Peak power ratings with convection and conduction cooled power supplies

Many open frame power supplies now offer two power ratings, one with convection or conduction cooling and one where external forced air is applied.  As some applications require low acoustic noise levels, for example in healthcare where patient comfort is important, fan-less cooling is preferred.  This can be achieved through operating a power supply at its convection rating, and if it is also capable of conduction cooling, a combination of both.

If the output load significantly varies with time it may be possible to utilize a power supply with a peak power rating.  This allows a lower power product to be selected, saving cost and reducing its size, as the convection cooled peak power rating is often the same as the forced air continuous rating. 

For example, modern hospital beds are fitted with electric motors that can adjust the angle of the bed to allow the patient to sit upright, or raise the lower portion to elevate the legs. These motors may only operate for short periods of time. The same will apply for dental chairs, thermal warmers for babies and incubators.

Power supply manufacturers will state the maximum peak power level and the length of time it can be drawn.  The datasheet or application notes indicate if the peak power rating is calculated using RMS or average power. Alternatively, examples may be given in the application notes or instruction manual with a list of components to be monitored and their maximum temperatures.

TDK-Lambda’s CUS600M power supply (Figure 1) has a convection cooled and RMS peak rating of 400W. It can deliver 600W peak for a maximum continuous duration of 10 seconds.

Figure 1: TDK-Lambda’s CUS600M power supply 

To determine the RMS power of a repetitive peak load, we shall use the example shown in Figure 2. OPa = minimum output power drawn, OPb = maximum output power, t = peak load time in seconds and T = quiescent load time in seconds.

 

Figure 2: Repetitive peak power load example

To calculate the RMS power we use equation 1.

Equation 1:  RMS Power = √((OPb² x t + OPa²xT)/(t + T))

It OPb=600W, OPa=100W, t=10s and T=20s, the maximum RMS power would be 356W.

Alternatively, if the power supply had an average power rating stated we would use equation 2.

Equation 2:  Maximum Average Power > ((OPb-OPa) x t/T) + OPa

For the previously used values that would calculate as 350W.

TDK-Lambda’s CUS400M power supply (Figure 3) can deliver 400W with forced air or, with a combination of convection and conduction cooling, provide up to 250W continuous output power and a peak power of 400W.

Figure 3: TDK-Lambda’s CUS400M power supply

Derating curves (Figure 4) are provided in the application notes as a guide rather than firm limits with the CUS600M, as it is expected that component temperatures will be measured and confirmed in the end system.

Figure 4: CUS400M peak power performance curves

Whereas many power supplies have peak power durations measured in seconds, the mechanical construction of this series provides additional cooling through the use of a metal baseplate. With a 230Vac input, the 400W peak rating applies up to 30 minutes with a 40^oC ambient, or 5 minutes with 115Vac at 30^oC. This makes this type of product very suitable for powering applications with occasional peak demands.

To ensure long term reliability, convection cooled power supplies should always have their critical component temperatures measured to ensure conformity with the manufacturer’s recommendations. This should be done in the end equipment at the worst-case conditions of ambient, input voltage and orientation, allowing the temperatures to fully stabilize.

For further advice and application support on this, or any other power supply related topic, please contact your local TDK-Lambda office.

Power Guy 

Using a Class I power supply in a Class II construction

I have to admit that I was a little skeptical when I was first told it was possible to use a Class I power supply (with an earth ground connection) in a Class II (no earth ground connection) construction.  After some discussion with a colleague, he pointed out that if certain actions are taken, it is perfectly safe - even in a medical application.

A general statement of safety is that a product must have two levels of protection between live (primary) parts and the end user.  If one level of protection fails, the end user is still safe.

A Class I example would be a clothes dryer. Usually they have an earth ground connection which is securely connected to the drier’s metal enclosure.  This is to protect the user if the insulation on the AC input cable frays or the heater element malfunctions and makes contact with the enclosure.  The fault current would flow through the earth wire, tripping the home’s earth leakage breaker and the AC power would be disconnected.

For our clothes dryer example, one protection level is the insulation on the internal wiring, the second level is the protective earth connection.

As mentioned in previous blog articles, the home healthcare standard (IEC 60601-1-11) stipulates the need for Class II equipment, as the integrity of the safety earth connection cannot be guaranteed in the home environment.

TDK-Lambda’s medically certified open frame CUS600M series (see Figure 1) can be used in either Class I or Class II applications.  It has two levels of protection, achieved through the use of double or reinforced insulation.

Figure 1: CUS600M power supply

 

The CUS600M/EF versions though have a metal enclosure and fan fitted. See Figure 2.  This changes the situation for a Class II application as during a single fault condition, the metal cover may  become live. If the cover was accessible to the user, we would no longer have two levels of protection. Fortunately, there is a solution!

Figure 2: CUS600M/EF power supply

 

First, the power supply must have 1 x MOPP (Means of Patient Protection) from the input to ground (chassis) and 1 x MOPP from the output to ground. 

Our CUS600M/EF has that - see Figure 3.

Figure 3: CUS600M/EF MOPP isolation barriers

Second, ensure the output touch current does not violate the safety requirements of the end equipment.

In our case the CUS600M touch current (enclosure leakage) is very low, <100µA, which should be acceptable in most applications.

Third, the power supply chassis should have 1 x MOPP isolation from the final equipment enclosure.

From Figure 4 it can be seen that we now have achieved our two levels of protection, even without the use of an earth ground connection.

Figure 4: CUS600M/EF isolation from the final enclosure

The 1 x MOPP isolation between the power supply and the system enclosure can be achieved by mounting the power supply on a plastic / non-conductive insulating plate or by mounting the unit on plastic / non-conductive stand-offs. See Figure 5.

Figure 5: Power supply with a metal chassis mounted on plastic / non-conductive stand-offs

Last, the EMC performance must not be adversely affected

The EMI performance of the CUS600M open frame power supply in a Class II application already meets EN55032-B for both conducted and radiated emissions.  The same applies to its immunity performance.

 

Even a Class I modular power supply like QM series can be used in this manner too, as the output to chassis isolation is 1 x MOPP. It should be noted that many other modular power supplies just have basic (non MOPP) isolation.

For further advice and application support on this, or any other power supply related topic, please contact your local TDK-Lambda office.

Power Guy

Buck & Buck-Boost Converter Operating Ranges

This is a follow-on to a recent post where I discussed the difference between a buck, boost and buck-boost converter.  Now we will review the operating ranges of a buck and a buck-boost converter.

As a quick recap - buck and buck-boost DC-DC converters are widely used in power supply designs, and have been for many years.  They are popular because of their simplicity, low cost and high efficiency.  There is no transformer used in the design, and as such, there is no isolation between the input voltage and the output voltage.  Manufacturers like TDK-Lambda offer both buck and buck-boost converters.  With less components and complexity, a buck converter will offer a lower cost, higher efficiency and either a smaller package or more output power than an isolated converter.

As with any power supply and DC-DC converter, there are limits to their operation.  A programmable power supply like TDK-Lambda’s GH10-150 is rated to operate from 0 to 10V with a maximum current of 150A with a maximum output power of 1500W.  It is rather unreasonable to expect it to deliver 5V at 300A.

The main restriction of a non-isolated (step down) buck DC-DC converter is that the input voltage has to be higher than the output voltage. One example is the i6A4W010A033V-001-R which has an input range of 9 to 53Vdc, an output adjustment range of 3.3 to 40V and a maximum output current of 10A.  Figure 1 shows the relationship between the input voltage and the allowable output voltage.  Only the maximum output power restricts the amount of output current that can be produced.

Figure 1: i6A4W 10A buck converter output versus input voltage

A non-isolated buck boost (step-up / step-down) DC-DC converter has different constraints to its operation, besides the rated output power, current and voltage.  The TDK-Lambda i7C series has quite clear operating parameters on its datasheet, so we will use that as an example.

The part number i7C4W008A120V-001-R has an input voltage range of 9 to 53V, an output adjustment range of 9.6 to 48V and a maximum output current of 8A. In the datasheet the operating range is defined by two plots. These show the valid input and output voltage operating range and the maximum output current against input and output voltage.

Figure 2 is a pictorial representation of the valid input and output voltage operating range stated in the datasheet.  Note this differs significantly from the buck converter discussed previously, as the buck-boost topology allows it to generate voltages lower and higher than the input voltage.

 

Figure 2: i7C 8A valid input and output voltage operating range

From Figure 3, we can see the x axis matches the 9.6 to 53V input range stated on the datasheet and Figure 2.  The y axis has a maximum limit of 8A for the output current. There are four plots for different output voltages.

Figure 3: i7C 8A Maximum output current vs the input and output voltage

As an example, a machine has 24Vdc available from an existing AC-DC DIN rail power supply. A new feature, which requires 48Vdc at 3A is required.  One way of generating this additional output voltage is to use a non-isolated DC-DC converter, like the i7C4W008A120V-001-R. We would use the purple plot (48Vo) and see that the maximum current we can safely draw from the converter is around 5A.  If the DIN rail power supply had a 24V battery back-up feature and the AC power failed, the i7C would continue to deliver 48V at 3A until the battery discharged down to 15V.

When a buck-boost DC-DC converter has a low input voltage, the input current switched by the FET is much larger than when it is operating at a high input voltage. This is the main restriction to the amount of output power it can deliver.

Like any power supply or DC-DC converter, having determined that the electrical parameters have been met, proper thermal management then has to be followed to ensure long term, reliable operation.

Figure 4: TDK-Lambda’s i7C 300W buck-boost DC-DC converter

 

Power Guy

What are buck, boost and buck-boost DC-DC converters?

Buck, boost and buck-boost DC-DC converters are widely used in power supply designs, and have been for many years.  They are popular because of their simplicity, low cost and high efficiency.  There is no transformer used in the design, and as such, there is no isolation between the input voltage and the output voltage.

 

In this post I will explain the differences between these three converters and a high level review on how they function..(As a note the simplified schematics do show diodes and switches, in reality FETs are used as synchronous rectifiers to reduce losses and improve efficiency.)

 

A buck converter reduces voltage and the output voltage is lower than the input voltage. See Figure 1.

Figure 1: Buck converter

 

When transistor S is turned on, energy is stored in inductor L as the current flows to the load and capacitor C is charged. When S is off, the energy stored in L is released and current flows into the load and circulates via diode D. Capacitor C also provides energy to the load.  This is repeated at a high frequencies, greater than 100,000 times a second.  The length of the time S is turned on defines the output voltage.

 

A boost converter increases voltage and the output voltage is higher than the input voltage. See Figure 2.

Figure 2: Boost converter

 

When transistor S is turned on, current flows through inductor L, through transistor S back to the input. During this period energy is stored in the inductor.  When transistor S is off, the inductor acts a voltage source in series with the input voltage.  The inductor’s stored energy is circulated through diode D to the load. This charges capacitor C to a higher level than the input voltage. Again, the length of the time S is turned on defines the output voltage.

 

This boost converter topology is also used in most Power Factor Control (PFC) sections of AC-DC power supplies. The control IC is different of course, as its purpose is to ensure the AC input current drawn is sinusoidal in shape.  At high line voltages greater than 240Vac the DC input may be higher than the voltage on capacitor C.  This will reduce the PFC boost converter’s performance and the power factor will be degraded slightly.

 

A buck-boost converter is a combination of a buck and boost converter. The output voltage can be higher or lower than the input voltage. See Figure 3.

Figure 3: Buck-boost converter

 

As you can see the circuit is more complicated and has more components.  S2, L, and D2 is the boost converter (S1 being on) and S1, L and D1 the buck section (S2 being off).

 

Many manufacturers like TDK-Lambda offer both buck and buck-boost converters.  With less components and complexity, a buck converter will offer a lower cost, higher efficiency and either a smaller package or more output power.

Figure 4: TDK-Lambda’s i7C 300W buck-boos tDC-DC converter

 Power Guy

Selecting a High Voltage Programmable Power Supply

High-voltage power supplies are used in many scientific and industrial applications including research, development, process control, power conditioning, test and measurement.  Sometimes a fixed output power supply may be used, rather than one with a variable or programmable output, which lowers the initial acquisition cost.

As technology rapidly advances, new markets are identified or production levels ramp up, voltage, current and power requirements can change significantly.  This can result in a need for a new high voltage supply or one with more features or functions.  Specifying a programmable power supply is a sound alternative, ensuring flexibility both in the near and long term. 

The decision as to which attributes should be considered and how may they benefit the user is an important one.  When specifying and evaluating programmable power supplies, users should look for as many of the following features and functions as possible.

High voltage outputs

Scientific instruments can require tens of kilovolts to perform their specialized tasks.  The power supply needs to be able to provide stable, regulated voltages with a range of outputs that could be as high as 50 kV and power levels of 1kW.  Even if the current application requires less, having a higher rated adjustable power supply provides future flexibility.

Compact size

Space within a 19” rack is often at a premium and the power supply competes with other instruments for this space.  Selecting a supply that is 2U rather than 3U in height will reduce the overall rack height or allow additional system functionality to be added.  A shorter depth may mean that a shallower rack can be used, consuming less space in a laboratory or on a factory floor, and saving costs.

Input voltage, active PFC and efficiency

A power supply that operates just from a 230Vac input restricts operation in many countries that also use 115Vac.  In the Americas or Japan, 208Vac may not be readily available in the desired location, requiring an additional electrical circuit to be wired in by an electrician.  Ideally chose a power supply that has the ability to operate from a wide range 110 to 230Vac input.

The power supply should have active power factor correction (PFC). This ensures that a sinusoidal input current is drawn from the AC supply, reducing the RMS line current and increases the available output power that can be drawn from an AC outlet or breaker panel.  Active PFC also reduces the harmonic distortion of the AC current which avoids an adverse impact on any sensitive instruments on the same AC feed.

A high efficiency power supply consumes less electricity and generates less internal heat.  A supply that is 90% efficient wastes half the power of an 80% efficient model, and allows other system instruments to operate cooler.

Easy operation

Engineers should not have to spend their valuable time reading instruction manuals to be able to program a complex power supply.  Choose one that has an intuitive, easy-to-use graphical display.  Ensure that the supply has both coarse and fine adjustment for accurate output voltage and current setting.  Ideally a product should utilize encoders, rather than potentiometers, for longer field life and the ability to program the magnitude of the steps.

Figure 1: TDK-Lambda’s FLX-HV series front panel display

Quiet operation

Loud or annoying audible fan noise can cause operators and nearby personnel to become fatigued. Scientific equipment will often not be operating continuously and the high voltage power supply will not require as much airflow for cooling at light loads.  Selecting a power supply that has a variable speed fan will reduce audible noise and prolong the life of the fan.

Digital interfaces

For remote or automated operation a standard digital interface is essential.  Chose a standard interface like USB or LAN. The manufacturer may include additional features in additional to status and programming capability, like being able to see the total operating hours and fault history.  Check to see if the manufacturer offers a GUI (Graphical User Interface) which will save time and effort to get the equipment running.

Safeguards and safety agency certification

When working with high voltages, protective functions are critical.  Rackmount power supplies need to manage the internal heat generation, and must be capable of protecting the (often expensive) external load from damage due to an output overvoltage or overcurrent condition.  IEC 61010-1 is an industry wide safety standard, allowing the product to be CE marked for easy importation into the European Union.  Compliance to EN61000-6-2 for immunity and EN61000-6-3 for emissions will reduce susceptibility to external electrical noise and avoid the power supply from interfering with other equipment or instrumentation.

Load arcs

Load arc events are common in high-voltage applications, and require a power supply that responds in a controlled and predictable manner. TDK-Lambda’s FLX-HV series for example will count load arc events, and if three or more arcs are detected in a five-second period, the unit will shut down for a 10-second interval. Arc activity is shown on the front panel display and reported on the remote interface.  An integrated arc counter records load arcs and can be read back via the remote interface, and reset to zero if required.  The FLX-HV supply also includes a second non-resettable arc counter remote interface query.

The manufacturer and product series

Selecting a global manufacturer like TDK-Lambda is also recommended. If your product may be exported, technical support is likely to be more accessible than a supplier that is focused on just one region.

The correct choice of a programmable high voltage power supply will provide you with flexibility, reliability and ease of use.  If your budget allows, select a higher wattage model for expansion and use in another project.  Remember, with a programmable product, the output voltage and current limits can always be set lower.

Some manufacturers offer a range of products, like the FLX-HV series mentioned earlier which has nine models ranging from 10kV to 50kV and 200W to 1,000W.

Figure 2: FLX-HV high voltage power supply

For more information visit FLX-HV series

Power Guy

Avoiding noise issues when operating power supplies in parallel

Operating power supplies in parallel is commonly used to increase the available output power or to provide system redundancy in the event of a power supply failure.  Not all power supplies can be connected in this manner, so please consult the manufacturer’s documentation first.

One method is “active” current sharing and is available as standard, or as an option, on most power supplies rated 1,000W or higher.  An internal high impedance circuit monitors the output current and compares its voltage level to the other units via a parallel connection (PC) wire.  A common connection (COM) serves as the return wire.  The power supply output voltage is automatically adjusted up or down to balance the output currents between the paralleled power supplies.  See Figure 1.

Figure 1: Two power supplies connected in parallel

At first glance, this looks perfectly acceptable. When the system is operating however, it may be observed that the power supplies are oscillating very slightly.  This is not a function of the power supplies malfunctioning when in parallel, but actually may be due to noise pick-up or noise currents circulating in the wiring.

The first thing to check is that the wiring between the PC and COM connections is twisted, short as possible and routed away from any potentially noisy cables.

If that does not solve the problem it may be due to how the negative remote sense is wired.  Looking at Figure 2, we can see that the COM connection is internally connected to the negative sense connection and as a result creating a potential noise loop.  The oscillation may be the result of the currents flowing in the negative load cables affecting the sensitive parallel and sensing circuitry.

Figure 2: Noise loop within the parallel, sensing and load system wiring

The solution for this is to disconnect the wire between the two COM pins and connect the negative remote sense wiring at the load. It will also compensate for voltage drops in the negative load cables.  See Figure 3.

Figure 3: Negative remote sense cables connected to the load and COM link removed

With this configuration, the internal signal common is isolated from noise on the power cables and any voltage differentials. If desired, the positive remote sense terminals can be connected to the positive of the load to compensate for voltage drops in those cables too.

Power Guy

How can I increase a power supply’s hold-up time?

What is hold-up time?

When an AC-DC power supply’s input voltage is interrupted, during a brown out condition or a very brief power failure, the DC output will only remain within regulation for a short period of time.  This is specified on the power supply datasheet as the hold-up time.  During this hold-up time the power supply relies on energy stored in its capacitors to maintain operation.

Figure 1 shows a simple block diagram of a power supply.

Figure 1: Power supply block diagram

The AC input voltage is filtered, rectified and boosted to provide a DC bus voltage of around 390V. The DC-DC converter section of the power supply provides primary-secondary isolation and reduces the 390V bus down to the desired DC output voltage.  The function of the high voltage bus electrolytic capacitor C1 is to reduce the ripple voltage on the 390V bus and store energy to keep the DC-DC converter operational during brief interruptions to the AC input.

Depending on the application, the length of the hold-up time varies from a half or full cycle of the incoming AC 50/60Hz voltage.  This is typically 8 to 20ms at 100% load, but is normally sufficient to avoid electronic equipment from having to restart or reboot.

When is extended hold-up time required?

The medical industry’s concern regarding hold-up time has increased since the release of the EN 60601-1-2; 2015 (Ed4) immunity standard.  Primarily created to address the growing number of products used in home healthcare, this standard specifies multiple AC voltage dips ranging from 20ms to 5 seconds.  The longer outages are addressed by batteries or ensuring that no harm will occur to the patient or operator if the power supply output voltage drops out of the regulation band.

Airborne equipment is covered by the DO-160 standard.  Section 16 refers to power input, simulating conditions of aircraft power from before engine start (using auxiliary ground based power) to after landing, including emergencies.  The requirement is for a hold-up time of at least 200ms.

What techniques are available to increase hold-up time?

There are various methods to extend power supply hold-up time, each with advantages and disadvantages.  As the amount of energy stored in a capacitor C is calculated as: ½ x C x V², to increase that energy storage and hence the hold-up time, either the amount of capacitance or the voltage on the capacitor has to increase. Since V is squared, an increase in the value of V will have a greater impact.

The following examples are based on a hypothetical system requiring a load of 150W at 12V, with a minimum output voltage requirement of 11.5V as the output decays to zero; 200ms is the desired hold-up time.

1.      Using a higher rated power supply and operating it at a reduced load

If we were to use the 150W 12V output TDK-Lambda RWS150B-12 power supply and operate it at 100% load, we would have a hold-up of just over 30ms based on the evaluation test data.  See Figure 2.

Figure 2: Hold-up time versus output load for the RWS150B-12 power supply

As expected, the hold-up time is dependent on the output load drawn. The greater the load, the quicker C1’s stored energy is depleted. To obtain 200ms hold-up, we could use the TDK-Lambda’s 1500W rated CUS1500M-12 power supply. See Figure 3.

Figure 3: Hold-up time versus output load for the CUS1500M-12 power supply

The larger value of “C1” in the CUS1500M-12 would provide enough energy to hold-up a 150W load for over 200ms.

This would be a simple off the shelf solution, but a much larger, more expensive power supply would be required.

2.      Adding capacitance across the power supply output terminals or load

Figure 3: Adding load capacitance

At first glance adding additional capacitance (C3) across the output seems like an easy solution.   Based on the equation 2 in the appendix, however, C3 would have to be a massive 4,595,745uF.

C = 2 x Pout x t / (V² – Vend²)

C = 2 x 150 x 0.18 / (12² - 11.5²)

Note as the power supply already has 20ms of hold-up capability, t is reduced to 180ms (0.18s).

Even with a supercap this would consume a large amount of space.  One other major concern is the over-current characteristics of the power supply during initial turn on.  An uncharged C3 would appear to the power supply control circuit as a dead short across the output.  The power supply would most likely fail to establish a 12V output when initially turned on.

3.      A customized power supply with a larger high voltage bus capacitor (C1)

As previously mentioned, the energy stored in a capacitor is equal to ½ x C x V², so adding capacitor C1a across the high 390Vdc bus has a greater effect than adding capacitance across the 12V output.  See Figure 4.

Figure 4: Adding high voltage bus capacitance

As the DC bus is not accessible on most power supplies, adding capacitors would involve creating a custom or modified standard design. This would involve engineering charges and safety re-certification fees, plus time to make the modification.

If the power supply to be modified had a hold-up time of 20ms, increasing it to 200ms would require adding the equivalent of nine more C1 capacitors.  As C1 typically occupies 5 to 6% of the internal space of a power supply, it would increase the size of the power supply by around 50% for the same product height.

A power module based solution could also be created using a non-isolated AC-DC 360Vdc output converter (TDK-Lambda’s PF series) and a high voltage input isolated DC-DC 12V output converter (TDK-Lambda PH-A series). This again would require a custom board design with engineering and safety certification charges.

4.      A 48V or 60V output AC-DC power supply and a wide range input DC-DC Converter

For an off-the-shelf standard product solution, a 48V output AC-DC power supply could be used with an isolated wide-range input 18 to 75V DC-DC converter with a 12V output.  See Figure 5.  The DC-DC converter may require a heatsink or cold plate for cooling.

Figure 5: 48V or 60V power supply and an isolated wide range input DC-DC converter

In addition to the hold-up inside the 48V output AC-DC power supply, capacitor C1 can be used for additional energy storage.  We have taken advantage of the energy storage formula ½ x C x V² as V is now 48V rather than 12V in scenario 1.  The efficiency of the DC-DC converter is considered as 90%.  The hold-up of the AC-DC power supply is 20ms, requiring an additional 180ms (t).

C = 2 x P x t / (Eff x (V² – Vend²))

For our example, the required value of C1 would be 2 x 150 x 0.18 / (0.9 x (48² – 18²)) which calculates as 30,300uF.     

If the 48V AC-DC power supply was replaced by one that had a 60V output, the additional capacitance could be reduced to 18,315uF. A 72V output power supply would reduce that further to 12,345uF.

5.      A 48V output AC-DC power supply and a wide range input non-isolated DC-DC Converter

In this case, the chosen DC-DC converter is non-isolated (for higher efficiency, smaller size and lower cost) having a wide input range of 9 to 53V. See Figure 6. A non-isolated DC-DC converter would not require heatsinking.

Figure 6: 48V power supply and a non-isolated DC-DC converter

The efficiency of the non-isolated DC-DC (TDK-Lambda i6A series) converter is considered as 96%.  The hold-up of the AC-DC power supply as 20ms, requiring an additional 180ms (t).

C = 2 x P x t / (Eff x (V² – Vend²))

For our example, the required value of C1 would be 2 x 150 x 0.18 / (0.96 x (48² – 9²)) which calculates as 25,304uF.

Summary

Method	Additional capacitance	Pros	Cons
Larger power supply	None	Standard part	Cost and size of bigger supply
Larger output cap	4,595,745uF	Standard part	Size and potential start-up issues
Larger HV bus cap	9 x C1 (~9,000uF)	Custom solution	Eng. cost and development time
48V AC-DC + isolated DC-DC	30,300uF	Standard parts	Space for DC-DC and heatsinking
60V AC-DC + isolated DC-DC	18,315uF	Uncommon 60V AC-DC Standard DC-DC	Space for DC-DC and heatsinking
72V AC-DC + isolated DC-DC	12,345uF	Uncommon 72V AC-DC Standard DC-DC	Space for DC-DC and heatsinking
48V AC-DC + non-isolated DC-DC	25,345uF	Standard parts	Space for DC-DC

Appendix - Calculating the required capacitance

Below are the equations for calculating the required hold-up capacitance.  The units of measure are Energy – Joules, Power – Watts, time – seconds, Voltage – Volts, Capacitance – Farads, Efficiency – Percentage.

Energy E is the product of the output power Pout and time t

Equation 1:

E = Pout x t

Stored energy (E) is half the product of the Capacitance (C) and the voltage (V) squared

E = 0.5 x C x V²

Rearranging for C we get

 C = 2 x E/V²

Note: The voltage on capacitor C will drop as it discharges into the load.  At some point the voltage will be too low for the load to function leaving unused energy in the capacitor.  That voltage point will be referred to as “Vend”.  In the scenarios 2, 4, 5, 6 a voltage of 11.5V is used.

Our “useful” energy for hold-up will be the initial minus the remaining energy.

E = (0.5 x C x V²) – (0.5 x C x Vend²)

Factoring the equation we get:

E = 0.5 x C x (V² – Vend²) or C = 2 x E / (V² – Vend²)

Substituting for E from equation 1 we have

Equation 2:

C = 2 x Pout x t / (V² – Vend²)

In cases where a separate DC-DC converter is used, that converter will not be 100% efficient (Eff) and we need to adjust the value of our AC-DC output power Pout to compensate:

P = Pout / Eff

Equation 3:

C = 2 x P x t / (Eff x (V² – Vend²))