tmp_pdf_text.txt

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FORECAST-AWARE  ROLLING-HORIZON  OPTIMIZATION  FOR  CONSTRAINED  HYBRID  
WIND-STORAGE
 
DISPATCH
 
David  Valenta
1
 
North
 
Carolina
 
State
 
University
 
Raleigh,
 
NC,
 
USA
 
dvalent2@ncsu.edu
 
Chris  Qin
2
 
Washington
 
State
 
University
 
Vancouver,
 
WA,
 
USA
 
chris.qin@wsu.edu
  
ABSTRACT  Hybrid  wind  farms  can  either  sell  wind  power  immediately  or  store  energy  for  later  hours  when  market  value  may  be  higher.  The  hard  part  is  that  the  controller  must  make  those  decisions  before  future  wind  generation  and  electricity  prices  are  known.  This  paper  presents  a  forecast-aware  rolling-horizon  dispatch  framework  for  the  Pyron  wind  farm  case  study  using  raw  ERCOT  locational  marginal  price  data  and  compressed-air  energy  storage  assumptions  from  PNNL.  The  method  uses  causal  ridge  regression  to  predict  wind  power,  then  solves  a  constrained  mixed-integer  linear  program  in  Gurobi  to  choose  direct  wind  delivery,  charging,  discharging,  curtailment,  and  state  of  charge.  The  storage  model  enforces  wind-only  charging,  no  grid  charging,  grid  export  limits,  storage  power  limits,  state-of-charge  bounds,  no  simultaneous  charging  and  discharging,  and  chronological  state  carryover.  The  best  forecasting  model  achieved  21.24  MW  RMSE  and  13.62  MW  MAE  on  the  common  comparison  set.  The  best  deterministic  rolling-horizon  controller  used  a  48-hour  planning  window  and  reduced  COVE  by  6.25%  relative  to  baseload.  Adding  uncertainty-aware  forecast  scenarios  improved  the  best  tested  deployable  case  to  23.19%  COVE  reduction  and  30.19%  revenue  gain  over  baseload;  seven  scenarios  remained  close  at  23.03%  COVE  reduction.  The  perfect-information  oracle  upper  bound  reached  32.83%  COVE  reduction.  The  results  show  that  storage  value  depends  on  forecast  quality,  horizon  length,  scenario  design,  and  physical  constraints  together  rather  than  on  any  single  model  component.
 
[1,2,3,4,5]
 Keywords:  wind-storage  dispatch;  rolling  horizon;  mixed-integer  linear  programming;  ridge  regression;  ERCOT;  CAES;  COVE.  
1.  INTRODUCTION  A  wind  farm  with  storage  is  more  flexible  than  a  wind  farm  alone.  Without  storage,  wind  is  sold  when  it  is  generated.  With  storage,  part  of  the  wind  can  be  held  and  sold  later.  This  creates  a  planning  problem:  the  controller  has  to  decide  whether  energy  should  be  delivered  directly,  stored,  released,  or  curtailed.
 
[1,2]
 The  planning  problem  is  difficult  because  both  wind  generation  and  electricity  price  move  through  time.  A  perfect  future-knowing  optimizer  can  always  look  ahead  and  choose  the  best  hours.  A  real  controller  cannot  do  that.  It  must  use  forecasts,  update  the  battery  state  after  real  operation,  and  then  solve  again.
 
[5,6]
 This  paper  frames  the  project  as  a  ladder.  First,  the  forecast  model  is  tested  by  comparing  predicted  wind  power  to  realized  wind  power.  Second,  the  best  forecast  is  passed  to  a  deterministic  rolling-horizon  Gurobi  dispatcher.  Third,  the  dispatcher  is  upgraded  with  multiple  forecast  scenarios  to  account  for  uncertainty.  Finally,  an  oracle  case  is  reported  only  as  an  upper  bound,  not  as  a  realistic  controller.  
 Figure  1:  End-to-end  pipeline.  The  forecast  supplies  the  information,  Gurobi  solves  the  
dispatch
 
plan,
 
storage
 
carries
 
energy
 
across
 
time,
 
and
 
the
 
grid
 
receives
 
delivered
 
power.
 
 Figure  2:  Information  cases  used  in  the  paper.  Baseload  is  the  reference  case,  causal  and  
scenario
 
cases
 
are
 
realistic,
 
and
 
oracle
 
is
 
only
 
an
 
upper
 
bound.
 The  main  claim  is  therefore  not  that  one  fixed  horizon  always  wins.  The  main  claim  is  that  hybrid  wind-storage  dispatch  should  be  evaluated  as  an  information  system.  The  same  physical  battery  can  look  valuable,  weak,  or  nearly  optimal  depending  on  what  the  controller  knows  and  how  often  it  replans.  This  is  why  the  paper  reports  forecasting  accuracy,  deterministic  horizon  results,  scenario  results,  and  oracle  upper-bound  results  together.  
Table
 
1:
 
Paper
 
ladder
 
and
 
what
 
each
 
layer
 
changes.
 
Layer
 
Question
 
answered
 
Baseload
 
What  happens  if  the  farm  does  not  strategically  shift  
storage?
 
Forecast
 
model
 
Which  causal  model  predicts  wind  power  best  before  
dispatch?
 


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Rolling
 
horizon
 
How  far  should  Gurobi  look  ahead  with  imperfect  
forecasts?
 
Scenarios
 
Does  planning  over  several  plausible  futures  improve  
robustness?
 
Oracle
 
How  much  value  is  available  if  future  uncertainty  
disappeared?
 
2.  SYSTEM  AND  DATA  The  case  study  is  the  Pyron  wind  farm  in  West  Texas.  The  energy  value  is  computed  using  raw  ERCOT  locational  marginal  price  data,  where  LMP  is  the  market  price  in  USD/MWh  at  a  specific  grid  location  and  hour.  Storage  parameters  are  based  on  compressed-air  energy  storage  because  the  prior  storage  comparison  made  CAES  a  strong  candidate  for  long-duration  shifting.
 
[2,3]
 
Table
 
1:
 
Main
 
input
 
data
 
and
 
assumptions.
 
Item
 
Value
 
Wind
 
generation
 
Pyron
 
hourly
 
generation
 
Market
 
value
 
raw
 
ERCOT
 
LMP,
 
USD/MWh
 
Storage
 
type
 
CAES-equivalent
 
storage
 
Grid
 
export
 
limit
 
249
 
MW
 
Charging
 
source
 
wind
 
only
 
Optimizer
 
Gurobi
 
MILP
 
Comparison
 
point
 
baseload
 
Baseload  is  the  reference  case.  It  means  the  wind  farm  follows  a  fixed  direct-delivery  rule  without  strategic  storage  shifting.  Every  improvement  percentage  in  the  dispatch  sections  is  reported  relative  to  that  baseload  case.  The  paper  uses  revenue  and  COVE  in  a  careful  way.  Revenue  is  a  dollar  value  or  revenue  metric  produced  by  each  result  runner.  COVE  is  the  cost  of  valued  energy:  it  goes  down  when  more  energy  is  delivered  during  valuable  price  hours.  Because  the  deterministic  rolling-horizon  and  scenario  runners  store  revenue  on  different  reporting  scales,  the  safest  cross-proposal  comparison  is  the  percent  improvement  over  baseload  inside  each  block.  Within  each  block,  the  revenue  and  COVE  numbers  are  directly  comparable.  
 Figure  3:  Revenue  and  COVE  calculation.  Realized  delivered  power  and  raw  realized  
LMP
 
determine
 
hourly
 
value;
 
COVE
 
improves
 
when
 
valued
 
delivered
 
energy
 
increases.
 
3.  FORECASTING  LAYER  The  forecast  model  used  in  the  final  ladder  is  causal  ridge  regression.  Causal  means  the  model  only  uses  information  that  would  be  available  before  the  operating  hour.  Ridge  regression  is  a  linear  model  with  a  penalty  that  prevents  the  coefficients  from  becoming  too  large.  In  plain  terms,  it  learns  a  stable  relationship  between  recent  wind  behavior  and  future  wind  power.
 
[7,8]
 The  forecast  comparison  was  kept  separate  from  dispatch  so  the  first  question  could  be  answered  cleanly:  which  wind  power  model  gives  the  best  power  prediction?  The  causal  ridge  model  achieved  the  lowest  common-set  RMSE  at  21.24  MW  and  MAE  at  13.62  MW,  beating  lag-1  persistence,  a  power-curve  model,  and  the  earlier  diagnostic  prediction  files.  RMSE  means  root  mean  squared  error.  It  measures  how  far  the  prediction  is  from  the  actual  wind  power,  with  large  mistakes  punished  strongly.  MAE  means  mean  absolute  error.  It  measures  the  average  size  of  the  miss.  A  lower  RMSE  and  MAE  means  the  forecast  gives  Gurobi  a  better  picture  of  the  future.  
 Figure  4:  Forecast  methods  in  plain  terms.  The  final  dispatch  ladder  uses  causal  ridge  
because
 
it
 
had
 
the
 
strongest
 
common-set
 
forecast
 
accuracy.
 


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 Figure  5:  Forecast  model  RMSE  comparison.  The  causal  ridge  forecast  has  the  lowest  
error,
 
so
 
it
 
is
 
used
 
as
 
the
 
forecast
 
input
 
for
 
the
 
dispatch
 
experiments.
 
Table
 
2:
 
Forecast
 
methods
 
compared
 
before
 
dispatch.
 
Method
 
What
 
it
 
means
 
Causal
 
ridge
 
learns
 
from
 
past
 
wind/power
 
values
 
only;
 
no
 
future
 
leakage
 
Lag-1
 
persistence
 
assumes
 
the
 
next
 
value
 
is
 
close
 
to
 
the
 
most
 
recent
 
value
 
Power
 
curve
 
maps  wind  speed  to  power  using  a  fixed  physics-style  
curve
 
Prior
 
NQF/RNN
 
files
 
older  neural-network  diagnostic  outputs  used  only  as  
comparison
 
The  important  point  is  that  the  forecasting  experiment  is  not  a  dispatch  result  by  itself.  Forecasting  is  the  first  rung  of  the  ladder  because  it  decides  what  information  Gurobi  receives.  If  the  forecast  is  weak,  the  optimizer  can  still  produce  a  mathematically  valid  plan,  but  that  plan  may  be  valid  for  the  wrong  future.  
 Figure  6:  Train,  validation,  and  test  RMSE.  The  causal  ridge  model  stays  stable  across  
data
 
splits,
 
which
 
is
 
why
 
it
 
was
 
selected
 
for
 
the
 
dispatch
 
ladder.
 The  example  week  shows  the  practical  meaning  of  the  forecast  error.  The  model  usually  follows  the  broad  shape  of  the  wind,  but  it  cannot  know  every  sudden  jump  or  drop.  Dispatch  must  therefore  be  able  to  recover  from  missed  peaks,  missed  valleys,  and  wrong  timing.  
 Figure  7:  Example  week  of  actual  and  predicted  power.  The  forecast  follows  the  main  wind  pattern  but  still  misses  some  peaks  and  dips,  which  motivates  rolling-horizon  
replanning.
 
4.  DISPATCH  OPTIMIZATION  After  forecasting,  dispatch  is  solved  as  a  mixed-integer  linear  program.  Mixed-integer  means  some  variables  are  continuous,  such  as  MW  charged  or  discharged,  while  one  variable  is  binary,  meaning  storage  must  choose  a  mode.  The  model  cannot  charge  and  discharge  at  the  same  time.
 
[5,6,9]
 Revenue  =  sum_t  lambda_t  P_del(t)      (1)  COVE  =  Cost  /  sum_t  lambda_t  P_del(t)      (2)  SoC(t+1)  =  SoC(t)  +  eta  P_ch(t)  -  P_dis(t)      (3)  Revenue  is  computed  from  realized  delivered  power  multiplied  by  realized  raw  LMP.  COVE  is  lower  when  the  same  fixed  cost  is  supported  by  more  price-weighted  delivered  energy.  Therefore,  higher  revenue  and  lower  COVE  usually  point  in  the  same  direction,  but  COVE  is  the  main  storage-value  metric  used  for  comparison.  In  code  form,  the  calculation  is  simple:  for  each  hour,  the  simulator  records  delivered  power  after  the  storage  constraints  are  applied,  multiplies  that  realized  delivered  power  by  the  realized  hourly  price,  and  sums  the  result  over  the  test  period.  COVE  uses  the  same  realized  delivered  power  in  the  denominator,  weighted  by  price.  This  makes  the  metric  reward  energy  delivered  in  valuable  hours  more  than  energy  delivered  in  low-price  hours.  


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 Figure  8:  Constraint  summary.  These  rules  prevent  the  optimizer  from  creating  
physically
 
impossible
 
storage
 
behavior.
 
Table
 
3:
 
Key
 
decision
 
variables.
 
Variable
 
Meaning
 
P_dir(t)
 
wind
 
sent
 
directly
 
to
 
the
 
grid
 
P_ch(t)
 
wind
 
used
 
to
 
charge
 
storage
 
P_dis(t)
 
stored
 
energy
 
released
 
P_del(t)
 
total
 
delivered
 
power
 
SoC(t)
 
storage
 
energy
 
level
 
before
 
hour
 
t
 
u(t)
 
charge/discharge
 
mode
 
The  direct-wind  variable  is  important  because  not  all  wind  automatically  becomes  sold  energy.  Some  wind  may  be  used  to  charge  storage,  some  may  be  delivered  directly,  and  some  may  be  curtailed  if  the  plan  or  grid  limit  does  not  allow  it.  This  prevents  the  model  from  receiving  free  extra  revenue  during  realized  execution.  
5.  ROLLING-HORIZON  EXECUTION  A  rolling  horizon  solves  a  future  planning  window  but  executes  only  the  first  short  part  of  the  plan.  Then  the  real  battery  state  is  updated  and  the  problem  is  solved  again.  This  matters  because  forecasts  become  less  trustworthy  farther  into  the  future.  
 Figure  9:  One  rolling-horizon  step.  The  optimizer  solves  ahead,  executes  only  the  first  
step,
 
carries
 
the
 
realized
 
SoC
 
forward,
 
and
 
repeats.
 The  deterministic  rolling-horizon  sweep  tested  24,  48,  72,  and  168  hours  using  the  selected  causal  ridge  forecast.  The  best  deployable  deterministic  case  was  48  hours,  with  6.25%  COVE  reduction  and  $7.61M  in  the  reported  revenue  metric.  The  168-hour  case  was  worse  under  forecasts  because  it  optimized  too  far  into  uncertain  information.  This  is  the  main  mechanism  behind  the  rolling-horizon  result.  A  24-hour  horizon  is  sometimes  too  short  because  the  controller  cannot  see  enough  future  price  movement  to  justify  charging.  A  168-hour  horizon  sees  more  future  hours,  but  those  future  hours  are  forecasted  and  therefore  contain  more  error.  The  48-hour  case  was  the  best  compromise  in  the  deterministic  test.  
Table
 
4:
 
Deterministic
 
rolling-horizon
 
revenue
 
and
 
COVE.
 
Case
 
Revenue
 
COVE
 
COVE
 
gain
 
Baseload
 
$7.13M
 
7.274
 
0.00%
 
24
 
h
 
$7.38M
 
7.033
 
3.31%
 
48
 
h
 
$7.61M
 
6.819
 
6.25%
 
72
 
h
 
$7.59M
 
6.833
 
6.06%
 
168
 
h
 
$7.54M
 
6.878
 
5.44%
 


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 Figure  10:  Deterministic  rolling-horizon  result.  The  48-hour  window  performs  best  
because
 
it
 
looks
 
ahead
 
enough
 
to
 
use
 
storage
 
but
 
not
 
so
 
far
 
that
 
forecast
 
error
 
dominates.
 
 Figure  11:  Revenue  and  COVE  for  the  deterministic  rolling-horizon  proposal.  Compared  with  baseload,  48  hours  gives  the  best  COVE  reduction  and  highest  deterministic  rolling  
revenue
 
metric.
 
 Figure  12:  Deterministic  horizon  scorecard.  The  table-style  figure  reports  revenue,  
COVE,
 
and
 
COVE
 
gain
 
for
 
each
 
planning
 
horizon.
 
6.  SCENARIO-AWARE  DISPATCH  A  single  forecast  gives  one  future  path.  Scenario-aware  dispatch  gives  the  optimizer  several  plausible  futures.  The  purpose  is  not  to  predict  the  exact  future  perfectly.  The  purpose  is  to  choose  storage  actions  that  are  still  good  across  different  possible  wind  and  price  outcomes.
 
[10,11]
 
 Figure  13:  Scenario  logic.  The  shaded  band  represents  several  possible  futures  around  a  
middle
 
forecast;
 
the
 
optimizer
 
chooses
 
actions
 
that
 
work
 
well
 
across
 
the
 
band.
 The  scenario  sweep  tested  1,  3,  5,  7,  and  10  scenarios  using  the  selected  forecast  and  a  48-hour  planning  window.  The  best  tested  result  was  the  three-scenario  case:  30.19%  revenue  gain  and  23.19%  COVE  reduction  over  baseload.  The  seven-scenario  case  was  very  close  at  29.92%  revenue  gain  and  23.03%  COVE  reduction.  Ten  scenarios  performed  worse  because  the  controller  became  too  conservative  and  missed  some  valuable  dispatch  opportunities.  
Table
 
5:
 
Scenario
 
cases
 
tested.
 
Case
 
Purpose
 
1
 
scenario
 
single
 
forecast
 
path
 
3
 
scenarios
 
small
 
uncertainty
 
band;
 
best
 
tested
 
5
 
scenarios
 
adds
 
more
 
high/low
 
combinations
 
7
 
scenarios
 
larger
 
uncertainty
 
set;
 
nearly
 
tied
 
with
 
best
 
10
 
scenarios
 
widest
 
tested
 
set;
 
became
 
too
 
conservative
 
Table
 
6:
 
Scenario
 
revenue
 
and
 
COVE.
 
Case
 
Revenue
 
COVE
 
COVE
 
gain
 
Baseload
 
$271.87M
 
0.216
 
0.00%
 
1
 
$337.32M
 
0.174
 
19.40%
 
3
 
$353.95M
 
0.166
 
23.19%
 
5
 
$353.12M
 
0.166
 
23.01%
 
7
 
$353.22M
 
0.166
 
23.03%
 
10
 
$341.86M
 
0.172
 
20.47%
 


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More  scenarios  do  not  automatically  mean  better  performance.  A  small  number  of  scenarios  can  protect  the  plan  against  obvious  forecast  misses.  Too  many  scenarios  can  make  the  plan  hedge  against  extreme  cases  that  do  not  occur  often  enough  to  justify  the  lost  revenue.  
 Figure  14:  Scenario  count  comparison.  Three  scenarios  produced  the  best  tested  COVE  
result;
 
seven
 
scenarios
 
was
 
nearly
 
tied,
 
while
 
ten
 
scenarios
 
over-hedged.
 
 Figure  15:  Revenue  and  COVE  for  the  scenario  proposal.  Scenario  dispatch  beats  
baseload
 
in
 
both
 
revenue
 
and
 
COVE,
 
with
 
the
 
strongest
 
tested
 
case
 
at
 
three
 
scenarios.
 
 Figure  16:  Scenario  scorecard.  The  table-style  figure  compares  revenue  gain  and  COVE  
gain
 
for
 
the
 
tested
 
scenario
 
counts.
 
 Figure  17:  Revenue-COVE  tradeoff.  Points  farther  up  and  to  the  right  improve  both  
revenue
 
and
 
COVE
 
relative
 
to
 
baseload.
 


--- PAGE 7 ---

 Figure  18:  Representative  week  for  the  best  scenario  case.  The  bottom  panel  shows  
chronological
 
state
 
of
 
charge
 
staying
 
inside
 
the
 
storage
 
limits.
 
7.  ORACLE  UPPER  BOUND  The  oracle  case  gives  Gurobi  the  realized  future  wind  and  realized  future  price.  This  is  not  a  real-life  controller  because  it  knows  the  future.  It  is  included  only  to  show  the  upper  bound:  how  much  value  would  be  available  if  forecast  error  disappeared.  The  oracle  result  increased  as  the  horizon  grew.  The  best  oracle  case  used  a  168-hour  horizon  and  reached  32.83%  COVE  reduction  over  baseload.  This  is  the  ceiling  that  the  realistic  causal  controllers  are  trying  to  approach.  
Table
 
7:
 
Oracle
 
upper-bound
 
revenue
 
and
 
COVE.
 
Case
 
Revenue
 
COVE
 
COVE
 
gain
 
Baseload
 
$7.13M
 
7.274
 
0.00%
 
24
 
h
 
$9.95M
 
5.215
 
28.30%
 
48
 
h
 
$10.39M
 
4.995
 
31.32%
 
72
 
h
 
$10.55M
 
4.921
 
32.35%
 
168
 
h
 
$10.62M
 
4.885
 
32.83%
 
The  oracle  behaves  differently  from  the  causal  case.  When  the  future  is  known  exactly,  a  longer  planning  window  is  helpful  because  there  is  no  forecast  error  penalty.  This  is  why  168  hours  is  best  for  oracle  but  not  best  for  the  realistic  deterministic  rolling  case.  
 Figure  19:  Oracle  upper-bound  horizon  sweep.  Longer  look-ahead  helps  when  the  future  
is
 
known
 
exactly.
 
 Figure  20:  Revenue  and  COVE  for  the  oracle  proposal.  The  oracle  is  not  deployable,  but  
it
 
gives
 
a
 
useful
 
ceiling
 
for
 
what
 
perfect
 
information
 
could
 
achieve.
 
 Figure  21:  Final  project  ladder.  Forecasting  supplies  the  input,  rolling  horizon  improves  deterministic  dispatch,  scenarios  improve  uncertainty  handling,  and  oracle  gives  the  
non-deployable
 
upper
 
bound.
 


--- PAGE 8 ---

 Figure  22:  Compact  scorecard  of  the  main  results.  Each  rung  answers  a  different  
question
 
in
 
the
 
project.
 
8.  DISCUSSION  The  results  explain  why  optimization  alone  is  not  enough.  Gurobi  can  solve  the  mathematical  problem  very  well,  but  it  can  only  optimize  the  information  it  is  given.  If  the  forecast  is  wrong,  a  longer  horizon  can  make  the  optimizer  confidently  plan  around  the  wrong  future.  This  is  why  the  deterministic  48-hour  horizon  beat  the  168-hour  horizon  under  causal  forecasts.  The  scenario  controller  helped  because  it  reduced  dependence  on  one  exact  forecast  path.  Instead  of  assuming  one  future,  it  considered  several  plausible  futures  and  selected  actions  that  were  less  fragile.  The  result  was  a  large  jump  from  6.25%  COVE  reduction  in  the  deterministic  rolling  case  to  23.19%  in  the  best  scenario  case.  The  gap  between  the  best  scenario  result  and  the  oracle  result  is  also  meaningful.  The  oracle  upper  bound  was  32.83%,  while  the  best  deployable  scenario  case  was  23.19%.  That  remaining  gap  is  the  value  of  better  forecasting,  better  scenario  calibration,  and  potentially  better  price  uncertainty  modeling.  A  reviewer  should  read  the  three  main  dispatch  numbers  as  different  information  cases,  not  as  contradictory  results.  Baseload  is  the  lower  comparison  point.  The  48-hour  causal  rolling  result  is  the  best  deterministic  forecast  case.  The  three-scenario  result  is  the  best  tested  uncertainty-aware  causal  case.  The  oracle  is  the  future-knowing  upper  bound  and  is  not  deployable.  
Table
 
8:
 
Main
 
ladder
 
results.
 
Layer
 
Best
 
result
 
Forecast
 
causal
 
ridge,
 
21.24
 
MW
 
RMSE
 
Rolling
 
horizon
 
48
 
h,
 
6.25%
 
COVE
 
reduction
 
Scenarios
 
3
 
scenarios,
 
23.19%
 
COVE
 
reduction
 
Seven-scenario
 
check
 
23.03%
 
COVE
 
reduction
 
Oracle
 
upper
 
bound
 
168
 
h,
 
32.83%
 
COVE
 
reduction
 
The  most  important  practical  result  is  that  the  scenario  method  closes  part  of  the  gap  between  deterministic  causal  control  and  the  oracle  
upper  bound.  The  deterministic  causal  controller  reached  6.25%  COVE  reduction.  The  best  scenario  case  reached  23.19%.  The  oracle  reached  32.83%.  This  means  uncertainty  handling  captured  a  large  fraction  of  the  value  that  was  unavailable  to  a  single-forecast  controller.  The  remaining  gap  is  not  a  failure  of  Gurobi.  It  is  mainly  an  information  gap.  The  optimizer  can  only  act  on  the  forecast  distribution  it  receives.  If  the  scenario  set  misses  the  true  high-price  or  high-wind  event,  the  plan  may  still  charge  or  discharge  at  the  wrong  time.  This  is  why  future  work  should  focus  on  calibrated  probabilistic  forecasting  rather  than  simply  adding  more  solver  complexity.  
 Figure  23:  Gap  to  the  oracle  upper  bound.  Scenario-aware  dispatch  closes  much  more  of  
the
 
available
 
value
 
than
 
the
 
single
 
deterministic
 
rolling-horizon
 
controller.
 
9.  WHY  THE  RESULT  HAPPENS  The  mechanism  can  be  explained  with  one  example.  Suppose  the  forecast  says  that  price  will  rise  tomorrow.  A  deterministic  optimizer  may  charge  today  and  wait.  If  the  price  spike  does  not  happen,  that  stored  energy  may  be  released  at  a  worse  time.  A  rolling  horizon  helps  because  the  controller  can  correct  the  plan  when  tomorrow  gets  closer.  A  scenario  controller  helps  even  more  because  it  does  not  trust  only  one  version  of  tomorrow.  The  best  scenario  count  was  not  the  largest  scenario  count.  Three  scenarios  performed  best  because  they  gave  the  optimizer  a  useful  low-middle-high  picture  without  making  it  defend  against  too  many  unlikely  paths.  Seven  scenarios  was  close,  which  suggests  that  moderate  uncertainty  modeling  is  useful.  Ten  scenarios  did  worse  because  the  plan  became  too  careful  and  reduced  valuable  discharge  activity.  This  result  is  important  for  hybrid  wind  farms  because  storage  dispatch  is  mostly  a  timing  problem.  The  storage  device  does  not  create  new  wind.  It  changes  when  wind  energy  is  sold.  Therefore,  the  controller  wins  when  it  moves  energy  from  low-value  hours  into  high-value  hours  while  respecting  storage  limits.  Forecast  error  directly  damages  this  timing  decision.  


--- PAGE 9 ---

 Figure  24:  Simple  mechanism  map.  Forecasting,  rolling  replanning,  scenarios,  and  
constraints
 
work
 
together
 
to
 
produce
 
more
 
valued
 
delivered
 
energy.
 
10.  LIMITATIONS  The  results  should  be  interpreted  as  a  constrained  historical  backtest,  not  as  a  guarantee  of  future  market  performance.  The  controller  was  evaluated  on  the  available  Pyron  and  ERCOT  historical  series.  Market  rules,  congestion  patterns,  turbine  behavior,  and  storage  cost  assumptions  can  change  over  time.  The  scenario  construction  used  a  practical  residual-based  design.  That  was  enough  to  show  the  value  of  uncertainty-aware  dispatch,  but  a  publishable  next  step  would  calibrate  the  scenarios  more  formally  using  quantile  regression,  conformal  prediction,  or  another  probabilistic  forecasting  method.  That  would  let  the  paper  state  not  only  that  scenarios  help,  but  also  whether  the  scenario  band  has  statistically  correct  coverage.  The  paper  also  reports  COVE  as  a  valued-energy  metric  rather  than  a  full  project-finance  model.  A  full  techno-economic  analysis  would  include  capital  cost,  operations  and  maintenance,  storage  lifetime,  degradation,  taxes,  financing  assumptions,  and  market  participation  rules.  Those  items  are  outside  the  main  claim  here,  which  is  about  forecast-aware  dispatch  structure  under  fixed  storage  assumptions.  
11.  CONCLUSION  This  paper  developed  a  forecast-aware  optimization  ladder  for  hybrid  wind-storage  dispatch.  The  main  lesson  is  that  the  best  controller  is  not  just  the  best  forecaster  and  not  just  the  best  optimizer.  It  is  the  best  pairing  of  forecast  information,  rolling-horizon  execution,  uncertainty  representation,  and  physical  storage  constraints.  For  the  Pyron  wind-storage  case,  the  causal  ridge  model  gave  the  best  tested  wind  power  forecast,  the  48-hour  rolling  horizon  gave  the  best  deterministic  causal  dispatch  result,  and  the  three-scenario  uncertainty-aware  controller  gave  the  best  tested  deployable  COVE  reduction.  The  oracle  result  shows  that  more  value  is  theoretically  available,  but  only  if  future  information  improves.  
ACKNOWLEDGMENTS  The  author  thanks  Dr.  Chris  Qin,  Nora  Hosseiniimeni,  Zach  Lawrence,  and  Jessica  Yao  for  guidance,  prior  project  materials,  and  discussions  that  helped  shape  the  storage  constraints  and  comparison  structure.  
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