Wind Farm Optimization<br />3<br />Currently wind energy contributes 2% of worldwide electricity consumption.<br />Planned increase in USA by 2030 – 10 fold.<br />Advancing wind energy would require optimal wind farm design strategies.<br />Critical aspects in wind farm design include (not limited to)<br /><ul><li>Farm layout
Motivation<br /><ul><li>The net power generated by a wind farm is reduced by the wake effects, which can be offset by optimizing the farm layout.
A combination of different types of turbines is expected to further improve the power generation capacity and the economy of a wind farm. Commercially available turbines provide a set of discrete choices.</li></ul>5<br /><ul><li>Exploration of the influence of key farm planning factors such as the farm size and the number of turbines, within the context of layout optimization would be uniquely helpful.</li></ul>www.wind-watch.org<br />
Existing Wind Farm Optimization Methods<br />6<br />Grid based approach<br />Yields a computationally expensive mixed-integer problem for large number of turbines<br />Array layout approach<br />Restricts turbine locating and introduces a source of sub-optimality<br /><ul><li>Do not simultaneously optimize the selection of wind turbines
Assume a constant induction factor</li></li></ul><li>Research Objectives<br />Develop and use an analytical wind farm model that avoids conventional restrictions in layout planning.<br />Implement a generalized Mixed-discrete Particle Swarm Optimization to simultaneously optimize (i) the selection of turbine rotor diameters, and (ii) the layout of the wind farm.<br />Explore the influences of the farm size and the number of turbines on the net performance of the optimized wind farm<br />7<br />
Basic Components of the UWFLO Framework<br />Power Generation Model<br /><ul><li>Develops a turbine influence matrix based on the wake effects
Considers a variable induction factor and partial wake-rotor overlap
Determines the net power generated by the wind farm</li></ul>Optimization Framework <br /><ul><li>Implements awind farm cost model
Simultaneously optimizes the selection of differing types of turbines
Maximizes the net power generation using the PSO algorithm</li></ul>8<br />
UWFLO Power Generation Model<br />The flow pattern inside a wind farm is complex, primarily due to the wake effects and the highly turbulent flow. <br />Rotor averaged velocity is determined from the flow profile*<br />Step 1<br /> Transformed co-ordinates are evaluated <br /> based on wind direction <br />10<br />* Cal et al., 2010<br />
Mutual Influence of Turbines<br />Step 2<br /> An influence matrix is defined as<br /> where Turbine-i influences Turbine-j if<br />Step 3<br /> The turbines are ranked in the increasing order of their x-coordinate. Power generated by turbines is calculated in the increasing order of their rank.<br />11<br />
Step 4<br /> Effective velocity of wind approaching Turbine-j:*<br /> The power generated by turbine-j:<br />Step 5<br /> Power generated by the farm: Farm Efficiency:<br />Power Generated by the Wind Farm<br />12<br />Coefficient of power<br />Power generated by a standalone turbine<br />* Katic et al., 1986<br />
Wake Model<br />UWFLO uses Frandsen’s wake model*,which calculates the diameter of the growing wake and the wake velocity as:<br />Wake spreading constant<br />However, UWFLO has the flexibility to use any standard wake model.<br />13<br />* Frandsen et al., 2006<br />
UWFLO – Problem Definition<br />An unidirectional uniform wind at 7.09 m/s and at 0o to X-axis is considered.<br />15<br />Cost Constraint: Applied when optimizing the selection of wind turbines<br />
Wind Farm Cost Model<br />Quadratic response surface based cost models* are developed to represent the farm cost, as a function of the turbine rotor diameters and number of turbines.<br />To this end we used data for wind farms in the state of New York*<br />16<br /> For wind farm with non-identical turbines<br />The cost per KW of power produced is given by<br />* Chowdhury et al., IDETC2010<br />
Particle Swarm Optimization (PSO)<br />Swarm Motion*<br />Solution Comparison<br />The constraint dominance principle** is used.<br />PSO can appropriately address the non-linearity and the multi-modality of the wind farm model.<br />17<br />* Kennedy and Eberhart, 1985<br />** Deb et al., 2002 (NSGA-II) <br />
Generalized Approach to MDNLO - Principles<br />Divides the variable space into continuous and discrete variable spaces.<br />Implements continuous optimization as the primary search strategy<br />Approximates candidate solutions to nearby feasible discrete locations based on certain criterion.<br />Saves computational expense by evaluating criterion functions only at feasible discrete locations.<br />Implemented through non-gradient based optimization algorithms<br />18<br />
Vertex Approximation Techniques<br />In the discrete variable domain, the location of a candidate solution can be defined by a local hypercube<br />Nearest Vertex Approach (NVA)<br />Approximates to the nearest discrete location based on Euclidean distance.<br />Shortest Normal Approach (SNA)<br />Approximates to the discrete location with shortest normal to the connecting vector.<br />19<br />
Experimental Scale Wind Farm<br />The UWFLO model has been validated** against a wind tunnel experiment on a scaled down farm.*<br />20<br />Meanrotor diameter of commercial turbines: 75mScaled down to experimental dimensions: 0.12mResulting feasible set of diameters at the experimental scale:<br />* Cal et al., 2010; ** Chowdhury et al., IDETC2010<br />
22<br />Case 2 – Identical Turbines<br />Identical turbines, with rotor diameter, D = 0.12m, are considered<br />Original continuous PSO was used in this case<br />Approximated power curve: The power generated is assumed to remain constant at the rated power (0.385W) for U > Rated speed (6.17m/s)<br /><ul><li>To investigate the influence of the number of turbines, we optimize five wind farms with 6, 9, 12, 15, and 18 turbines laid out in 14D x 6D wind farm
To investigate the influence of the farm size, we optimize five wind farms with a length to breadth ratio of 7/3. </li></li></ul><li>UWFLO – Influence of the Number of Turbines<br />23<br />
UWFLO – Influence of the Farm Size<br />Cost information relating the farm size to the total cost was not readily available.<br />24<br />
Concluding Remarks<br /><ul><li>The proposed UWFLO technique allows simultaneous optimization of (i) the selection of turbine rotor diameters, and (ii) the layout of the wind farm.
To this end the developed mixed-discrete PSO is found to be highly effective. The nearest vertex approach performs better than the shortest normal approach.
This wind farm optimization technique increases the power generation by 44% compared to the array layout (at no additional cost).
The determination of the appropriate number of turbines, and the farm size is crucial to optimal wind farm design. </li></ul>25<br />
Future Work<br /><ul><li>In future research, each commercially available turbine, with a unique combination of rotor diameter, hub height, and performance characteristics, will be explicit considered.
Future research will also consider the variability of the speed and direction of wind, in the case of commercial wind farms.</li></ul>26<br />
Selected References<br />World Wind Energy Report 2008. Bonn, Germany, February 2009.<br />Katic, I., Hojstrup, J., and Jensen, N. O. A Simple Model for Cluster Efficiency. In Proceedings of European Wind Energy Conference and Exhibition (Rome, Italy 1986).<br />Frandsen, S., Barthelmie, R., Pryor, S, Rathmann, O, Larsen, S, Hojstrup, J, and Thogersen, M. Analytical Modeling of Wind Speed Deficit in Large Offshore Wind Farms. Wind energy, 9, 1-2 (2006), 39-53.<br />Grady, S. A., Hussaini, M. Y., and Abdullah, M. M. Placement of Wind Turbines Using Genetic Algorithms. Renewable Energy, 30, 2 (February 2005).<br />Sisbot, S., Turgut, O., Tunc, M., and Camdali, U. Optimal positioning of Wind Turbines on Gökçeada Using Multi-objective Genetic Algorithm. Wind Energy (2009).<br />Mosetti, G., Poloni, C., and Diviacco, B. Optimization of Wind Turbine Positioning in Large Wind Farms by Means of a Genetic Algorithm. Journal of Wind Engineering and Industrial Aerodynamics, 54, 1 (January 1994), 105-116.<br />Kennedy, J. and Eberhart, R. C. Particle Swarm Optimization. In Proceedings of the 1995 IEEE International Conference on Neural Networks ( 1995), 1942-1948.<br />Cal, R. B., Lebron, J., Kang, H.S., Meneveau, C., and Castillo, L., “Experimental study of the horizontally averaged flow structure in a model wind-turbine array boundary layer”, Journal of Renewable and Sustainable Energy, 2, 1 (2010).<br />Lebron, J., Castillo, Cal, R. B., Kang, H. S., and Meneveau, C., 2010, “Interaction Between a Wind Turbine Array and a Turbulent Boundary Layer,” Proceeding 49th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, January 4-9.<br />27<br />