Type 3223

The Type 3223 controls the performance outputs of Type 3254 through four control signals:

  1. the normalized compressor frequency \(\nu\),

  2. the operating mode,

  3. the defrost mode,

  4. the indoor unit fan speed ratio.

Inputs

1. On / Off signalreal

On / Off signal for the controller. Zero is interpreted as Off, and all nonzero values are interpreted as On.

2. Temperature setpointreal

Setpoint for controlling the room temperature.

3. Fan speed settinginteger \(\in \{0, 1, 2, 3\}\)

Setting for the indoor unit fan speed:

\(1\)

low

\(2\)

medium

\(3\)

high

When this input is set to \(0\), the controller determines the appropriate setting automatically. A specific air flow rate can be assigned to each setting, see control file.

4. Return temperaturereal

Temperature to be controlled (typically the indoor temperature).

5. Outdoor temperaturereal

The temperature of the outdoor air.

6. Minimum frequency valuereal \(\geq 0\)

The value of the frequency control signal under which the controller will saturate.

7. Maximum frequency valuereal \(\geq 0\)

The value of the frequency control signal over which the controller will saturate.

8. Operating modeinteger \(\in \{-1, 0, 1\}\)

\(0\)

always in cooling mode

\(1\)

always in heating mode

\(-1\)

automatic heating/cooling mode
9. Defrost mode overrideinteger \(\in \{-1, 0, 1, 2\}\)

Manual defrost mode setting:

\(0\)

defrost mode (no heat output)

\(1\)

recovery mode

\(2\)

steady-state mode

A value of \(-1\) triggers automatic defrost cycles.

10. Frequency levels numberinteger \(> 0\)

The number of values \(N\) that the command signal can take between its minimum and maximum values (inputs 4 and 5, respectively). The command signal levels are evenly spaced, i.e. the \(i^\text{th}\) value is equal to \(\frac{i}{N} (\nu_\text{max} - \nu_\text{min}) + \nu_\text{min}\).

11. PI gainreal \(\geq 0\)

Gain constant \(k_c\) for the PI controller. It affects both the proportional and integral parts.

12. Integral time constantreal \(\geq 0\)

Integral time constant \(\tau_i\) of the controller. The integral gain will be the PI gain divided by this value; if \(k_c\) is the PI gain, then the integral gain is \(k_i = \frac{k_c}{\tau_i}\) High values of time integral time will thus result in low integral gains. The only exception is when the integral time is set to zero, which disables the integral action (i.e. sets the integral gain to zero).

13. Tracking time constantreal \(\geq 0\)

Tracking time constant \(\tau_t\) for the anti-windup. This is used to decrease the integral action whenever the control variable (i.e. the frequency) is saturated. The tracking gain will be the PI gain divided by this value; if \(k_c\) is the PI gain, then the tracking gain is \(k_t = \frac{k_c}{\tau_t}\) High values of time tracking time will thus result in low tracking gains. The only exception is when the tracking time is set to zero, which disables the tracking action (i.e. no anti-windup). Providing a negative tracking time will set it to the same value as the integral time.

14. Proportional setpoint weightreal \(\geq 0\)

The weight of the setpoint in the proportional error. A higher weight will result in a faster response to a setpoint change, but it will also increase the overshoot.

Parameters

1. Operating mode deadbandreal \(\geq 0\)

The width of the error signal deadband (centered on \(0\)) in which the operating mode will keep its previous value if set to auto (\(\text{input 8} = -1\)), to avoid oscillations.

2. Minimum fixed operating mode durationreal \(\geq 0\)

The minimum time period during which the operating mode must remain the same. This is to prevent switching back and forth too quickly; to disable this feature, set the duration to zero.

3. Monotonous frequency minimum duration

To ensure that the frequency does not oscillates too much, it is forced to be monotonous (or constant) for a duration specified by this parameter. Set the duration to zero to disable this behaviour.

4. Maximum number of iterationsinteger \(> 0\)

Number of iterations after which the controller’s output will stick to its current value in order to avoid oscillations and promote convergence.

5. Logical Unit — cooling modeinteger \(\geq 10\)

The logical unit which will be assigned to the data file which contains the heat pump control parameters for cooling mode.

6. Logical Unit — heating modeinteger \(\geq 10\)

The logical unit which will be assigned to the data file which contains the heat pump control parameters for heating mode.

Outputs

1. Normalized compressor frequencyreal \(\geq 0\)

The value of the compressor frequency computed by the controller to reach the setpoint. When it is not zero, it is restricted to the interval \([\nu_\text{min}, \nu_\text{max}]\) (see inputs 6 and 7).

2. Fan speed ratioreal \(\geq 0\)

The fan speed ratio associated with the specified fan speed setting (see input 3).

3. Operating modeinteger \(\in \{0, 1\}\)

If the input 8 is set to \(0\) or \(1\), the same value is provided as output. If it is set to \(-1\), the operating mode is selected automatically from the room temperature error.

4. Defrost modeinteger \(\in \{1, 2, 3\}\)

If the input 9 is set to \(1\), \(2\) or \(3\), the same value is provided as output. If it is set to \(0\), the defrost mode is selected automatically from the outdoor temperature.

5. Recovery penaltyreal \(\in [0, 1]\)

Correction factor for the heating capacity when the heat pump operates in recovery mode. See recovery penalty.

Control file

The control file contains more advanced parameters for the Type 3223. Those parameters include tables, which can be cumbersome to enter in the simulation studio, and are more easily entered in a separate file. Two control file examples (for cooling and heating operation) are shown below, along with short explanations for each parameter described in the files.

Cooling control file

Example of cooling control file.
 1!# Control file for cooling mode operation of Type 3223.
 2!#
 3!# Control operating range
 4!#   The error signal is defined as Tset - Tr.
 5!#   Minimum error value under which the frequency is maximum,
 6!#   in degree celsius.
 7     -2
 8!#   Maximum error value over which the frequency is zero,
 9!#   in degree celsius.
10     2.5
11!#
12!# Air flow rate control
13!#   Number of air flow rates
14     3
15!#   Normalized air flow rate values
16     1       0.827   0.608
17!#   Error values and deadband values (in degree celsius)
18!#   Note:   the number of lines must be equal to the number
19!#           of air flow rates minus one.
20!#   Error   deadband
21     -2.25   0.5
22     -1.25   0.5
23!#
24!# Minimum frequency
25!#   Number of outdoor temperature (To) values
26     3
27!#   To values
28!#   Lower normalized frequency limit values
29             10              14              40
30     0.614           0.316           0.175           0.263
31!#
32!# Boost frequency
33!# Boost frequency maximum duration (hours), scaling factor
34     0.5     0.8421
35!#   Number of outdoor temperature zones, number of air flow rates
36      2  3
37!#   Oudtoor temperature values and deadband values (in degree celsius)
38!#   Note:   the value of To + db/2 of a line should be smaller
39!#           than the value of To - db/2 of the next line.
40!#           The number of lines must be equal to the number of
41!#           outdoor temperature zones minus one.
42!#   To      db
43     11      2
44     20      2
45!# Normalized air flow rates values
46   0.608     0.827   1
47!# Normalized boost frequency values
48   0.543     0.649   0.895
49   0.456     0.614   0.755
50   0.649     0.789   1.334
Lines 7 and 10: control operating range

Those values define the room temperature error range \([e_\text{min}, e_\text{max}]\) over which the frequency is modulated. See control operating range for more details.

Line 16: air flow rate values

The indoor unit volume air flow rate values corresponding to each level (low / medium / high, see input 3), normalized by the rated air flow rate (parameter 9 of Type 3254). It should be in increasing order for heating mode control files, and in decreasing order for cooling mode control files.

Lines 21–22: parameters for the error deadbands

Fan speed level control relies on deadbands to prevent oscillating between two levels. (See fan speed level control for more details.) With \(n\) different levels, there should be \(n - 1\) deadbands. In this case, \(n = 3\) so there are two deadbands. Each deadband is defined by its center (first column) and its width (second column). Each row thus corresponds to a different deadband, and rows should be ordered so that the first column is in increasing order (lowest value at the top, and highest value at the bottom).

Lines 29–30: compressor frequency lower limit

The lower limit of the compressor frequency \(\nu_0\) can depend on the outdoor temperature \(T_o\). Different values of \(\nu_0\) can be assigned to specific temperature ranges. The first line represents the limits of each temperature interval (it should be ordered in increasing order). The second line specifies the value of \(\nu_0\) in each interval. The dependency provided in the example could be represented as follow:

../_images/min-freq.pdf
Line 34: boost frequency settings

The maximum duration of operation at boost frequency and the scaling factor.

Lines 36, 43–44, 46, 48–50: boost frequency values

To avoid oscillations between two boost frequency values, deadbands are used to model the outdoor tempertature dependency (see boost frequency). Assuming there are \(n\) temperature zones, there should be \(n - 1\) deadbands. In this example \(n = 3\) (see line 36), so there are two deadbands, corresponding to the lines 43 and 44. Each line specify the center then the width of the deadband. The lines should be ordered so that the centers are in increasing order (the smallest at the top), and different deadbands should not overlap.

Since the boost frequency values also depend on the indoor air flow rate, the normalized air flow rate value are also specified (in increasing order, see line 46). Finally, the boost frequency values are given as a table, whose columns correspond to the air flow rate levels given above. Thus if there are \(m\) flow rate levels, the dimensions of the table are \(n \times m\).

Heating control file

Example of heating control file.
 1!# Control file for heating mode operation of Type 3223.
 2!#
 3!# Control operating range
 4!#   The error signal is defined as Tset - Tr.
 5!#   Minimum error value under which the frequency is zero,
 6!#   in degree celsius.
 7     -2.5
 8!#   Maximum error value over which the frequency is maximum,
 9!#   in degree celsius.
10     3
11!#
12!# Air flow rate control
13!#   Number of air flow rates
14     3
15!#   Normalized air flow rate values
16     0.608   0.827   1
17!#   Error values and deadband values (in degree celsius)
18!#   Note:   the number of lines must be equal to the number
19!#           of air flow rate minus one.
20!#   Error   deadband
21     1.25    0.5
22     2.25    0.5
23!#
24!# Minimum frequency
25!#   Number of outdoor temperature (To) values
26     4
27!#   To values
28!#   Lower normalized frequency limit values
29             -5              3               7               18
30     0.5833          0.4833          0.3             0.1667          0.2667
31!#
32!# Maximum frequency
33   1.9833
34!#
35!# Defrost cycles parameters
36!#   Tcutoff: defrost cutoff temperature (in degree celsius)
37!#   t_df: the defrost duration, during which the heat pump
38         operates in cooling (in minutes)
39!#   t_h:  duration of heating mode operation in a cycle
40!#   t_rec: duration of the transient (recovery) period
41!#   Tmin: temperature under which a constant t_rec is used
42         instead of the linear dependance
43!#   Tcutoff t_df
44     6       5
45!#   t_h parameters: a + b * exp(c * (Tout+d)) (in minutes)
46!#   a       b       c       d
47     37.39   16.64   0.235   -2.118
48!#   t_rec parameters: m * Tout + p for Tout > Tmin
49      (in minutes and degree celsius)
50!#   m       p       Tmin
51     -0.931  10.798  -28

Note

Up to the line 30, the heating and cooling control files describe the same parameters—although sometimes with different values. Those parameters aren’t described here, to avoid redundancy.

Line 33: maximum frequency

The maximum frequency of the compressor, normalized by the rated frequency. There is no “boost” frequency in heating mode, since outdoor temperature is low and compressor overheating is not a concern.

Line 44: cutoff temperature \(T_c\) and defrost duration \(\tau_\text{df}\)

The cutoff temperature is the outdoor temperature limit above which no defrost is needed (see defrost cycles). The defrost duration is the time during which the heat pump works in cooling mode to remove the frost that formed on the outdoor unit exchanger.

Line 47: parameters for the heating operation duration \(\tau_\text{h}\)

Heating operation duration is the time during which the heat pump is not operating in defrost mode, i.e. the recovery and steady-state periods.

Line 51: parameters for the recovery period duration \(\tau_\text{rec}\)

When finishing a defrost operation, the heat pump goes through a recovery phase before reaching the steady-state. During the recovery period, the capacity of the heat pump is affected, but it recovers gradually over the period.

In-depth features

Control operating range

The frequency is modulated using a PI (proportional-integral) controller when the temperature error signal \(e = T_r - T_\text{set}\) is within a certain range \([e_\text{min}, e_\text{max}]\) (\(T_r\) is the input 4 and \(T_\text{set}\) the input 2). When \(e \notin [e_\text{min}, e_\text{max}]\), the frequency \(\nu\) is either set to zero or to its maximal value \(\nu_\text{max}\), depending on the operating mode.

mode

\(\pmb{e < e_\text{min}}\)

\(\pmb{e > e_\text{max}}\)

heating

\(0\)

\(\nu_\text{max}\)

cooling

\(\nu_\text{max}\)

\(0\)

The value of \(e_\text{min}\) and \(e_\text{max}\) also depend on the operating mode. In the example control files, these values are the following:

mode

\(\pmb{e_\text{min}}\)

\(\pmb{e_\text{max}}\)

heating

−2.5 °C

3 °C

cooling

−2 °C

2.5 °C

Fan speed level control

The fan speed level is selected automatically from the value of the temperature error \(e = T_r - T_\text{set}\), unless it is set explicitly (see input 3). To prevent oscillations between two fan speeds, deadbands are used to manage the transition between modes. For example, in the figure below, the fan speed goes from low to medium when the error drops below −1.5 °C, but in order to return to the low speed level, the error must exceeds −1 °C.

../_images/fan-deadbands.pdf

Illustration of the deadbands defined in the example control files.

Each speed level is associated with an air flow rate value, specified in the control file (line 16 in the examples).

Boost frequency

In cooling mode, high outdoor temperatures may cause overheat if the compressor is running at full speed for too long. The maximum compressor frequency is therefore limited to a safe value. However, when starting up the compressor can sometimes run temporarily at a higher frequency, called the boost frequency, to reach the setpoint faster.

../_images/max-freq.pdf

At full regime, the compressor operates about 20 % faster than its “safe” maximum speed for 30 minutes, then lowers its speed to avoid overheating.

This behaviour can be reproduced by the Type 3223, using two parameters: the duration of the boost frequency operation and the ratio between the maximum frequency and the boost frequency (aka the scaling factor). In the example above, the duration would be half an hour, and the scaling factor would be \(\frac{1}{1.2} \approx 0.833\). Check out line 34 of the example control file to see how to specify these parameters.

The value of the boost frequency (1.2 in the example above) should also be specified. However, this value may depend on the outdoor temperature \(T_o\) and the indoor unit fan speed. The latter is divided into fan speed levels, and each level is associated with a set of boost frequency values. The dependency with \(T_o\) is modelled using temperature intervals, the same approach as for the minimum frequency but with deadbands to avoid oscillations between two different compressor speeds. Each interval defines a temperature zone, which is also associated with a set of boost frequency values.

../_images/boost-freq.pdf

The boost frequency value depends on the outdoor temperature zone and on the fan speed level.

To correctly specify the boost frequency values, three things are needed:

  • The deadbands that allow to determine the temperature zones (each deadband is defined by its center and its width).

  • The normalized air flow rate corresponding to each fan speed level.

  • The table with the boost frequency values.

Check the end of the example control file to see how to include them.

Defrost cycles

Each defrost cycle is divided into three phases:

  1. The defrost operation, where the heat pump operates in cooling mode to bring heat in the outdoor unit.

  2. The recovery phase, where the capacity increases gradually towards its steady-state value, as it is affected by transient processes.

  3. The steady-state phase, where the heat pump operates normally.

Each phase has a certain duration, noted respectively \(\tau_\text{df}\), \(\tau_\text{rec}\) and \(\tau_\text{ss}\). The duration of the whole heating operation period (\(\tau_\text{rec} + \tau_\text{ss}\)) is noted \(\tau_\text{h}\).

../_images/defrost-cycle.pdf

Duration of each phase

The duration \(\tau_\text{df}\) is constant (line 44 of the heating control file), but \(\tau_\text{rec}\) and \(\tau_\text{ss}\) vary with the outdoor temperature. The dependency is specified through two regressions of the outdoor temperature, one for \(\tau_\text{rec}\) and one for \(\tau_\text{h}\) (from which one can deduce \(\tau_\text{ss}\)).

\[\begin{split}\frac{\tau_\text{rec}}{\text{min}} = \left\{ \begin{array}{lr} p + m\,\dfrac{T_o}{\text{°C}} & \text{if } T_o \geq T_\text{min} \\ 37 & \text{if } T_o < T_\text{min} \end{array} \right.\end{split}\]
\[\frac{\tau_\text{h}}{\text{min}} = a + b\, \exp\left[c\left(\frac{T_o}{\text{°C}} + d\right)\right]\]

The parameters \(a\), \(b\), \(c\), \(d\), \(p\), \(m\) and \(T_\text{min}\) must be provided at the end of the heating control file.

Cutoff temperature

Since defrost is only necessary below a certain temperature level, defrost cycles are not triggered whenever the \(T_o\) is above a cutoff temperature \(T_c\) for a certain period. Specifically, cycles are not triggered if the the time \(\tau_\text{oc}\) during which \(T_o > T_c\) is bigger than the time \(\tau_\text{uc}\) during which \(T_o < T_c\).

../_images/cutoff-temperature.pdf

Illustration of the cutoff temperature. In this case, \(\tau_\text{oc} > \tau_\text{uc}\) so there would be no defrost cycles.

The cutoff temperature must be provided in the control file; see line 44 of the example heating control file.

Recovery penalty

To quantify how the heating capacity is affected by transient processes in the recovery phase, the Type 3223 computes a correction factor—called the recovery penalty—to apply to the steady-state capacity value. Since the Type 3254 is in charge of finding this capacity value, the Type 3223 outputs the recovery penalty so that it can be provided to the Type 3254 (input 14).