On Target Heliostat Calibration

Posted in Simulation

Mark

MarkGeiger@posteo.de


Geiger SP19

Simple Power Estimation of Heliostats

A very simple approach of estimating heliostat efficiencies. In this implementation shading and blocking effects are ignored:

double PowerEstimation::estimateHeliostatEfficiency(Vector3 &sunVector, const 
Heliostat &heliostat, const Receiver &receiver)
{
    Vector3 position = heliostat.getPos();
    Vector3 target = receiver.getPos();

    // Ray vector from heliostat to AimPoint
    Vector3 rayFull = target.add(position.multiply(-1.0));
    Vector3 ray = rayFull.normalize();
    Vector3 normalVector = calcHeliostatNormalVector(heliostat, sunVector, target);

    // efficiency = shading * cos * reflectivity * blocking * transmission * intercept
    double cosine = normalVector.dot(ray); // cos for normalized vectors
    double etaShade = 1.0; // no shading
    double etaBlock = 1.0; // no blocking
    double transmission = 0.99326 - 1.046e-4 * rayFull.length() + 1.7e-8 * pow(rayFull.length(), 2)
                          - 2.845e-12 * pow(rayFull.length(), 3);
    double areaAperture = receiver.getLength() * receiver.getWidth();
    double imageDiameter = rayFull.length() * 0.015; // image has diameter of 1.5 m in 100 m distance,
    double imageArea = M_PI * pow(imageDiameter/2.0, 2); // assumer circular spot
    // area as square of diameter

    double etaIntercept = 1;
    if (imageArea > areaAperture)
    {
        etaIntercept = areaAperture / imageArea;
    }

    return etaShade * cosine * heliostat.getReflectivity() * etaBlock * transmission * etaIntercept;
}

References

[1] Vijayakumar, Sethu & Schaal, Stefan. (2000). Locally Weighted Projection Regression: An O(n) Algorithm for Incremental Real Time Learning in High Dimensional Space. Proceedings of the Seventeenth International Conference on Machine Learning (ICML 2000). Vol. 1.

[2] Pfahl, Andreas, et al. "Progress in heliostat development." Solar Energy 152 (2017): 3-37.

[3] Liu, Hechen, and Markus Schneider. "Similarity measurement of moving object trajectories." Proceedings of the 3rd ACM SIGSPATIAL International Workshop on GeoStreaming. ACM, 2012.

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