Peak Shaving and Price Saving

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Peak Shaving and Price Saving
Algorithms for self-generation
David Craigie ____________________________________
___________________Supervised by Prof. Andy
Philpott Dr Golbon Zakeri
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Today
1/25

• Demand side management
• Contracting Self-Generation
• The Peak Shaving Problem
• The Peak Shaving Algorithm
• Example using UoA demand data
• The stochastic problem
• Conclusions
• Future Work
• Questions

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Demand Side Management
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• Conservation
• Load Shifting
• Contracting
• Self-Generation

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Contracting Self-Generation
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• CFDs dont alter optimal self-generation
  strategy
• Charge (in period t)
• where dt demand realised in period t
• pt spot market price in period t
• dc swap volume
• pc strike price
• (based on Mercury Energys Swap Contracts)

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The Peak Shaving Problem
4/25

• The deterministic peak shaving problem can be
  stated
• Given a load profile, price profile and a
  capacity of generation, find the optimal
  allocation of a limited quantity of generator
  fuel with a sunk cost in order to minimize the
  cost of electricity consumption.
• Or
• Allow for an unlimited amount of fuel but at a
  given unit cost. However, the algorithm is the
  same in either case, only the stopping criterion
  changes.

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The Peak Shaving Problem

• Objective
• where
• di demand in period i MWh
• pi spot market price in period i /MWh
• si fuel used in period i L
• e generator efficiency MWh/L
• c maximum demand charge /MWh
• N number of periods
• md average of m highest load realisations
  during N MWh
• By setting e 1 and removing constant terms

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• Constraints
• (i) Total fuel allocation cannot exceed available
  quantity
• (ii) Fuel allocation in any period cannot exceed
  generator capacity
• (iii) The maximum demand quantity must be equal
  to the greatest sum of m demands after
  generation
• where Mi is the set giving the ith way of
  choosing m periods from a
• possible N.

The Peak Shaving Problem
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The Peak Shaving Algorithm
7/25

• The combinatorial number of maximum demand
  constraints makes the Peak Shaving Problem
  intractable for the RSM.
• However, we can use a greedy algorithm that will
  give the same solution as the RSM but without the
  computational cost.
• At every iteration the algorithm will choose a
  period to allocate fuel to that will give the
  maximum savings. It will cease allocation to that
  period when either capacity of the generator is
  reached, fuel supply is exhausted or savings need
  to be recalculated.

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Peak Shaving Example
8/25

• Suppose we will be charged for the average of
  the highest 2 load realizations in the following
  five period demand profile, at a rate of 30/MWh
• p172 p268 p360 p465
  p585 /MWh
• Initial Cost 15(1211)
  3,317

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Peak Shaving Example
9/25

• Suppose we have 16MWh worth of fuel, but the
  capacity in any one period is 4MWh. We seek the
  allocation of fuel among the 5 periods that will
  obtain the greatest savings
• Iteration 1
• Decision Allocate 4MWh to period 5 (12MWh
  remaining)

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Peak Shaving Example
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• Iteration 2
• Decision Allocate 1MWh to period 4 (11MWh
  remaining)
• Current Load Profile

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Peak Shaving Example
11/25

• Iteration 3
• Saving for 2,4 1/2 x (68 65) 1/2 x 15
• Decision Allocate 2MWh to period 3 (9MWh
  remaining)

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Peak Shaving Example
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• Iteration 4
• Saving for 2,3,4 1/3 x (68 65 60) 2/3
  x 15
• In general the savings from an n-period MD set
  tie are
• 1/n x (p1 p2 pn) (n-1/n) x c
• Thus the best tie to consider will be the
  highest priced n periods where n maximizes the
  above expression
• Decision Allocate 2MWh to periods 2,3 and 4
  (3MWh remaining)

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Peak Shaving Example
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• Iteration 5
• Decision Allocate 1MWh to periods 2 and 4 (1MWh
  remaining)
• Iteration 6
• Decision Allocate 1MWh to period 1 - STOP

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Peak Shaving Example
14/25

• Before
• Cost 3,317
• After
• Cost 2,081

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UoA Example
15/25

• Using demand data from 18 Symonds St
  (Engineering Building) for the month of August
  (1488 periods) and price data from OTA reference
  node.
• Using a 100kW generator at 3.6kWh/L with 14000L
  of fuel. Maximum demand charge of 8/kWh
  multiplied by the average of the 10 highest load
  realisations.
• Before 36,164 After 32,102

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Dual Simplex Approach
16/25

• We can solve a relaxed version of the LP by
  removing all the maximum demand constraints. This
  solution will (most likely) be infeasible in the
  original problem, but we know at least one of the
  constraints it violates, so we can add that
  constraint and resolve using the Dual Simplex
  Algorithm.
• We continue to add constraints until they cease
  to change the solution. By doing this we will
  obtain all the binding constraints from the
  optimal solution of the original problem.
• Depending on how many of the maximum demand
  constraints are binding in the optimal solution
  of the original LP, this may be a faster
  approach.

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Dual Simplex Approach

• Iteration 1
• Iteration 2
• Iteration 3
• etc

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• Scenario tree for prices (3 periods only)

Stochastic Problem
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• N 3, m 2. Complete Stochastic LP
  formulation

Stochastic Problem
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Stochastic Problem
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• Use Dual Simplex approach
• Iteration 1
• Iteration 2
• etc

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Stochastic Problem
21/25

• Dynamic Programming Approach

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Stochastic Problem
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• Dynamic Programming Approach
• This approach works when the size of the maximum
  demand set is 1 (as in the recursion above) or
  close to 1. However when m10, we need to store
  10 demands and consequently the state space
  explodes (curse of dimensionality).
• To overcome this problem, we might consider
  storing the 1st and 10th highest demands and
  interpolating between these.

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Conclusions
23/25

• Under normal market conditions, self generation
  using diesel generators is not economical.
• However, if fuel is needed as a backup supply and
  is approaching expiration there is an optimal way
  to use it.
• Formulated as an LP the Peak Shaving problem is
  intractable for the RSM.
• A relatively simply greedy algorithm exists that
  will determine the optimal allocation.
• Alternatively, a dual simplex approach can be
  employed.
• The stochastic problem is significantly larger
  and requires a large number of constraints if
  formulated using an SLP or an enormous state
  space if formulated as a DP.

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Future Work

• Is the stochastic problem more sensitive to
  demand or price uncertainty? Are we better to use
  the SLP and trim the scenario tree, or the DP and
  interpolate the state space?
• Is back-up generation really worth it? Given that
  peak shaving can reduce the cost of this security
  of supply, how risk averse does one need to be
  for back-up generation to be a sensible strategy.
• The level of contracting does not alter the
  optimal self generation plan but the converse is
  not necessarily true. Does the added security of
  back-up generation alter the optimal contract
  spot mix.
• Other demand side questions
• Would a liquid hedge market enable large
  consumers to more effectively manage price risk
  and at less cost?
• Can better contracts be negotiated by consumers
  acting as a group?
• What about demand side bids?
• Every little bit counts Are there optimal
  conservation strategies? How valuable are they?

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Thank You For Listening. Questions?