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Wind Power Scheduling With External Battery.Pinhus DashevskyAnuj BansalWind Energy Advantages of wind energy:It is abundantly available everywhere and is free of cost.A pollution free means of generating electricityReduces 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 IntroductionReliable 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 ObjectiveTo 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.

AssumptionsThe 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) 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 < PA probabilistic constraint makes the problem nonlinear Ways to Solve (I)Dynamic ProgrammingThis proves difficult because of state dependency, nonviolation today drains a battery which might cause state violation tomorrowWays to Solve (II)Lagrangian Convex OptimizationRelax the Constraint but impose a penalty and maximize the profitCheck the Constraint if probability is low Decrease penaltyIf Probability of violation is highIncrease penaltyEach iteration of Lagrangian takes a long time There is no way to know how quickly you converge

Ways to Solve (III)Markov Decision ProcessFind stationary probabilities that maximize the profitThe issue is that the decision in our problem is continuousSince X_t [0, Battery used + W(t)]So you would need to discretize outputs otherwise this problem is infinitely largeOur MethodUse to simulation and heuristics to establish Lower Bounds on profitUpper Bounds are easily established by taking Expectation of the W(t) over [0,T]Contending AlgorithmsGreedyConservativeHybridsTargetSmart Target

Performance (uniform)Violation (uniform)Hybrids (Normal(50,50)ViolationsRealistic Wind

Solving WeibullPercent Violation (Weibull)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 situationThis 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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