# Generation capacity adequacy assessment - intuition behind two state model

While doing some reading on the power system resource adequacy studies I have noticed that the standard (baseline?) model for generation availability is the two state model - assumes two possible capacities, zero and maximum. It also requires that the capacities from different units are independent. While I think I get the independence reasoning for conventional and wind/hydro generation and why sometimes it cannot be achieved (e.g. wind capacities at different locations might be driven by the same weather systems - it can be windy or calm in the whole power system at some time $$t$$). I have a problem understanding the logic behind using two state model.

The papers are quite advanced and they talk about more complicated scenarios and thus, authors do not explain the two state model assumptions in detail. From what I have seen there's usually just something along the lines: "generating units are usually represented by a two state model" or "two-state model is well suited for modeling conventional generators". But I haven't been able to find a proper answer to WHY the two state model is justified here.

My question is whether the assumption of operating under two states, zero and maximum, is justified for conventional and unconventional generation. It might be super obvious but I just can't see why this is true.

## 2 Answers

In reliability studies, the availability of conventional plants is modelled with two states, available and unavailable. A plant can be unavailable due to scheduled maintenance or due to an outage. In order to model the outages, you need some information for the mean time to failure and the mean time to repair, which can be used to model the transition between the two states. From my personal experience, it is easier to work with the Forced Outage Rate, which can be estimated from above. With a fast search I found an introductory text here.

Note that a power plant might include several turbines and each one could be modelled separately. For example if a plant has two turbines $$A,B$$ and each one assumes two states $$\{available, outage\}$$, there are 4 states in total. In most papers I would assume that plants are modelled as a single entity due to data unavailability. From my experience working at a system operator, I think it is not unheard that a plant operates below the nominal capacity due to some reason (outage or other).

The classic Reliability assessment assumes that a device either works or not. Additionally, you can assume some derated states. For example, consider a Power plant with $$P_{max} = 100MW$$.

You can model it as $$0$$ or $$100$$. You can model it as $$0$$, $$50$$ or $$100$$. Usually, it is for conventional power plants.

• Think this is an almost correct explanation. The way I finally understood it is that we can model the generator to be in two states: the resource (generator) is available or is not available (e.g. due to maintenance). Which I think differs a bit from your answer or simply you used simplified reasoning. To me, modelling the generator as working or not working is a bit different from modelling it as available and not available. Because as you pointed out, we can model it 0, 50 or 100. So even though it can be available, it does not necessarily work? Does that make sense? May 29 at 12:16
• Consider a realistic case study Do you allow a power plant work in derated mode (50%) ? or if there is anything wrong with it then you will fix the issue and get back to 100% ? May 29 at 21:55