Understanding the Changes in Variable b Formulas for NIV and PAR Tags
The formulas for calculating NIV and PAR tags have been adjusted to accommodate situations where the first Accepted Bid or last Accepted Offer needs to be untagged. By expanding the range of variable b, the solutions are made more precise to avoid multiple valid outcomes. The modifications aim to ensure a single unique solution and eliminate potential for overlapping ranges that could lead to multiple solutions.
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Mod_07_18 Variable b The formulas used to calculate NIV and PAR tags rely on determining values for b (the rank of a particular action) and beta (the proportion of that action) needed in order to satisfy the equation; The proposals allow variable b to have a wider range so that they can account for situations where the entirety of the first Accepted Bid or last Accepted Offer needs to be untagged (from 1 <= b <= N to 0 <= b <= N+1): Normally for other BOAs which need to be wholly untagged this can be satisfied by having b be the action before or after the one which needs to be entirely untagged, with an associated value for beta of zero; However under the current wording this was not possible to have happen for when the first Accepted Bid or last Accepted Offer needs to be wholly untagged: to be correct this would require b = 0 or b = N+1 with a value of zero for beta, or else having b = 1 or b = N with a value of one for beta; The approach of changing the allowed values for b was chosen, rather than the approach of letting beta equal to one, because if beta can equal one then in the other situations where a BOA needs to be wholly untagged there would be multiple solutions possible, where for example b = 5 and beta = 1 would be an equally valid result as b = 6 and beta = 0 but with different outcomes in terms of which BOAs are tagged. The value of beta in these situations is also explicitly stated to ensure there is no possibility of multiple solutions being mathematically valid, even if they would not have an impact on the results; The language for the bounds of the values for b and beta was also changed to in the range to make it explicit that the bounds previously stated in parentheses were being defined as the allowed range, rather than it just being implied as the range of the value for b and beta.
Mod_07_18 Variable b The change in the language ensures that there is no potential for multiple solutions, leaving only the possibility for a single unique solution: The previous style of language to set the value of TNIV would have resulted in situations where multiple solutions are possible due to overlapping ranges, for example if the action b was the first Accepted Offer in the ranked set, then the last Accepted Bid in the ranked set would meet conditions for having a rank between 1 to M, and having a rank between M to b-1, which means it would be required to have two different values for TNIV; The intention, which is reflected in the proposed wording, was to set the value of TNIV to potentially different levels for: All BOAs in the direction opposite to the NIV; All BOAs before that determined to have rank b; All BOAs after that determined to have rank b; BOA with rank b.
Mod_07_18 Variable b Example 1 (1/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEA = P5 QAOu5 = 100 QAOuk x TINIVuk = 200 QRTAG = 50 Ranked Set Flagged Tagged 6 PMEA 5 4 3 2 1 QRTAG QRTAG is the sum of the initial tagged bids & offers. Indicates how much tagging is required to bring sum of tagged bids & offers to zero
Mod_07_18 Variable b Example 1 (2/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEA = P5 QAOu5 = 100 QAOuk x TINIVuk = 200 QRTAG = 50 b =5, = 0.5 Ranked Set Flagged Tagged 6 PMEA 5 4 3 2 1 QRTAG QRTAG is the sum of the initial tagged bids & offers. Indicates how much tagging is required to bring sum of tagged bids & offers to zero
Mod_07_18 Variable b Example 1 (3/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEA = P5 QAOu5 = 100 QAOuk x TINIVuk = 200 QRTAG = 50 b =5, = 0.5 PIMB = P5 Ranked Set Flagged Tagged 6 PMEA QRTAG PIMB 5 4 3 2 1 QRTAG is the sum of the initial tagged bids & offers. Indicates how much tagging is required to bring sum of tagged bids & offers to zero
Mod_07_18 Variable b Example 2 (1/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEA = P5 QAOu5 = 100 QAOuk x TINIVuk = 200 QRTAG = 100 Ranked Set Flagged Tagged 6 PMEA 5 4 3 2 1 QRTAG QRTAG is the sum of the initial tagged bids & offers. Indicates how much tagging is required to bring sum of tagged bids & offers to zero
Mod_07_18 Variable b Example 2 (2/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEA = P5 QAOu5 = 100 QAOuk x TINIVuk = 200 QRTAG = 100 b =6, = 0 (same as b =5, = 1) Ranked Set Flagged Tagged 6 PMEA 5 4 3 2 1 QRTAG QRTAG is the sum of the initial tagged bids & offers. Indicates how much tagging is required to bring sum of tagged bids & offers to zero
Mod_07_18 Variable b Example 2 (3/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEA = P5 QAOu5 = 100 QAOuk x TINIVuk = 200 QRTAG = 100 b =6, = 0 (same as b =5, = 1) PIMB = P4 Ranked Set Flagged Tagged 6 PMEA QRTAG 5 PIMB 4 3 2 1 QRTAG is the sum of the initial tagged bids & offers. Indicates how much tagging is required to bring sum of tagged bids & offers to zero
Mod_07_18 Variable b Example 3 (1/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEA = PCAP QAOu3 = 100 QAOuk x TINIVuk = 0 QRTAG = 300 Ranked Set Flagged PMEA=PCAP Tagged 3 2 1 QRTAG QRTAG is the sum of the initial tagged bids & offers. Indicates how much tagging is required to bring sum of tagged bids & offers to zero
Mod_07_18 Variable b Example 3 (2/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEA = PCAP QAOu3 = 100 QAOuk x TINIVuk = 0 QRTAG = 300 b =4, = 0 (same as b =3, = 1) Ranked Set Flagged PMEA=PCAP Tagged 3 2 1 QRTAG QRTAG is the sum of the initial tagged bids & offers. Indicates how much tagging is required to bring sum of tagged bids & offers to zero
Mod_07_18 Variable b Example 3 (3/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEA = PCAP QAOu3 = 100 QAOuk x TINIVuk = 0 QRTAG = 300 b =4, = 0 (same as b =3, = 1) PIMB = P3 Ranked Set Flagged PMEA=PCAP Tagged PIMB 3 2 1 QRTAG is the sum of the initial tagged bids & offers. Indicates how much tagging is required to bring sum of tagged bids & offers to zero
Mod_07_18 Variable b Example 4 (1/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEA = PFLOOR QAOu1 = 100 QAOuk x TINIVuk = 0 QRTAG = 200 Ranked Set Flagged PMEA = PFLOOR Tagged 6 PMEA 5 4 3 2 1 QRTAG QRTAG is the sum of the initial tagged bids & offers. Indicates how much tagging is required to bring sum of tagged bids & offers to zero
Mod_07_18 Variable b Example 4 (2/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEA = PFLOOR QAOu1 = 100 QAOuk x TINIVuk = 0 QRTAG = 200 b =0, = 0 (same as b =1, = 1) Ranked Set Flagged PMEA = PFLOOR Tagged 6 PMEA 5 4 3 2 1 QRTAG QRTAG is the sum of the initial tagged bids & offers. Indicates how much tagging is required to bring sum of tagged bids & offers to zero
Mod_07_18 Variable b Example 4 (3/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEA = PFLOOR QAOu1 = 100 QAOuk x TINIVuk = 0 QRTAG = 200 b =0, = 0 (same as b =1, = 1) PIMB = P1 Ranked Set Flagged PMEA = PFLOOR Tagged 6 PMEA 5 4 3 2 1 PIMB QRTAG is the sum of the initial tagged bids & offers. Indicates how much tagging is required to bring sum of tagged bids & offers to zero
Mod_08_18 TPAR Current drafting assumes QPAR > 0; As a parameter which states over what absolute volume of balancing market accepted bids/offers will we create the volume weighted average price, no need for it ever to be negative; But there is a mathematical possibility that if QPAR were to be a negative number then there could be more than one unique answer, for example with QNIV = 5 and QPAR = -6: (Clause 11) If -QPAR <= QNIV <= QPAR: - (-6) <= 5 <= 6, 6 <= 5 <= 6, false so If statement fails; (Clause 12) If QNIV > QPAR: 5 > -6, true so If statement passes; (Clause 13) If QNIV < - QPAR: 5 < - (-6), 5 < 6, true so If statement passes. While it is not expected to happen in reality, this modification is being proposed to ensure that is unambiguously understood to be the case and also to ensure compliance for certification purposes by making it explicit that QPAR > 0 is expected.
