Mod_07_18 – Variable b The formulas used to calculate NIV and PAR tags in the rules 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 original version of the proposal allowed 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): However while the proposal seems to adequately cover this scenario, on the basis of analysis presented in queries it appears that the modification proposal text does not cover all situations. For example, when there are only actions in a single direction (inc or dec), meaning that all actions should be untagged to meet the NIV, and if the order that is “b” is not at the edges of the ranked set, by using an approach which sets b to be the action after the one which needs to be entirely unflagged, and having beta equal zero, results in an incorrect outcome where: all actions up to b have TNIV equal to 1; then b has TNIV equal to beta and therefore equal to zero; and all actions after b have TNIV equal to 1; rather than all actions having TNIV equal to 1 as intended.

Mod_07_18 – Variable b Version 2 of the modification incorporates an approach raised by participants at the previous meeting: Allow beta to equal 1. This creates a situation where there can now two valid results in situations where the entirety of a bid offer acceptance quantity should be untagged, e.g. b = 2 beta = 1 or b = 3 beta = 0. Therefore also add wording to clarify which result is the one used for all following pricing processes: the one with beta = 1 achieves the correct result. Other minor changes: Changed language from “any rank k < b” etc. to “each rank k where k < b” etc.; V1 of the mod had “…where the Net Imbalance Volume Quantity (QNIVukφ) is a negative value” in paragraph 9 before (a), this should be “…positive value”.

Mod_07_18 – Variable b – E.g. 1 Mod v1 correct (1/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEAφ = PCAP QAOu3φ = 100 ∑QAOukφ x (1 – TINIVukφ) = 300 QRTAGφ = -300 Ranked Set Flagged Tagged PMEA=PCAP   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 – E.g. 1 Mod v1 correct (2/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEAφ = PCAP QAOu3φ = 100 ∑QAOukφ x (1 – TINIVukφ) = 300 QRTAGφ = -300 b = 4, β = 0 (same as b = 3, β = 1) Ranked Set Flagged Tagged PMEA=PCAP   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 – E.g. 1 Mod v1 correct (3/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEAφ = PCAP QAOu3φ = 100 ∑QAOukφ x (1 – TINIVukφ) = 300 QRTAGφ = -300 b = 4, β = 0 (same as b = 3, β = 1) PIMBφ = P3 Ranked Set Flagged Tagged PMEA=PCAP   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 – E.g. 2 Mod v1 incorrect (1/4) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEAφ = P3 QAOu2φ = 100 ∑QAOukφ x (1 – TINIVukφ) = 100 QRTAGφ = -100 Ranked Set Flagged Tagged   PMEA 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 – E.g. 2 Mod v1 incorrect (2/4) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEAφ = P3 QAOu2φ = 100 ∑QAOukφ x (1 – TINIVukφ) = 100 QRTAGφ = -100 b = 3, β = 0 (same as b = 2, β = 1) Ranked Set Flagged Tagged   PMEA 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 – E.g. 2 Mod v1 incorrect (3/4) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEAφ = P3 QAOu2φ = 100 ∑QAOukφ x (1 – TINIVukφ) = 100 QRTAGφ = -100 b = 3, β = 0 (same as b = 2, β = 1) PIMBφ = P2 Ranked Set Flagged Tagged   PMEA 3 PIMB 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 – E.g. 2 Mod v2 correct (4/4) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEAφ = P3 QAOu2φ = 100 ∑QAOukφ x (1 – TINIVukφ) = 100 QRTAGφ = -100 b = 3, β = 0 (same as b = 2, β = 1) PIMBφ = P3 Ranked Set Flagged Tagged   PMEA 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 – E.g. 3 Mod v1 correct (1/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEAφ = PFLOOR QABu1φ = -100 ∑QABukφ x (1 – TINIVukφ)= 200 QRTAGφ = 200 Ranked Set Flagged Tagged PMEA =   PFLOOR 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 – E.g. 3 Mod v1 correct (2/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEAφ = PFLOOR QABu1φ = -100 ∑QABukφ x (1 – TINIVukφ)= 200 QRTAGφ = 200 b = 0, β = 0 (same as b = 1, β = 1) Ranked Set Flagged Tagged PMEA =   PFLOOR 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 – E.g. 3 Mod v1 correct (3/3) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEAφ = PFLOOR QABu1φ = -100 ∑QABukφ x (1 – TINIVukφ)= 200 QRTAGφ = 200 b = 0, β = 0 (same as b = 1, β = 1) PIMBφ = P1 Ranked Set Flagged Tagged PMEA =   PFLOOR 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_07_18 – Variable b – E.g. 4 Mod v1 incorrect (1/4) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEAφ = P1 QABu3φ = -50 ∑QABukφ x (1 – TINIVukφ)= 50 QRTAGφ = 50 Ranked Set Flagged Tagged   6 PMEA 5 4 3 2 1  PMEA 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 – E.g. 4 Mod v1 incorrect (2/4) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEAφ = P1 QABu3φ = -50 ∑QABukφ x (1 – TINIVukφ)= 50 QRTAGφ = 50 b = 1, β = 0 (same as b = 2, β = 1) Ranked Set Flagged Tagged   6 PMEA 5 4 3 2 1  PMEA 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 – E.g. 4 Mod v1 incorrect (3/4) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEAφ = P1 QABu3φ = -50 ∑QABukφ x (1 – TINIVukφ)= 50 QRTAGφ = 50 b = 1, β = 0 (same as b = 2, β = 1) PIMBφ = P2 Ranked Set Flagged Tagged   6 PMEA 5 4 3 2  PIMB 1  PMEA 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 – E.g. 4 Mod v2 correct (4/4) Dark Red = +ve Unflagged / Untagged Light Red = +ve Flagged / Tagged Dark Blue = -ve Unflagged / Untagged Light Blue = -ve Flagged / Tagged Values PMEAφ = P1 QABu3φ = -50 ∑QABukφ x (1 – TINIVukφ)= 50 QRTAGφ = 50 b = 1, β = 0 (same as b = 2, β = 1) PIMBφ = P1 Ranked Set Flagged Tagged   6 PMEA 5 4 3 2 1  PMEA 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