Wind Power Scheduling With External Battery. Pinhus Dashevsky Anuj 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

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 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 Rate Ramp 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 Formulation Wind 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 Formulation Schedule Outputs To maximize Profit Max ∑c(X_t) S.T. ∑(  {abs(∆X_t)>R}/n < P Bused_t-1+W(t) – X_t > 0 The solution to this problem would allow us to build optimal size batteries Use 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 penalty If Probability of violation is high Increase 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 Method Use 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 Algorithms Greedy Conservative Hybrids Target Smart Target

Performance (uniform)

Violation (uniform)

Hybrids ( Normal (50,50 )

Violations

Realistic Wind

Solving Weibull

Percent Violation (Weibull)

Conclusions Finding 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

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