Integral

This integrations provides the Riemann sum of the values provided by a source sensor. The Riemann sum is an approximation of an integral by a finite sum.

The integration sensors are updated whenever the source changes and, optionally, based on a predefined time interval. Source sensors with higher sampling frequency provide more accurate results.

Configuration

To add the Integral integration to your Home Assistant instance, use this My button:

Name

The name the sensor should have. You can change it again later.

Input sensor

The entity providing numeric readings to integrate.

Integral method

Riemann sum method to be used.

Precision

Round the calculated integration value to at most N decimal places.

Metric prefix

Metric unit to prefix the integration result.

Integration time

SI unit of time to integrate over.

Max sub-interval

Applies time-based integration if the source did not change for this duration. This implies that at least every max sub-interval, the integral is updated. If you don’t want time-based updates, enter 0.

YAML configuration

Alternatively, this integration can be configured and set up manually via YAML as well. To enable the Integration sensor in your installation, add the following to your configuration.yamlThe configuration.yaml file is the main configuration file for Home Assistant. It lists the integrations to be loaded and their specific configurations. In some cases, the configuration needs to be edited manually directly in the configuration.yaml file. Most integrations can be configured in the UI.[Learn more] file:

# Example configuration.yaml entry
sensor:
  - platform: integration
    source: sensor.current_power

Configuration Variables

source string Required

The entity ID of the sensor providing numeric readings.

name string (Optional)

Name to use in the frontend.

Default:

source entity ID integral

unique_id string (Optional)

An ID that uniquely identifies the integration sensor. Set this to a unique value to allow customization through the UI.

round integer (Optional, default: 3)

Round the calculated integration value to at most N decimal places.

unit_prefix string (Optional, default: None)

Metric unit to prefix the integration result. Available units are k, M, G and T.

unit_time string (Optional, default: h)

SI unit of time to integrate over. Available units are s, min, h and d.

method string (Optional, default: trapezoidal)

Riemann sum method to be used. Available methods are trapezoidal, left and right.

max_sub_interval time (Optional, default: 0)

Applies time-based integration if the source did not change for this duration. This implies that at least every max sub-interval, the integral is updated. If you don’t want time-based updates, enter 0.

The unit of source together with unit_prefix and unit_time is used to generate a unit for the integral product (e.g. a source in W with prefix k and time h would result in kWh). Note that unit_prefix and unit_time are also relevant to the Riemann sum calculation.

Integration method

The Riemann Sum is an approximation of an integral by a finite sum and is therefore intrinsically inaccurate. Nonetheless, depending on the method used, values can be more or less accurate.

The integration method defines how to calculate the area under the source sensor when it changes. Regardless of the method used, the integration will be more accurate if the source updates more often. The config max_sub_interval can be used to trigger integration when the source sensor is constant.

Trapezoidal

The trapezoidal method follows the Trapezoidal rule. This method is the most accurate of the currently implemented methods, if the source updates often, since it better fits the curve of the intrinsic source.

Left

The left method follows the Left rule. The method underestimates the intrinsic source, but is extremely accurate at estimating rectangular functions which are very stable for long periods of time and change very rapidly (e.g. such as the power function of a resistive load can jump instantly to a given value and stay at the same value for hours). If your source keeps its state for long periods of time, this method is preferable to the trapezoidal.

Right

The right method follows the Right rule. The method is similar to the left method, but overestimates the intrinsic source. Again it is only appropriate to be used with rectangular functions.

Energy

An integration sensor is quite useful in energy billing scenarios since energy is generally billed in kWh and many sensors provide power in W (Watts).

If you have a sensor that provides you with power readings in Watts (uses W as unit_of_measurement, device_class of power), then you can use the integration sensor to track how much energy is being spent. Take the next manual YAML configuration as an example:

sensor:
  - platform: integration
    source: sensor.current_power
    name: energy_spent
    unit_prefix: k
    round: 2
    max_sub_interval:
      minutes: 5

This configuration will provide you with sensor.energy_spent which will have your energy in kWh, as a device_class of energy.