Active Heave Compensation

How does active heave compensation work?

An active heave compensator consists of at least:

  1. An actuator, which may be a linear (e.g. cylinder) or rotary (e.g. winch) actuator, with position measurement.
  2. A motion reference unit (MRU), which may be placed on the AHC in case of an inline AHC or on the vessel in case of an integrated AHC.
  3. Some form of manipulation of the actuator position, that is sufficiently fast to be able to follow vessel motion (e.g. hydraulic motor).

When the active heave compensation mode is turned on the control system keeps the payload stationary when seen from a stationary reference frame, by actively counteracting the wave motion using the actuator. 

Active heave compensation can reach efficiencies above 90%. Active heave compensators usually work best for longer wave periods.

The main types of AHC

There are many types of active heave compensators, here are some of the main ones:

  1. Electric rotary AHC, usually best suited for lighter payloads.
  2. Hydraulic rotary AHC, for heavy payloads.
  3. Deck based sheave AHC, for retrofitting.
  4. Topside inline AHC, for basic AHC tasks topside.
  5. Subsea inline AHC, combines AHC with many of the properties of an adaptive PHC.
Norwegian Dynamics can supply all of these types, but we recommend from a cost perspective to choose inline AHC. The subsea version of the inline AHC is currently the most versatile lifting tool in the market.

How much energy is consumed?

A simple example, 100t is compensated in air for a sinusoidal movement with amplitude 1 m and period 10 s. Assume that the AHC is an inline AHC with the following properties:

  1. 10:1 gas to oil ratio and 4 m stroke.
  2. Efficiency of AHC components 90%.
  3. 50 % energy regeneration.
How much energy is spent during 10 hours of operation?

For an inline AHC the payload is kept at mid position by passive gas pressure. It is brought out from mid position by the hydraulic motor. So our energy consumption will be:
W = \int_{0}^{10\,\mathrm{h}} F \, \dot{S} \, dt
 
We know that the AHC need to add energy during half the cycle and energy is regenerated during half the cycle, it will look like this:
Energy plot for active heave compensation

In the first red area we need to add energy to extend the cylinder, then we let the cylinder retract and regenerate energy until we reach mid stroke where we need to add energy to retract further, finally we regenerate energy by letting the cylinder extend to mid position. It can be shown that the force that the AHC system has to provide is:

F = m g \left[ \left( \frac{S_\mathrm{max}(R – 0.5)}{S_\mathrm{max}(R – 0.5) – S} \right)^{\gamma} – 1 \right]

Since S follows the sinusoidal motion we can rewrite it as:

F = m g \left[ \left( \frac{S_\mathrm{max}(R – 0.5)}{S_\mathrm{max}(R – 0.5) – \zeta\cos{\omega t}} \right)^{\gamma} – 1 \right]

Our integral can then be written as:

W = \int_{0}^{10\,\mathrm{h}} m g \left[ \left( \frac{S_\mathrm{max}(R – 0.5)}{S_\mathrm{max}(R – 0.5) – \zeta\cos{\omega t}} \right)^{\gamma} – 1 \right] \, \zeta \omega \sin{\omega t} \, dt
 

Due to symmetry we can integrate like this:
W = \int_{0}^{10\,\mathrm{h}} \left| m g \left[ \left( \frac{S_\mathrm{max}(R – 0.5)} {S_\mathrm{max}(R – 0.5) – \zeta\cos{(\omega t)}} \right)^{\gamma} – 1 \right] \, \zeta \omega \sin{(\omega t)} \right| \, dt

And finally we adjust for the efficiencies and get:
W = \int_{0}^{10\,\mathrm{h}} \left| m g \left[ \left( \frac{S_{\mathrm{max}}(R – 0.5)} {S_{\mathrm{max}}(R – 0.5) – \zeta \cos(\omega t)} \right)^{\gamma} – 1 \right] \, \zeta \omega \sin(\omega t) \right| \, dt \cdot \frac{(1-\eta_{\mathrm{regen}})}{\eta_{\mathrm{AHC}}} \

By numerical integration we find that to be 207 MJ or 57 kWh.

So as we can see even for a heavy payload being compensated for a significant amount of time the required battery capacity isn’t super big, comparable to an EV battery.

For more accurate calculations that includes friction, hydraulic losses, more accurate efficiency models for pump/motors/battery, accurate equation of state, etc. please contact Norwegian Dynamics.