Abstract:
An apparatus and method for measuring or controlling the Outdoor Air Fraction (OAF) ratio through economizer or outdoor air dampers and cabinet to total system airflow and mixed-air humidity ratio and wetbulb temperature for HVAC equipment. An OAF exceeding the minimum regulatory requirements wastes energy and contributes to global warming. OAF is used to optimize economizer damper position either manually or automatically using an economizer Fault Detection Diagnostic controller and actuator to meet minimum outdoor airflow requirements. After the outdoor air damper position is optimized, the mixed-air humidity ratio and mixed-air wetbulb temperature are determined and used with the measured mixed-air drybulb and supply-air drybulb temperatures to evaluate evaporator airflow, cooling capacity, and heating capacity, and, if necessary, provide a visual or electronically-transmitted error code signal indicating maintenance requirements to check or correct economizer damper position, cabinet leakage, airflow, cooling or heating capacity, and/or other faults for the HVAC system.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    The present invention relates to Heating, Ventilating, and Air Conditioning (HVAC) systems and in particular to outdoor air introduced into buildings during HVAC operation through economizer outdoor air dampers or non-economizer outdoor air dampers. 
         [0002]    Buildings are required to provide a minimum flow of outdoor air into their HVAC systems per the American Society of Heating Refrigeration and Air-Conditioning Engineers (ASHRAE) Standard 61.1 (ANSI/ASHRAE 62.1-2010. Standard Ventilation for Acceptable Indoor Air Quality) and the California Energy Commission (CEC) Building Energy Efficiency Standards for Residential and Nonresidential Buildings (CEC-400-2012-004-CMF-REV2). When the outdoor airflow exceeds the minimum required airflow, the additional airflow may introduce unnecessary hot outdoor air when the HVAC system is cooling the building, or introduce unnecessary cold outdoor air when the HVAC system is heating the building. This unnecessary or unintended outdoor airflow reduces space cooling and heating capacity and efficiency and increases cooling and heating energy consumption and the energy costs required to provide space cooling and heating to building occupants. Known methods for measuring the amount of outdoor airflow to meet minimum requirements introduced into buildings are inaccurate and better methods are required to improve thermal comfort of occupants, reduce cooling and heating energy usage, and improve cooling and heating energy efficiency. 
         [0003]    U.S. Pat. No. 6,415,617 (Seem 2002) discloses a method for controlling an air-side economizer of an HVAC system using a model of the airflow through the system to estimate building cooling loads when minimum and maximum amounts of outdoor air are introduced into the building and uses the model and a one-dimensional optimization routine to determine the fraction of outdoor air that minimizes the load on the HVAC system. The &#39;617 patent does not provide apparatus or methods to measure the Outdoor Air Fraction (OAF) defined as the ratio of outdoor airflow through the economizer or non-economizer dampers to total system airflow. Nor does the &#39;617 patent provide methods to adjust the economizer outdoor air damper minimum damper position until OAF is within the allowable minimum regulatory requirement. 
         [0004]    US Patent application publication No. 2015/0,309,120 (Bujak 2015) discloses a method to evaluate economizer damper fault detection for an HVAC system including moving dampers from a baseline position to a first damper position and measuring the fan motor output at both positions to determine successful movement of the baseline to first damper position. The &#39;120 publication does not teach how to measure the OAF or electronically control the actuator to adjust the economizer outdoor air damper minimum damper position until OAF is within the allowable minimum regulatory requirement. 
         [0005]    U.S. Pat. No. 7,444,251 (Nikovski 2008) discloses a system and method to detect and diagnose faults in HVAC equipment using internal state variables under external driving conditions using a locally weighted regression model and differences between measured and predicted state variables to determine a condition of the HVAC equipment. The &#39;251 patent does not provide apparatus or methods to measure the OAF. The &#39;251 patent does not provide apparatus or methods to measure the OAF. Nor does the &#39;251 patent provide methods to adjust the economizer outdoor air damper minimum damper position until OAF is within the allowable minimum regulatory requirement or measure the temperature difference across the evaporator or heat exchanger to determine whether or not the sensible cooling or heating capacities are within tolerances. 
         [0006]    U.S. Pat. No. 6,223,544 (Seem 2001) discloses an integrated control and fault detection system using a finite-state machine controller for an air handling system. The &#39;544 method employs data regarding system performance in the current state and upon a transition occurring, determines whether a fault exists by comparing actual performance to a mathematical model of the system under non-steady-state operation. The &#39;544 patent declares a fault condition in response to detecting an abrupt change in the residual which is a function of at least two temperature measurements including: outdoor-air, supply-air, return-air, and mixed-air temperatures. The &#39;544 patent measures the mixed-air temperature with a single-sensor and without a minimum temperature difference between outdoor and return air temperatures. The &#39;544 patent does not provide apparatus or accurate methods to measure the OAF. Nor does the &#39;544 patent provide methods to adjust the economizer outdoor air damper minimum damper position until the OAF is within the allowable minimum regulatory requirement or measure the temperature difference across the evaporator or heat exchanger to determine whether or not the sensible cooling or heating capacities are within tolerances. 
         [0007]    Thus, known methods and apparatus currently do not exist to accurately measure the outdoor airflow through economizer or non-economizer outdoor air dampers. The present invention provides an apparatus and method to accurately measure and establish the OAF to optimize economizer damper position either manually or automatically using an economizer fault detection diagnostic (FDD) controller and actuator to meet ASHRAE 62.1 minimum outdoor airflow requirements. Optimizing the OAF will improve space cooling and heating efficiency, save energy, and reduce carbon dioxide emissions. 
       BRIEF SUMMARY OF THE INVENTION 
       [0008]    The present invention addresses the above and other needs by providing a method for determining the Outdoor Air Fraction (OAF), (the ratio of outdoor airflow through the economizer or non-economizer outdoor air dampers and/or cabinet, to the total airflow introduced into the air conditioner evaporator or heat exchanger) and the mixed-air humidity ratio and mixed-air wetbulb temperature, for packaged and split-system HVAC equipment equipped with economizer or non-economizer outdoor air dampers. An outdoor airflow exceeding the American Society of Heating Refrigeration and Air-Conditioning Engineers (ASHRAE) Standard 62.1 minimum outdoor air requirements wastes space cooling and heating energy and increases carbon dioxide emissions contributing to global warming. The OAF measurements are used to optimize the minimum economizer or non-economizer outdoor air damper position to meet but not exceed ASHRAE 62.1 minimum outdoor airflow requirements. The present invention provides a method to measure OAF versus damper actuator voltage at the initial damper position, fully-open-damper maximum damper position, and closed-damper position. The present invention uses these measurements and matrix algebra to calculate coefficients for a quadratic regression equation of OAF versus control voltage in order to establish the optimal economizer damper position actuator control voltage to adjust the damper to achieve the optimally minimum OAF to just meet outdoor airflow regulatory requirements to reduce over ventilation and save energy. After the economizer damper position is optimized, the mixed-air wetbulb temperature is determined to measure evaporator entering air drybulb and wetbulb temperatures and supply air drybulb temperature to evaluate temperature split, sensible cooling or heating capacity, and refrigerant charge Fault Detection Diagnostics (FDD) in order to determine whether or not the evaporator airflow, sensible cooling or heating capacity, and refrigerant charge of the air conditioning system, needs to be adjusted or corrected. 
         [0009]    In accordance with one aspect of the invention, there is provided a method for accurately measuring mixed air temperature by positioning an averaging temperature sensor in the passage between the mixed air chamber of the HVAC system and the air conditioner evaporator and furnace/heat exchanger of the HVAC system. The averaging temperature sensor is preferably formed into a quasi-rectangular or quasi-circular spiral in the shape of the passage in order to measure the average temperature of air flowing through the mixed-air chamber from the return duct and the outdoor air dampers. The mixed-air drybulb temperature measurement is considered accurate when the difference between return drybulb temperature and outdoor air drybulb temperature is preferably at least 10 degrees Fahrenheit and more preferably at least 20 degrees Fahrenheit. OAF measurements made at lower temperature differences will have slightly lower accuracy. 
         [0010]    In accordance with another aspect of the invention, there is provided a method for recursively computing mixed air humidity ratio W* s . An initial value of mixed air wetbulb temperature t* m  is made based on a drybulb temperature measurement. A saturation pressure at wetbulb temperature p ws  is computed using the estimate of t* m . An updated value of W* s  is computed from p ws . The process is repeated using updated value of W* s  until it converges. 
         [0011]    In accordance with yet another aspect of the invention, there is provided a method for measuring the sensible temperature split across the evaporator in cooling mode or the sensible temperature rise across the heat exchanger in heating mode. The sensible temperature split for cooling, or for temperature rise for heating, can be used to evaluate over ventilation, airflow, sensible cooling capacity, sensible heating capacity, and/or refrigerant charge FDD information. 
         [0012]    In accordance with still another aspect of the invention, there is provided a method to use sensors to transmit temperature or humidity measurement data using wires or wirelessly to a device or controller in order to display, store, or use the data to measure the OAF or to provide measurement data to an economizer controller or outdoor air damper controller where the controller uses the data to calculate the measured OAF and compares the measured OAF to a minimum outdoor airflow specification for a building conditioned space and occupancy, and communicates a low-voltage signal to an actuator to energize the actuator to adjust the damper position to establish an optimally minimum damper position to provide an OAF within tolerances of the minimum outdoor airflow based on regulatory requirements for a building conditioned space and occupancy. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
         [0013]    The above and other aspects, features and advantages of the present invention will be more apparent from the following more particular description thereof, presented in conjunction with the following drawings wherein: 
           [0014]      FIG. 1  shows a portable (for example, hand held) apparatus for measuring the outdoor air fraction (OAF) through economizer outdoor air dampers or manual outdoor air dampers. 
           [0015]      FIG. 2  shows the electronic components of a portable measurement instrument or control device mounted to an HVAC system for measuring OAF or evaluating HVAC FDD. 
           [0016]      FIG. 3  shows an air handler of a Heating, Ventilation, and Air Conditioning (HVAC) system with manually adjusted outdoor air dampers according to the present invention with measurement instrument or controller capable of receiving measurements using either wired connections or wirelessly. 
           [0017]      FIG. 4  shows an averaging temperature sensor formed into a quasi-rectangular or quasi-circular spiral in the shape of the passage according to the present invention. 
           [0018]      FIG. 5  shows the air handler of an HVAC system with an economizer controller and actuator used to adjust outdoor air dampers according to the present invention with measurement instrument or controller capable of receiving measurements using either wired connections or wirelessly. 
           [0019]      FIG. 6  shows the air handler of an HVAC system with an economizer controller and actuator used to adjust outdoor air dampers according to the present invention with measurement instrument or controller mounted on the HVAC hardware. 
           [0020]      FIG. 7  shows a method for OAF optimization on an HVAC system while the HVAC system is operating, according to the present invention. 
           [0021]      FIG. 8  shows a method for Fault Detection Diagnostic (FDD) evaluation on an HVAC system while the HVAC system is operating, according to the present invention. 
           [0022]      FIG. 9  provides a chart showing the OAF versus economizer damper actuator control voltage on an HVAC system according to the present invention. 
           [0023]      FIG. 10  shows a chart of damper position data, and equations 7, 9, 11, and 19, according to the present invention. 
           [0024]      FIG. 11  shows a lookup table for calculating the target temperature split difference (δT t ) based on the evaporator entering mixed-air drybulb temperature, t m , and evaporator entering mixed-air wetbulb temperature, t* m , according to the present invention. 
           [0025]      FIG. 12  shows a chart of gas furnace manufacturer minimum acceptable temperature rise data versus airflow for 253 models. 
           [0026]      FIG. 13  shows a chart of heat pump manufacturer minimum acceptable temperature rise data versus outdoor air temperature for 12 different models. 
           [0027]      FIG. 14  shows a chart of hydronic heating coil manufacturer minimum acceptable temperature rise versus hot water temperature for 35 models. 
       
    
    
       [0028]    Corresponding reference characters indicate corresponding components throughout the several views of the drawings. 
       DETAILED DESCRIPTION OF THE INVENTION 
       [0029]    The following description is of the best mode presently contemplated for carrying out the invention. This description is not to be taken in a limiting sense, but is made merely for the purpose of describing one or more preferred embodiments of the invention. The scope of the invention should be determined with reference to the claims. 
         [0030]    Where the terms “about” or “generally” are associated with an element of the invention, it is intended to describe a feature&#39;s appearance to the human eye or human perception, and not a precise measurement. Drybulb temperature measurements at indicated without asterisks and corresponding wetbulb temperatures are indicated by the addition of an asterisk. 
         [0031]      FIG. 1  shows a handheld measurement device  40  and  FIG. 2  shows the electronic components of measurement devices  40 ,  40   a  or  40   b  (see  FIGS. 3, 5 and 6 ). The measurement devices  40 ,  40   a  and  40   b  preferably include a low-voltage power supply or external power source  313 , a signal conditioner  301 , an ac-dc converter  303 , microprocessor with flash memory  305 , wireless communication electronic technology  42   b , and a display  42  or  42   a  for receiving, processing, transmitting and displaying measurements from temperature sensors  24 ,  28 ,  28 *,  30 ,  30 *, and  32 , and voltage  27  (see  FIGS. 3, 5 and 6 ). The measurement device  40  may also provide an input keypad  41  to enter the required OAF r  or other data, and a battery or a low-voltage power supply  313 . The measurement devices  40   a  and  40   b  may also provide a low-voltage input  27  and a common input  27   a  to measure damper actuator voltage for controlling the position of outdoor air dampers  50  and return dampers  52  shown in  FIGS. 5 and 6 . 
         [0032]    An air handler  10  of a packaged Heating, Ventilation, Air Conditioning (HVAC) system with manually adjusted outdoor air dampers  50  is shown in  FIG. 3 , and an averaging temperature sensor  24  is shown in  FIG. 4  formed into a quasi-rectangular or quasi-circular spiral in the shape of the mixed-air passage  22 . A flow of outdoor air  16  enters a mixed air chamber  12  of the air handler  10  through adjustable dampers  50 . A flow of return air  18  enters a mixed air chamber  12  of the air handler  10  through adjustable dampers  52 . The outdoor air flow and return air flow combine in a mixed air flow  22  that flows through an air filter  26  and evaporator  29 , and into a chamber  14  containing a draw-through blower fan  33  and gas or electric heat exchanger  31 . A flow of heated or cooled air  20  is then provided through supply ducts to the conditioned space. The averaging temperature sensor  24  is located on the inlet side of the air filter  26  adjacent to the evaporator  29  of the mixed air passage. The averaging temperature sensor  24  is generally perpendicular to the path of mixed airflow  22 , on the inlet of air filter and upstream of the evaporator  29 , blower fan  33  and heat exchanger  31 . The averaging temperature sensor  24  is used to measure the mixed-air drybulb temperature t m . 
         [0033]    The outdoor air dampers  50  and return air dampers  52  are coupled by a gear assembly so when outdoor air dampers  50  are opened, the return air dampers  52  close, and vice versa. Closing the outdoor air dampers  50  reduces the volumetric airflow rate of the outdoor air  16  into the mixed air chamber  12  and opens the dampers  52  to increase the volumetric airflow rate of return air  18  into the mixed air chamber  12 . Preferably, the positions of the dampers  50  and the dampers  52  are coupled by the gear assemblies  50   a  and  52   a  so that opening the dampers  50  closes the dampers  52 , and opening the dampers  52  closes the dampers  50 , to maintain a generally consistent volumetric airflow rate into the mixed air chamber  12 . 
         [0034]    The temperature sensor  28  measures the return air drybulb temperature, t r , and temperature sensor  30  measures the outdoor air drybulb temperature t o . The temperature sensor  32  is used to measure the supply air drybulb temperature t s , used with the return air drybulb or mixed air drybulb to calculate the temperature split decrease across the evaporator in cooling mode or the temperature split increase across the heat exchanger in heating mode. The mixed-air drybulb temperature, t m , measurement is considered minimally accurate when the difference between return drybulb temperature, t r , and outdoor air drybulb temperature, t o , is preferably at least ten degrees Fahrenheit and is considered more accurate when the difference between return drybulb temperature, t r , and outdoor air drybulb temperature, t o , is at least 20 degrees Fahrenheit. The measurement device  40  (see  FIG. 1 ) is connected to the sensors  24 ,  28 ,  30 , and  32  by cables  44 , or wirelessly communicates with the sensors  24 ,  28 ,  30 , and  32 . When the air handler  10  includes an actuator A to adjust outdoor air dampers  50  and return dampers  52  (see  FIG. 5 ), the measurement device  40  may also provide low-voltage inputs to measure damper actuator voltage for controlling the position of outdoor air dampers  50  and return dampers  52 . 
         [0035]    The return air drybulb temperature t r , and the return air wetbulb temperature t* r , are preferably measured in well-mixed return air. The outdoor air drybulb temperature t o  and outdoor air wetbulb temperature t* o  are preferably measured in well-mixed outdoor air entering an economizer  49  controlling the outdoor air flow  16   b  into the mixed air chamber  12  through outdoor air dampers  50 . 
         [0036]    The averaging temperature sensor  24  shown in  FIG. 4  is preferably a Resistance Temperature Detector (RTD) or thermistor or thermocouple sensor, preferably formed into a quasi-rectangular or quasi-circular spiral in the shape of the in the shape of the mixed-air passage  22  or the mixed-air chamber  12 . The averaging temperature sensor  24  may further be an infrared averaging sensor or temperature sensor array consisting of one or more RTD, thermistors, or thermocouple sensors used to measure the mixed air drybulb temperature, t m . 
         [0037]    An air handler  10   a  of a packaged HVAC system with an economizer controller  56  and actuator  54  used to adjust outdoor air dampers is shown in  FIG. 5 . The flow of outdoor air  16  enters the mixed air chamber  12  of the air handler  10  through the adjustable dampers  50 . The flow of return air  18  enters the mixed air chamber  12  of the air handler  10  through the adjustable dampers  52 . The outdoor air flow and return air flow combine in the mixed air flow  22  that flows through the air filter  26  and the evaporator  29 , and into the chamber  14  containing the draw-through blower fan  33  and the gas or the electric heat exchanger  31 . The flow of heated or cooled air  20  is then provided through supply ducts to the conditioned space. The averaging temperature sensor  24  is located on the inlet side of the air filter  26  adjacent to the evaporator  29  of the mixed air passage. The averaging temperature sensor  24  is generally perpendicular to the path of mixed airflow  22 , on the inlet of air filter and upstream of the evaporator  29 , blower fan  33  and heat exchanger  31 . The averaging temperature sensor  24  is used to measure the mixed-air drybulb temperature t m . 
         [0038]      FIG. 5  shows outdoor air dampers  50  and return air dampers  52  controlled and coupled by a gear assembly  50   a ,  52   a  and actuator  54  so when outdoor air dampers  50  are opened by the actuator, the return air dampers  52  close, and vice versa. The actuator  54  is controlled by a controller  56  using a voltage signal carried by a cable  45   a  and measured by the hand held measurement device  40   a  using a low-voltage sensor  27  and ground probe  27   a . Closing the outdoor air dampers  50  reduces the volumetric airflow rate of the outdoor air  16  into the mixed air chamber  12  and opens the dampers  52  to increase the volumetric airflow rate of return air  18  into the mixed air chamber  12 . Preferably, the positions of the dampers  50  and the dampers  52  are controlled and coupled by the gear assembly  50   a ,  52   a  so that opening the dampers  50  closes the dampers  52 , and opening the dampers  52  closes the dampers  50 , to maintain a generally consistent volumetric airflow rate into the mixed air chamber  12 . 
         [0039]    The sensor  28  measures the return air drybulb temperature, t r , and the optional temperature sensor  28 * measures the return air wetbulb temperature, t* r , respectfully. The temperature sensor  30  measures the outdoor air drybulb temperature, t o , and the optional temperature sensor  30 * measures the outdoor air wetbulb temperature, t* o , respectively. The temperature sensor  32  is used to measure the supply air drybulb temperature, t s , used with the return air drybulb or mixed air drybulb to calculate the temperature split decrease across the evaporator in cooling mode or the temperature split increase across the heat exchanger in heating mode. The mixed-air drybulb temperature, t m , measurement is considered minimally accurate when the difference between return drybulb temperature, t r , and outdoor air drybulb temperature, t o , is preferably at least ten degrees Fahrenheit and considered more accurate when the difference between return drybulb temperature, t r , and outdoor air drybulb temperature, t o , is at least 20 degrees Fahrenheit.  FIG. 5  shows a portable (for example, hand held) measurement device  40   a . The measurement device  40   a  is connected to the temperature sensors  24 ,  28 ,  28 *,  30 ,  30 *, and  32  by cables  44 , or wirelessly communicate with the sensors temperature  24 ,  28 ,  28 *,  30 ,  30 *, and  32 . 
         [0040]    An air handler of a HVAC system  10   b  and including a measurement instrument or control device  40   b  mounted to an HVAC system  10   b  is shown in  FIG. 6 . The controller device  40   b  may be connected to the temperature sensors  24 ,  28 ,  28 *,  30 ,  30 *, and  32  by cables  44 , or may wirelessly communicate with the temperature sensors  24 ,  28 ,  28 *,  30 ,  30 *, and  32 , and is connected to the actuator  54  by the cable  44   b  to control the dampers  50  and  52  using a voltage signal. The measurement and controller device  40   b  preferably includes a low-voltage power supply or external power source, signal conditioner, microprocessor, wireless communication electronic technology  42   b , and display  42   a  for receiving, processing, transmitting and displaying measurements from the temperature sensors  24 ,  28 ,  28 *,  30 ,  30 *, and  32 . 
         [0041]    The measurement device  40   b  may also provide low-voltage outputs to control the actuator A for controlling the position of outdoor air dampers  50  and return dampers  52 . The measurement device  40   b  may also be wired or wireless and provide economizer damper position and Outdoor Air Flow (OAF) measurements and operational Fault Detection Diagnostic (FDD) signals through a built-in display or external display through wireless communication signals to a building energy management system, standard thermostat, WIFI-enabled thermostat, internet-connected computer, internet telephony system, or smart phone indicating maintenance requirements to check and correct outdoor air damper position, evaporator airflow and/or refrigerant charge of the air conditioning system. 
         [0042]      FIG. 6  further shows an optional temperature sensor  37  which may be used to measure the inlet hot water supply  35  temperature for a hydronic heating system for calculating target temperature split using the hydronic heating minimum acceptable target temperature rise equation shown in  FIG. 14 . Other than including the measurement and controller device  40   b  mounted to the HVAC system  10   b  and the optional temperature sensor  37  and the inlet hot water supply  35 , the HVAC system  10   b  shares the features of the HVAC system  10   a  described in  FIG. 5 . 
         [0043]      FIG. 7  shows a method for optimizing OAF on an HVAC system while the HVAC system is operating according to the present invention. The method includes starting the optimization at step  100 , measuring return air temperature t r  outdoor air temperature t o , and mixed air temperature t m  at step  101 , and waiting for at least 5 minutes for sensors to measure air temperature at step  102 . If the fan operational time is less than 5 minutes, then the method includes continuing to loop through step  101  to measure air temperatures until the fan has operated for at least 5 minutes according to step  102 . 
         [0044]    After 5 minutes of fan operational time, the method includes checking if the absolute value of the return-air minus outdoor-air temperature difference, δT ro , is greater than a minimum temperature difference, preferably 10 degrees Fahrenheit, at step  104  according to the following equation. 
         [0000]      δ T   ro   =|t   r   −t   o |≧10  Eq. 1
   Where, δT ro =absolute value of the return-air minus outdoor-air drybulb temperatures (F),
       t r =return-air drybulb temperature (F), and   t o =outdoor-air drybulb temperature (F).   
       
 
         [0048]    If the absolute value of the return-air minus outdoor-air temperature difference is not greater than 10 degrees Fahrenheit, then the method loops back to step  100 . 
         [0049]    If the temperature difference is greater than 10 degrees Fahrenheit, then the method includes computing the Outdoor Air Fraction (OAF) from t r , t o  and t m  at step  106  using the following equation. 
         [0000]    
       
         
           
             
               
                 
                   OAF 
                   = 
                   
                     
                       
                         t 
                         r 
                       
                       - 
                       
                         t 
                         m 
                       
                     
                     
                       
                         t 
                         r 
                       
                       - 
                       
                         t 
                         o 
                       
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
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                   3 
                 
               
             
           
         
       
       
         Where, OAF=outdoor air fraction (dimensionless),
       t m =mixed-air drybulb temperature (F).   
     
       
     
         [0052]    The method may be implemented manually on units without a damper actuator. The method may be further implemented on units with an analog economizer controller with temperature sensors and low-voltage output signals to measure, adjust and correct the OAF using a damper actuator. The method may be further implemented on units with a digital economizer controller with microprocessor with FDD capabilities, temperature sensors and low-voltage output signals to control a damper actuator, and low-voltage output actuator control signals to measure, adjust and correct the OAF using a damper actuator and evaluate low airflow, low cooling capacity or low heating capacity. The controller may be able to take temperature measurements at specific initial, maximum, and closed economizer damper actuator control voltages, and use this information to calculate regression equation coefficients for the OAF versus economizer damper actuator voltage and with use the target minimum OAF based on regulatory requirements with the regression equation to solve for the optimal actuator voltage to achieve the target minimum OAF using the quadratic formula, and adjust the economizer dampers as necessary to achieve the optimally minimum OAF and then measure the OAF to verify the optimally minimum OAF is within an accepted tolerance of the minimum OAF r  based on regulatory requirements for the building and occupancy. A preferred accepted tolerance is within plus or minus ten percent of the minimum OAF r  based on regulatory requirements for the building and occupancy. 
         [0053]    At step  108 , the method includes checking the measured outdoor air fraction (OAF) to determine whether or not it is within ten percent of the minimum required outdoor air fraction (OAF r ) based on regulatory standards. 
         [0000]      0.9×OAF r ≦OAF≦1.1×OAF r   Eq. 5
 
         [0054]    At step  110 , the method includes fully opening the economizer dampers and looping back to step  100  and measuring t r , t o  and t m  at the maximum damper position and computing and storing the maximum Outdoor Air Fraction (OAF max ) based on t r , t o  and t m  at step  106  using Equation 2. For an HVAC system with an economizer damper actuator, opening the dampers involves adjusting the damper actuator control voltage to the maximum voltage, typically 10V, and looping back to step  100  and measuring t r , t o  and t m  at the maximum damper position and computing and storing the maximum Outdoor Air Fraction (OAF max ) based on t r , t o  and t m  at step  106  using Equation 2. 
         [0055]    Repeating step  110 , the method includes fully closing the economizer dampers and looping back to step  100  and measuring t r , t o  and t m  at the closed damper position and computing and storing the closed Outdoor Air Fraction (OAF closed ) based on t r , t o  and t m  at step  106  using Equation 2. For an HVAC system with an economizer damper actuator, closing the dampers involves adjusting the damper actuator control voltage to the minimum voltage, typically 2V, and looping back to step  100  and measuring t r , t o  and t m  at the closed damper position and computing and storing the closed Outdoor Air Fraction (OAF closed ) based on t r , t o  and t m  at step  106  using Equation 2. 
         [0056]    At step  112 , the present invention method includes developing the regression equations used to adjust the damper position to the optimize Outdoor Air Fraction (OAF o ) to meet regulatory requirements per the following equations. 
         [0000]        y   i   =ax   i   2   +bx   i   +c   Eq. 7
 
         [0000]    Where, y i =outdoor air fraction (OAF) based on economizer damper position (dimensionless),
       x i =economizer damper position or control voltage varying from 2V closed to 10V fully open (Volts),   a=regression coefficient,   b=regression coefficient, and   c=regression coefficient.
 
The regression equation coefficients are calculated using a least square method based on measuring OAF at the initial, maximum, and closed damper position at the economizer actuator control voltages for each damper position using the following matrix equations for the quadratic regression.
       
 
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                                  
                                 
                                   y 
                                   i 
                                 
                               
                             
                           
                         
                         
                           
                             
                               ∑ 
                               
                                 y 
                                 i 
                               
                             
                           
                         
                       
                       ] 
                     
                     
                        
                       Y 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   9 
                 
               
             
           
         
       
     
         [0000]    The method includes solving the above equation based on three OAF measurements at the initial, maximum, and closed damper positions by multiplying the inverse of the 3×3 matrix A times 1×3 matrix C to obtain the coefficients of the quadratic regression using the following equation. 
         [0000]        C=X   −1   Y   Eq. 11
 
         [0000]    Where, X −1 =inverse of the 3×3 matrix X calculated according to the following equation,
       C=1×3 matrix C containing coefficients, a, b, and c of the quadratic regression equation, and   Y=1×3 matrix Y noted in the above equation.
 
The method includes solving the inverse of the 3×3 matrix X using the following equations.
       
 
         [0000]    
       
         
           
             
               
                 
                   X 
                   = 
                   
                     [ 
                     
                       
                         
                           h 
                         
                         
                           k 
                         
                         
                           n 
                         
                       
                       
                         
                           i 
                         
                         
                           l 
                         
                         
                           o 
                         
                       
                       
                         
                           j 
                         
                         
                           m 
                         
                         
                           p 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   Eg 
                   . 
                   
                       
                   
                    
                   13 
                 
               
             
             
               
                 
                   
                     X 
                     
                       - 
                       1 
                     
                   
                   = 
                   
                     
                       1 
                       
                         det 
                          
                         
                             
                         
                          
                         X 
                       
                     
                      
                     
                       [ 
                       
                         
                           
                             
                               
                                 l 
                                  
                                 
                                     
                                 
                                  
                                 b 
                               
                               - 
                               om 
                             
                           
                           
                             
                               
                                 n 
                                  
                                 
                                     
                                 
                                  
                                 m 
                               
                               - 
                               kp 
                             
                           
                           
                             
                               ko 
                               - 
                               nl 
                             
                           
                         
                         
                           
                             
                               oj 
                               - 
                               ip 
                             
                           
                           
                             
                               
                                 h 
                                  
                                 
                                     
                                 
                                  
                                 p 
                               
                               - 
                               ni 
                             
                           
                           
                             
                               ni 
                               - 
                               ho 
                             
                           
                         
                         
                           
                             
                               im 
                               - 
                               lj 
                             
                           
                           
                             
                               kj 
                               - 
                               hm 
                             
                           
                           
                             
                               hl 
                               - 
                               ki 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   15 
                 
               
             
             
               
                 
                   
                     1 
                     
                       det 
                        
                       
                           
                       
                        
                       X 
                     
                   
                   = 
                   
                     1 
                     
                       hlp 
                       - 
                       imn 
                       + 
                       jko 
                       - 
                       hmo 
                       - 
                       jln 
                       - 
                       ikp 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   17 
                 
               
             
           
         
       
     
         [0000]    Where, detX=determinant of matrix X which cannot equal zero.
 
After calculating the 1×3 matrix C coefficients a, b, and c, using the above equations, the method includes calculating the position or control voltage, x r , required for economizer dampers to achieve the required minimum OAF r , to meet regulatory requirements using the following quadratic formula.
 
         [0000]    
       
         
           
             
               
                 
                   
                     x 
                     r 
                   
                   = 
                   
                     
                       
                         - 
                         b 
                       
                       + 
                       
                         
                           
                             b 
                             2 
                           
                           - 
                           
                             4 
                              
                             
                               a 
                                
                               
                                 ( 
                                 
                                   c 
                                   - 
                                   
                                     OAF 
                                     r 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     
                       2 
                        
                       a 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   19 
                 
               
             
           
         
       
     
         [0000]    Where, OAF r =the required minimum OAF r , to meet regulatory requirements, and
       X r =the economizer actuator control voltage setting to achieve the required minimum OAF r , to meet regulatory requirements.
 
After step  112 , the present invention includes looping back to step  100  and measuring t r , t o , and t m , computing final OAF in step  106 , and checking whether or not the OAF is within acceptable tolerance of preferably ten percent of OAF r  in step  108 .
       
 
         [0064]      FIG. 9  provides a graph showing measurements of outdoor air fraction (OAF) versus economizer damper actuator position control voltage from closed to maximum open on an HVAC system according to the present invention. The economizer damper control voltage is determined using measurements of initial, maximum, and closed damper OAF and voltage.  FIG. 10  illustrates how measurement data are used in a least squares method to determine coefficients of the quadratic regression Eq. 7.  FIG. 10  provides a table of OAF measurements (y i ) based on damper actuator voltage (x i ).  FIG. 10  shows measurement data entered into matrix X and matrix Y in Eq. 9.  FIG. 10  shows the inverse matrix X is multiplied by matrix Y to calculate the matrix C quadratic regression coefficients in Eq. 11.  FIG. 10  shows how the quadratic formula is used with the required minimum OAF r  per regulatory requirements to calculate the required damper actuator control voltage x r  in Eq. 19. The required damper actuator control voltage (x r ) is used to adjust the dampers, and the outdoor air fraction is measured per step  100  through step  106  of  FIG. 7  to verify that the new OAF is preferably within an acceptable tolerance of the minimum allowable OAF r  per regulatory requirements per step  108 . Preferably, the optimization is performed when the difference between outdoor-air temperature and return-air temperature is at least 10 degrees Fahrenheit and more preferably at least 20 degrees Fahrenheit. 
         [0065]      FIG. 11  illustrates the lookup table for calculating the target temperature split difference (δT t ) where the independent variables are the evaporator entering mixed-air drybulb temperature, t m , and evaporator entering mixed-air wetbulb temperature, t* m , and the dependent variable is the target temperature split difference (δT t ). 
         [0066]    The HVAC manufacturer protocols or regulatory standards require accurate measurement of mixed-air drybulb, t m , and mixed-air wetbulb, t* m , entering the evaporator in order to lookup the required or target temperature difference across the evaporator (defined as the difference between mixed-air drybulb, t m , minus supply-air drybulb, t s , temperature) to diagnose and correct improper evaporator airflow or low cooling capacity. Low airflow can cause ice to form on the air filter and evaporator which blocks airflow and reduces cooling capacity and efficiency. Low cooling capacity can be caused by many faults including excess outdoor airflow, dirty or blocked air filters, blocked evaporator caused by dirt or ice buildup, blocked condenser coils caused by dirt or debris buildup, low refrigerant charge, high refrigerant charge, refrigerant restrictions, and non-condensable air or water vapor in the refrigerant system. 
         [0067]    The HVAC manufacturer protocols or regulatory standards also require accurate measurement of mixed-air drybulb, t m , and mixed-air wetbulb, t* m , entering the evaporator in order to lookup the required or target superheat (defined as the difference between refrigerant suction temperature and evaporator saturation temperature) in order to diagnose and correct refrigerant charge or other faults which can cause improper superheat outside published tolerances established by the manufacturer or regulatory agency. Superheat must be within published tolerances in order to maintain proper cooling capacity and efficiency and prevent liquid refrigerant from entering and damaging the refrigerant system compressor. Not having a method to accurately measure mixed-air drybulb, t m , or wetbulb, t* m , will cause improper airflow and refrigerant system FDD as well as improper setup and operation of economizers and economizer FDD systems required by regulatory agencies. 
         [0068]    Calculating the humidity ratios (Ibm/Ibm) of return-air W r , outdoor-air, W o  and mixed-air W m  in step  114  are preferably performed using the following equations based on the Hyland Wexler formulas from the 2013 ASHRAE Handbook. 
         [0000]        p 1 ws =EXP[ C   1   /t*   r   +C   2   +C   3   t*   r   +C   4   t*   r   2   +C   5   t*   r   3   +C   6  ln( t*   r )]  Eq. 21
 
         [0000]    Where, p1 ws =saturation pressure at wetbulb temperature (psia) for the return air.
       t* r =measured return air wetbulb temperature +459.67 (R)   C 1 =−1.0440397 E+04,   C 2 =−1.1294650 E+01,   C 3 =−2.7022355 E−02,   C 4 =1.2890360 E−05,   C 5 =−2.4780681 E−09,   C 6 =6.5459673 E+00,
 
and
       
 
         [0000]    
       
         
           
             
               
                 
                   
                     W 
                     r 
                     * 
                   
                   = 
                   
                     0.621945 
                      
                     
                       [ 
                       
                         
                           p 
                            
                           
                               
                           
                            
                           
                             1 
                             ws 
                           
                         
                         
                           
                             p 
                             a 
                           
                           - 
                           
                             p 
                              
                             
                                 
                             
                              
                             
                               1 
                               ws 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   23 
                 
               
             
           
         
       
     
         [0000]    Where, W* r =humidity ratio corresponding to saturation at the return air wetbulb temperature, t* r  (Ibm/Ibm),
       p a =ambient air pressure (psia),
 
and
       
 
         [0000]    
       
         
           
             
               
                 
                   
                     W 
                     r 
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             1093 
                             - 
                             
                               0.556 
                                
                               
                                 t 
                                 r 
                                 * 
                               
                             
                           
                           ) 
                         
                          
                         
                           W 
                           r 
                           * 
                         
                       
                       - 
                       
                         0.24 
                          
                         
                           ( 
                           
                             
                               t 
                               r 
                             
                             - 
                             
                               t 
                               r 
                               * 
                             
                           
                           ) 
                         
                       
                     
                     
                       ( 
                       
                         1093 
                         + 
                         
                           0.444 
                            
                           
                             t 
                             r 
                           
                         
                         - 
                         
                           t 
                           r 
                           * 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   25 
                 
               
             
           
         
       
     
         [0000]    Where, W r =return air humidity ratio (Ibm/Ibm). 
         [0077]    Computing humidity ratio of outdoor air W o  (Ibm/Ibm) at step  114  is preferably performed using the following equations: 
         [0000]        p 2 ws =EXP[ C   1   /t*   o   +C   2   +C   3   t*   o   +C   4   t*   o   2   +C   5   t*   o   3   +C   6  ln( t*   o )]  Eq. 27
 
         [0000]    Where, p2 ws =saturation pressure at wetbulb temperature (psia) for the outdoor air,
       t* o =measured outdoor air wetbulb temperature +459.67 (R), and       
 
         [0000]    
       
         
           
             
               
                 
                   
                     W 
                     o 
                     * 
                   
                   = 
                   
                     0.621945 
                      
                     
                       [ 
                       
                         
                           p 
                            
                           
                               
                           
                            
                           
                             2 
                             ws 
                           
                         
                         
                           pa 
                           - 
                           
                             p 
                              
                             
                                 
                             
                              
                             
                               2 
                               ws 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   29 
                 
               
             
           
         
       
     
         [0000]    Where, W* o =humidity ratio corresponding to saturation at the outdoor air wetbulb temperature, t* o  (Ibm/Ibm),
 
and
 
         [0000]    
       
         
           
             
               
                 
                   
                     W 
                     o 
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             1093 
                             - 
                             
                               0.556 
                                
                               
                                 t 
                                 o 
                                 * 
                               
                             
                           
                           ) 
                         
                          
                         
                           W 
                           o 
                           * 
                         
                       
                       - 
                       
                         0.24 
                          
                         
                           ( 
                           
                             
                               t 
                               o 
                             
                             - 
                             
                               t 
                               o 
                               * 
                             
                           
                           ) 
                         
                       
                     
                     
                       ( 
                       
                         1093 
                         + 
                         
                           0.444 
                            
                           
                             t 
                             o 
                           
                         
                         - 
                         
                           t 
                           o 
                           * 
                         
                       
                       ) 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   31 
                 
               
             
           
         
       
     
         [0000]    Where, W o =outdoor air humidity ratio (Ibm/Ibm). 
         [0079]    The method includes preferably calculating an initial value of the mixed-air humidity ratio W m  from the OAF m , W r , and W o  at step  114  using the following equation. 
         [0000]        W   m   =W   r   −[W   r   −W   o ]OAF m   Eq. 33
 
         [0000]    Where, W m =humidity ratio at the mixed-air conditions (Ibm/Ibm). 
         [0080]    Estimating an initial value of mixed-air wetbulb temperature (t* m ) at step  116  is preferably setting an initial value of mixed-air wetbulb temperature (t* m ) to the mixed-air drybulb temperature minus 10 degrees Fahrenheit in cooling mode (t* m =t m −10). Computing saturation pressure (p ws ) for the mixed-air wetbulb temperature (t* m ) at step  118  is preferably performed using the initial or previous time-step estimate of the mixed-air wetbulb temperature, t* m , in the following equation. 
         [0000]        p   ws =EXP[ C   1   /t*   m   +C   2   +C   3   t*   m   +C   4   t*   m   2   +C   5   t*   m   3   +C   6  ln( t*   m )]  Eq. 35
 
         [0000]    Where, p ws =saturation pressure at wetbulb temperature (psia)
       t* m =mixed-air wetbulb temperature +459.67 (i.e., converted to degrees Rankine).
 
The method includes calculating the saturation humidity ratio (W m) at step  118  from the saturation pressure (p ws ) using the following equation.
       
 
         [0000]    
       
         
           
             
               
                 
                   
                     W 
                     m 
                     * 
                   
                   = 
                   
                     0.621945 
                      
                     
                       [ 
                       
                         
                           p 
                           ws 
                         
                         
                           pa 
                           - 
                           
                             p 
                             ws 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   37 
                 
               
             
           
         
       
     
         [0000]    Where, W* m =humidity ratio at the mixed-air saturation pressure (p ws ) (Ibm/Ibm). 
         [0082]    The method includes calculating a new estimate of mixed-air wetbulb temperature (t* m ) at step  120 , preferably performed using the following equation including the previous step mixed-air wetbulb temperature (t* m     i-1   ) estimate. 
         [0000]    
       
         
           
             
               
                 
                   
                     t 
                     m 
                     * 
                   
                   = 
                   
                     0.5 
                      
                     
                       [ 
                       
                         
                           t 
                           
                             m 
                             
                               i 
                               - 
                               1 
                             
                           
                           * 
                         
                         + 
                         
                           
                             
                               1093 
                                
                               
                                 W 
                                 m 
                               
                             
                             + 
                             
                               0.444 
                                
                               
                                 W 
                                 m 
                               
                                
                               
                                 t 
                                 m 
                               
                             
                             - 
                             
                               1093 
                                
                               
                                 W 
                                 m 
                                 * 
                               
                             
                             + 
                             
                               0.24 
                                
                               
                                 t 
                                 m 
                               
                             
                           
                           
                             
                               W 
                               m 
                             
                             - 
                             
                               0.556 
                                
                               
                                 W 
                                 m 
                                 * 
                               
                             
                             + 
                             0.24 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   Eq 
                   . 
                   
                       
                   
                    
                   39 
                 
               
             
           
         
       
     
         [0000]    Where t* m =new estimate of mixed-air wetbulb temperature (F), and
       t* m     i-1   =previous step mixed-air wetbulb temperature (F).       
 
         [0084]    The new estimate of mixed-air wetbulb temperature is tested for convergence at step  122 , to evaluate whether or not the absolute value of the change in Δt* m  is less than or equal to 0.01 degrees Fahrenheit using the following equation. 
         [0000]      |Δ t*   m |≦0.01  Eq. 41
 
         [0085]    If the absolute value of the change in Δt* m  is less then or equal to 0.01 degrees Fahrenheit, then the method includes proceeding to step  124  to check whether or not the unit is operating in cooling mode. If step  124  determines that the absolute value of the change Δt* m  is not less than or equal to 0.01 degrees Fahrenheit, then steps  118 ,  120 , and  122  are preferably repeated calculating p ws  and W* s  a new estimate of t* m  until the absolute value of the recursive change in wetbulb temperature Δt* m  is less than or equal to 0.1 degrees Fahrenheit. 
         [0086]    At step  124  the method includes storing coefficients a, b, and c, and the economizer actuator control voltage, x r , to meet the minimum outdoor air fraction, OAF r , to meet regulatory requirements, maximum OAF max , closed OAF closed , mixed-air drybulb temperature t m , mixed-air wetbulb temperature, t* m , and return and outdoor air drybulb and wetbulb temperature measurements, t r , t* r , t o , and t* o , and proceeding to step  126 . 
         [0087]    At step  126 , the method includes checking whether or not to evaluate HVAC FDD, and if not, ending the OAF optimization method at step  128 , or going to step  129  and proceeding to step  131  and starting the HVAC FDD evaluation method shown in  FIG. 8 . 
         [0088]      FIG. 8  shows a method for performing an FDD evaluation on an HVAC system while the HVAC system is operating according to the present invention. The method starts at step  130  and includes first checking whether or not the ventilation fan has been operating continuously for greater than 24 hours at Step  132 . If the fan has been operating continuously for greater than a maximum fan run time FT max , for example 24 hours, the method includes reporting a fan on continuously fault at step  134 . 
         [0089]    If the fan has not been operating continuously, then the method proceeds to Step  136  and checking whether or not the HVAC system is in cooling or heating mode. If in cooling mode, the method includes detecting and diagnosing low airflow and low cooling capacity faults in steps  138  through  158 . In some embodiments in cooling mode, the method includes performing FDD of refrigerant superheat based on t* m  and t o  in steps  138  through  158 . If in heating mode, the method includes steps for detecting and diagnosing low heating capacity faults in steps  154  through  182 . 
         [0090]    At step  138 , the method includes checking if the cooling system has been operating for at least a minimum cooling run time, preferably five minutes, and if not, then the method includes checking short cycle cooling operation for five successive cycles (i.e., failing the test of step  138  five consecutive times) at Step  140 , and if yes, then generating an FDD alarm signal reporting a cooling short cycle fault at Step  142 . 
         [0091]    After the minimum fan run time of cooling system operation at Step  144 , the method includes calculating the actual temperature split difference (δT a ) based on the mixed-air drybulb temperature (t m ) minus the supply-air temperature (t s ) according to the following equation. 
         [0000]      δ T   a   =t   m   −t   s   Eq. 43
 
         [0092]    At step  144 , the method also includes calculating the target temperature split difference (δT t ) across the cooling system evaporator and the temperature split difference ΔTS defined as the actual temperature split minus the target temperature split. The method includes calculating the target temperature split difference (δT t ) using a target temperature split lookup table shown in  FIG. 11 , where the independent variables are the evaporator entering mixed-air drybulb temperature, t m , and evaporator entering mixed-air wetbulb temperature, t* m . The method also includes calculating the target temperature split difference (δT t ) using the following equation. 
         [0000]      δ T   t   =C   7   +C   8   t   m   +C   9   t   m   2   +C   10   t*   m   +C   11   t*   m   2   +C   12 ( t   m   ×t*   m )  Eq. 45
 
         [0000]    Where, δT t =target temperature difference between mixed-air and supply-air in cooling mode (F),
       t m =measured mixed-air drybulb temperature (F),   t* m =mixed-air wetbulb temperature (F),   C 7 =−6.509848526 (F),   C 8 =−0.942072257 (F −1 ),   C 9 =−0.009925115 (F −2 ),   C 10 =1.944471104 (F −1 ),   C 11 =−0.0208034037991888 (F −2 )   C 12 =−0.000114841 (F −2 )       
 
         [0101]    At step  144 , the method also includes calculating the delta temperature split difference (ΔTS) based on the actual temperature split difference (δT a ) minus the target temperature split difference (δT t ) using the following equation. 
         [0000]      Δ TS=δT   a   −δT   t   Eq. 47
 
         [0000]    Where, ΔTS=delta temperature split difference between actual temperature split and target temperature split (F). 
         [0102]    At step  146  the method checks whether or not the temperature split difference ΔTS is within plus or minus a temperature split threshold, preferably ±3 degrees Fahrenheit (or a user input value). If ΔTS is within plus or minus the temperature split threshold (or the user input value), then the cooling system is within tolerances, no FDD alarm signals are generated, and the method loops back to continue checking proper operation of the cooling system by repeating steps  144  and  146 . 
         [0103]    At step  148 , the method checks whether or not the temperature split difference (ΔTS) is less than a negative minimum temperature split difference threshold, preferably less than −3 degrees Fahrenheit (or a user input value). If the method determines the temperature split difference (ΔTS) is less than the negative minimum temperature split difference threshold (or the user input value), then the method includes providing an FDD alarm signal reporting a low cooling capacity fault at step  152  to check for low cooling capacity which can be caused by many faults including excess outdoor airflow, dirty or blocked air filters, blocked evaporator caused by dirt or ice buildup, blocked condenser coils caused by dirt or debris buildup, low refrigerant charge, high refrigerant charge, refrigerant restrictions, or non-condensable air or water vapor in the refrigerant system. 
         [0104]    At step  148 , if the method determines that the temperature split difference (ΔTS) is not greater than the negative minimum temperature split difference threshold, then the method includes providing an FDD alarm signal at step  150  reporting a low airflow fault to check for low airflow which can cause ice to form on the air filter and evaporator which blocks airflow and severely reduces cooling capacity and efficiency. 
         [0105]    At step  136  if the method determines the system is in heating mode, then the method includes proceeding to step  154 . 
         [0106]    At step  154 , the method includes checking if the heating system has been operating for greater then a minimum heater run time, preferably five minutes, and if no, then the method includes checking short cycle heating operation for 5 successive cycles at Step  156 , and if yes, then generating an FDD alarm signal reporting a heating short cycle fault at Step  158 . 
         [0107]    After at least the minimum heater run time of heating system operation at Step  160 , the method includes calculating the actual temperature rise (δTR a ) for heating based on the supply-air temperature minus the mixed-air temperature according to the following equation. 
         [0000]      δ TR   a   =t   s   −t   m   Eq. 49
 
         [0108]    At step  162 , the method includes checking whether or not the heating system is a gas furnace, and if the method determines the heating system is a gas furnace, then the method proceeds to step  164 . 
         [0109]    At step  164 , the method includes calculating the minimum acceptable target supply-air temperature rise for a gas furnace which is preferably a function of airflow and heating capacity based on furnace manufacturer temperature rise data shown in  FIG. 12 , and is preferably 30 degrees Fahrenheit as shown in the following equation. 
         [0000]      δ TR   t     furnace   =30  Eq. 51
 
         [0000]    Where, δTR t     furnace   =minimum acceptable furnace temperature rise.
 
The minimum acceptable furnace temperature rise may vary from 30 to 100 degrees Fahrenheit or more depending on make and model, furnace heating capacity, airflow, and return temperature.
 
         [0110]    At step  164 , the method also includes calculating the delta temperature rise for the gas furnace heating system, ΔTR furnace , according to the following equation. 
         [0000]      Δ TR   furnace   =δT   a   −δTR   t     furnace     Eq. 53
 
         [0111]    At step  170  the method includes calculating whether or not the delta temperature rise for the furnace is greater than or equal to zero degrees Fahrenheit according to the following equation. 
         [0000]      Δ TR   furnace   =δT   a   −δTR   t     furnace   ≧0  Eq. 55
 
         [0112]    At step  170 , if the method determines the delta temperature rise for the furnace is greater than or equal to zero degrees Fahrenheit, then the gas furnace heating system is considered to be within tolerances, no FDD alarm signals are generated, and the method includes a loop to continue checking the temperature rise while the furnace heating system is operational using steps  160  through  170 . 
         [0113]    At step  170 , if the method determines the delta temperature rise for the furnace is less than zero degrees Fahrenheit, then proceeds to step  172 . 
         [0114]    At step  172 , for a gas furnace heating system, the method includes preferably providing at least one FDD alarm signal reporting a low heating capacity fault which can be caused by excess outdoor airflow, improper damper position, improper economizer operation, dirty or blocked air filters, low blower speed, blocked heat exchanger caused by dirt buildup, loose wire connections, improper gas pressure or valve setting, sticking gas valve, bad switch or flame sensor, ignition failure, misaligned spark electrodes, open rollout, open limit switch, limit switch cycling burners, false flame sensor, cracked heat exchanger, combustion vent restriction, improper orifice or burner alignment, or non-functional furnace. 
         [0115]    At step  162 , the method includes checking whether or not the heating system is a gas furnace, and if the method determines the heating system is not a gas furnace, then the method proceeds to step  170 . 
         [0116]    At step  174 , the method includes checking whether or not the heating system is a heat pump, and if the method determines the heating system is a heat pump, then the method proceeds to step  176 . 
         [0117]    At step  176 , the method includes measuring the target temperature rise for heat pump heating based on the minimum acceptable target temperature rise which is preferably a function of outdoor air temperature as shown in the following equation based on heat pump manufacturer minimum acceptable temperature rise data shown in  FIG. 13 . 
         [0000]      δ TR   t     heat pump     =[C   21   t   o   2   +C   22   t   0   +C   23 ]  Eq. 57
 
         [0000]    Where, δTR t     heat pump   =minimum acceptable heat pump temperature rise,
       C 21 =0.0021 (F −1 ),   C 22 =1.845 (dimensionless), and   C 23 =8.0 (F).
 
Temperature rise coefficients may vary depending on user input, heat pump make and model, heat pump heating capacity, airflow, outdoor air temperature, and return temperature. Minimum temperature rise coefficients for a heat pump are based on outdoor air temperatures ranging from −10 F to 65 Fahrenheit, airflow from 300 to 400 cfm/ton, and return temperatures from 60 to 80 degrees Fahrenheit.
       
 
         [0121]    At step  176 , the method also includes calculating the delta temperature rise for the heat pump heating system according to the following equation. 
         [0000]      Δ TR   heat pump   =δT   a   −δTR   t     heat pump     Eq. 58
 
         [0122]    At step  178 , the method includes calculating whether or not the delta temperature rise for the heat pump heating system is greater than or equal to zero degrees Fahrenheit according to the following equation. 
         [0000]      Δ TR   heat pump   =δT   a   −δTR   t     heat pump   ≧0  Eq. 59
 
         [0123]    At step  178 , if the method determines the delta temperature rise for the heat pump is greater than or equal to zero degrees Fahrenheit, then the heat pump heating system is considered to be within tolerances, no FDD alarm signals are generated, and the method includes a loop to continue checking the temperature rise while the heat pump heating system is operational using steps  160  through  178 . 
         [0124]    At step  178 , if the method determines the delta temperature rise for the heat pump is less than zero degrees Fahrenheit, then the method proceeds to step  172 . 
         [0125]    At step  172 , for a heat pump heating system, the method includes preferably providing at least one FDD alarm signal reporting a low heating capacity fault to check the system for low heating capacity which can be caused by many faults including excess outdoor airflow, improper damper position, improper economizer operation, dirty or blocked air filters, blocked heat pump indoor coil caused by dirt buildup, improper thermostat setup or malfunction, loose wire connections, blocked outdoor coil caused by ice, dirt or debris, defective capacitor or relay, failed outdoor coil fan motor or capacitor, failed reversing valve or improper reversing valve control, improper refrigerant charge, refrigerant restriction (filter drier or expansion device), non-condensable air or water vapor in system, malfunctioning defrost controller, high airflow above 450 cfm/ton, failing compressor (locked rotor, leaking valves, etc.), or non-functional heat pump. 
         [0126]    At step  174 , if the method determines the heating system is not a heat pump, then the method proceeds to step  180 . 
         [0127]    At step  180 , the method measures the target temperature rise for the hydronic heating system based on the minimum acceptable target supply-air temperature rise according to the following equation which is preferably a function of hot water supply temperature and may vary from 18 to 73 degrees Fahrenheit depending on airflow, coil heating capacity, and hot water supply temperature, t hw , as shown in  FIG. 14 . 
         [0000]      δ TR   t     hydronic     =[C   25   t   hw   +C   26 ]  Eq. 61
 
         [0000]    Where, δTR t     hydronic   =minimum acceptable hydronic temperature rise,
       C 25 =0.35 (F −1 ), and   C 26 =−24 (F).       
 
         [0130]    The method also includes the following simplified equation to measure the target temperature rise for the hydronic heating system for all systems regardless of hot water supply temperature as shown in  FIG. 14 . 
         [0000]      δ TR   t     hydronic     =C   27   Eq. 62
 
         [0000]    Where, δTR t     hydronic   =minimum acceptable hydronic temperature rise,
       C 27 =19 degrees Fahrenheit (F).       
 
         [0132]    At step  180 , the method also includes calculating the delta temperature rise for the hydronic heating system according to the following equation. 
         [0000]      Δ TR   hydronic   =δT   a   −δTR   t     hydronic     Eq. 63
 
         [0133]    At step  182 , the method includes calculating whether or not the delta temperature rise for the hydronic heating systems greater than or equal to zero degrees Fahrenheit according to the following equation. 
         [0000]      Δ TR   hydronic   =δT   a   −δTR   t     hydronic   ≧0  Eq. 65
 
         [0134]    At step  182 , if the method determines the delta temperature rise for the hydronic heating system is greater than or equal to zero degrees Fahrenheit, then the hydronic heating system is considered to be within tolerances, no FDD alarm signals are generated, and the method includes a loop to continue checking the temperature rise while the hydronic heating system is operational using steps  160  through  182 . 
         [0135]    At step  182 , if the method determines the delta temperature rise for the hydronic heating system is less than zero degrees Fahrenheit, then the method proceeds to step  172 . 
         [0136]    At step  172 , for a hydronic heating system, the method includes preferably providing at least one FDD alarm signal reporting a low heating capacity fault to check the system for low heating capacity which can be caused by many faults including excess outdoor airflow, improper damper position, improper economizer operation, dirty or blocked air filters, blocked hydronic coil caused by dirt buildup, improper thermostat setup or malfunction, loose wire connections, failed or stuck hydronic control valve, defective capacitor or relay, low hot water temperature setting, failed water heater or boiler, leak or loss of hydronic fluid, failed capacitor, high airflow above 450 cfm/ton, air in hydronic system, or non-functional hydronic circulation controller or pump. 
         [0137]    In some embodiments, the method includes providing FDD alarms regarding the following faults: excess outdoor air, damper actuator failure, low airflow, low cooling capacity, or low heating capacity. In some embodiments the present invention includes methods to communicate FDD alarms using wired or wireless communication to display error codes or alarms on the present invention apparatus through a built-in display or external display through wired or wireless communication signals to a building energy management system, standard thermostat, WIFI-enabled thermostat, internet-connected computer, internet telephony system, or smart phone indicating maintenance requirements to check and correct outdoor air damper position, evaporator airflow and/or refrigerant charge of the air conditioning system. 
         [0138]    While the invention herein disclosed has been described by means of specific embodiments and applications thereof, numerous modifications and variations could be made thereto by those skilled in the art without departing from the scope of the invention set forth in the claims.