Control_output not equal to sum of all pid values

[andreid1303]

Describe the bug
I found that when target temperature is archived and Integral is changing slowly the control output is switching fro say 60% to 30% and back in an hour.

To Reproduce
Steps to reproduce the behavior:
Here is the current state:

hvac_modes: heat, off
min_temp: 10
max_temp: 25
preset_modes: none, away, eco, boost, comfort, home, sleep, activity
current_temperature: 21
temperature: 21
hvac_action: heating
preset_mode: home
away_temp: 16
eco_temp: 10
boost_temp: 21.5
comfort_temp: 20
home_temp: 21
sleep_temp: 19
activity_temp: 17.5
control_output: 30
kp: 35
ki: 0.017
kd: 20000
ke: 1.2
pid_mode: auto
pid_i: 60.8
pid_p: 0
pid_d: 0
pid_e: 20.5
pid_dt: 0.6851170063018799
friendly_name: House Smart Thermostat
supported_features: 401

The output is 30 while
pid_i: 60.8
pid_p: 0
pid_d: 0
pid_e: 20.5

Expected behavior

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Desktop (please complete the following information):

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• Browser [e.g. chrome, safari]
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Smartphone (please complete the following information):

• Device: [e.g. iPhone6]
• OS: [e.g. iOS8.1]
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Additional context
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