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Applications of Calculus

Applications of Calculus. Optimizing Power Output on a Solar Power System. By: Alex Bryson. Terms to Know. Volts – electromotive force, inversely related to temperature Current - flow of electric charge, dependant on irradiance

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Applications of Calculus

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  1. Applications of Calculus Optimizing Power Output on a Solar Power System By: Alex Bryson

  2. Terms to Know • Volts – electromotive force, inversely related to temperature • Current - flow of electric charge, dependant on irradiance • Watts – amount of power is measured in watts, power produced • Kilowatt Hours(Kwh) – power usage measured by kwh • MPP- max power point • Irradiance – the solar energy from the sun

  3. Problem • MPP is always changing because it is dependent on multiple variables • Temperature of the panels • Intensity of the sun • Shading or snow block • Each input of Voltage and Current form a new curve

  4. Finding the MMP • The Maximum Power Point is where the slope/derivative of the power curve is equal to zero. • To find the mpp: • Take the inputs from the panels (volts and current) • Determine the slope of the curve • If it is not zero, make adjustments to move to where it is equal to zero

  5. The Math • These equations show how the inverter establishes the MPP P = power I = current V = volts • Using the voltage and current inputs and these equations an inverter can tell whether it needs to allow more or less current to flow to achieve the MPP

  6. Basic Power Curve **In this example assume the sunlight is constant The change from g(x) to f(x) is an increase in temperature Power Output g(x) = mpp f(x) Voltage

  7. Basic Power Curve **In this example assume the sunlight is constant The change from g(x) to f(x) is an decrease in current Power Output g(x) = mpp f(x) Voltage

  8. MPP- November and December The MPP shift due to temperature changes or suns intensity. The vertical shifts came from changes in suns intensity. The horizontal shifts came from temperature changes

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