Here we explain the data required for determining regenerative-power requirements and regen-resistor selection for the controlled motion of servomotor systems.

By Hurley Gill • Senior applications and systems engineer | Kollmorgen

Electric AC servomotors are either synchronous or asynchronous motors used in a closed-loop (servo) configurations for precise output control. Control over motion outputs — which can include position, velocity, and torque — relies on feedback signals from sensors on the machinery or its motor(s) to the motor controllers (drive amplifiers). When a position loop is closed around the velocity loop, the bidirectional servo mechanism controls:

• The motor’s physical position, velocity, and/or torque to accomplish some specific purpose and
• The motor’s response to everchanging loads, disturbances, and commands.

The required feedback signals may be generated either from multiple feedback devices coupled to the motor/load or an individually coupled feedback sensor (from which the other necessary feedback signals are derived). Independent of position, a velocity loop can command the bidirectional velocity and torque while controlling motor velocity, current, and response to everchanging loads, disturbances, and commands.

Servomotors and their kinetic and electric energies

DC brush servomotor designs have been around for more than fifty years and AC asynchronous servomotors since the mid 1980s. But today in the automation industry, the term rotary servomotor typically refers to actuators based on permanent-magnet (PM) AC synchronous motor technology. Similarly, linear servomotor typically refers to linear actuators based on a PM AC synchronous motor design. These motors actuate rotational axes or linear axes traversing vertical, horizontal, or other planes.

Every servomotor’s precisely controlled (and often repeated) accelerations, traverses, decelerations, and dwells over a defined time period are represented by a motion profile. Each segment of a motion profile has an associated quantity of energy stored or dissipated as a function of the controlled motion’s velocity and loads. Kinetic energy is stored by the total moment of inertia or mass and the commanded (and achieved) axis velocity. Assuming no potential energy sources, energy used to accelerate an axis to its commanded velocity is supplied by the servo drive’s power source. Likewise, a deceleration of that same mass or rotating inertia requires by some physical means, the absorption or dissipation of the stored mechanical energy. Energy absorption or dissipation occurs when the motor enters power-generation operation:

• During normal decelerations (normal machine operation) or
• During event-driven stop functions — as during a controlled motion in a NEC Category 1 emergency stop (e-stop) or Category 2 priority stop (p-stop) — i.e., with drive control power applied to minimize event-driven stop times.

When a servomotor system is in the process of recovering axis kinetic energy during a controlled deceleration, the servomotor enters a power-regeneration mode … converting excess mechanical energy back to electricity. By design, its drive returns that energy back to the same power source used to originally supply energy to the motor. If the power source was a battery, the returned power would simply recharge that battery. More common AC-line input-power drives absorb the resulting additional energy (joules) via their DC-bus capacitance (over and above nominally stored joules). An increased DC-bus voltage (pumping up the DC bus) is the physical effect of this additional energy absorbed by the DC-bus capacitors.

However, the DC-bus capacitance and maximum resulting voltage is limited by a drive’s design and selected capacitors. In manufacturing settings, the typical servomotor is powered by pulse width modulation (PWM) of the DC bus via a full-wave three-phase bridge rectifier circuit (typically supplied by 208 up to 480 Vac notwithstanding lower voltage requirements).

Whenever a servomotor slows down (whether there is an external servo-loop closed around the motor or not) it’s possible for kinetic energy to return to the drive’s power source. Upon axis deceleration, the mechanically stored energy is converted back to electrical energy … and any energy not lost to mechanical frictions or dissipated within the motor (as when the motor acts as an alternator) must be absorbed by the drive. This happens when the internally generated voltage of the motor’s electromotive force (emf) exceeds drive-supplied voltage. Then generated emf becomes the dominant power source — reversing the current within the motor’s windings. That in turn causes a braking action on the axis.

Question about regenerated energy: What happens when the controlled motion defined by an axis’ motion-profile requires the servomotor to convert (regenerate) more energy than the DC-bus capacitors can safely absorb for a given servo drive?

Answer: Additional energy exceeding the DC bus capacitance storage capacity must be diverted so the DC bus voltage remains below its maximum safe-operating value during both normal operation and stop-function events. Exceeding DC bus voltage should cause the drive to fault and shut down. This excess energy can be handled with one or more of the following approaches:

1. Increase total DC-bus capacitance for a higher energy absorption capability. This may be accomplished by adding an external capacitance module to the subject DC bus or by connecting multiple drives together for a common/shared DC bus.
2. Present and return excess energy back onto the AC line source by adding an AC line-regeneration module. The drawback with this method is how it can add significant cost and size to the drive system electronics.
3. Use the servo drive’s regeneration circuit to dissipate the excess DC-bus energy across a regeneration (regen) power resistor. This is an often-used solution.

A regen resistor is a resistive-power device used to dissipate the pumped-up DC-bus energy — to dissipate the excess. DC-bus voltage is controlled by dumping power to the regen resistor and (as long as the regen circuit’s power-dumping capability exceeds the power the motor is returning) the DC-bus voltage will fall. Repeatedly switching a regeneration resistor on and off across the DC-bus capacitors in a controlled manner will keep DC-bus voltage within a safe range between the rectified AC line voltage (nominal DC bus) and the upper DC-bus voltage limit set by the drive electronics.

If a regen resistor is undersized or there is no regen resistor where one is needed, the production speeds could be degraded, and the machine could even shutdown due to nuisance tripping caused by overvoltages … blown or tripped protection circuity … and/or drive component damage.

Regeneration resistor questions: How does an engineer determine if a regen resistor is required? If such a resistor is required, what should its resistance and wattage values be?

Answer: Simply put, we must evaluate the power flow over a machine’s motion cycle. If the power flow as energy/time from the motor to the drive has significant power distribution to the drive’s DC-bus capacitors, the system will require a power resistor to dissipate excess regenerative power. Otherwise, power flow will need to be lowered. This regenerative analysis is simplified by considering total returned energy rather than the exact details of the power flow. The mechanical kinetic energy E(k) less all applicable losses E(el) and E(f) and any external forces E(ext-f) for each deceleration of an axis summed together is compared against the drive’s DC-bus capacitors energy storage capacity E(caps). If the total recovered energy Er(total) is greater than the additional storage capacity of the DC-bus capacitance E(caps) then a regen resistor is required.

A regen resistor with a continuous power capacity greater than the application’s requirement should be selected to satisfy ( Pc_req = (Er(total) – E(caps))/t_total). For multi-axis machines with a common DC-bus capacitance, the total continuous power requirement Pc_req(total) is determined by summing continuous power requirements of each axis for the number of axes being served by the common DC bus. Expressed as an equation, this Pc_req(total) is:

Pc_req(A1) + Pc_req(A2) + … Pc_req(Axis#).

But first, we need to calculate kinetic energy less losses Er(n) for each deceleration (n) of the axis under consideration with Er(n) = E(k) – E(el) ± (ext-f) – E(f) and:

Er(n) = ½(J_load + J_motor) ωm²
– 3(I²_dec × Rm/2) t_dec
± (T_ext × Δωm/2) t_dec)
– (Tf × Δωm/2) t_dec.

Where Er(total) = Er(1) + Er(2) + Er(3) + … Er(n).

For each axis under consideration, we must determine each represented motion segment of an axis’ motion-profile with potential recovered kinetic energy (joules) to be absorbed or dissipated. Each defined deceleration segment within an axis’ motion profile will potentially present some recovered kinetic energy Er(n) requiring absorption by the DC-bus capacitance — and potential further dissipation by a regen resistor. Hence, each deceleration of each axis should be considered.

It’s straightforward to calculate the sum of each axis’ recovered energies Er(total) to be dissipated over a machine’s cycle time (or for any specific deceleration n). That in turn determines the minimum required continuous power capability of the selected regen resistor:

Where t_total = Axis cycle time
Pc_req(total) = Pc_req(A1) + Pc_req(A2) + … Pc_req(A#)
Any given axis (A#) with a resulting Er(n) < 1 is set = 0.

Note that the calculated Pc_req for any given axis (A#) can become quite small for motion profiles with large dwells between active motion. In these cases, the regeneration resistor is typically selected to satisfy peak power requirements rather than the average requirement over time. Also, multi-axis machines often have situations involving one axis returning energy while another concurrently consumes energy — so the net returned energy can approach or be zero. That’s why unless all machine axes will concurrently return energy (as during controlled motion-stop functions) engineers should consider the timing of all returned energy.

Once the total continuous power (Pc_req(total)) requirement is known for normal operation (and not stop functions) further refinement can be achieved by subtracting additional DC-bus capacitance absorption capability.

Accounting for peak power conditions

Proper regen-resistor selection also requires calculation of peak requirements (Ppk_req). The values are calculated much like Pc_req values, but typically for the peak (maximum) power on the motor just prior to deceleration onset … at time zero (t_0) of the power regenerative mode.

Peak power question: When do the highest-power worst-case (wc) conditions determining peak energy Er(n) or Er(wc) and its absorption requirements occur?

Answer: These conditions are generally defined by the motion segment with the highest mass or moment of inertia and velocity — represented as E(k). But it is the worst-case recovered energy Er(wc) that must be absorbed regardless of the time period over which the deceleration occurs.

Independently decelerated axes under normal machine operation can and often do require recovered kinetic energy dissipation above the DC-bus capacitance storage capacity by other means — such as using the DC-bus capacitance shared by multiple drives, for example. Sometimes it’s easier to set the peak regen capability based on the peak possible returned energy set by the drive’s ac input line and its peak output current … less a little margin for losses. A 20% margin for losses is a good rule of thumb. In other words, for a three-phase servomotor the upper-bound peak power (VA) is equal to 0.8 · (AC-line Vac) · (Drive peak phase current) ·√3.

Of course, safety is a top design objective for most machine designs (and their axes). Best practices for designing servo-controlled motion demand the shortest possible stop times for controlled-motion p-stops and e-stops with few exceptions. Ideally, each servo-controlled axis of a machine should be able to stop controlled motion in the shortest possible time for maximal protection of human, machine, and product. Satisfying this requirement for controlled motion requires a separate evaluation of each axis’ resulting recovered energy for the stop-function Er(sf):

Er(wc) or Er(sf) = E(k) – 3(I²_dec × Rm/2) t_dec
± (T_ext × Δωm/2) t_dec)
– (Tf × Δωm/2) t_dec

Where E(k) = ½(J_load + J_motor) ⋅ ωm² = Specific kinetic energy E(k) used for determining maximum resulting recovered Er(wc) or Er(sf) for the specific axis under consideration.

Note: The required I_dec developed by the motor’s application must fall within the motor’s peak current capability Ipk(motor) and the proposed servo drive’s peak current Ipk(drive) capability for the defined time (t_dec). Otherwise:

• The desired t_dec must be increased and/or
• A different servomotor should be chosen and/or
• A different drive with a higher capacity should be chosen.

With that, I_dec(required) ≤ Ipk(motor) and Ipk(drive) capability where Ipk is the peak RMS phase (Ø) current and I_dec:

In addition, Ppk_req = Er(n)/t_dec where Er(n) = Er(wc) for worst-case (wc) instantaneous peak under normal axis operation or Er(sf) for stop functions such as p-stops or e-stops — are two separate evaluations.

No part of the DC-bus capacity E(caps) is considered as in (Er(n) – E(caps))/t_dec) because the available DC-bus capacity before a stop-function occurrence can’t be guaranteed or easily determined. The maximum value R_regen(Ω) for any selected regen resistor mustn’t exceed:

Where Ppk_req(total) represents the rate of energy needing to be drained from the DC bus. This is the maximum possible resistance value for the defined condition of the application that will continuously keep DC-bus operation under its maximum value VDC_max(fault).

Of course, the regen resistor’s peak wattage requirement (Ppk_req) and selection can be affected by using shortest possible stop time as during stop functions. For some individual axes or multiple machine axes with a shared DC bus, the defining deceleration — and determining factor for regen resistor selection — is based on best-practice design evaluations for controlled stops. Here, the regen resistor is selected based on peak-wattage requirements. Otherwise, when a regen resistor is required for normal axis operation, Pc_req is the typical dominating criteria.

Again, be careful of motion-profiles with significant dwell times relative to total cycle time (t_total) … especially relative to the calculated normal operation Ppk_req.

Balancing competing resistor objectives

A motor-drive sizing program should look at each motion segment for calculating Pc_req and determine the worst-case Ppk_req for normal axis operation … though typical sizing programs require separate evaluation for deceleration events with unique values. All e-stop and p-stop functions for a given axis are typically set to the same minimum deceleration stop time.

For multiple axis machines with a shared and common DC bus, the simultaneous deceleration of all axes during a stop-function event requires a resistance value so VDC bus stays below VDC_max(fault).

Specification tip: When possible, select the regen-resistor manufacturer’s standard ohms value — or one within their published range. Engineers should ensure that the manufacturer’s published maximum continuous/peak current is not exceeded by selecting a regen resistor:

• With high enough resistance while also
• Ensuring the regen resistor ohm value is low enough to keep DC-bus voltage below the drive’s maximum (fault) value

For the latter that means Vmax = VDC_max(fault) – 1 during normal operation (normal axis’ decelerations/stops) and during any e-stop or p-stop. For any selected regen resistor R_regen(Ω) the maximum shunt current from DC-bus capacitance may be calculated:

Within the defined application, the selected regen resistor maximum instantaneous or pulse, peak wattage is calculated:

The selected regen resistor’s capability must meet the following conditions:

1. Pc_resistor (wattage) > axis’ calculated required Pc_req.

2. Ppk_resistor (wattage) > axis’ calculated required Ppk_req (under all conditions).

3. R_regen(Ω) must be within the selected drive’s specified regen resistor range, where the external resistance may be presented as an ohms range and/or a preferred standard value by the drive manufacturer.

4. As mentioned earlier, the maximum value R_regen(Ω) for any selected regen resistor mustn’t exceed:

That’s true even for simultaneous deceleration of all axes as during a full machine stop as defined by Ppk_req(total) = Ppk_req(A1) + Ppk_req(A2) + Ppk_req(A3) + … + Ppk_req(A#). The selected R_regen(Ω) should be less than the maximum possible resistance for the defined application condition that will let the DC bus continuously remain under its maximum value VDC_max(fault).

5. R_regen(Ω) > Pc_req(total)/I²_shunt(drive max) and the selected R_regen(Ω) should be greater than the minimum possible resistance for the selected drive’s or resistor’s defined maximum possible regen shunt current capability. This limits continuous-operation regen current to something less than maximum shunt-current capability.

For many regen resistors the peak/pulse wattage capability is established by a rule-of-thumb fixed multiple (say, tenfold or fifteenfold) the published continuous capability. Instantaneous peak capability like the continuous capability of a given regen resistor is a function of its physical design, materials, duty-cycle (used and applied), and manufacturing process … and in all cases, the resistor’s peak capacity should be published or otherwise defined. Once a motor-duty-rated regen resistor has been selected, more specific capabilities versus requirements can be reviewed using non-linear differential equations when all required application and resistor information is known.

About the author: Hurley Gill is senior applications and systems engineer at Kollmorgen located in Radford, Va. He’s a 1978 engineering graduate of Virginia Tech who has been engaged in the motion control industry since 1980s. He can be reached at hurley.gill@kollmorgen.com.

Click here for the second part of this series — and an example of how to specify a system for a rotary servo axis needing a regenerative resistor.