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Wind Power Scheduling With External Battery.

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.

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Wind Power Scheduling With External Battery.

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  1. Wind Power Scheduling With External Battery. PinhusDashevsky Anuj Bansal

  2. 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.

  3. 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. 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

  9. 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

  10. Problem Difficulty • ∑({abs(∆X_t)>R}/n < P • A probabilistic constraint makes the problem nonlinear

  11. Ways to Solve (I) • Dynamic Programming • This proves difficult because of state dependency, • nonviolation today drains a battery which might cause state violation tomorrow

  12. 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

  13. 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

  14. 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]

  15. Contending Algorithms • Greedy • Conservative • Hybrids • Target • Smart Target

  16. Performance (uniform)

  17. Violation (uniform)

  18. Hybrids (Normal(50,50)

  19. Violations

  20. Realistic Wind

  21. Solving Weibull

  22. Percent Violation (Weibull)

  23. 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

  24. Thank You • Any Questions:

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