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Introduction

Heat Load Components

Electrical Analogue Model for an Airconditioned Rom

Control Strategies for Energy Conservation in Room A/C units

Description of the Simulink Model of the System

Selected Simulation Results
 
 
 

      [ This article was prepared for a short-term course conducted by Department of Electrical Engg., NIT Calicut in 2000.]

Demand Side Management considers room air conditioner load as one of the most suitable loads to implement direct customer load control in order to exercise peak demand control as well as energy consumption control in Supply systems. In DSM, the room A/C units located at customer premises are directed to enter energy/demand saving control modes by means of control signals issued from sub stations either via remote radio link or via power line carrier communication link at distribution level when the Utility wants to exercise demand control during periods of power shortage. A prior contractual arrangement with the customer is of course implicit. Two popular control techniques employed in room A/C units in order to limit their energy consumption and their average power demand are examined in this lecture using SIMULINK simulation as the study tool. It may be noted that these and similar control strategies have been in use for many years in Western Power Systems for implementation of Direct Load Control.

The room A/C unit contains two a.c single phase motors-one for the compressor and one for the Air Fan. The air fan runs continuously whereas the compressor motor is on an ON/OFF cycle mode operation. The thermostat and its setting decide the state of the compressor motor. The bimetallic type thermostat trips the compressor motor when the inside temperature exceeds the thermostat setting by a small value (due to thermostat hysteresis) and the compressor motor is switched on when the inside temperature goes below the setting by the same small value. In a 1.5T room A/C unit the compressor motor is rated for 2kW and the fan motor is rated for 149W.It has been found from experimental observations that the daily duty factor (defined as the ratio of total compressor motor ON time to the total time for which the A/C unit was operational) usually varies from 0.4 to 0.5 in the case of an A/C unit selected properly. Also the duty factor for operation between 9:00AM to 6:00PM has been found to have a range of 0.5-0.6.This implies that if the unit is powered for 24hrs a day, an 1.5T unit is likely to consume 20 to 25 units of electrical energy every day. Considerable energy saving opportunity exists in the case of room A/C units at the expense of slight/negligible discomfort to the occupants. The conventional bimetallic thermostat based controller will have to be replaced by Electronic Sensor based controller in order to exercise the kind of control covered in this lecture.

The basic components of a room A/C unit are the compressor, air cooled condenser, expansion valve, evaporator, two motors and air filter. The refrigerant absorbs heat from the evaporator and rejects it to the condenser. The fan draws in air from outside and circulates it over the condenser to cool it. The fan also draws in outside air through the compressor compartment for ventilation of the conditioned space. The amount of ventilating air is controlled by a damper position in its path. The room air enters the evaporator chamber, goes over the cooling coils and comes back into the room through the air filter.

The expansion valve used room A/C units is of capillary tube type. The capillary tube holds back the refrigerant gas while releasing the liquid only into the cooling coil. The length of the tube and its diameter are the controlling factors in its performance. Once the compressor stops, the capillary tube will equalize pressures in the system in about half a minute. This is a distinct advantage, for the compressor is free to start on no load when it is switched on next time. Hence it is very vital that the controller ensures that at least half a minute is allowed before the compressor is switched on again after being switched off. Usually more than this minimum time will be available due to the large time constants in the thermal system, delays involved in the temperature sensing and the hysteresis band available in the thermostat. But when the temperature sensing is done electronically and the bimetallic thermostat is replaced by an electronic thermostat it may be necessary to build in electronic logic to ensure that the compressor motor remains off for at least a minute after it is stopped once.

2.  Heat Load Components

Cooling load calculations room A/C units deal with heat gains of two kinds:
 

Sensible Heat gains to the space include:

A further load classification that is frequently used is based on the sources of heat. Loads are
External, if they come from without the conditioned space. These are either sensible or latent.
Internal, if they are produced within the conditioned space. This too may be either sensible or latent heat.

3.  Electrical Analogue Model for an Air Conditioned Room

The dynamic behaviour of the air-conditioned room has been modeled from fundamental physical principles. The model thus obtained is a lumped parameter electrical analog model where each parameter represents a physical quantity. However, accurate measurement of these quantities would be difficult because in reality they are distributed parameters.

Several variables, such as, temperature, solar radiation, humidity, wind speed, air infiltration etc influence the flow and storage of heat in a room in a very complex manner. Representation of every component and process in detail will make modeling very difficult and the model becomes intractable. Therefore, assumptions are made to obtain a simple, yet fairly accurate model. The effect of only major variables like temperature, solar radiation, air infiltration, humidity and internal heat is taken into account while developing the model. The lumped parameter model thereby is shown in Fig.1.

The walls, base and roof of the room are represented by a T network formed by R_w and C_w, where R_w represents the equivalent thermal conduction resistance and C_w represents the thermal storage capacity of the room (walls, base and roof). The average air infiltration is represented by an equivalent resistance R_c.C_i represents the thermal capacitance of the air inside the room. T_o is the outside temperature, T_w is the wall temperature and T_i is the inside temperature.

The heat removed by the air conditioner is represented by a current source I_ac in the figure. The value of this source is I_ac multiplied by a switching function S(t).S(t) is 1 when the compressor motor is ON and 0 when compressor motor is OFF.

Normally the temperature of air at the fan outlet in a room A/C unit is kept within a small band around a set temperature by thermostatic control. When the air conditioning unit compressor is switched off all the refrigerant return to a liquid state in a short time and when thermostat switches the compressor motor on it takes a little time for the vapor system to come to steady state. However, this time is small and once the vapor system comes to steady state the heat removal rate and the compressor load remains essentially constant since the outlet air temperature is maintained more or less constant. Thus neglecting the load and heat removal rate variations during switching on transients, it may be safely assumed that, whenever the compressor is ON the heat removal rate and compressor load are at a fixed level. Hence the representation of air conditioner heat removal rate by a constant current source is justifiable. Also the energy consumption by the compressor motor is thus proportional to the total ON period of the motor over a day or equivalently to the average duty factor over the day.

Most of the solar radiation and part of the internal heat do not heat the inside air directly; rather their energy is first absorbed by the walls, roof and other mass inside the room and then it is delivered to the inside air. Therefore these two components (solar radiation and the portion of internal heat sources involved in this indirect heating of air) are combined to give the source I_s represented by a current source in the electrical analogue. This current source is connected across C_w to represent the heat storage effect.

I_inst is the current source to represent the instantaneous component of internal heat sources such as bulbs, fans etc, which heat up air inside directly. I_cond is the current source used to represent the heat addition due to the condensation of water vapor in the room A/C unit evaporator tubes. This condensation takes place only when the unit is ON. This usually represents only a small addition to the heat load and hence is neglected in the simulation study reported here.

There is an unavoidable delay between the air temperature and the actuating temperature of a thermostat due to thermal time lags in the sensing unit. This delay serves the useful function of avoiding too frequent switchings of the unit under heavy load conditions and also avoids the compressor motor starting on loaded condition. The sensing system is not shown in Fig.1.However it was modelled by a first order transfer function in the simulation model.

The model parameters for a typical room of 6mx6mx4m have been calculated/estimated using standard calculation practices used in Air Conditioning calculations. These values are listed below.

R_w = 0.004 ⁰C/W
R_c = 0.01 ⁰C/W
C_w = 6,000,000 J/⁰C
C_i = 175,000 J/⁰C
I_ac = 7500W(for a 2T unit)

The source functions T₀,I_s,I_inst are available in the form of table of hourly values.T₀ is arrived at by temperature records on June 22^nd at Calicut and the solar radiation heat gain is calculated by using standard solar radiation curves for the appropriate data relevant for Calicut. The roof area was taken as the solar radiation incidence area and the solar radiation on side walls were ignored.

The source I_inst was estimated through knowledge of electrical equipment used inside the room and their use pattern

The plots of these source functions-T₀ ,I_s and I_inst-, obtained by interpolating between the hourly values, are shown in Fig.2,Fig3 and Fig.4 respectively.

In an electrical analogue for a thermal system temperature difference is analogous to potential difference, heat flow is analogous to current, thermal resistance is analogous to electrical resistance and thermal capacity or thermal storage is analogous to electrical capacitance.

The governing equations of the system can be obtained by writing Kirchoff’s current law at the two nodes where the unknowns are T_w and T_i.

The system equations after simplifying are cast into the form of two first order differential equations with coupling. This form is suitable for solution by numerical methods.

4.  Control Strategies for Energy Conservation
 

Three control modes are implemented in an Electronic thermostat. They are ‘NORMAL’ , ‘HOLD’ and ‘RAMP’.

In the NORMAL mode the Electronic thermostat behaves as a normal thermostat with the only difference that since the temperature is sensed electronically and the setting is done electronically much more flexibility will be available in the Electronic thermostat. In a bimetallic strip based thermostat the range of set temperature available is limited and even if the user wants to save energy by increasing the set temperature, the range available is limited. Also, the hysteresis band in such a thermostat can not be adjusted. These shortcomings are solved in an Electronic thermostat.

When HOLD mode is chosen in an Electronic thermostat the duty ratio of the room A/C unit is kept constant from that time instant onwards. Normally the duty ratio, i.e the ratio of ON Time to total duration of a switching cycle , goes on varying as the outside temperature and solar radiation increase. The peak in the heat load on the unit takes place after the peak in the outside temperature and solar incidence. This is due to the thermal time lag introduced by the large heat capacity of walls, base and roof. Usually the room A/C unit faces maximum load after 90 to 120 minutes of outside temperature and solar radiation reaching a peak. The duty ratio will reach a peak at this time if the unit is on NORMAL mode. It could be as high as 0.8 in a properly sized unit and it could approach unity if the sizing is not proper. And if the unit is undersized the unit will remain ON continuously for hours together during this period and yet the room temperature may increase. Not allowing the compressor motor to go off periodically affects the heating in compressor motor and is detrimental to its life. In the HOLD mode the duty ratio, the ON time and the OFF time of the room A/C unit is kept constant disregarding the set temperature and allowed band around it. The price paid is the increasing temperature inside. Usually a supplementary control that overrides this mode will have to be built in to avoid the inside temperature becoming too high for the comfort of users. But it is possible to arrange the HOLD mode duration in such a way that the discomfort to the user is marginal and unnoticeable. Considerable energy saving will be possible by using this mode. Moreover the compressor motor life will be extended.

But what is the value of ON time and OFF time that will be used to decide the condition of compressor motor in the HOLD mode ? Two possibilities exist and both are used in actual implementations.In the first case the average duty factor in the last hour immediately prior to the HOLD command is calculated and a fixed time interval, usually 15min,is divided as per this duty factor .For e.g let the room A/C unit be running with an average duty factor of 0.4 at the time of receiving HOLD command. Then the room A/C unit will be cycled at the rate of 6 minutes ON and 9 minutes OFF till the HOLD command is removed. In the second method the ON duration and OFF duration of the last cycle of ON/OFF is used as the held value of ON duration and OFF duration. The values used pertain to the last ON/OFF cycle completed and does not refer to the ongoing cycle of switching at the time of incidence of HOLD command. The HOLD logic has to see to it that at least one complete cycle of switching has taken place before the room A/C unit is put on HOLD. In fact it is better that the HOLD logic ensures that at least two switch-offs have taken place before HOLD is obeyed. This is to ensure that the unit does not go into HOLD mode with a large ON Time. This will happen at starting of the unit. The first cycle ON time of a room A/C unit will be large since the heat load will be high at the time of powering the unit. If the unit is asked to go into HOLD during or immediately after the first cycle the held ON time will be large and instead of energy conservation it will result in more consumption. Thus the HOLD logic must wait for a steady state cycle i.e it must record at least two switch-offs of compressor motor before it puts the unit on HOLD. This logic is used in the simulated system.

The HOLD command on a unit should be removed and it should be allowed to go back into NORMAL mode only after the heat load has gone down well below the peak level. When the hold mode is terminated the normal set temperature value comes back into effect and the unit remains in ON condition for a laong time before settling down to a cyclic operation. Many room A/C units released from HOLD mode simultaneously can put a large peak demand on the distribution system – the very thing the Utility was trying to avoid by asking all the room A/C units in the distribution area to go into HOLD mode by remote radio control. The duration of this large ON period will depend on the set temperature value and the heat load at the time of releasing the HOLD command. Hence, if the unit is put on HOLD it should be released only after the day has cooled down. The optimum HOLD period would be from 12:00 noon to 8:00PM or so in our climate.

The HOLD mode suffers from virtual loss of control on the inside temperature and the consequent possibility of noticeable user discomfort. The RAMP mode offers a solution to this. In this mode the thermostatic action remains i.e., the thermostat tripping controls the ON/OFF cycle. But the set temperature is no more a constant. In the RAMP mode, the set temperature is ramped up first from its NORMAL mode value @ 1⁰C/hr or 2⁰C/hr till the set value reaches about 28⁰C or 29⁰C.And after that it is ramped down at the same rate till it reaches the NORMAL mode setting. There is effective control on the inside temperature and at the same time considerable energy saving is possible. This mode has been by far more popular than HOLD mode.

5.  Description of the SIMULINK Model of the System

The room A/C unit system, with the parameter values and source function given earlier, was simulated in MATLAB-SIMULINK in order to estimate the possible energy savings under different modes of control. The simulation model developed is shown in Fig.5.

A ‘hierarchical block’ approach was used in the development of the model. The fig.5 shows the top layer model. The major parts of the system are embedded in the subsystem blocks.

There are five subsystem models at this level. They are the input sources model, the A/C Room Model, the ON/OFF Control Model, the Hold Mode Control Block and the Ramp Mode Model. The remaining components at the top-level model are for signal outputting and signal observation.

The Input Source Model is expanded in Fig.6a.It contains three look up table elements needed for the three source functions-the outside temperature, the solar radiation heat gain and the instantaneous component of internal heat gain. The tabular values are entered against time in minutes and the look up table elements do interpolation if needed. A clock element through a gain block of gain 1/3600 convert the simulation time in seconds into minutes and provides the time information into the look up tables.

The Hold Mode Control Block is expanded in Fig.6b.It contains two step function elements and a summer. The first step function outputs a unit step with transition at an instant which is a parameter that can be set by opening that element. Similarly the second one outputs a negative unit step at a designated time point later. Addition of these two gives the HOLD mode control signal.

The Ramp Mode Block is expanded in Fig.7.It is an enabled model and it is executed only when the ‘Ramp Mode ON’ step source element at top level goes high. This block has a look up table inside which outputs the linearly increasing and decreasing temperature reference in force while RAMP mode lasts. A threshold switch element at the top level directs the correct set temperature value for NORMAL and RAMP modes into the subsequent blocks.

5.1 The A/C Room Model

The A/C Room Model is expanded in Fig.8.This subsystem accepts five inputs. The source functions make for three. The fourth input is the information that the room A/C unit has been powered. This is provided by a step source ‘Power ON’. The fifth input is the compressor motor ON/OFF signal and is needed to decide the switching function value S(t) needed for solving the differential equations. The model has two outputs and they are the sensed inside temperature and the true inside temperature. This block implements the two coupled first order differential equations describing the analogue electrical model of the room A/C system using gain blocks, summing blocks and two integrators. The delay involved in sensing the inside temperature is modeled using the transfer element. A first order transfer function is used.

5.2 The ON/OFF Control Model

The ON/OFF Control Model accepts the sensed room temperature, the HOLD command and the temperature setting as the inputs. It provides seven outputs one of which –ON/OFF Control- is the information about the state of compressor motor. This block is expanded in Fig.9.This block models the thermostat in the NORMAL mode and RAMP mode and decides whether the compressor motor should be switched ON or OFF. It also keeps a record of the ON time and OFF time during the last completed cycle, the total ON time and OFF time since the start of simulation and the count of switching ON & switching OFF operations since the start of simulation. These six variables are also provided as simulation outputs. In the HOLD mode this block checks to verify that at least two switch OFF operations have taken place. If not it will wait for that to take place. After that the last cycle ON and OFF times are accepted as the relevant fixed ON and OFF times till the HOLD mode lasts and suitable ON/OFF control signal will be issued. All the while ON/OFF times, total ON/OFF times and ON/OFF counts will be updated and outputted. 

This block uses five subsystems of its own and four data store memory elements of SIMULINK to perform its functions. At the top layer of this block the received sensed temperature is compared with the set temperature and the difference is passed on to a relay block with hysteresis (simulating the thermostat). The relay output is the ON/OFF control signal in the NORMAL mode. The HOLD mode signal received at the top layer is passed on to a subsystem called Hold Initiation Block (expanded in Fig.9a) where it is passed on to its output after verifying that at least two OFF operations have taken place. This HOLD signal is used as the threshold signal in a switch element and the switch element will pass on the relay output or the signal from Hold Mode Timing Block as the compressor motor ON/OFF Control signal to the Room Model depending on the Hold Command output value from Hold Initiation Block.

The compressor motor ON/OFF Control signal goes to four subsystems in addition to the output. The unipolar format is used for this signal i.e. ON is represented by a value of 1 and OFF by 0 (not –1).The Total ON/OFF Time Block (expanded in Fig.9b) receives this signal and integrates it to obtain the Total ON time of the unit. Subtracting this signal from 1 makes a signal that uses 1 to represent OFF and 0 represent ON and on integration results in Total OFF time output.

The two subsystems called ON Count Block and OFF Count Block (expanded in Figs 9c and 9d) keep the count of ON and OFF operations of the compressor motor from the ON/OFF signal received from top layer. They make use of two data store memory elements named ONCOUNT and OFFCOUNT. These two subsystems are SIMULINK Triggered elements and both execute at the rising edge of respective trigger signals. The trigger for ON Count Block is the ON/OFF Control signal and for the other it is the complement of ON/OFF Control signal. At the rising edges, the subsystems add 1 to the present memory contents and execute a write operation into the same memory locations. Triggered execution and non-zero time steps used by the simulator avoid a ‘racing condition’.

The next subsystem ON/OFF Duration Block (expanded in Fig.9e) keeps track of the ON and OFF times during the ongoing cycle of switching and at the end of the cycle writes these values into two data store memory elements defined for that purpose and named ON and OFF stores. Integrators with reset function are used to integrate the received ON/OFF Control Signal and its complement to find out the current ON time and OFF time. At the end of integration the integrator contents are written into ON and OFF data sore memory elements by ‘Memory Store Write’ elements contained in the next level subsystems On Time Store Write and Off Time Store Write. These are triggered subsystems in order to avoid updating the memory content while the integration is going on. The integrators are reset at the edge of reset signal after the write operation is over. The required delay between the memory write edge and integrator reset edge is implemented by using the transportation delay block. Thus the Data Store Memories called ON and OFF will always contain the ON and OFF time durations in the last completed cycle of compressor motor switching. Also the ongoing ON time and OFF time are available at the integrator outputs and these are made available to the top layer.

These current time values go into the last subsystem Hold Mode Timing Block (expanded in Fig.9f). This block reads the last completed cycle ON/OFF values from the relevant data stores. The current time is compared with the last completed cycle time and the difference is passed on to a ZCD. The ZCD element outputs sets and resets a SR Flip Flop and the FF output can be used as the ON/OFF Control Signal for compressor motor. Very accurate determination of zero crossing by the ‘Hit Crossing’ elements in SIMULINK prevents the values contained in the Data Store Memory elements named ON and OFF from drifting away from the values they contained at the beginning of HOLD mode. The unused output of SR FF is terminated using the ‘Terminator’ element at the top layer in order to avoid error messages while simulating.

6. Selected Simulation Results

Various simulation runs using the developed model were carried out using SIMULINK 2.1 in MATLAB 5.1.Some representative outputs are discussed in this section. The aim of this lecture was to illustrate how a reasonably complex system can be simulated in SIMULINK by developing a suitable simulation model. Many runs with variations in system parameters and source functions will be needed to evaluate completely the efficacy of the control strategies under varying conditions and at various locations.

The system was simulated in the NORMAL mode to study the effect of thermostat setting on the daily energy consumption. The effect of sensing delay was examined by running the simulation with various sensing delays. Also the effect of changing the hysteresis in the thermostat was investigated.Fig.10 shows the growth of ON time of the unit over a day and shows clearly that most of the energy consumption takes place during the 10:00AM to 6:00PM period. Also the daily duty factor is seen to be about 0.35.Fig.11 shows similar information for hysteresis band of ± 4⁰C.The total hours of energy consumption has come down and there is a long period for which the unit remained OFF continuously (the flat portion in the curve).

Fig.12 shows the variation of total daily operation hours against the set temperature in the NORMAL mode. The delay in sensing the inside temperature is seen to result in longer operation hours at all settings. And doubling the hysteresis band value has the effect of decreasing the total time of operation. But the most significant point is the extent of possible energy savings by setting the thermostat to higher levels. For example revising the thermostat setting from 21⁰C to 24 ⁰C results in 1.85 hours less of operation and it amounts to about 25% energy savings on 21⁰C setting basis.The duration of unit operation seems to be almost proportional to the thermostat setting for any band value and sensing delay.
 
 

Fig.13 shows the effect of HOLD mode between 12:00Noon to 8:00PM on energy consumption at various thermostat settings. It can be seen that the energy consumption has come down by a factor of about 0.87 at all settings. This represents 13% energy savings at all setting.

But this saving came at a price.The inside temperature goes above set value during the HOLD mode.Fig.14 shows the maximum inside temperature for various cases and it can be seen clearly that HOLD mode with high temperature setting in the thermostat is as good as switching off the unit!

Fig.15 shows the variation of ON duration in switching cycles and clearly shows that the ON duration is held constant during the HOLD mode. It also shows that there is a large period of operation immediately after the HOLD mode is released.

The total number of switching operations for various cases are shown in Fig.16.The simulation results verify the expected relation between the number of switching operations and the relevant variables like the set temperature, hysteresis band and sensing delay. Lower the set temperature higher the frequency of switching. Higher the hysteresis band lower the number of switching operations. And higher sensing delay lowers the number of switchings.

Fig.17 shows the set temperature and the inside temperature in the case the unit operated in the RAMP mode from 9:00AM to 7:00PM.The thermostat setting before enabling the RAMP mode was 21⁰C and after the RAMP mode operation is over the set temperature comes back to the same value. The ramp rate was 1⁰C/hr, going up to 26⁰C at 2PM and then coming back 21⁰C at 7PM.The total ON period without RAMP mode was 7.6 hours and with RAMP mode it was 7 hrs. This represents energy savings of about 10%.