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In order to approximate the flow-based domain, the input of the functions gtso or ˜gtso must be known. For that, we first have to find out how the characteristics vector Ch is composed. Thus we want to find out which characteristics have influence on the flow-based domain. The first step is to identify possible candidates. From Chapter2, a list of relevant candidates are derived:

1. Renewable energy forecast is the forecast of solar and wind energy.

2. Consumption forecast is the forecast of the amount of electricity consumers will use.

CHAPTER 4. CHARACTERISTICS 4.4. EQUIVALENCE CLASSES

3. Congestion forecast is the forecast of flow on the branches in the network. 4. Known outages are the branches and generators that are non-functional.

5. Generation shift keys are the forecasts of the increase/decrease of import/export mapped to the generators.

6. Day of the week is an indicator for demand of electricity. 7. Season is an indicator for the possible temperature and weather.

The forecast of renewable energy and the forecast of consumption, can be done quite accurate. To forecast the congestion, the entire design of the electrical network must be taken into account. Making a program which can simulate the entire electrical network and the change in flow in this electrical network would be time consuming and the correctness that is gained by making this very accurate, detailed program would be nullified by the errors made by the use of forecasts. The information about known outages is not very useful, because it cannot be coupled directly to a specific branch b(n) or directly to the design of the flow-based domain. The reason that this is not possible has to do with the publication of the parameters within the flow-based model by the TSOs. After the TSOs have calculated the parameters within the flow-based model they publish the parameters on the different platforms, for example at [11]. In this publication every row in the PTDF- matrix (and corresponding RAM-value) corresponds to a certain branch b(n), every b(n) has a unique number which is published with the constraint. This number is fixed, so every time it appears it refers to the same branchb(n), but it is unknown which physical branch b(n) corresponds to which number in the publication. This makes it impossible to couple a known outage to a specific constraint or the design of the flow-based domain. The influence of the generation shift keys on the parameters within the flow-based model is important, but a problem with the this forecast is that it is only useful if a change in a generation shift key can be related to a specific constraint for branchb(n) or to the design of the flow-based domain, which is not the case. The day of the week (and hour of the day) and season can be of influence on the parameters within the flow-based model and this information is known. Concluding, we only consider the following likely candidates: renewable energy forecast, consumption forecast, day of the week, hour of the day and season.

4.4

Definition of Equivalence Classes

To find out if there is a relation between certain characteristics and the flow-based domain we have to define a certain concept of equality. If we have a definition of equality we can determine when a characteristic is ‘equal’ for two different data points (in our case, hours) and what the consequence is from this equality for the flow-based domain.

The natural definition of equality would be that the characteristics have the exact same value. The only problem is that our data is very detailed and our data-set is limited. As a consequence, we (almost) never have the same value for a certain characteristic, which makes it impossible to find hours with the exact same value for even one char- acteristic, let alone for all the characteristics. This is why we define equivalence classes. Two values of one characteristic are called ‘equal’ if they are in the same equivalence class.

4.5. CHARACTERISTIC ANALYSIS METHODS CHAPTER 4. CHARACTERISTICS

Assume we have characteristic vectors Chh1 _{and Ch}h2 _{for two hours h}

1 and h2. We

split up the domains Dk inli sub-domains, where li is specific for a certainChi. For those sub-domains holds: D1 =D11 ∪. . .∪ D l1 1 and ∀i, j (i6=j)D i 1∩ D j 1 =∅, .. . ... ... Dk =Dk1∪. . .∪ D lk k and ∀i, j (i6=j)D i k∩ D j k=∅, These sub-domains are used to define our equivalence class.

Chh1 _≈Chh2 _{⇐⇒ for allithe values ofCh}h1

i andCh h2

i are in the same sub-domainD j i. If the characteristics vector of two hours (Chh1 _{and Ch}h2_{) are in the same equivalence}

class, we call them ‘equal’.

Note, that each domain can be split up into sub-domains in many different ways. In our case we use the average value of a certain characteristic Chi to define the middle of the entire domain Di. After that the standard deviation of characteristicChi defines the size of the sub-domains. Each domain, which is not the first or last domain, has a length equal to 1 time the standard deviation. For example if we split up the domain Di of characteristic Chi in 5 sub-domains the split up is as in Figure 4.7.

Figure 4.7: Example of the split up of domainDi of characteristicChi, where li= 5.

4.5

Analyse Methods to find the Characteristic of Influence