Let us first define a schematic disaster as a random event E with a low probability of occurrence p (say p=0.05) in each year and a high cost C (including social cost, represented by means of unitary not served energy costs). If we include not served energy as special generation plants and we use a Spot price based on marginal costs, an occurrence of E will be characterised by a period with very high prices. Suppose there is a project which is only useful in the case of disaster periods, where it can get a great net income NI(E). Let us call ENI the project expected net income discounted at a rate i, that is:

Let PI be the project's investment cost (we can suppose PI is sure and is made in time period t=0).

Then if ENI>PI, the project would be convenient (let us forget management flexibility for a while). So you would spend PI surely today, and the waiting time W before your first net income will be geometric with parameter p=0.05. That is, the expected value of W is 20 years. It is difficult to find an independent investor for such a business.

A very big insurance company BC is needed to make contracts with independent investors in the following terms:

1) BC will pay annually a fixed prime to the independent investor.

2) The independent investor will transfer to BC the quantity NI(E), in the case that E occurs. BC must be aware of the risk that the independent investor would not be able to get the amount NI(E) during the disaster event E. Perhaps financial mechanisms will have to be designed.

Now BC has a stochastic programming problem. For only one independent project, the value NI(E) is well known. But if many projects are done in the same market, NI(E) will decrease. BC may calculate how many projects like P are profitable in expected value, and afterwards it could ask for bids. Another way is to decide how much to pay for a project, as a part of p*NI(E). When this quantity attains a required level (depending on investment costs), some projects will be constructed and NI(E) will fall again below the required level.

The first approach corresponds to using the primal solution of the stochastic programming problem. The second one uses the dual solution.

The type of stochastic programming problem to be solved depends on the system characteristics. The low p Bernouilli type probability distribution of disasters produces analogies in the corresponding scenario structure. Sometimes, a schematic formulation is possible using only two situations, the normal one (expected values given E do not occur) and the disastrous one (expected values given E occur), on a conditional probability base. In this approach scenarios are sequences of situations.

In hydro-thermal systems where inflows are random with an important variance, a disaster could arise if a long run of low inflows occurs. A project P will be represented by a gas turbine of low investment cost and corresponding high variable cost. Normally a company like BC does not exist, and the Regulatory authority has to take its place, defining some system of "power remuneration" to complement income from energy sales. Many problems arise in practical systems with that kind of complements. Furthermore, there is available information about negative linear correlation between the hydrological situation in pretty distant regions, many times in different countries. Only countries of the size of Brazil are able to profit of complementary basins without international co-ordination.

Other applications are possible, like disasters from hurricanes, outage of very big generation plants, changes in internal regulations, changes in international trade, etc. Applications are not limited to electricity markets.

A final comment about BC. The nature of things is such that BC could be interested in promoting disasters ... and it will be a powerful organisation. If very few BCs exist, perhaps it would be good that governments share their stocks. If a lot of BCs develop, they would have to publish their disaster statistics, in such a way that consumers can make an informed choice.

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