Analysing the impact of high frequency power modulation on the cell stability

A L U M I N I U M S M E LT I N G I N D U ST RY Analyzing the impact on the cell stability power modulation on a scale of minutes M. Dupuis, GeniSim Inc., and V. Bojarevics, University of Greenwich More and more aluminium smelters will have to play an active Introduction role to maintain the regional electrical grid stability. Trimet smelters in Germany have been playing that role for a long Reference [1] presents the work done in the Trimet Hamburg smelter time already [1]. Smelters can do that by performing high fre- to test high frequency power modulation. Fig. 1 presents a picture of quency power modulation, which for the cell operation means the cell technology used in that smelter. It was originally a Reynolds amperage modulation over periods of minutes, rather than P19 cell technology, later retrofitted to operate at 180 kA [2]. The hours. Because a smelter represents a significant load on the authors had access to an existing MHD-Valdis model of that retro- grid, with power modulation it can be used as a buffer to help fitted cell technology developed for another modeling study [3]. maintain the global grid balance between production and con- Fig. 2 presents the MHD-Valdis model, while Fig. 3 shows the ori- sumption. ginal P19 busbar design. A power grid can experience both long term and short term imbal- The busbar network was modified to reduce the intensity of the ance. Trimet have been involved in helping the grid to manage both vertical component of the magnetic field (Bz). Despite the improve- types of load imbalances, notably pioneering a high frequency power ment, the Bz intensity is still not ideal as we can see in Fig. 4. One of modulation to address the gird short term imbalance of the order of the particular features of the MHD-Valdis model is the ability to minutes. Contrary to a long-term power modulation lasting several rapidly compute the magnetic field using a volume element integral hours and more, short term power modulation events do not indi- equation formulation which eliminates the need to mesh the air vol- vidually induce a significant cell thermal response. They just need ume. To compute the magnetic field, the code solves first for the to be globally balanced in a sequence of equal amounts of positive passage of the electric current in the busbar and in the cell itself. It and negative power changes. They may have a destabilizing effect on then calculates the current density in the metal pad and the resulting the cell bath / metal interface by inducing extra cell voltage noise, magnetic field. From these it computes the Lorentz force that drives detrimental to current efficiency. This investigation studied this ef- the metal movement and deforms the interface between the metal fect using a new version of the code MHD-Valdis that now supports the coding of amperage modulation events into the simulation. Fig. 1: Potroom of the Trimet Hamburg smelter Fig. 2: MHD-Valdis model of the Trimet 180 kA cell © GeniSim Fig. 4: Vertical component of the magnetic field Bz in Fig. 3: Original P19 busbar design the middle of the metal 54 pad for the 180 kA cell ALUMINIUM · 1-2/2021

SPECIAL A L U M I N I U M S M E LT I N G I N D U ST RY accumulated at the bottom of the cell and the bath floating on top of Fig. 5: Steady state depth averaged metal flow for the 180 kA cell the metal. Fig. 5 presents the steady state flow in the metal pad; Fig. 6 presents the bath / metal interface deformation due to the Lorentz Fig. 6: Steady state position of the bath-metal interface for the 180 kA cell force and to the bath and metal flow as computed by MHD-Valdis. Fig. 7: Typical MHD-Valdis cell stability analysis where the Standard stability analysis of the Trimet 180 kA cell obtained bath-metal interface growth rate has been fitted From the steady state solution presented above, the cell stability is Fig. 8: Transient analysis results for the Trimet 180 kA cell normally analysed by imposing a perturbation on that steady state, at 4.2 cm ACD with a usual user imposed initial perturbation and then calculating the evolution of that perturbation with time. If the cell is stable, that perturbation will die out with a negative growth rate. Fig. 7 illustrates such a decaying wave with a calculation of that negative growth rate, for such a stable case. The cell is critically stable when the logarithm of the wave growth rate is zero. For the Trimet 180 kA design, the cell is predicted to be about critically stable at 4.2 cm ACD and 17 cm of metal pad thick- ness. Fig. 8 presents the typical MHD-Valdis transient wave evolu- tion analysis for that situation. The initial imposed perturbation is not decaying with time, in fact the wave amplitude is growing, but extremely slowly – an indication that 4.2 cm ACD is just a bit below the critical stability ACD. Since the goal of the new type stability analysis will be the study of the impact of an amperage modulation event, the above stabil- ity analysis was repeated without imposing an initial perturbation. If the starting point of the transient analysis is exactly the steady state solution, the dynamic solution evolution would simply maintain that initial steady state solution. Because the steady state solution is not 100% converged, the solution is evolving with a small-scale oscillation. If at 4.2 cm ACD the cell is on the unstable side of the stability limit, this ‘butterfly effect’ infinitesimal perturbation would be sufficient to grow a wave that will eventually short circuit the cell, given enough time. This transient long evolution without a significant perturbation from the initial “steady state” is presented in Fig. 9. Introduction of the Trimet high frequency power modulation event In [1], Fig. 4 presents a typical high frequency power modulation event which is reproduced here in Fig. 10. It is a 30 MW extra power consumption from a 190 MW base power level that was ramped up and down in less than 15 seconds, and lasted about 15 minutes. From this extra power consumption, we deduced that the line amperage was increased by about 15 kA from 180 kA to 195 kA, as indi- cated in [4], considering the corresponding increase of the cell volt- age. Since it is hard to evaluate from that graph the duration of the ramp rate, the ramping duration we estimated to last for 2 seconds, while the overshoot was neglected. The new version of the code MHD-Valdis includes the option to add an arbitrary rate of change for the line amperage during the transient calculation. Hence, with the new code version, it is pos- sible to schedule amperage modulation events to occur during the simulation. Stability analysis of the Trimet 180 kA with high frequency power modulation For the first stability analysis test, we scheduled a very short am- perage modulation ‘pulse’. This amperage modulation pulse is much shorter than the 15 minutes duration of the typical modulation re- ported in [1], the intention being to study the perturbation effect of ALUMINIUM · 1-2/2021 55

A L U M I N I U M S M E LT I N G I N D U ST RY Fig. 9: Transient analysis results for the Trimet 180 kA cell a pulse on the bath / metal interface. That short pulse was scheduled at 4.2 cm ACD without the usual initial perturbation using 2 seconds ramp up, then a short 15 seconds holding time and finally a 2 seconds ramp down to the base amperage. Fig. 11 presents Fig. 10: A high frequency power modulation the obtained transient solution for a run without an imposed pertur- qualification event presented in [1] bation using the marginally stable 4.2 cm ACD. From Fig. 11 we can observe that the amperage modulation pulse generated a significant Fig. 11: Transient analysis results for the Trimet 180 kA cell at 4.2 cm ACD perturbation which is equivalent to the interface wave perturbation without the usual initial perturbation but with an amperage modulation normally imposed at the beginning of the transient evolution. pulse (+15 kA) occurring at 15 seconds into the simulation The second stability test was an attempt to reproduce the Trimet high frequency qualification test as closely as possible. At 15 seconds 56 into the simulation, a 2 seconds ramp from the base 180 kA amper- age to 195 kA was scheduled. That 195 kA operation was maintained for 900 seconds, then the amperage was dropped down to 180 kA in 2 minutes. In this case, the ACD was set to 4.5 cm, the usual operat- ing ACD according to [3]. Fig. 12 presents the results obtained. The metal pad short circuits the cell by touching the anode before the end of the power modulation. Knowing that the cell is critically stable at 4.2 cm ACD at 180 kA and 17 cm of metal pad thickness, it can be calculated that at 195 kA, the ACD required to be critically stable is 4.9 cm. As seen in [5], the cell stability can also be increased by increasing the metal pad thickness. So far, the metal pad thickness has been kept at relatively low 17 cm. Fig. 13 presents the results of the exactly the same power modulation but this time using a slightly raised 18 cm of metal pad thickness. As we can see, the cell stability has increased enough so that the cell is now close to being critically stable even at 195 kA. Complementary analysis of the thermal response using Dyna / Marc MHD-Valdis was designed to study the cell stability by solving the evolution of the bath / metal interface over a time scale relevant to the physics of this problem. MHD-Valdis was optimized to solve the prob- lem as efficiently as possible for the evolution of the interface over a period of 2 000 seconds (~ half an hour), using the 0.25 second time step, which requires close to 24 hours elapse time on a regular PC. Another software is required to study the thermal impact of high frequency power modulation, in this case, we used the Dy- na / Marc dynamic cell simulator. Due to its thermal mass, the ther- mal response of a cell is much slower than the MHD response, so we are talking about a time scale of hours instead of minutes. Fig. 14 presents the thermal evolution of an approximation of the Tri- met 180 kA for 3 hours of normal operation at 180 kA. The cell dynamic simulation starts from a steady state condition in under- feeding mode, as the Fig. 14 indicates, in 3 hours the feed rate has changed 2 times, we can see the cell thermal response to those changes of feeding rate. Contrary to MHD-Valdis, Dyna / Marc can solve this 3 hours transient evolution using a 6 seconds time step in a few wall clock seconds. Fig. 15 presents the cell thermal evolution due to the 900 seconds power modulation event, clearly showing the impact of the power modulation on the cell temperature evolution. The impact is not that significant, and it will only become a problem if many such events occur in sequence, and if they are always on the power addition side. Conclusions The impact of high frequency power modulation of the cell stability has been analyzed using an updated version of the code MHD-Valdis that supports the coding of amperage adjustment events during the transient evolution of the MHD wave. The results demonstrate that a very short ALUMINIUM · 1-2/2021

SPECIAL A L U M I N I U M S M E LT I N G I N D U ST RY Fig. 12: Transient analysis results for the Trimet 180 kA cell at 4.5 cm ACD Fig. 15: Transient thermal analysis results for the Trimet 180 kA cell without the usual initial perturbation, but with a 900 seconds amperage for operation with a 15 minutes power modulation (scale of green modulation event (+15 kA) occurring at 15 seconds into the simulation curves are on the left and blue curves are on the right) Fig. 13: Transient analysis results for the Trimet 180 kA cell amperage pulse introduces a perturbation to the bath / metal interface. at 4.5 cm ACD and the rised 18 cm metal pad thickness without A longer amperage modulation of 15 minutes at 15 kA (or about the usual initial perturbation but with a 900 seconds amperage 8%, from the 180 kA base amperage, corresponding to about 15% modulation event occurring at 15 seconds into the simulation power modulation) is long enough to amplify the wave to harmful level if the cell is operating close to the critical stability level before Fig. 14: Transient thermal analysis results for the amperage modulation. To be able to endure power modulation the Trimet 180 kA cell in normal operation events of that magnitude without compromising the current effi- ciency, the cell must be away from this critical stability in its normal ALUMINIUM · 1-2/2021 operating condition. Thermally, this intensity and duration of a single power modulation event is too short to affect the cell operation. References [1] B. Sachs et al., High Frequency Power Modulation – Trimet smelters pro- vide primary control power for stabilizing the frequency in the electricity grid, Light Metals 2013, 659-662. [2] T. Reek, The Hamburg Smelter – A Study of the Cathode Performance, Light Metals 2009, 347-351. [3] V. Bojarevics and J. W. Evans, Mathematical modelling of Hall-Héroult pot instability and verification by measurements of anode current distribution, Light Metals 2015, 783-788. [4] T. Reek, A Novel Approach to Power Modulation, 10th Australasian Alu- minium Smelting Technology Conference, 2011. [5] M. Dupuis and V. Bojarevics, Performing MHD cell stability sensitivity analysis using MHD-Valdis, ALUMINIUM 96 (1/2), 2020, 62-67. Authors Dr. Marc Dupuis is a consultant specialized in the applications of mathematical modelling for the aluminium industry since 1994, the year when he founded his own consulting company GeniSim Inc. (www.genisim.com). Before that, he graduated with a Ph.D. in chemical engineering from Laval University in Quebec City in 1984, and then worked ten years as a research engineer for Alcan International. His main research interests are the development of math- ematical models of the Hall-Héroult cell dealing with the thermo-electric, thermo-mechanic, electro-magnetic and hydrodynamic aspects of the problem. He was also involved in the design of experimental high amperage cells and the retrofit of many existing cell technologies. Dr. Valdis Bojarevics is an internationally recognized specialist in the field of computational magneto-hydro-dynamics (MHD), especially in developing ori- ginal computational models for a wide range of practical applications and sup- porting physical experiments in the electro-metallurgical industry. He has been invited to several internationally leading research centres for collaborative work: 1991 and 1992 Ecole Federale de Lausanne (Switzerland), 1993 Madylam labo- ratory, Grenoble (France), 1993-1995 Reynolds Metals Research Centre (Ala- bama, USA. In 1995 he was invited to join the computational modelling group at the University of Greenwich. He is currently a professor at that University. Contact: [email protected] 57