Integration
To integrate the values of a time series, select Methods → Convert time series → Integrate time series (power to energy) from the menu bar or the context menu of the time series in the Project Explorer (see the following figure), or use the key combination <Ctrl>+<Shift>+<I>.
In the window that opens (see following figure), the time series to be processed are selected with Select time series. A multiple selection is possible.
Select whether the respective existing time series should be overwritten with the integrated values or whether a new time series should be created in addition.
The following figure shows an example of the integration of a time series with the unit kW. The integrated time series has the unit kWh.
The result time series corresponds to the integral of the initial time series.
For each data point of time j, the integration interval is defined as the distance between time (j) and time (j+1), see following schematic diagram. For equally spaced time series the integration interval corresponds to the sample time (step size) of the time series. The corresponding values of the data points are called x(j) and x(j+1).
The rectangle rule is applied: only the current data point x(j) is used to calculate the integral value. This applies to both equally spaced and unequally spaced time series.
Differentiate
To differentiate the values of a time series, select Methods → Convert time series → Differentiate (energy to power) from the menu bar or the context menu of the time series in the Project Explorer, see the following figure, or use the key combination <Ctrl>+<Shift>+<D>.
In the window that opens (see following figure), use Select time series to select the time series to be processed. A multiple selection is possible.
Select whether the respective existing time series should be overwritten with the differentiated values or whether a new time series should be created in addition.
The following figure shows a simple example for the derivation of an energy time series.
An application example of differentiation is the calculation of the loading and unloading capacities of a storage facility by deriving the energy content of the storage facility (see following figure).
The result time series corresponds to the differential quotients of the initial time series.
For each data point of time j, the differentiation interval is defined as the time interval between this data point and the following data point, i.e., time (j) and time (j+1), see following schematic diagram. For equally spaced time series the integration interval corresponds to the sample time (step size) of the time series. The corresponding values of the data points are named x(j) and x(j+1).
To determine the slope between points x(j) and x(j+1), a simple two-point method (secant method) is used. The difference between the slope of the secant and the slope of the tangent is approximately proportional to the difference between the two values x(j) and x(j+1).
