# Sizing VFDs for optimal operating efficiency

## A new control strategy and implementation system optimize variable frequency drive (VFD) efficiency to meet cooling-air requirements.

**Learning Objectives:**

- Explain the impact of variable frequency drive (VFD) enclosure parameters on VFD performance and operational reliability.
- Analyze the VFD's efficiency and its ability to meet enclosure cooling-air requirements with the new control strategy.
- Outline the new control strategy and implementation system developed to optimize VFD efficiency.

The VFD enclosure cooling-air fan should be sized by the mechanical engineer by considering cooling-air load, temperature entering the enclosure, and the allowable operating temperature. The enclosure cooling load is caused by the drive inefficiency, resulting in increased air dry-bulb temperature. Required cooling-air volume should be calculated assuming that the VFD enclosure load will be carried out as the sensible load only.

The actual VFD enclosure cooling load during design and off-design conditions must be verified from monitoring data; otherwise, the enclosure cooling load could be substantially higher when compared with data from a VFD manufacturer. The actual enclosure-load deviation is due to the different patterns of the static and dynamic hydraulic-pressure losses in various systems. The design cooling-airflow rate (CAFR_{DES}) will be determined based on the maximum anticipated ambient temperature (T_{AMB MAX}) surrounding the VFD enclosure and by a manufacturer's allowable VFD enclosure maximum operating temperature (T_{OPR MAX}).

The following four equations determine major enclosure operational parameters in British system thermal units:

1. Q_{DES/OFF-DES} = Q_{TOT} = Q_{SEN} = 1.085 x (T_{EXT MAX} - T_{ENT MAX}) x CAFR_{DES} = 4.5 x ∆E x CAFR_{DES }

2. CAFR_{DES} = Q_{DES} / [1.085 x (T_{EXT MAX} - T_{ENT MAX})]

3. T_{OPR MAX }= (T_{ENT MAX} + T_{EXT MAX}) / 2

4. T_{EXT MAX} = 2 x (T_{AMB MAX }- T_{ENT MAX})

Where:

Q_{DES/OFF-DES}, Q_{SEN}, Q_{TOT} = VFD enclosure design/off-design, sensible, and total cooling load

T_{ENT MAX} = Maximum anticipated dry-bulb cooling-air temperature entering the VFD enclosure; depends on the location of the enclosure (i.e., in the air conditioned area, in the area with mechanical-free cooling, etc.)

T_{AMB MAX} = Manufacturer's allowable dry-bulb ambient air temperature surrounding the VFD enclosure, which represents the enclosure's maximum allowable operating temperature T_{OPR MAX}

T_{EXT MAX} - T_{ENT MAX} = Temperature differential between maximum cooling-air dry-bulb temperatures exiting and entering the VFD enclosure

∆E = Enthalpy differential for cooling-air exiting and entering the VFD enclosure.

Design cooling-air conditions entering the VFD enclosure are related to the design cooling-air dry-bulb temperature, relative humidity, air density, and humidity ratio.

Because VFD manufacturers allow high dry-bulb temperature and relative humidity of cooling air entering the enclosure, the moist loaded air is always present in the enclosure. As indicated by the first equation, the enclosure's total cooling load should be equal to its sensible load. However, if the VFD enclosure design's cooling-air flow rate is specified in the equations, the enclosure's optimal operating conditions can be satisfied without a moisture exchange. If these specifications aren't met, it might result in moisture deposition in the enclosure.

Figure 1 demonstrates the impact of T_{OPR MAX} on the design relative cooling-air (RCAFR_{DES}). The T_{OPR MAX} varied from 104° to 122°F. This is the conservative approach, because the actual T_{OPR MAX} might be higher due to the T_{EXT} increase associated with heat removal caused by a greater VFD power-loss factor. Compensating for the increase in T_{OPR MAX} will require employing an oversized VFD. The higher operating temperature of the VFD enclosure will lead to increased T_{EXT MAX}, which can be calculated in the last equation.

T_{ENT MAX} depends on the location of the enclosure and varies from 50°F for an air conditioned area to 100°F for mechanical-free cooling with a once-through ventilation system. The top graph in Figure 1 indicates that RCAFR_{DES} is drastically reduced when T_{ENT MAX} drops from 100° to 90°F, which coincides with VFD enclosure cooling-air temperature differentials increasing from 8° to 28°F. A further reduction of T_{ENT MAX} and the correlated increase in the enclosure's temperature differential leads to a lower reduction of the design's relative cooling-airflow rate.

Figure 1 also indicates that, for the considered conditions, the maximum design cooling-airflow rate of 100% occurs at T_{ENT MAX} = 100°F and T_{EXT MAX} = 108°F (i.e., at T_{OPR MAX} = 104°F). The increase in allowable VFD enclosure operating temperature from 104°F (shown in the top graph of Figure 1) to 113°F (shown in the middle graph of Figure 1) leads to the reduction in RCAFR_{DES} from 100% to 30.8%. It also causes the VFD enclosure's temperature differential to increase from 8°F (at T_{ENT MAX} =100°F and T_{EXT MAX} = 108°F; see Figure 1, top graph) to 26°F (at T_{ENT MAX} =100°F and T_{EXT MAX }= 126°F).

The further increase in allowable operating temperature from 104° to 122°F (shown in the bottom graph of Figure 1) leads to the additional reduction in RCAFR_{DES} from 100% (see Figure 1, top graph) to 18.2%. It also causes the VFD enclosure's temperature differential to further increase from 8°F (at T_{ENT MAX} =100°F and T_{EXT MAX} = 108°F; see Figure 1, top graph) to 44°F (at T_{ENT MAX} =100°F and T_{EXT MAX} = 144°F).

Therefore, RCAFR_{DES} could be noticeably reduced by lowering the cooling-air temperature entering the enclosure. The reduction of TENT from 100° to 50°F could lead to the RCAFR_{DES} decreasing from 100% to 7.4% (shown in the top graph of Figure 1).

Given equal load conditions, the reduction in cooling-air temperature entering the VFD enclosure leads to an increased exiting cooling-air temperature, causing an increase of the temperature differential and correlated reduction in cooling-airflow rate. Maintaining a lower operating temperature at the same load and cooling-air temperature entering the enclosure will require a lower cooling-air temperature exiting the VFD enclosure and a higher relative airflow rate compared to the design magnitude (shown in the first graph of Figure 1).

Further analysis demonstrates how the cooling-air temperature exiting the VFD enclosure impacts the enclosure's operating temperature of 70°F and flow rate at constant entering-air temperature. A wide variety of operating temperatures, from 75° to 100°F, might apply by adjusting the VFD enclosure's cooling-airflow rate. For instance, the increase in the enclosure operating temperature from 75°F to 85°F will allow the reduction in cooling-airflow from 100% to 33.3%. The increase in operating temperature from 75° to 100°F will reduce required cooling-airflow from 100% to 16.7%.

**VFD enclosure moisture deposits, moisture-exchange control **

While VFD manufacturers' statistical data show how the enclosure's elevated dry-bulb operating temperature impacts VFD service life and reliability, frequency-controller electronic equipment make apparent the negative impact of moisture residing in the VFD enclosure. The conditions with no moisture exchange in the enclosure could be found from the following equations:

5. ∑M_{ENT} =∑M_{EXT }

Equation 5 could be modified as:

6. (CAFR_{ENT} / D_{ENT}) x HR_{ENT} = (CAFR_{EXT} / D_{EXT}) x HR_{EXT }

Thus, equation 5 is equivalent to:

7. HR_{ENT} = HR_{EXT }

Where:

∑M_{ENT} = cumulative amount of air moisture entering the enclosure, pounds of water per minute

∑M_{EXT} = cumulative amount of air moisture exiting the enclosure, pounds of water per minute

D_{ENT} and D_{EXT} = density of the cooling-air entering and exiting the enclosure, cubic feet per pound of dry air

HR_{ENT} and HR_{EXT} = humidity ratio of the cooling-air entering and exiting the VFD enclosure, pounds of water/pounds of dry air.

The conditions of equalized entering and exiting moisture amounts in the enclosure can be achieved by varying the cooling-airflow rate. The required airflow rates to satisfy these conditions are governed by the following equations:

8. Q_{DES/OFF-DES} = Q_{TOT} = Q_{SEN }= 1.085 x (T_{EXT MAX} - T_{ENT MAX}) x CAFR_{DES} = 4.5 x ∆E x CAFR_{DES }

9. CAFR_{DES} = Q_{DES} / [1.085 x (T_{EXT MAX} - T_{ENT MAX})]

10. HR_{ENT} = HR_{EXT}

Given the fixed cross-section area for the particular VFD enclosure, the variation in the amount of cooling-air through the enclosure will result in respective change in the enclosure cooling-air velocity. There are three operational scenarios that have to be considered to determine the required cooling-airflow rate via the enclosure:

- HR
_{EXT}= HR_{ENT}: No control actions are required. - HR
_{EXT}< HR_{ENT}: The cooling-air's moisture is separating from the air and dropping off into the enclosure because the cooling-air velocity is lower than the critical air velocity, which is necessary to carry the moisture suspended in the air at a given load. Under these conditions, the cooling-airflow rate through the enclosure must be increased until HR_{EXT}= HR_{ENT}. - HR
_{EXT}> HR_{ENT}: The air velocity exceeds its critical magnitude at a given load. Under these conditions, the cooling-airflow could be reduced. However, the rate of reduction is limited by the maximum allowable cooling-air temperature exiting the enclosure (see Figure 1) to prevent the cooling-air operating temperature from exceeding the allowed magnitude. The alternative control strategy would be to maintain constant cooling-airflow at its design magnitude. This approach, however, isn't the best for energy conservation due to the increased energy usage by the enclosure's cooling fans and associated cooling equipment during design and off-design conditions, which results in lowering the VFD's operational efficiency.

The system's schematics shown in Figure 2 outline the specifics of the VFD enclosure's developed variable operating temperature and cooling-airflow control. This control system achieves the optimal operating temperature by resetting the exiting air's temperature set point at a given VFD enclosure's entering-air temperature and cooling load. If the enclosure's operating air temperature is maintained above its optimal value of 75°F, then the service life of the VFD is reduced.

On the other hand, when the operating air temperature gets below 75°F, the overall VFD efficiency is lower due to the additional energy expenditure to maintain cooling-air below optimal conditions. The selection of the optimal cooling-air operating temperature and exiting-air humidity ratio will increase the VFD's service life and reduce its energy consumption, thus, increasing overall operational efficiency. A multispeed, cooling-air fan-motor control could also be employed to realize the system control strategy as shown in Figure 2.

Figure 3 depicts the three-way VFD enclosure's comparative control parameters with constant and variable cooling-airflow rate. In comparison, the cooling-air operating temperature, humidity ratio, and cooling load with moisture exchange are all assumed to be related to the same conditions adopted for the data gathered earlier from the monitored parameters for a 125-hp VFD servicing a secondary loop chilled-water pump.

The top graph in Figure 3 shows cooling-air operating temperatures of the VFD enclosure for the current mode when the enclosure cooling fans are not controlled and cooling-airflow remains relatively constant and close to its design magnitude per the manufacturer's specification (i.e., about 604 cfm). The current control strategy uses on/off cooling fans control for two cooling fans, depending on the VFD operational status. When the VFD is on, the cooling fans are running. When the VFD is off or switched to the VFD bypass mode, the cooling fans are turned off.

The second set of operating temperatures in the first graph of Figure 3 represents the increased design cooling-airflow calculated using Equation 2.

The third set of operating temperatures on the top graph in Figure 3 is related to the variable cooling-airflow rate, which is applied to match the VFD enclosure's operating temperatures to the current control strategy. The second graph from the top of Figure 3 shows the humidity ratio of the cooling-air entering the VFD enclosure. The second graph from the top of Figure 3 also gives the humidity ratio of the air exiting the enclosure at the current control strategy with constant airflow specified by the VFD manufacturer. This control, as other articles show, leads to the moisture exchange in the enclosure when HR_{EXT} > or < HR_{ENT}. Finally, the second graph from the top of Figure 3 also shows the exiting-air humidity ratio with suggested variable or increased design flow rate. In both cases, HR_{EXT} = HR_{ENT} and no moisture exchange takes place in the enclosure.

The third graph from the top in Figure 3 shows comparative magnitudes of the cooling-airflow rates for the considered options. The calculated design cooling-airflow, based on the developed methodology, is by the factor of 1.6 higher as compared with the cooling-airflow magnitude suggested by the VFD manufacturer. This increase of cooling-airflow via VFD enclosure is necessary to eliminate the moisture exchange.

The application of developed variable cooling-airflow control is advantageous from an energy-conservation point of view when compared with current control strategies It also might further benefit switchover from traditional VFD control to VFD↔VFD bypass control to reduce a system's electrical motors' overall design power demand, according to a study.

During investigations, the system was operating with constant and inadequate cooling-airflow rate, which caused protracted periods during which the magnitudes of HR_{EXT} and HR_{ENT} were not equalized, resulting in residual moisture being present in the enclosure. When the suggested control strategy -either a variable or permanently oversized cooling-airflow rate- was implemented to maintain HR_{EXT} = HR_{ENT}, there was no moisture exchange in the enclosure during design and off-design VFD operations.

The third graph in Figure 3 also depicts power demand for the enclosure cooling fans. The power demand fluctuates between its maximum and minimum values of 0.175-kW and 0.0466-kW loads, respectively, in correlation with the enclosure's daily cooling-airflow. The enclosure cooling-air fans' cumulative daily power demand for variable air control (0.073 kW) is lower as compared with permanently increased cooling-airflow (0.175 kW), allowing 900 kWh/year in energy savings. The last graph in Figure 3 depicts relative values of the VFD enclosure's sensible, latent, and total load.

Figure 3 also indicates that if the existing control strategy is applied for enclosure cooling then both sensible and latent cooling loads will be present, causing moisture exchange in the VFD enclosure. When the control strategy with variable cooling-airflow or increased design cooling-airflow is realized, the total load always will be equal to the VFD enclosure's sensible load only. This will preclude moisture exchange from occurring in the VFD enclosure. A similar control strategy could also be used for VFDs with no enclosures.

**Alexander L. Burd** is president and **Galina S. Burd** is a project manager and vice president at Advanced Research Technology. Alexander Burd has 35 years of experience in the design, research, and optimization of HVAC and district energy systems with verified monitored electrical and thermal energy savings for large facilities and energy utilities. Galina Burd has more than 25 years of design and research experience in the HVAC and architectural engineering field and has co-authored many technical and research papers both in the U.S. and Europe.