Wind Power Scheduling With External Battery.

Pinhus DashevskyAnuj Bansal

Wind Energy Advantages of wind energy:

It is abundantly available everywhere and is free of cost.

A pollution free means of generating electricity

Reduces dependency on the non-renewable sources of energy.

Low cost when compared to other clean sources of energy.

US and wind energy:

According to reports of the American Wind Energy Association, wind energy accounts for 31% of the newly generated capacity installed over the 5 years. 2009-13.

Wind Energy and Future Prospects.

Wind Penetration Level refers to the fraction of energy produced by wind compared to the total generating capacity of a nation.

As of 2011, US had a penetration level of 3.3% which is expected to rise to 15% by 2020.

With such high penetration levels, the wind energy integration in the grid has to be highly reliable and uniform.

However, the variability of winds causes a major problem in efficient forecasting and distribution of the power.

Problem Introduction• Reliable power systems require a balance

between demand load and generation within acceptable limits. • supply and demand shocks create power surges

• Wind energy generation cannot be forecasted with sufficient accuracy due to the inherent variability of the wind.

• The variability makes wind a poor energy source.

Problem Scope and Objective

• To schedule the distribution of wind power generated at a farm into the city grid.

• The objective is to maximize profits which comes from providing energy per watt.

• There is a penalty imposed for non uniform power distribution.

• An external battery is provided which can be used to smoothen the non uniform generation by absorbing/supplying in cases of excess/shortage of power generation.

Assumptions• The wind power forecasting has been done assuming

Uniform, Normal and Wiebull distributions.

• Each unit of power supplied results in $1 profit.

• Penalty of $10 is imposed if the power input to the grid changes by more than 5 units between two consecutive time frames.

• Battery used has a capacity of 100 units of power.

• The rate at which the battery can accept or deliver electrical energy is unrestricted.

• Wind power is measured only at discrete time intervals.

Ramp RateRamp rate is defined as the difference

consecutive power outputs.

∆(x_t,x_t-1)<R in discrete time

∂x/∂t<R in continuous time

For smooth distribution of power, this ramp rate is limited by a quantity R. Violation of this limit is subjected to a penalty.

• Our objective is to maximize profits by reducing the ramp rate violations over a given time period T.

Model FormulationWind is a stochastic process W(t) with output Power

In our model Power goes between [0,100]

Battery has Battery capacity, current Battery used

System decides how much goes to the grid

The rest goes to Battery

Any remaining power that cannot be stored by the battery is lost

S (W(t), X_t-1, Bcap, Bused_t-1, R) outputs X_t

Mathematical FormulationSchedule Outputs To maximize Profit

Max ∑c(X_t)

S.T. ∑({abs(∆X_t)>R}/n < PBused_t-1+W(t) – X_t > 0

The solution to this problem would allow us to build optimal size batteriesUse wind much more efficiently

Problem Difficulty∑({abs(∆X_t)>R}/n < P

A probabilistic constraint makes the problem nonlinear

Ways to Solve (I)Dynamic Programming

This proves difficult because of state dependency,

nonviolation today drains a battery which might cause state violation tomorrow

Ways to Solve (II)Lagrangian Convex Optimization

Relax the Constraint but impose a penalty and maximize the profit

Check the Constraint if probability is low Decrease penaltyIf Probability of violation is highIncrease penalty

Each iteration of Lagrangian takes a long time

There is no way to know how quickly you converge

Ways to Solve (III)Markov Decision Process

Find stationary probabilities that maximize the profit

The issue is that the decision in our problem is continuous

Since X_t [0, Battery used + W(t)]

So you would need to discretize outputs otherwise this problem is infinitely large

Our MethodUse to simulation and

heuristics to establish Lower Bounds on profit

Upper Bounds are easily established by taking Expectation of the W(t) over [0,T]

Contending AlgorithmsGreedy

Conservative

Hybrids

Target

Smart Target

Performance (uniform)

0 10 25 50 75 100 500 10000

10000

20000

30000

40000

50000

60000Profit vs Battery capacity (Uniform wind

distribution)

Conserva-tive

Battery Capacity (percent of the max wind)

Profit ($)

Violation (uniform)

025 75

500

0

5

10

15

20

Conservative

Percent Violation (uniform distributed wind)

Conservativegreedy

Battery Capacity

Percent Violation

Hybrids (Normal(50,50)

0 10 25 50 75 100 500 10000

10000

20000

30000

40000

50000

60000

Profit vs Battery capacity (normal)Conservative

Greedy

Hybrid

hand off

Target 30

Smart Target 30

Battery Capacity (percent of the max wind)

Profit ($)

Violations

0 10 25 50 75 100 500 10000

5

10

15

20

25

30

35

40

45

50

Percent Violation (normally distributed wind)

Conservative

greedy

hand off

Hybrid

Target 30

Smart Target 30

Battery Capacity

Percent Violation

Realistic Wind

Solving Weibull

0 10 25 50 75 100 500 10000

5000

10000

15000

20000

25000

30000

Profit vs Battery capacity (Weibull wind)

Conservative

Greedy

target 25

Smart Target 25

Smart Target 30

Battery Capacity (percent of the max wind)

Profit ($)

Percent Violation (Weibull)

0 10 25 50 75 100 500 10000

10

20

30

40

50

60

Percent Violation (uniform distributed wind)

Conservative

greedy

target 25

Smart Target 25

Smart Target 30

Battery Capacity

Percent Violation

ConclusionsFinding a Lower Bound Heuristic is Useful.

Unfortunately it is not a simple task.

It is more feasible to focus on creating a Heuristic for one situation

This problem remains difficult but finding a Lagrange that does better than our Heuristic is still possible and that can teach us a lot about the problem

Thank YouAny Questions: