Transcript presentation

Kevin Kim
PENSA Summer 2011
Energy Markets: Overview
Demand
RTO
Energy Consumer
Supply
Power Generators
Schedule
Unit Commitment Problem
 How much demand do we need to meet tomorrow?
 How should we schedule our generators to meet 100%
of this demand?
 How do we minimize overages/shortages in energy?
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Challenge 1: Random Demand
 How much demand do we have to satisfy tomorrow?
 How should we schedule our power generators
tomorrow to meet this demand?
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Challenge 2: Generator Limitations
 Many plants take several hours to warm up before they
can be used.
 Some plants turn on quickly, but they’re much more
expensive and can’t generate as much power
Coal Plant
~10 hours to turn on.
~$50/MW
Maxed at ~500 MW
Natural Gas Plant
~0.1 hours to turn on
~$300/MW
Maxed at ~20 MW
Now, the biggest challenge….
WIND ENERGY
 Clean, renewable, and low cost/MW.
 However, wind is VOLATILE.
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Challenge 3: Random Supply
 With wind energy, part of our energy supply is also
random.
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Predicted wind
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Wind Energy: News
 Department of Energy
 Target of 20% wind
penetration by 2030
 Google
 $5 billion project to
build 350-mile cable on
the east coast to power
offshore wind farms.
We solve the unit commitment
problem with a math model….
Model: Basic Algorithm
Predict demand and wind for tomorrow (t=1).
2. Schedule generators based on these forecasts.
3. Now, at tomorrow (t=1), change the outputs of the
faster generators to correct for errors in forecast
4. Run the following cases and compare costs:
1.
1.
2.
3.
4.
5% wind penetration
20% wind penetration
40% wind penetration
60% wind penetration
Model: A Sneak Peek
min
𝑓𝑢𝑒𝑙
𝑡′
𝑖
(𝐶𝑖
∗ 𝑝𝑡,𝑡 ′,𝑖 )
𝑠. 𝑡 𝑝𝑡,𝑡 ′,𝑖 ≥ 𝑝𝑖𝑚𝑖𝑛 ∗ 𝑢𝑡,𝑡 ′,𝑖
𝑝𝑡,𝑡 ′,𝑖 ≤ 𝑝𝑖𝑚𝑎𝑥 ∗ 𝑢𝑡,𝑡 ′ ,𝑖
𝑜𝑛
𝑦𝑡,𝑡
′ ,𝑖
+
𝑜𝑓𝑓
𝑦𝑡,𝑡 ′,𝑖
𝑢𝑡,𝑡 ′,𝑖 − 𝑢
𝑜𝑛
𝑦𝑡,𝑡
′ ,𝑖 +
𝑜𝑓𝑓
𝑦𝑡,𝑡 ′,𝑖 +
…..…
≤1
𝑜𝑛
= 𝑦𝑡,𝑡
′ ,𝑖 +
min(𝑡 ′ +𝜏𝑖𝑜𝑛 −1,𝑇)
𝑡,𝑡 ′ −1,𝑖
𝑜𝑓𝑓
𝑦𝑡,𝑡 ′,𝑖
𝑜𝑓𝑓
𝑦𝑡,𝑡 ′′ ,𝑖 ≤ 1
𝑡 ′′ =1
𝑜𝑓𝑓
min(𝑡 ′ +𝜏𝑖 −1,𝑇)
𝑡 ′′ =𝑡 ′ +1
𝑜𝑛
𝑦𝑡,𝑡
′′ ,𝑖 ≤ 1
Sample Output
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Predicted wind
Actual Demand
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Total Actual Power
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The cost of randomness
What if we could predict wind…
What if wind were constant…
The reality
Future Work
 Reduce shortages in stochastic wind cases
 Reduce cost in stochastic wind cases.
 Analyze effects of offshore wind.