Abstract:
A system and method for controlling a system that includes fixed speed and variable speed compressors are described. The method generally allows the system, for example, a heating, ventilating, and air condition (HVAC) system that includes fixed speed and variable speed compressors, to maximize unit modulating capability. The method allows the use of a variable speed compressor that is relatively smaller, which can lead to cost savings, easier installation, manufacturing, etc.

Description:
FIELD 
       [0001]    The embodiments disclosed herein relate generally to a system and method for controlling a system that includes fixed speed and variable speed compressors. 
       BACKGROUND 
       [0002]    Control of a compressor utilized in a refrigeration circuit within a refrigeration system is known. Improvements in control of refrigeration systems that include a compressor may be made. 
       SUMMARY 
       [0003]    The embodiments described herein are directed to a system and method for controlling a system that includes a fixed speed compressor and a variable speed compressor. The method generally allows the system, for example, a refrigeration or a heating, ventilating, and air condition (HVAC) system that includes fixed speed and variable speed compressors, to maximize unit modulating capability. The method allows the use of a variable speed compressor that has relatively smaller capacity, which can lead to cost savings, easier installation, manufacturing, etc. 
         [0004]    In some embodiments, the system includes one variable speed compressor, at least one fixed speed compressor, a condenser and an evaporator. In some examples, the system can include more than one variable speed compressor. In some examples, the system can further include a control unit that is configured to control the system by executing a control program or algorithm that is stored in a memory of the control unit. 
         [0005]    In some examples, the system includes first and second fixed speed compressors, and the control unit is configured so that the fixed speed compressors and the variable speed compressor operate in certain operational stages. 
         [0006]    The term “operational stage” means the operational state of each of the compressors. The term “operating mode” refers to a capacity of the compressors operating in a certain operational stage. 
         [0007]    The operational state of the fixed speed compressor can be the on state or the off state. The operational state of the variable speed compressor can be the off state, variable speeds ranging from a minimum speed to a maximum speed. In some examples, the operational stages include the following: Stage 0, Stage 1 min, Stage 1 max, Stage 2 min, Stage 2 max, Stage 3 min and Stage 3 max. 
         [0008]    At Stage 0, the first and second fixed speed compressors and the variable speed compressor operate in the off state so that the speeds of the fixed speed compressors and the variable speed compressor are at 0 revolutions per second (rps). 
         [0009]    At Stage 1 min, the speed of the variable speed compressor ramps up from 0 rps until a minimum speed is reached. In some examples, the speed of the variable speed compressor ramps up at a constant rate and/or a variable rate. In some examples, the ramp rate can be different or the same as that in the other operational stages. For example, the ramp rate in Stage 1 min can be the same as or different from that of Stage 1 max, Stage 2 max, and/or Stage 3 max. In some examples, the ramp rate is predetermined. In some instances, the ramp rate is predetermined based on the type of compressors utilized, e.g., manufacturer, size, etc. of the compressors. The first fixed speed compressor and the second fixed speed compressor operate in the off state so that their speeds are at 0 rps. 
         [0010]    At Stage 1 max, the speed of the variable speed compressor can ramp up from the minimum speed to a maximum speed. In some examples, the speed of the variable speed compressor ramps up at a constant rate and/or a variable rate. The first fixed speed compressor and the second fixed speed compressor operate in the off state so that the speeds are at 0 rps. 
         [0011]    At Stage 2 min, the first fixed speed compressor operates in the on state and the second fixed speed compressor operates in the off state so that the speed of the second fixed compressor is at 0 rps. The speed of the variable speed compressor is set at or ramped down to a minimum speed. Note that the minimum speed of Stage 2 min can be different from the minimum speed of Stage 1 min. 
         [0012]    At Stage 2 max, the first fixed speed compressor operates in the on state and the second fixed speed compressor operates in the off state so that the speed of the second fixed compressor is at 0 rps. The speed of the variable speed compressor ramps up from a minimum speed to a maximum speed. In some examples, the speed of the variable speed compressor ramps up at a constant rate and/or a variable rate. Note that the maximum speed of Stage 2 max can be different from the maximum speed of Stage 1 max. 
         [0013]    At Stage 3 min, both the first fixed speed compressor and the second fixed speed compressor operate in the on state. The speed of the variable speed compressor is set at or ramped down to a minimum speed. Note that the minimum speed of Stage 3 min can be different from the minimum speed of Stage 1 min and/or the minimum speed of Stage 2 min. 
         [0014]    At Stage 3 max, both the first fixed speed compressor and the second fixed speed compressor operate in the on state. The speed of the variable speed compressor ramps up from a minimum speed to a maximum speed. In some examples, the speed of the variable speed compressor ramps up at a constant rate and/or a variable rate. Note that the maximum speed of Stage 3 max can be different from the maximum speed of Stage 2 max and/or the maximum speed of Stage 2 max. 
         [0015]    In some examples, the stages listed above, that is, Stage 0, Stage 1 min, Stage 1 max, Stage 2 min, Stage 2 max, Stage 3 min and Stage 3 max, occur sequentially in the listed order when the load is increasing. In some examples, the stages listed above occur in reverse order when the load is decreasing. 
         [0016]    In some examples, the control unit implements an algorithm to control the operation of the compressors. The algorithm generally involves modulating the speed of a variable speed compressor relative to the fixed speed compressors based on a measured parameter and a set point of the measured parameter. In some examples, the control unit implements an algorithm to control the operation of the compressors using a PI controller. 
         [0017]    In some instances, the algorithm can involve: 
         [0018]    (a) measuring a parameter, for example, discharge air temperature (DAT); 
         [0019]    (b) determining a PI capacity value based on the parameter measured in (a) and a set point using the PI controller; 
         [0020]    (c) determining an operating mode based on the PI capacity value determined in (b); 
         [0021]    (d) operating the fixed speed and variable speed compressors based on the determination made in (c); 
         [0022]    (e) determining an operating mode after (d); 
         [0023]    (f) determining the operational state of the fixed speed compressor; 
         [0024]    (g) operating the fixed speed compressor based on the determination made in (f); 
         [0025]    (h) determining a speed of the variable speed compressor using the PI controller; and 
         [0026]    (i) operating the variable speed compressor based on the determination made in (h). 
         [0027]    In some examples, in step (c), the PI capacity value is compared to one or more preconfigured values to determine the operating mode, where the operating mode indicates the applicable operational stage(s) based on the determined PI capacity value. In some examples, the preconfigured values are based on the configuration of the system, for example, the type of compressors used, the number of compressors used etc. 
         [0028]    In some instances, the determination made in steps (c) and (e) can depend on whether there is a capacity/stage gap for the variable speed compressor relative to the fixed speed compressors. 
         [0029]    In some examples, the ramp rate in the operational stage(s) is limited using the PI controller. In some examples, limiting the ramp rate involves determining a change in speed of the variable speed compressor using the PI controller, comparing the determined change to a predetermined value, and based on the comparison, limiting the ramp rate of the variable speed compressor. 
         [0030]    Other aspects of the invention will become apparent by consideration of the detailed description and accompanying drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0031]    Referring now to the drawings in which like reference numbers represent corresponding parts throughout. 
           [0032]      FIG. 1  is a schematic illustration of a system for controlling the operation of fixed speed and variable speed compressors, according to one embodiment. 
           [0033]      FIGS. 2A-2C  are flow charts of the processes involved in controlling the fixed speed and variable speed compressors, according to one embodiment. 
           [0034]      FIGS. 3A and 3B  illustrate the overall concept of the term “capacity/stage gap(s)”, according to one embodiment. 
           [0035]      FIG. 4  shows a graph of the relation between the operating modes and operational stages where there is no capacity/stage gap, i.e., where a capacity/stage overlap, according to one embodiment. 
           [0036]      FIG. 5  shows a graph of the relation between the operating modes and operational stages where there is a capacity/stage gap, according to one embodiment. 
       
    
    
     DETAILED DESCRIPTION 
       [0037]    The embodiments described herein are directed to a system and method for providing control in a system that includes a variable speed compressor and at least one fixed speed compressor. In some examples, the system can include more than one variable speed compressor. 
         [0038]    The system can be any system that utilizes a variable speed compressor and one or more fixed sped compressors, including, but not limited to, water source heat pumps, unitary systems, split systems, self-contained systems, outdoor air units and airside, terminal devices and generally any temperature control equipment that utilizes one or more variable speed compressor and one or more fixed speed compressor. Airside and terminal devices include air handlers, make-up air gas heating systems, ventilation fans, blower coil air handlers, HVAC fan coil units, electric wall fins, unit ventilators and variable air volume units. 
         [0039]    In some examples, the system can be a large tonnage unit. In some instances, the large tonnage unit has an overall compressor capacity between about 6 to about 12 tons. In some other examples, the system can be a larger tonnage unit. In some instances, the larger tonnage unit has an overall compressor capacity between about 12.5 to about 162.0 tons. 
         [0040]      FIG. 1  provides a schematic illustration of one embodiment of the disclosed system (see system  100  in  FIG. 1 ). The system  100  includes a variable speed compressor  105 , a first fixed speed compressor  108  and a second fixed speed compressor  112 . 
         [0041]    Note that  FIG. 1  shows an example of a system including one variable speed compressor  105  and two fixed speed compressors  108  and  112 . However, the number of each of the compressors that can be included in the system  100  can be any number that is suitable for use in a refrigeration and/or a HVAC system. Further details of a system that includes more than one variable speed compressor is provided at the end of the Detailed Description below. 
         [0042]    The term “fixed speed compressor” means a compressor that operates at a fixed speed. The first fixed speed compressor  108  and the second fixed speed compressor  112  can be connected to motors  116  and  119 , respectively, and can be operated as is generally known in the art. The first fixed speed compressor  108  and the second fixed speed compressor  112  can be controlled, for example, by a control unit  121  (note that the control unit  121  will be discussed more in detail below) so that each of the first fixed speed compressor  108  and the second fixed speed compressor  112  operates in the on state or off state. In the on state, each of the first fixed speed compressor  108  and the second fixed speed compressor  112  operates at a fixed speed, e.g., a speed at anywhere between 25 and 100 revolutions per second (rps). In some examples, one or both of the motors  116  and  119  are induction motors. In some instances, one or both of the fixed speed compressors  108  and  112  run on a 60 HZ power supply, and one or both of the fixed speed compressors  108  and  112  operate at a fixed speed of about 60 rps. In the off state, each of the first fixed speed compressor  108  and the second fixed speed compressor  112  operates at 0 rps. 
         [0043]    The term “variable speed compressor” means a compressor that operates at variable speeds, as generally understood in the art. The variable speed compressor  105  can be connected to a motor  124  that is driven by a variable speed drive  126 , as is generally known in the art. The speed of the variable speed compressor  105  can be controlled, for example, by the control unit  121 , so that the variable speed compressor  105  operates at variable speeds, for example, a range of speeds including a minimum speed and a maximum speed. The minimum speed can be, for example, about 25 rps, and the maximum speed can be, for example, 100 rps. Note that these speeds are provided as examples only. In some examples, the minimum speed and/or the maximum speed will depend on the configuration of the system  100  utilized, for instance, the type of variable speed compressor used, the capacity of the variable speed compressor relative to the fixed speed compressors, etc. When the variable speed compressor  105  is turned off, the variable speed compressor  105  operates at 0 rps. 
         [0044]    Each of the fixed speed compressors  108  and  112  and the variable speed compressor  105  can be any compressor type that is suitable for use in a refrigeration and/or a HVAC system, and can include, but is not limited to, reciprocating, scroll, rotary, screw, centrifugal, etc. 
         [0045]    In some examples, each of the fixed speed compressors  108  and  112  and the variable speed compressor  105  can be in fluid communication with a condenser  129  and a cooling coil  131 . The cooling coil  131 , the condenser  129  and the compressors  105 ,  108 , and  112  can utilize a refrigeration loop that is generally known in the art. In some instances of the refrigeration loop, the compressors  105 ,  108 , and  112  can feed high-pressure and high-temperature refrigerant gas to the condenser  129 . The refrigerant vapor that is delivered to the condenser  129  then can enter into a heat exchange relationship with a fluid, for example, air. In some embodiments, the condensed liquid refrigerant from the condenser  129  then can flow through an expansion device (not shown) to an evaporator (not shown). In some instances, when an evaporator is used, a secondary liquid, e.g., water, that has flowed into the evaporator then can enter into a heat exchange relationship with the low pressure/low temperature liquid refrigerant to chill the temperature of the secondary liquid. The chilled secondary liquid can then run through the cooling coil  131 , and the refrigerant liquid in the evaporator can undergo a phase change to a refrigerant vapor as a result of the heat exchange relationship with the secondary liquid. It will be appreciated that if an evaporator is not employed, the cooling coil  131  may act as the evaporator in the system  100 . The refrigerant vapor then can return to the compressors  105 ,  108 , and  112  to complete the refrigeration loop. 
         [0046]    The system  100  also can include a sensor  135  for measuring a parameter. In some examples, the parameter can be a discharge air temperature (DAT) and/or a space temperature. 
         [0047]    The control unit  121  of the system  100  generally can include a processor (not shown), a memory (not shown), a clock (not shown), an input/output (I/O) interface (not shown) and a PI controller (not shown) and can be configured to receive data as input from various components within the system  100 , and send command signals as output to various components within the system  100 . 
         [0048]    In some examples, during operation, the control unit  121  can receive information, for instance, from the first fixed speed compressor  108 , the second fixed speed compressor  112 , the variable speed compressor  105 , and/or the sensor  135  through the I/O interface, process the received information using the processor based on an algorithm stored in the memory, and then send command signals, for instance, to the components involved in the refrigeration loop including the first fixed speed compressor  108 , the second fixed speed compressor  112 , and/or the variable speed compressor  105 . 
         [0049]    For example, the control unit  121  can receive information regarding the DAT from the sensor  135 , process the data, and then based on the data, send a command signal to the variable speed compressor  105  so as to control the speed of the variable speed compressor  105  and/or send a command signal to the first fixed speed compressor  108  and/or the second fixed speed compressor  112  to control the operation of the respective compressors  108  and  112 . It is to be realized that the control unit  121  can be configured to receive information and send command signals to other components that are generally known to be included in a system that utilizes fixed speed and variable speed compressors. 
         [0050]    Details of the various algorithms that can be stored in the memory will now be provided below. 
         [0051]    Generally, the system  100  is configured so that command signals are sent from the control unit  121  to the fixed speed compressors  108  and  112  and the variable speed compressor  105 , and after receiving the command signals, the respective compressors  105 ,  108  and  112  operate, for example, in the following operational stages: Stage 0, Stage 1 min, Stage 1 max, Stage 2 min, Stage 2 max, Stage 3 min and Stage 3 max. Details of each of the stages are provided below. 
         [0052]    At Stage 0, each of the first fixed speed compressor  108 , the second fixed speed compressor  112  and the variable speed compressor  105  operates in the off state so that the speed of each of the fixed speed compressors  108  and  112  and the variable speed compressor  105  is at 0 rps. 
         [0053]    At Stage 1 mil, the speed of the variable speed compressor  105  ramps up from 0 rps until a minimum speed is reached. In some examples, the speed of the variable speed compressor  105  ramps up at a constant rate and/or a variable rate. In one implementation, the constant rate and/or the variable speed is predetermined. In some examples, the constant rate is an increase of about 2 rps. In some examples, the variable rate is a rate that varies between 2 and 4 rps. In other examples, the constant rate and/or the variable rate can be determined based on the configuration of the system  100 . In some examples, a PI controller can be used to limit the ramp rate as will be discussed below. The first fixed speed compressor  108  and the second fixed speed compressor  112  operate in the off state so that the speeds are at 0 rps. 
         [0054]    At Stage 1 max, the speed of the variable speed compressor  105  can ramp up from a minimum speed to a maximum speed. In some examples, the speed of the variable speed compressor  105  ramps up at a constant rate and/or a variable rate. In one implementation, the constant rate and/or the variable speed is predetermined. In some examples, the constant rate is an increase of about 2 rps. In some examples, the variable rate is a rate that varies between 2 and 4 rps. In other examples, the constant rate and/or the variable rate can be determined based on the configuration of the system  100 . In some examples, a PI controller can be used to limit the ramp rate as described below. The first fixed speed compressor  108  and the second fixed speed compressor  112  operate in the off state so that the speeds are at 0 rps. 
         [0055]    At Stage 2 min, the first fixed speed compressor  108  operates in the on state and the second fixed speed compressor  112  operates in the off state so that the speed of the second fixed compressor is at 0 rps. The speed of the variable speed compressor  105  is set at a minimum speed. 
         [0056]    At Stage 2 max, the first fixed speed compressor  108  operates in the on state and the second fixed speed compressor  112  operates in the off state so that the speed of the second fixed compressor is at 0 rps. The speed of the variable speed compressor  105  ramps up from a minimum speed to a maximum speed. In some examples, the speed of the variable speed compressor  105  ramps up at a constant rate and/or a variable rate. In one implementation, the constant rate and/or the variable speed is predetermined. In some examples, the constant rate is an increase of about 2 rps. In some examples, the variable rate is a rate that varies between 2 and 4 rps. In other examples, the constant rate and/or the variable rate can be determined based on the configuration of the system  100 . In some examples, a PI controller can be used to limit the ramp rate as will be discussed below. 
         [0057]    At Stage 3 min, both the first fixed speed compressors  108  and the second fixed speed compressor  112  operate in the on state. The speed of the variable speed compressor  105  is set at a minimum speed. 
         [0058]    At Stage 3 max, both the first fixed speed compressor  108  and the second fixed speed compressor  112  operate in the on state. The speed of the variable speed compressor  105  ramps up from a minimum speed to a maximum speed. In some examples, the speed of the variable speed compressor  105  ramps up at a constant rate and/or a variable rate. In one implementation, the constant rate and/or the variable speed is predetermined. In some examples, the constant rate is an increase of about 2 rps. In some examples, the variable rate is a rate that varies between 2 and 4 rps. In other examples, the constant rate and/or the variable rate can be determined based on the configuration of the system  100 . In some examples, a PI controller can be used to limit the ramp rate as will be discussed below. In some instances, Stage 3 max is the full capacity for the exemplary set of compressors  105 ,  108  and  112 . 
         [0059]    In some examples where the PI controller is used to limit the ramp rate, limiting the ramp rate involves determining a change in speed of the variable speed compressor using the PI controller, comparing the determined change to a predetermined value, and based on the comparison, limiting the ramp rate of the variable speed compressor. The predetermined value can be, e.g., 2 rps. In some example, if the determined change is greater than a predetermined value where the load is increasing, the ramp rate is limited to the predetermined value. Otherwise, the ramp rate may not be limited. In some examples, if the determined change is less than a predetermined value where the load is decreasing, the ramp rate is limited to the predetermined value. Otherwise, the ramp rate may not be limited. 
         [0060]    In some examples, the minimum speed and/or the maximum speed of the variable speed compressor  105  for each of the respective stages can be different from or the same as one another. For instance, the minimum speed of the variable speed compressor  105  in Stage 1 min can be different from or the same as that of Stage 2 min and/or Stage 3 min. Likewise, the maximum speed of the variable speed compressor  105  in Stage 1 max can be different from or same as that of Stage 2 max and/or Stage 3 max. In some instances, the minimum speed and maximum speed selection is a tradeoff among, for example, factors including cost, energy efficiency and acoustics. In some other examples, the minimum speed and/or maximum speed is (are) predetermined for the selected variable speed compressor  105 . For instance, the minimum speed and/or maximum speed is (are) predetermined based on the size and model of the variable speed compressor  105  utilized. In some examples, the algorithm described below utilizes the minimum speed and/or maximum speed to normalize dynamic behavior of the system  100 . 
         [0061]    In some examples, the operational stages listed above, that is, Stage 0, Stage 1 min, Stage 1 max, Stage 2 min, Stage 2 max, Stage 3 min and Stage 3 max, can occur sequentially in the listed order when the load is increasing. Note that the compressors are not required to operate in all of the operational stages. That is, the system  100  is capable of modulating between the operational stages so that the compressors operate in only a subset of the listed operational stages. The subset of the operational stages in which the compressors  105 ,  108  and  112  operate can be determined by an algorithm, for example the algorithm that is discussed in detail below. 
         [0062]    In some examples, the operational stages listed above can occur in reverse order when the load is decreasing, for example, in the following sequential order: Stage 3 max, Stage 3 min, Stage 2 max, Stage 2 min, Stage 1 max, Stage 1 min and Stage 0. 
         [0063]    Generally, the control unit  121  can be configured to implement the disclosed method of controlling the system  100  as illustrated in  FIGS. 2A-2C . In general, the process described in  FIGS. 2A-2C  is executed by the processor executing program instructions (algorithm(s)) stored in the memory of the control unit  121 . 
         [0064]    With reference to  FIG. 2A , in one embodiment, the disclosed method or algorithm  200  initiates at step  206  and proceeds to step  209  where a determination is made as to a parameter using the sensor  135 . In some examples, the parameter can be space temperature. In some other examples, the parameter can be discharge air temperature (DAT). In the description that follows, the algorithm  200  will be described using DAT as the parameter. However, it is to be realized that the space temperature can replace the DAT in the description that follows. 
         [0065]    After step  209 , the algorithm  200  proceeds to  215  where a determination is made as to a PI capacity value using the PI controller. In some examples, the PI capacity value is determined based on the DAT measured in step  209  and a set point of the DAT. In some examples, the PI capacity value can be determined, for example, by applying a gain value to the difference between the measured DAT and the set point. In some examples, the gain value can be adjusted, for example, by considering the supply air flow across an evaporator coil. In some instances, the PI controller has a deadband of about 0.5 to about 1° F. so that when the DAT is about 0.5 to about 1° F. above the set point, the algorithm  200  continues, and when the DAT is about 0.5 to about 1° F. below the set point, the algorithm  200  ends. In some instances, a wider deadband can be used at Stage 0 to Stage 1 min to minimize cycling. Note that cycling refers to the cycling step  235  in  FIG. 2C , which will be discussed in further detail below. 
         [0066]    After step  215 , a determination is made as to an operating mode based on the PI capacity value at  221 . The operating mode is a parameter that is used by the algorithm  200  to indicate the applicable operational stage(s) based on the determined PI capacity value. In some examples, the operating mode is determined by comparing the PI capacity value with preconfigured values, for example, using a lookup table. In some examples, the operating mode is determined by normalizing the PI capacity value based on the configuration of the system  100 . In some examples, the preconfigured values are based on the configuration of the system, for example, the type of compressors used, the number of compressors used, etc. 
         [0067]    In some examples, the type of parameters used for the operating mode depends on whether there is(are) capacity/stage gap(s) for the variable speed compressor  105  relative to the fixed speed compressors  108  and  112 . 
         [0068]    The meaning of “capacity/stage gap(s)” will now be described with reference to  FIGS. 3A and 3B .  FIGS. 3A and 3B  illustrate the overall concept of the term “capacity/stage gap(s)”. The term “capacity/stage gap(s)” generally refers to the gap in capacity of the variable speed compressor  105  relative to the fixed speed compressors  108  and  112 . The term “capacity” means the tons the compressor will produce based on certain operating conditions. 
         [0069]    Generally, the “capacity/stage gap(s)” concept illustrates how the algorithm  200  modulates the operation of the fixed speed compressors  108  and  112  and the variable speed compressor  105  based on the configuration of the system  100 . The modulation of the operation of the fixed speed compressors  108  and  112  and the variable speed compressor  105  can be done by adjusting the speed of the variable speed compressor  105  and/or by a cycling operation to meet a set point of the PI controller. 
         [0070]    Each of a first stage capacity box  302 , a second stage capacity box  308  and a third stage capacity box  310  in  FIGS. 3A and 3B  indicates a capacity range of the variable speed compressor  105  under different operating states of the variable speed compressor  105  and the first fixed speed compressor  108  and the second fixed speed compressor  112 . In particular, the first stage capacity box  302  indicates a capacity range  305  of the variable speed compressor  105  when both the first fixed speed compressor  108  and the second fixed speed compressor  112  are turned off. The second stage capacity box  308  indicates a capacity range  309  of the variable speed compressor  105  when the variable speed compressor  105  is operating between a minimum speed and a maximum speed, and the first fixed speed compressor  108  is turned on and the second fixed speed compressor  112  is turned off. The third stage capacity box  310  indicates a capacity range  312  of the variable speed compressor  105  when the variable speed compressor  105  is operating between a minimum speed and a maximum speed, and both the first fixed speed compressor  108  and the second fixed speed compressor  112  are turned on. 
         [0071]    Referring to  FIG. 3A , in some examples, there is no capacity/stage gap when a maximum capacity of the capacity range in one stage overlaps a minimum capacity of the capacity range in the subsequent stage. In some examples, an overlapping region of the maximum capacity of the capacity range in one stage and the minimum capacity of the capacity range in the subsequent stage is about 2 to about 3%. In some examples, there is no capacity/stage gap if a maximum capacity  302  max of the capacity range  305  in the first stage capacity box  302  overlaps a minimum capacity  308  min of the capacity range  309  in the second stage capacity box  308  and/or if a maximum capacity  308  max of the capacity range  309  in the second stage capacity box  308  overlaps a minimum capacity  310  min of the capacity range  312  in the third stage capacity box  310  as shown in  FIG. 3A . 
         [0072]    Referring to  FIG. 3B , on the other hand, a capacity/stage gap is present when a maximum capacity of the capacity range in one stage does not overlap a minimum capacity of the capacity range in the subsequent stage. In particular, there is a capacity/stage gap  315  if the maximum capacity  302  max of the capacity range  305  in the first stage capacity box  302  does not overlap the minimum capacity  308  min of the capacity range  309  in the second stage capacity box  308  and/or if the maximum capacity  308  max of the capacity range  309  in the second stage capacity box  308  does not overlap the minimum capacity  310  min of the capacity range  312  in the third stage capacity box  310  as shown in  FIG. 3B . 
         [0073]    Generally, the presence or absence of the capacity/stage gap depends on the configuration of the system  100 , for instance, the type of variable speed compressor  105  utilized. For example, a capacity/stage gap may occur in systems where the variable speed compressor  105  has a small capacity relative to the fixed speed compressors  108  and  112 . In general, in the instance where the capacity/stage gap is present, the algorithm  200  will modulate the operation of the fixed speed compressors  108  and  112  and the variable speed compressor  105  by using a cycling operation, whereas in the instance where the capacity/stage gap is absent, the algorithm  200  will not use a cycling operation. 
         [0000]    Details of Algorithm where there is No Capacity/Stage Gap 
         [0074]    Referring back to  FIG. 2A , in some examples, if there is no capacity/stage gap, that is, where a capacity/stage overlap is present, then the parameters used for the operating mode in the algorithm  200  include Stage 1 min capacity, Stage 1 max capacity and Stage 2 max capacity. 
         [0075]      FIG. 4  shows a graph illustrating the overall relation between the operating modes on the x-axis, namely, Stage 1 min capacity  402 , Stage 1 max capacity  406  and Stage 2 max capacity  408 , and the operational stages on the y-axis, namely, Stage 0  411 , Stage 1 min  415 , Stage 1 max  418 , Stage 2 min  421 , Stage 2 max  425 , Stage 3 min  427  and Stage 3 max  431 . 
         [0076]    Referring to  FIG. 4 , Stage 1 min capacity  402  on the x-axis references the unit capacity when the variable speed compressor  105  is operating at Stage 1 min  415  on the y-axis, where both the first fixed speed compressor  108  and the second fixed speed compressor  112  are turned off; Stage 1 max capacity  406  on the x-axis references the unit capacity when the variable speed compressor  105  is operating at Stage 1 max  418  on the y-axis, where both the first fixed speed compressor  108  and the second fixed speed compressor  112  are turned off; and Stage 2 max capacity  408  on the x-axis references the unit capacity when the variable speed compressor  105  is operating at Stage 2 max  425  on the y-axis, where the first fixed speed compressor  108  is turned on and the second fixed speed compressor  112  is turned off. 
         [0077]    Referring to  FIG. 2A  and  FIG. 2B , after the operating mode has been determined at  221  as shown in  FIG. 2A , the algorithm proceeds to the steps in {circle around (1)}. Details of {circle around (1)} are provided in  FIG. 2B . 
         [0078]    The steps in {circle around (1)} now will be described with reference to  FIG. 2B . At  222 , the variable speed compressor  105 , the first fixed speed compressor  108  and/or the second fixed speed compressor  112  operate at the referenced operational stage based on the operating mode determined in  221 . 
         [0079]    Then, at  223 , a determination is made as to the DAT, and at  224 , a determination is made as to a PI capacity value using the PI controller. In some examples, the PI capacity value is determined based on the DAT measured in step  223  and the set point of the DAT. 
         [0080]    The algorithm  200  then proceeds to  225 , where a determination is made as to an operating mode based on the PI capacity value determined at  224 . In some instances, the parameters used for the operating mode can further include Stage 1 max cap+5 and Stage 2 max cap+5. In some examples, Stage 1 max cap+5 and Stage 2 max cap+5 are used as dynamic buffers to prevent cycling between the referenced operating stage and a previous operating stage. Note that “+5” indicates a 5% differential in the PI capacity values for the respective operating modes, and references a dynamic buffer value. Note also that “+5” is only an example, and can be other values, for example, 0 to 20. 
         [0081]    The meaning of “dynamic buffer” will be described with reference to  FIG. 4 . As illustrated in  FIG. 4 , Stage 1 max capacity+5  446  on the x-axis references the unit capacity when the variable speed compressor  105  is operating at Stage 2 min  421  on the y-axis, where the first fixed speed compressor  108  is turned on and the second fixed speed compressor  112  is turned off, and Stage 2 max capacity+5  452  on the x-axis references the unit capacity when the variable speed compressor  105  is operating at Stage 3 min  427  on the y-axis, where the first fixed speed compressor  108  is turned on and the second fixed speed compressor  112  is turned on. 
         [0082]    In the instance where the PI capacity value determined in  224  is within a dynamic buffer value and the operating mode is determined to be, for example, Stage 1 max cap+5  446  on the x-axis, cycling does not occur between Stage 2 min  421  and Stage 1 max  418  in the region  438  on the y-axis. If, for example, the operating mode is determined to be Stage 2 max cap+5  452 , cycling does not occur between Stage 3 min  427  and Stage 2 max  425  in the region  441  on the y-axis. If the operating mode is determined to be Stage 1 min capacity  402 , cycling does not occur between Stage 1 min  415  and Stage 0  411  in the region  435  on the y-axis. 
         [0083]    Referring back to  FIG. 2B , after step  225 , a determination is made as to the operational state of the first fixed speed compressor  108  and/or the second fixed speed compressor  112  at  226 . A determination is also made as to the speed of the variable speed compressor  105  based on the PI capacity value at  227 . Then, at  228 , the first fixed speed compressor  108  and/or the second fixed speed compressor  112  is operated based on the determination made in  226 , and at  229 , the variable speed compressor  105  is operated based on the determination made in  227 . 
       Details of Algorithm in the Presence of Capacity/Stage Gap 
       [0084]    In some examples, if a capacity/stage gap is present, then the parameters used for the operating mode in the algorithm  200  include Stage 1 min capacity. Stage 1 max capacity, Stage 2 min capacity, Stage 2 max capacity and Stage 3 min capacity.  FIG. 5  shows a graph illustrating the overall relation between the operating modes, namely, Stage 1 min capacity  502 , Stage 1 max capacity  506 , Stage 2 min capacity  509 , Stage 2 max capacity  513  and Stage 3 min capacity  516 , and the operational stages, namely, Stage 0  521 , Stage 1 min  524 , Stage 1 max  531 , Stage 2 min  536 , Stage 2 max  539 , Stage 3 min  541  and Stage 3 max  545 . The operating modes are provided on the x-axis, while the operational stages are provided on the y-axis. 
         [0085]    Referring to  FIG. 5 , Stage 1 min capacity  502  references the unit capacity when the variable speed compressor  105  is operating at Stage 1 min  524 , where both the first fixed speed compressor  108  and the second fixed speed compressor  112  are turned off; Stage 1 max capacity  506  references the unit capacity when the variable speed compressor  105  is operating at Stage 1 max  531 , where both the first fixed speed compressor  108  and the second fixed speed compressor  112  are turned off; Stage 2 min capacity  509  references the unit capacity when the variable speed compressor  105  is operating at Stage 2 min  536  where the first fixed speed compressor  108  is turned on and second fixed speed compressor  112  is turned off; Stage 2 max capacity  513  references the unit capacity when the variable speed compressor  105  is operating at Stage 2 max  539 , where the first fixed speed compressor  108  is turned on and the second fixed speed compressor  112  is turned off; and Stage 3 min capacity  516  references the unit capacity when the variable speed compressor  105  is at Stage 3 min  541  and both the first fixed speed compressor  108  and the second fixed speed compressor  112  are turned on. 
         [0086]    Referring to  FIGS. 2A and 2C , after the operating mode has been determined at  221 , the algorithm proceeds to the steps in {circle around (1)}. Details of {circle around (1)} are provided in  FIG. 2C . 
         [0087]    The steps in {circle around (1)} now will be described with reference to  FIG. 2C . At  232 , the variable speed compressor  105 , the first fixed speed compressor  108  and/or the second fixed speed compressor  112  operate at the referenced operational stage based on the operating mode determined in  221 . 
         [0088]    Then, the algorithm proceeds to  235  where the variable speed compressor  105 , the first fixed speed compressor  108  and/or the second fixed speed compressor  112  cycle between the referenced operational stage and a subsequent or previous operational stage. 
         [0089]    Generally, the reason cycling occurs in the presence of capacity/stage gap is explained as follows with reference to  FIG. 5 . During operation, the system  100  can have too much cooling if running at, for example, Stage 2 min  536 . In this instance, the DAT will become lower than the set point of the DAT, and as a result, the PI capacity value will decrease. When PI capacity value becomes less than, for example, Stage 1 max  531 , cycling will occur between Stage 1 max  531  and Stage 2 min  536  in the region  561  on the y-axis. 
         [0090]    Further details of the cycling operation will be described with reference to  FIG. 5 . 
         [0091]    Cycling can occur between Stage 0  521  and Stage 1 min  524  so that the variable speed compressor  105  cycles between the off state and a minimum speed as shown by region  555  on the y-axis. Cycling also can occur between Stage 1 max  531  and Stage 2 min  536  so that the variable speed compressor  105  cycles between a minimum and a maximum speed and the first fixed speed compressor  108  cycles between the on and off states as shown by region  561  on the y-axis. Cycling also can occur between Stage 2 max  539  and Stage 3 min  541  so that the variable speed compressor  105  cycles between a minimum and a maximum speed and the first fixed speed compressor  108  cycles between the on and off state as shown by region  569  in the y-axis. 
         [0092]    In some examples, the variable speed compressor  105 , the first fixed speed compressor  108  and/or the second fixed speed compressor  112  cycle a predetermined number of times, for example, 1-5 times. In other examples, the number of the times the variable speed compressor  105 , the first fixed speed compressor  108  and/or the second fixed speed compressor  112  cycle between the respective operational stages can depend on the PI capacity value. 
         [0093]    Referring back to  FIG. 2C , after step  235 , the algorithm  200  proceeds to  237  where a determination is made as to the DAT. Then, at  240 , a determination is made as to the PI capacity value based on the DAT determined in  237  and the set point of the DAT. Then, at  242 , a determination is made as to the operating mode. 
         [0094]    Referring to  FIG. 2C , after step  242 , a determination is made as to the operational state of the first fixed speed compressor  108  and/or the second fixed speed compressor  112  at  248 . A determination is also made as to the speed of the variable speed compressor  105  based on the PI capacity value at  259 . Then, at  252 , the first fixed speed compressor  108  and/or the second fixed speed compressor  112  is operated based on the determination made in  248 , and at  261 , the variable speed compressor  105  is operated based on the determination made in  259 . 
         [0095]    In the above-described examples, a system including two fixed speed compressors and one variable speed compressor is described. However, in some examples, the system  100  can include more than one variable speed compressor. In one implementation, one of the fixed speed compressors  108 ,  112  can be replaced with a variable speed compressor so that the system includes two variable speed compressors and one fixed speed compressor. The algorithm utilized in a system including two variable speed compressors and one fixed speed compressor would be the same as the algorithm  200  discussed above, except that one of the fixed speed compressors  108 ,  112  would be replaced with a variable speed compressor, and the variable speed compressor replacing one of the fixed speed compressors  108 ,  112  would switch between speeds rather than turning on and off. 
         [0096]    With regard to the foregoing description, it is to be understood that changes may be made in detail, especially in matters of the construction materials employed and the shape, size and arrangement of the parts without departing from the scope of the present invention. It is intended that the specification and depicted embodiment to be considered exemplary only, with a true scope and spirit of the invention being indicated by the broad meaning of the claims.