Design Parameters Analysis of Point Absorber WEC via an evolutionary-algorithm-based Dimensioning Tool
2. Parametric Analysis Definition
2.1. Reference Case Definition
- Generation plant with a single grid-connected WEC.
- The sea site for the commissioning and testing is located at PLOCAN.
- The WEC is a point absorber, which is one of the most suitable topologies for the installation of a direct-driven generator .
|Pnom||Rated Electric Power||220 kW (peak power)|
|Fnom||Maximum Force||220 kN|
|Vnom||Rated Speed||1 m/s|
|Snom||Maximum Stroke||4 m|
2.2. Parametric Analysis Set-up
|Parametric Analysis Cases||Analysis 1||Analysis 2||Analysis 3||Analysis 4||Analysis 5|
|Peak-Power Frequency Matching (f)||Location (c)||WEC (d)||PTO Force (b)||Control (e)|
|Reference Case||Two-Body Peak-Power Frequency Matching||PLOCAN||2-body WEC||220 kN||Reactive Control|
|Parametric Analysis||Maximum Peak-Power Frequency||SANTOÑA||1-body WEC||(37–660) kN||Damping Control|
|No Peak-Power Matching||IPS buoy|
3. Preliminary Dimensioning Algorithm
3.1. Optimization Problem Algorithm
Multi-Objective Differential Evolution Algorithm
- In each iteration (generation), the DE algorithm generates a new set (population) of candidate solutions (child population, Qt) from the initial set of solutions (parent population, Pt). The definition of the new set of solutions implies the specification of the particular values of the search space variables (see Section 3.3.1 for more information). The main differential characteristic of the DE algorithm, compared with other bio-inspired algorithms, is the definition of a new set of candidate solutions where each one is obtained from mutation of two randomly chosen candidate solutions by the sum of the weighted differences between them.
- In a second iteration step, the candidate solutions (Qt) are evaluated, calculating their objective function values (described in Section 3.3.2) and restricted values (described in Section 3.3.3) by means of a WEC mathematical model (described in Section 3.2) characterized for some particular values of the search space.
- The third iteration step evaluates and compares Qt together with Pt in order to determine the initial population of the following iteration (Pt+1). Subsequently, a joint set of solutions (Rt), from Pt and Qt, is ordered in terms of the multi-objective function values (dominance between solutions) by means of a non-dominated sorting algorithm based on NSGA-II. Besides, Rt is sorted in terms of restrictions accomplishing Deb’s rules. In this way, an order is established based on feasibility, when the solution accomplishes all the restrictions, and dominance, when the solution gets better values in both objective functions. Finally, Pt+1 is composed by the best solutions of Rt.
3.2. Mathematical Model of a WEC
3.2.1. Location and Operation States
|Tmin||Minimum Wave Period (of the operation range)||6 s||7 s|
|Tmax||Maximum Wave Period (of the operation range)||14 s||18 s|
|Tr||Maximum Occurrence Wave Period||8 s||10 s|
3.2.2. Point Absorber Dynamic Model
…=(Z11·Z22 − Z122)·(Z*11 + Z*22 + 2·Z*12)/|(Z11 + Z22 + 2·Z12)|2
3.2.3. PTO Power Loss Model
3.2.4. PTO Control Strategy
3.3. Optimization Problem Definition
3.3.1. Search Space
3.3.2. Objective Functions
- Minimum PTO electric extracted power in WEC operational Range III. The power extracted values of the profile should exceed the minimum value of the PTO rated power (PNOM, defined in Table 1) multiplied by a certain coefficient.
- Maximum PTO relative velocity in WEC operational Ranges II and III. The power extracted values of the profile should exceed the maximum value of the PTO rated velocity (vNOM, defined in Table 1) multiplied by a certain coefficient
- Maximum PTO relative displacement in WEC operational Ranges II and III. This restriction is applied over the amplitude of the relative movement (between 2 bodies in the case of IPS and 2-body devices; between the floating body and the sea floor in the case of 1-body WEC). It ensures that the relative movement amplitude does not reach the maximum value of the PTO maximum stroke SNOM (see Table 1), which should be limited by protections such as end stop springs or similar devices.
- WEC peak-power frequency in the neighborhood of the fr (1/Tr) value (see Table 3).
- Anti-Slamming  restriction in WEC operational Ranges II and III. This restriction ensures that the floating-body oscillatory-movement amplitude is less than its own draft (d1). The distance between the mass center of body 1 (floating body) and the sea water surface is restricted to the maximum value of the floating body draft multiplied by a certain coefficient.
- The first (ωr2 = 2π (Tr2−1)) produces the maximization of the oscillation amplitude in the submerged body. This peak-power frequency is related with the natural resonance frequency of body 2. It is usually sufficiently high to be out of the WEC operational Ranges II and III, due to the fact that the stiffness of the body 2 is small compared with its mass.
- The second (ωr1 = 2π (Tr1−1)) produces the maximization of the oscillation amplitude in the floating-body. This peak-power frequency is related with the natural resonance frequency of body 1. It is usually within the WEC operational Ranges II and III.
- The third (ωr12 = 2π (Tr12−1)) appears by the effect of the PTO and in a well-tuned device. It produces a peak in the power extraction frequency profile characterized by individual and relative velocities relatively manageable. The value of this frequency is usually between ωr1 and ωr2 [31,32,45]. This frequency, not usually considered a resonance frequency, is in the neighborhood of the resonance frequency of the two rigidly connected bodies [31,45].
4. Discussion of the Parametric Analysis Results
4.1. Parametric Analysis 1: Peak-Power Frequency Matching Restriction
4.2. Parametric Analysis 2: Location
4.3. Parametric Analysis 3: WEC Concept
4.4. Parametric Analysis 4: PTO Rated Force
4.5. Parametric Analysis 5: Energy Extraction Control Strategy
5. Discussion and Future Work
Conflicts of Interest
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Blanco, M.; Moreno-Torres, P.; Lafoz, M.; Ramírez, D. Design Parameters Analysis of Point Absorber WEC via an evolutionary-algorithm-based Dimensioning Tool. Energies 2015, 8, 11203-11233. https://doi.org/10.3390/en81011203
Blanco M, Moreno-Torres P, Lafoz M, Ramírez D. Design Parameters Analysis of Point Absorber WEC via an evolutionary-algorithm-based Dimensioning Tool. Energies. 2015; 8(10):11203-11233. https://doi.org/10.3390/en81011203Chicago/Turabian Style
Blanco, Marcos, Pablo Moreno-Torres, Marcos Lafoz, and Dionisio Ramírez. 2015. "Design Parameters Analysis of Point Absorber WEC via an evolutionary-algorithm-based Dimensioning Tool" Energies 8, no. 10: 11203-11233. https://doi.org/10.3390/en81011203