Technology Model Improvements

Aside from the methodological changes introduced by either of the NWP methods, improvements to the initial technology models are possible. The transfer functions used in the basic uncertainty work were simplistic, but function to prove that the technique works at a low level. Any advancement to the models will produce more

accurate transfer functions, and therefore more accurate power output forecasts for the VPP.

The two technologies which benefit from this advancement are wind turbines and PV arrays, because they have a dynamic range of output power and efficiency, whereas the micro CHP boiler is on or off, and has a relatively static range of power output.

The basic wind power profile used in the model is built using a total of 3 points: the cut-in point, the rated power point, and the cut-out speed. It is analogous to Figure 3.3, but that is only a theoretical power curve. A more realistic power curve is determined by measurement of an example of the wind turbine in question under test conditions, resulting in a curve which accurately maps the input speed to the power output. Compare and contrast the two curves in the figure below (Figure 4.6).

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Windspeed in m/s

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Measured Data Simple Model

Figure 4.6: Comparing Wind Power Curves

Clearly, there are key differences between the two, but the most apparent difference is the generation area that is cut-out between 20ms^-1 and 25ms^-1 by the early cut-out point for this turbine. The full ramifications of this difference will be discussed later, but it is apparent that the turbine will not achieve maximum power generation nearly as often as the basic model would indicate.

The basic PV array model has a similar inherent problem, because it assumes that the DC power produced by the array is converted perfectly into AC power. This is a false assumption, as the inverter electronics which govern the conversion are not perfect, and the conversion efficiency falls as the amount of DC power produced by the PV array falls; this can be thought of as a semi-fixed amount of power that is lost to the conversion process, which has a greater impact on efficiency. Figure 4.7, below, gives an example of a more realistic inverter efficiency curve.

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AC Output Power %

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Figure 4.7: Inverter Efficiency

If the basic inverter efficiency curve were to be shown on the same graph, it would lie at 100%, and the margin between the two curves is what introduces the error between the two methods.

In order to incorporate the more complicated power profiles (either power output curves, or inverter efficiency curves), changes are necessary in the methodology of the models. If the basic profiles are used, using the basic power curve for wind turbines and a flat inverter profile for PV arrays, the determination of the output value for each and every point is achievable using only a few logic tests.

Under basic operation, when determining the output power for the micro wind turbines the windspeed distribution is built first, using the mean windspeed data adjusted for height and the roughness length for the turbine. The turbine data contains

3 windspeeds, forming 5 sections: the off section from 0ms^-1 to the cut-in speed, the ramp section from the cut-in speed to the rated speed, the flat section at maximum power between the rated speed and the cut-out speed, the discontinuous section at the cut-out speed, and the off section after the cut-out speed, as shown in Figure 4.6. Of these 5 sections, the discontinuity can be ignored entirely as it cannot contain any quantity of probability. The 3 horizontal sections (at 0%, 100%, and 0% power respectively) can have their probabilities calculated easily by inspection of the windspeed distribution. Bearing in mind that the power output graph is discrete in nature, the remaining ramping region of the curve between 0% at the cut-in windspeed and 100% power at the rated power windspeed can be evaluated by determining the intersection windspeeds for the required power (the upper and lower boundaries for the discrete power), and then using these values with the windspeed’s cumulative distribution to evaluate the quantity of probability bounded by the 2 windspeeds. This is shown in Figure 4.8.

Figure 4.8: Old Method for Turbine Output Power

Similarly, the flat inverter characteristic used in the basic model decreased the difficulty of building the output power graphs. The power output produced by the stated solar insolation condition is determined first, and then the output power distribution is built using the RMSE insolation value. This produces a continuous output power distribution. Each discrete power point in the output is determined using the cumulative distribution function of the output power, and any output power which

Windspeed/ms^-1

Power Output

is greater than the inverter limit is assumed to have caused the inverter to shut-down to prevent overloading [88]. Thus the power regions which lie outside of the inverter limits are shifted respectively to produce 0 Watts AC power, as the inverter is shut-down in these regions.

Modifications are therefore necessary to accommodate the more accurate profiles. Of the two technologies, micro wind turbines are the more straightforward to modify. As has been discussed above, every discrete power point in the power output is evaluated to produce the output. The basic power curve requires an investigation into a single slope between the cut-in speed and the rated speed to determine the intersection points, whereas the more realistic power curve profile requires evaluation of every slope which makes up the power profile to determine the intersection points. The intersection points between the power and the windspeed are then used to lookup the probabilities from the CDF which are used to evaluate the probability for each discrete power point used in building the power output graph.

Each discrete power point in the power output refers to an output power which has an associated upper and lower boundary power. The basic technique requires that the two power points be checked against the single slope for intersection, and where these are found the corresponding probability can be read from the windspeed distribution. By checking against every slope instead of just one, the method can be expanded to cover the new turbine power curve, as shown in Figure 4.9, below. If more than one windspeed region is found to contribute to the power, the probabilities for each are added together to determine the probability, as in the example.

Figure 4.9 : New Technique for Turbine Output Power

The PV inverter efficiency curve is more problematic to implement when contrasted to the micro wind turbine method, as they are implemented in slightly different ways.

Referring back to the PV inverter efficiency curve, the inverter is more efficient at higher AC powers, and is 0% efficient at 0% AC power. The basic PV model does not contain inverter efficiency, however, and it is desirable to determine the power curve which will convert between the PV array’s DC power output and the inverter’s AC output, using the listed efficiency profile of the inverter. This power transfer curve can be produced by taking the reciprocal of the efficiency and multiplying by the AC power, but there is a small problem. The 0% efficiency value at 0% AC output power can take any value of DC power, as any value of input DC power multiplied by zero will give the correct result – that result also being zero.

By examining the points close to the 0% efficiency point the power curve can be seen to flatten vertically. Furthermore, in the efficiency region between 0% and the first efficiency point, it is easy to prove that the DC input power is a constant which can produce the power between 0 AC Watts and the power dictated by the first efficiency point. This forms a discontinuity in the power curve, at the end of which is the 0%

efficient point. As this 0% efficiency point lies at the end of a discontinuity, it is no longer required to be determined, as no quantity of probability can be contained by a discontinuity. Placing this point at 0 output power is also the intuitive solution, as the

Windspeed/ms^-1

Power Output

low efficiency is a result of diminishing input DC power from the PV array, hence the inverter output power will only rise above zero once the internal conversion losses have been overcome by rising input DC power. The power curve produced from the example inverter efficiency, Figure 4.7, is shown in Figure 4.10:

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DC Input Power %

AC Output Power %

Real Inverter Ideal Inverter

Figure 4.10: Derived Inverter Power Curve

This type of curve is of the same format as the wind turbine power curve, and the same techniques which are used in the building of the micro wind turbine power output, with the improved power curve, can be applied to the inverter power curve.

The fundamental difference between the two power curves is that the inverter curve does not have insolation along the x-axis, instead it has the PV array DC power.

To use the inverter power curve, it is first necessary to convert both axis of the power curve into real power units instead of percentages. This is done using the power limit for the inverter, and produces a derived power output curve. If the PV array DC power equation, (3.6), is considered:

P = PSTC × G/1000 × [1-b(T-25)]

It can be seen that this can be rearranged to find the insolation on the PV array in terms of the DC output power as a quadratic equation, explicitly:

[ ]

Using this expression, it is possible to determine the ratio between the insolation, G, and the DC output power, P, an example of which is shown in Figure 4.11. This relationship can be applied to the inverter power curve, adjusting the x-axis values to a corresponding insolation value. This derives a power curve which relates the insolation received by the PV array to the AC output power produced by the inverter.

Thus, this new power curve is in the same format as the wind turbine power curve (relating the input forecast variable to a power output). With the power curve in a similar style to the wind turbine power curve, the more sophisticated output power graph building process defined for micro wind turbines can be applied to the PV array power curve in the same fashion (Figure 4.11).

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Figure 4.11: DC and AC Power Output against Insolation