ALTERNATIVAS FORMULADAS Y EVALUADAS

Now, we consider the case of a player that is contemplating to purchase some amount of CRP

û

to satisfy some need. This presents an optimisation problem to the player, which can be stated as follows:

( )

(G

û

)

min

(5) Where:

( )

(

)

(

)

(

)

[

]

[

]

( ) (

)

û û o e o e G û û u f u du B u x f u du B x f û E u E B u x B x f 0 0 1 ( , ) 1 (0, ) 0 0 1 ( , ) 1 0, 0 0 π π ψ ψ ψ π π ψ ψ ψ = ⋅ + ⋅ = − ⋅ = − ⋅ = = ⋅ + = − = − ⋅ =

∫

∫

₍₆₎

In (6), ψ is a Bernoulli random variable indicating the random activation, or not, of the power delivery during the CRP availability interval. The probability of either outcome has to be evaluated according to the activation rule of the player and its knowledge of the underlying uncertainties it wishes to manage.

1 if CRP is activared 0 otherwise

ψ =

⎧_⎨

⎩

(7)

Moreover, the actual power delivery associated with the CRP, which is in the range, 0≤ ≤u uˆ is subject to the conditional probability distribution f

( )

uψ , which models the probability density function of the random event “u units of power are delivered given that the CRP is activated”.

The optimisation in (5) is subject to the following constraints:

b

x

u

F(

,

)≤

(8)

û

u

≤

≤

0

(9)

(û

)

R

R

,π

e

,π

s

≤

(10)

The other symbols present in (6) – (10) are:

o

π

Option price of CRP, €/MW.

e

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u

Amount of power delivered through the CRP, MW.

)

,

(u

x

B

Benefit associated with the delivery of u units of CRP, €.

b

x

u

F(

,

)≤

Technical and commercial constraints of the player (similar to SRP).

(û

)

R

R

,π

_e

,π

_s

≤

Risk constraint of the player. The player must keep some risk metric

(û

e s

)

R

,π

,π

below the administrative risk threshold

R

. The risk metric depends on the CRP volume

û

, the exercise price

π

_e and the statistics on the prices of alternatives

π

_s to CRP in the market (including doing nothing and incurring corresponding imbalances charges).

The player’s objective here is to maximise its expected benefits from buying a capacity of CRP uˆ less the cost of buying it in advance

( )π

_o

û

less its expected cost if the CRP is actually activated and deployed. As with the SRP, the player is facing technical and commercial constraints, which need to be fulfilled with any amount in the range

0

≤

u

≤

û

, (8), (9).

Unlike the SRP, however, the CRP optimisation process requires that the risk of the player be bounded from above, (10). The risk here is with the uncertain future delivery of the power and the uncertain price of an alternative (possibly cheaper) flexibility product, which could be acquired closer to real time. This is the key difference between the SRP and the CRP. The conditionality of the delivery of CRP provides extra flexibility for the player (on top of potentially solving a problem, like an SRP), which allows for risk management. Obviously, this extra flexibility comes at a price (a fixed-price conditional future power delivery

( )π

e

u

at the expense of a fixed upfront fee

( )π

o

û

).

The probability that a given volume of the optional power delivery is being exercised, i.e. f

(

uψ =1

)

, depends on the following factors throughout the periods before the expiration of the option:

- The expected need of the market player i.e.

F(u,x)≤b

.

- The difference between

π

_e and the expected cost of using alternative solutions (e.g. waiting and buying energy from the balancing market) those are able to meet (some or all of) the market player’s need.

- The probability density function of exercising the CRP.

The properties of the probability density function of a CRP being exercised are further assessed in Appendix G.

In the same way, Appendix G presents:

- an analysis of CRP optimisation by Lagrange’s method

- an example of an iterative approach to solve the optimisation problem for the CRP. This procedure to formulating the optimal price and volume signals is similar to the one developed for the SRP.

- The process to compute a “request curve” instead of (volume, price) pairs, like the curve presented in Figure 21. Indeed, in the same way as for the SRP, it is reasonable to think that a player may wish to “draw” an explicit relationship between its willingness to pay for an active demand product and its corresponding optimal volume.

Regarding the formulations of the optimisation problem for time-coupled CRP, players may be facing highly complex issues, which inevitably evolve over time. So the challenge outlined for SRP is also relevant for the CRP. It is actually more so given the conditionality of the CRP deployment. Hence,

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there may be needs for players to optimise the procurement of CRP in a dynamic fashion. Its complexity, however, is beyond the scope of this document especially if we start considering opportunities for resale of such products to third parties and the resale of CRP, which have already been activated (i.e. SRP) to third parties.

Each player is expected to develop its own portfolio of flexibility products (both SRP and CRP) and its own strategies for procuring those. The underlying optimisations should be part of the operational strategies of each player; these are expected to be modulated heavily by the prevalent regulation and available market and business opportunities.

4.5. Application of the price and volume signal calculation

In document Plan De Cierre Para El Botadero A Cielo Abierto De Residuos Solidos Del Municipio De Inirida - Guainia (página 69-73)