Fairfax reported that “Victoria is facing an unprecedented 72 days of possible power supply shortfalls over the next two years following the shutdown of the Hazelwood plant next week.” This was picked up by other media but a little more sense was injected by Giles Parkinson, Dylan McConnell and Tony Wood, including RenewEconomy and Radio National Breakfast. Since AEMO uses a probabilistic approach to reliability, I thought it would be helpful to graphically illustrate the meaning of reliability with probability distribution functions.

The figure is a stylised representation of the annual demand distribution (left plot) and generator availability distribution, with and without Hazelwood (right plots). I have added dashed lines when the VIC-NSW interconnector is included. Note that this is a stylised diagram and that the generator availability changes throughout the year. It also doesn’t include semi-dispatchable and non-dispatchable power (i.e. wind and solar) since these haven’t different contributions to reliability. Wind can normally be assumed to contribute 5 to 10% of rated capacity in Victoria. The plots are probability density functions (PDF’s) and can be converted to a cumulative density function (CDF), more commonly known as a load duration curve. In this case, I used the CDF algorithm designed by Preston and converted to a PDF.

The loss-of-load-probability (LOLP) can be calculated for each hour based on the generator availability. It can be thought of as the area bound by the intersection of the demand and supply curves. The LOLP for the peak hour of each day can be added to give the loss-of-load-expectation (LOLE) for a year. Most jurisdictions use LOLE as the standard reserve margin planning metric. The United States standard is a LOLE of 0.1 (‘one day in ten year’), meaning that an outage (of any duration) should only occur on one day in 10 years on average. A LOLE of 2.9 hours per year is used within the reliability standards used by France, Ireland and Belgium. Australia applies an Expected-Unserved-Energy (EUE) standard of 0.002% of annual consumption.

I have assumed a forced outage rate (FOR) of 5% to calculate the probability distribution functions (PDF) assuming that none have scheduled service. I have included all the generators in the table below. AEMO has precise data on forced outage but this information is not generally available as far as I know. The area bound by the curves should be seen as stylised and not precise.

The probability of unserved energy is determined by the intersection of the right tail of the demand distribution, with the left tail of the availability distribution. I have used a kernel density estimation (KDE) to draw the demand graph. The KDE is a non-parametric way to produce a smooth curve which can be extrapolated with a given confidence. Essentially AEMO extrapolates the right tail of the demand function and compares this to the availability function. AEMO refers to the extrapolation of “probability of exceedance (POE). If demand is greater than the reserve capacity, a “reserve shortfall” is flagged. This simply means that there is a non-zero probability of a demand shortfall. AEMO’s actual method is described here.

From the graph, it is clear that Hazelwood has extinguished Victoria’s surplus capacity and raised the possibility of unserved energy. The headline “72 days” is highly misleading but nonetheless, reserve margins have significantly tightened.

Appendix – Generators included (units and capacity in MW)

Hazelwood | 8 | 200 |

Loy Yang A | 3 | 560 |

1 | 500 | |

Loy Yang B | 2 | 500 |

Mortlake | 2 | 283 |

Newport | 1 | 510 |

Somerton | 4 | 40 |

Valley Power | 6 | 50 |

Yallourn | 2 | 380 |

2 | 360 | |

Bogong | 2 | 80 |

6 | 25 | |

Dartmouth | 1 | 185 |

Eildon | 2 | 60 |

2 | 7.5 | |

Hume | 1 | 29 |

Laverton North | 2 | 156 |

Murray 1 | 10 | 95 |

Murray 2 | 4 | 138 |

Jeeralang A | 4 | 53 |

Jeeralang B | 3 | 76 |

Bairnsdale | 2 | 47 |

West Kiewa | 4 | 15 |