2.3/kwh  

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Future  Research  Ø  Consider  supply  chains  that  span  larger  regions.  In  this  case  the  in-­‐bound  supply  chain  will  have  a  hub-­‐and-­‐spoke  structure.  

 Ø Develop  models  which  optimize  costs  and  the  social  impacts  of  co-­‐Ciring:  Ø  Use  a  Stackelberg  game  model:  

Ø  Leader:  Decision  makers  at  the  federal  level  that  identify  a  PTC  structure  

Ø  Followers:  Coal  plants  that  decide  on  the  amount  of  coal  to  displace.  

Ø  The  goal  is  to  a  PTC  which  optimizes  the  social  beneCits  without  sacriCicing  power  plants  proCits.       26  

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Questions?    

27  

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References  [1]  De,  S.,  M.  Assadi.  2009.  Impact  of  cofring  biomass  with  coal  in  power  plants:  A  techno-­‐economic  assessment.  Biomass  and  Bioenergy,  Vol.  33,  283-­‐293.    

[2]  Sondreal,  E.A.,  S.A.  Benson,  J.P.  Hurley,  M.D.  Mann,  J.H.  Pavlish,  M.L.  Swanson.  2001.  Review  of  advances  in  combustion  technology  and  biomass  cofring.  Fuel  Process  Technology,  71  7-­‐38.    

[3]  Caputo,  A.C.,  M.  Palumbo,  P.M.  Pelagagge,  F.  Scacchia.  2005.  Economics  of  biomass  energy  utilization  in  combustion  and  gasiCication  plants:  effects  of  logistic  variables.  Biomass  and  Bioenergy,  Vol.  28,  35-­‐51.    

[4]  Knowledge  discovery  framework.  US  Department  of  Energy.  https://bioenergykdf.net.    

[5]  Searcy,  E.,  P.  Flynn,  E.  Ghafoori,  A.  Kumar.  2007.  The  relative  cost  of  biomass  energy  transport.  Applied  Biochemistry  and  Biotechnology,  Vol.137,  639-­‐652.    

[6]    National  Energy  Technology  Laboratory.  http://www.netl.doe.gov/energyanalyses/hold/technology.html.  

 

28  

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Ø Tax  credits  are  necessary  for  production  of  the  renewable  energy  o  For  Mississippi,  cents  0.7/kwh  is  a  lower  bound  on  PTC    

Ø Increasing  PTC  impacts  positively  the  amount  of  renewable  energy  produced  o  At  $100/ton:  When  PTC  is  less  than  cents  2.1/kwh,  only  some  of  the  available  biomass  is  used    

Numerical  Results  

29  

The  impact  of  tax  credit  and  targeted  price  on  biomass  usage.  

0  

500  

1000  

1500  

2000  

2500  

3000  

3500  

4000  

0   0.5   1   1.5   2   2.5   3   3.5   4  

Biom

ass  usage  (1000  Tons)  

Tax  credit  (cents/kwh)  

50  ($/Ton)  

60  ($/Ton)  

70  ($/Ton)  

80  ($/Ton)  

90  ($/Ton)  

100  ($/Ton)  

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 Develop solution algorithms to solve the LP approximation model:  •  𝑀𝑎𝑥𝑖𝑚𝑖𝑧𝑒:𝑍=  ∑𝑗∈𝐶↑▒█■    ((  𝜎↓𝑗↑𝑝 + 𝜎↓𝑗↑𝑡 )  ∑𝑖∈𝑆↑▒𝑋↓𝑖𝑗  )  −  ∑𝑖∈𝑆,𝑗∈𝐶↑▒(𝑐↓𝑖𝑗↑𝑡 + 𝑐↓𝑖↑𝑏𝑚 ) 𝑋↓𝑖𝑗   

•                                                   −∑𝑗∈𝐶↑▒∑𝑙∈𝐿↑▒𝐼↓𝑙𝑗↑ 𝑌↓𝑙𝑗↑       

30  

Current  Research  

Subject  to:                            ∑𝑗∈𝐶↑▒𝑋↓𝑖𝑗  ≤ 𝑠↓𝑖                                         for  all    𝑖∈𝑆        (1)                            ∑𝑖∈𝑆↑▒𝑋↓𝑖𝑗  ≤∑𝑙∈𝐿↑▒𝑀↓𝑙𝑗↑𝑏𝑚 𝑌↓𝑙𝑗      for  all    𝑗∈𝐶      

 (2*)              ∑𝑙∈𝐿↑▒𝑌↓𝑙𝑗  ≤1          for  all    𝑗∈𝐶        (8)                            𝑋↓𝑖𝑗   ∈   𝑅↑+                                     for  all    𝑖∈𝑆,  𝑗∈𝐶              (5)                             𝑌↓𝑙𝑗   ∈{0,  1}                for  all    𝑙∈𝐿,𝑗∈𝐶    (9)  

∑𝑖∈𝑆,𝑗∈𝐶↑▒█■   𝐶↓𝑖𝑗 𝑋↓𝑖𝑗     

Complicating constraints:

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 Lagrangean relaxation model:  

𝑀𝑎𝑥:𝑍↑𝜆 =∑𝑖∈𝑆,𝑗∈𝐶↑▒█■   𝐶↓𝑖𝑗 𝑋↓𝑖𝑗   −∑𝑗∈𝐶↑▒∑𝑙∈𝐿↑▒𝐼↓𝑙𝑗↑ 𝑌↓𝑙𝑗↑     +  ∑𝑖∈𝑆↑▒( 𝑠↓𝑖 −█■   𝐶↓𝑖𝑗 𝑋↓𝑖𝑗 )  λ↓𝑖     

31  

Current  Research  

Subject  to:                        ∑𝑖∈𝑆↑▒𝑋↓𝑖𝑗  ≤∑𝑙∈𝐿↑▒𝑀↓𝑙𝑗↑𝑏𝑚 𝑌↓𝑙𝑗      for  all    𝑗∈𝐶      

 (2*)              ∑𝑙∈𝐿↑▒𝑌↓𝑙𝑗  ≤1          for  all    𝑗∈𝐶        (8)                            𝑋↓𝑖𝑗   ∈   𝑅↑+                                     for  all    𝑖∈𝑆,  𝑗∈𝐶              (5)                             𝑌↓𝑙𝑗   ∈{0,  1}                for  all    𝑙∈𝐿,𝑗∈𝐶    (9)  

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 For a give facility j and a given set of multipliers  λ↓𝑖 :  

𝑀𝑎𝑥:𝑍↑𝑗𝜆 =∑𝑖∈𝑆↑▒(█■   𝐶↓𝑖𝑗 −  λ↓𝑖 )𝑋↓𝑖𝑗   −∑𝑗∈𝐶↑▒∑𝑙∈𝐿↑▒𝐼↓𝑙𝑗↑ 𝑌↓𝑙𝑗↑                 Theorem:  The  LP-­‐relaxa7on  of  this  problem  provides  the  op7mal  solu7on.    

Lemma:  In  an  op7mal  solu7on  to  this  problem  plants  receive  shipments  from  a  single                                  supplier.  

32  

Current  Research  

Subject  to:                        ∑𝑖∈𝑆↑▒𝑋↓𝑖𝑗  ≤∑𝑙∈𝐿↑▒𝑀↓𝑙𝑗↑𝑏𝑚 𝑌↓𝑙𝑗                                          (2)              ∑𝑙∈𝐿↑▒𝑌↓𝑙𝑗  ≤1                                  (8)                            𝑋↓𝑖𝑗   ∈   𝑅↑+                               for            𝑖∈𝑆          (5)                             𝑌↓𝑙𝑗   ∈{0,  1}                        for            𝑙∈𝐿        (9)  

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The  dual  of  Lagrangean  relaxa7on  model  can  easily  be  solved  using    a  simple  inspec7on  procedure:          𝐼𝑓:𝑚𝑎𝑥↓𝑖  {0, 𝐶↓𝑖𝑗 −  λ↓𝑖 } = 𝐶↓𝑖∗𝑗 −  λ↓𝑖∗ >0,  𝑡ℎ𝑒𝑛:         █■𝐼𝑓:𝑚𝑎𝑥 {0,   𝑚𝑎𝑥↓𝑙 {𝑀↓𝑙𝑗 (𝐶↓𝑖∗𝑗 −  λ↓𝑖∗ )− 𝐼↓𝑙𝑗 }} = 𝑀↓𝑙∗𝑗 (𝐶↓𝑖∗𝑗 −  λ↓𝑖∗ )− 𝐼↓𝑙∗𝑗 >0,  𝑡ℎ𝑒𝑛: ↓ 

      𝑌↓𝑙∗𝑗↑ =1;   𝑌↓𝑙𝑗↑ =0  𝑓𝑜𝑟  𝑙  ∈  L/{l*}  𝑋↓𝑖∗𝑗↑ =   𝑀↓𝑙𝑗 ;   𝑋↓𝑖𝑗↑ =0  𝑓𝑜𝑟  𝑖  ∈  I/{i*}

 We  are  working  on  fine  tuning  the  algorithm.         33  

Current  Research