Spike clustering and re-onset risk

For each region, we measured the time from the start of one episode to the start of the next and divided it by the region's mean gap, which ranges from 11.5 hours (Queensland, South Australia) to 23.4 hours (Victoria). If onsets arrived at random at a constant rate (a Poisson process), the rescaled gaps would follow an exponential distribution.

57% of gaps are shorter than a tenth of the mean gap; an exponential distribution puts 10% there. The median rescaled gap is 0.065, against 0.69 for random arrival. A gamma distribution fitted to the rescaled gaps has shape 0.32, where 1 corresponds to random arrival and lower values to stronger clustering. Earthquake recurrence times give about 0.7 on the same statistic. The estimate depends on the episode definition: merging episodes separated by a few minutes would raise it.

The implication is that the onset hazard varies strongly in time. A model that treats onsets as independent events at a fixed rate will under-estimate risk shortly after a spike and over-estimate it during long quiet spells.

In the first 15 minutes after an episode ends, the probability of a new episode within 30 minutes is 44–49% in the mainland regions and 35% in Tasmania. The excess over each region's long-quiet rate (0.13–0.82%) halves in 22 minutes in Victoria, 23 in New South Wales, 24 in Queensland and 26 in South Australia and Tasmania. A power law fits the decay better than an exponential in all five regions, with 1.2 to 3 times lower weighted error. At 6 hours the probability is still above the long-quiet rate everywhere, from 2.9 times in South Australia to 26 times in Victoria (whose long-quiet rate is the lowest).

The halving time is nearly the same across regions with very different generation: coal in Queensland, wind and batteries in South Australia, hydro in Tasmania. That points to a common mechanism. Plausible candidates are the time it takes fast-start plant and batteries to respond to a high price, and the cadence of rebidding after one. We have not tested these here. An earlier analysis across the October 2021 move to 5-minute settlement found a similar decay time scale before and after the change (28–31 minutes before, 24–29 after), which argues against a purely administrative cause.

The onset rate is 29 times the long-quiet rate in the first 30 minutes after an episode ends, 7.4 times from 30 minutes to 2 hours, 3.0 times from 2 to 6 hours and 2.5 times from 6 to 24 hours. From 1 to 3 days it is 1.1 times; beyond 3 days there is no difference.

For risk management, recent spike history is informative for about a day and uninformative after that. Persistent multi-day drivers would appear as ratios above 1 at 1–7 days; once hour of day and season are controlled, there are almost none.

We grouped episodes by their peak price and measured how often a new episode started within 30 minutes of each one ending. The rate is 51% after episodes peaking at $300–500, 54% at $500–1,000, 51% at $1,000–3,000 and 48% at $3,000–5,000. After episodes that reached $5,000 or more it is 44% (90% interval 40–48%, 443 episodes). This is the opposite of earthquake catalogues, where larger shocks produce more aftershocks (Utsu's law).

A plausible mechanism is the supply response to a very high price. Batteries discharge, fast-start gas units commit and participants rebid capacity into lower price bands, which leaves more headroom in the following half hour. This is an interpretation; we did not measure the response directly in this analysis.

We chained episodes in the same region separated by at most 4 hours into clusters, giving 2,037 clusters with at least two episodes, and compared the largest and second-largest peak in each.

The probability that the second-largest peak is within a factor of 1.35 of the largest (at least 74% of its height) falls from 38% when the largest peak is $500–1,000 (419 clusters) to 20% at $1,000–3,000 (152) and 7% at $3,000–8,000 (73). Over the same range the median ratio of the second peak to the first falls from 0.67 to 0.11. In seismology the gap between a main shock and its largest aftershock is roughly constant (Båth's law); here it widens with size.

Above $8,000, where peaks are close to the market price cap, the repeat probability rises to 14% (289 clusters). At the cap the price is set administratively, so repeated cap-level intervals within a cluster produce identical peaks. The rise reflects the cap rather than a change in market behaviour.

The regions are linked by four interconnector paths: Queensland–New South Wales, New South Wales–Victoria, Victoria–South Australia and Victoria–Tasmania. For each episode start in region A, we computed the probability that an episode starts in region B within the following 30 minutes, among cases where B was not already in an episode. We divided that by B's probability of an episode starting in any 30-minute window.

For directly connected regions the ratio averages 8.9, ranging from 5.7 (Queensland to New South Wales) to 12.9 (Victoria to Tasmania). For regions two links apart it averages 3.9; for three links apart (Queensland to South Australia or Tasmania), 2.6. At high prices the coupling is tighter. When Victoria's price is at or above $5,000, South Australia's is too in 78% of intervals and New South Wales's in 79%, against base rates near 0.1%.

The decline with interconnector distance is consistent with how regional prices are set. While an interconnector is below its limit, adjacent regions are dispatched together and their prices move together. When the limit binds, their prices separate. Regions two or more links apart are coupled only through the regions between them, which dilutes the effect.