Applying Karush-Kuhn-Tucker (KKT) Optimality Conditions for Pricing Analysis in DAM Under

Applying Karush-Kuhn-Tucker (KKT) Optimality Conditions for Pricing Analysis in DAM under the proposed Future AS

Introduction to concepts

The simplified hypothetical DAM optimization problem is presented below.

Simplifications:

(i)  Transmission constraints, PTPs, block offers and bids are not considered

(ii)  A single AS product (generically called AS) is considered

(iii)  Load Resources are not considered

(iv)  Energy Offer and AS Offer are covering the entire MW range from LSL to HSL

(v)  No constraints on how much AS can be awarded to a single resource

(vi)  CiEnergyBid,CiEnergyOffer,CiASOffer are the submitted bids ($/MWh) , energy offers ($/MWh), AS offers ($/MW) respectively. For simplicity, these bids and offers are considered to be constant for the entire MW bid or offered.

(vii)  Resource commitment not considered – all Resources considered to be online and only online AS and Energy Offers considered

(viii)  All AS Offers from Generation Resources are considered to be inclusive with respect to their EOC.

(ix)  Temporal constraints not modeled

(x)  AS Self Arrangement set to zero

(xi)  Other simplifications compared to actual DAM ….

Optimization Problem

Minimize objective (cost) function:

Minimize Objective=Minimize -i=1NebCiEnergyBid×MWiEnergyBidAward+i=1NCiEnergyOffer×MWiEnergyOfferAward+i=1NCiASOffer×MWiASAward

Subject to:

Ignoring transmission constraints and focusing on power balance, AS procurement and Resource limit constraints, the set of constraints are given below:

System wide constraints:

a)  Power Balance: (Shadow price = λ)

i=1NMWiEnergyOfferAward-i=1NebMWiEnergyBidAward=0

b)  AS Procurement: (Shadow price = α)

i=1NMWiASAward-ASRequirement ≥0

Individual Energy Bid constraints:

c)  Energy Bid MW constraint for every energy bid i=1,2,3…Neb: (Shadow price = θieb respectively)

EnergyBidMWi-MWiEnergyBidAward ≥0

Individual Resource constraints:

Each Resource will have its own set of constraints to ensure awards are within bounds of its own upper (HSL/MPC) and low (LSL/LPC) limits.

d)  LSL Constraint for every modeled Generation Resource i=1,2,3…N: (Shadow price = θiLSL)

MWiEnergyOfferAward-LSLi ≥0

e)  HSL Constraint for every modeled Generation Resource i=1,2,3…N: (Shadow price = θiHSL)

HSLi-MWiEnergyOfferAward-MWiASAward ≥0

Analysis by Applying KKT optimality conditions:

The objective and constraints are combined to form the Lagrange function:

L=Objective- iShadowpricei×Constrainti

L= -i=1NebCiEnergyBid×MWiEnergyBidAward+i=1NCiEnergyOffer×MWiEnergyOfferAward+i=1NCiASOffer×MWiASAward- λi=1N∆MWiEnergyOfferAward-i=1Neb∆MWiEnergyBidAward-αi=1NMWiASAward-ASRequirement -i=1NebθiebEnergyBidMWi-MWiEnergyBidAward-i=1NθiLSLMWiEnergyOfferAward-LSLi-i=1NθiHSLHSLi-MWiEnergyOfferAward-MWiASAward

At optimal solution ∇L=0 (optimality condition)

i.e. the partial derivative of L with respect to each award MWiEnergyBidAward,MWiEnergyOfferAward,MWiASAward will equate to zero at the optimal solution.

Taking the partial derivative of L with respect to each award MWiEnergyBidAward,MWiEnergyOfferAward,MWiASAward we get:

∇LMW=0= -i=1NebCiEnergyBid×∆MWiEnergyBidAward+i=1NCiEnergyOffer×∆MWiEnergyOfferAward+i=1NCiASOffer×∆MWiASAward- λi=1N∆MWiEnergyOfferAward-i=1Neb∆MWiEnergyBidAward-αi=1N∆MWiASAward +i=1Nebθieb∆MWiEnergyBidAward-i=1NθiLSL∆MWiEnergyOfferAward+i=1NθiHSL∆MWiEnergyOfferAward+∆MWiASAward

Rearranging the terms by ∆MWiEnergyBidAward, ∆MWiEnergyOfferAward,∆MWiASAward we get:

f)  For each energy bid i=1,2,3,…Neb, the following equation holds true

CiEnergyBid= λ-θieb

If the energy bid i is marginal to the power balance constraint, then θieb=0 and the energy bid i sets the shadow price for the power balance constraint (System Lambda λ)

g)  For each Resource energy offer i=1,2,3,…N, the following equation holds true

CiEnergyOffer=λ-θiHSL+θiLSL

If the energy offer i is marginal to the power balance constraint, then in most cases, θiHSL=0,θiLSL=0 and the energy offer i sets the shadow price for the power balance constraint (System Lambda λ)

h)  For each Resource AS offer i=1,2,3,…N, the following equation holds true

CiASOffer=α-θiHSL

If the AS offer i is marginal to the AS procurement constraint, then in most cases, θiHSL=0and the AS offer i sets the shadow price for the AS procurement constraint (typically referred to as the AS MCPC α)

Pricing Analysis Example:

Let there be a Resource g whose capacity has been partly awarded energy and partly awarded AS such that the sum of the energy award and AS award equals Resource g HSL.

In this case:

MWgEnergyOfferAward+MWgASOfferAward=HSLg

The HSL constraint is binding, i.e. θiHSL>0

The LSL constraint is not binding, i.e. θiLSL=0

And,

CiEnergyOffer- λ+θiHSL=0

CiASOffer- α+θiHSL=0

Rearranging we get

λ-CiEnergyOffer=θiHSL

α-CiASOffer=θiHSL

Equating the two equations we get
λ-CiEnergyOffer=α-CiASOffer

This demonstrates that at the optimal solution Resource g is indifferent to whether its capacity is used for energy or AS. This is because for each MW sold from the resource for energy or AS, the additional revenue from energy or AS, over submitted offer price, is the same.

DAM Pricing Analysis Applying KKT Optimality Conditions– Future AS

The simplified DAM optimization problem under the proposed Future Ancillary Service framework is presented below.

Simplifications:

(i)  Transmission constraints, PTPs, block offers and bids are not considered

(ii)  Energy Offer are covering the entire MW range from LSL to HSL

(iii)  No constraints on how much AS can be awarded to a single resource but AS awards cannot exceed the MW amount in the AS Offer

(iv)  CiEnergyBid,CiEnergyOffer,CiRegUpOffer, etc. are the submitted bids ($/MWh) , energy offers ($/MWh), RegUp offers ($/MW), etc. respectively. For simplicity, these bids and offers are considered to be constant for the entire MW bid or offered.

(v)  Resource commitment not considered – all Resources considered to be online and only online AS and Energy Offers considered

(vi)  All AS Offers from Generation Resources are considered to be inclusive with respect to their EOC.

(vii)  Temporal constraints not modeled

(viii)  AS Self Arrangement set to zero

(ix)  Other simplifications compared to actual DAM ….

Optimization Problem

Minimize objective (cost) function:

Minimize -i=1NebCiEnergyBid×MWiEnergyBidAward+i=1NgCiEnergyOffer×MWiEnergyOfferAward+i=1Ng+NclCiRegUpOffer×MWiRegUpAward+i=1Nfg+NfclCiFRRSUpOffer×MWiFRRSUpAward+i=1Ng+NclCiRegDnOffer×MWiRegDnAward+i=1NfclCiFRRSDnOffer×MWiFRRSDnAward+i=1Ng+NclCiPFROffer×MWiPFRAward+i=1Ng+NclCiCR1Offer×MWiCR1Award+i=1Ng+NclCiSR1Offer×MWiSR1Award+i=1Nbl+Nfg+NfclCiFFR1Offer×MWiFFR1Award+i=1NblCiFFR2Offer×MWiFFR2Award+i=1NblCiCR2Offer×MWiCR2Award+i=1NblCiSR2Offer×MWiSR2Award

Subject to:

Ignoring transmission constraints and focusing on power balance, AS procurement and Resource limit constraints, the set of constraints are given below:

System wide constraints:

a)  Power Balance: (Shadow price = λ)

i=1NgMWiEnergyOfferAward-i=1NebMWiEnergyBidAward=0

b)  RegUp Procurement (including FRRS-Up): (Shadow price = α)

i=1Ng+NclMWiRegUpAward+i=1Nfg+NfclMWiFRRSUpAward-RegUpRequirement ≥0

c)  FRRS-Up maximum procurement limit: (Shadow price = ωFRRSUp)

MaxFRRSUp-i=1Nfg+NfclMWiFRRSUpAward≥0

d)  RegDn Procurement (including FRRS-Dn): (Shadow price = β)

i=1Ng+NclMWiRegDnAward+i=1NfclMWiFRRSDnAward-RegDnRequirement≥0

e)  FRRS-Dn maximum procurement limit: (Shadow price = ωFRRSDn)

MaxFRRSDn-i=1NfclMWiFRRSDnAward ≥0

f)  CR Procurement (CR1 & CR2): (Shadow price = γ)

i=1Ng+NclMWiCR1Award+i=1NblMWiCR2Award-CRRequirement ≥0

g)  CR1 minimum procurement : (Shadow price = ωCR1)

i=1Ng+NclMWiCR1Award- MinCR1≥0

h)  SR Procurement (SR1 & SR2): (Shadow price = δ)

i=1Ng+NclMWiSR1Award+i=1NblMWiSR2Award-SRRequirement ≥0

i)  SR1 minimum procurement : (Shadow price = ωSR1)

i=1Ng+NclMWiSR1Award- MinSR1≥0

j)  PFR+FFR1+FFR2 Procurement: (Shadow price = ϕ)

i=1Ng+NclMWiPFRAward+R×i=1Nbl+Nfg+NfclMWiFFR1Award+i=1NblMWiFFR2Award- PFRRequirement+R×FFRRequirement ≥0

k)  FFR1+FFR2 Maximum procurement limit : (Shadow price = ωFFR)

MaxFFR-i=1Nbl+Nfg+NfclMWiFFR1Award-i=1NblMWiFFR2Award≥0

l)  FFR1 Maximum procurement limit : (Shadow price = ωFFR1)

MaxFFR1-i=1Nbl+Nfg+NfclMWiFFR1Award≥0

Individual Energy Bid constraints:

m)  Energy Bid MW constraint for every energy bid i=1,2,3…Neb: (Shadow price = θieb respectively)

EnergyBidMWi-MWiEnergyBidAward ≥0

Individual Resource constraints:

Each Resource will have its own set of constraints to ensure awards are within bounds of its own upper (HSL/MPC) and low (LSL/LPC) limits.

n)  LSL Constraint for every modeled Generation Resource i=1,2,3…Ng: (Shadow price = θiLSL)

MWiEnergyOfferAward-MWiRegDnAward-LSLi ≥0

o)  HSL Constraint for every modeled Generation Resource i=1,2,3…Ng: (Shadow price = θiHSL)

HSLi-MWiEnergyOfferAward-MWiRegUpAward-MWiPFRAward-MWiCR1Award-MWiSR1Award ≥0

p)  AS Offer MW constraint for every modeled Generation Resource i=1,2,3…Ng: (Shadow price = θig-ASup,θig-ASdn respectively)

ASOfferMWi-MWiRegUpAward-MWiPFRAward-MWiCR1Award-MWiSR1Award ≥0

ASOfferMWi-MWiRegDnAward ≥0

q)  MPC & LPC Constraint for every modeled “Blocky” Load Resource i=1,2,3…Nbl: (Shadow price = θibl)

Note that a “blocky” Load Resource is awarded only one AS product.

MPCi-LPCi-MWiFFR1Award ≥0

or

MPCi-LPCi-MWiFFR2Award ≥0

or

MPCi-LPCi-MWiCR2Award ≥0

or

MPCi-LPCi-MWiSR2Award ≥0

r)  AS Offer MW constraint for every modeled “Blocky” Load Resource i=1,2,3…Nbl: (Shadow price = θibl-AS)

ASOfferMWi-MWiFFR1Award ≥0

or

ASOfferMWi-MWiFFR2Award ≥0

or

ASOfferMWi-MWiCR2Award ≥0

or

ASOfferMWi-MWiSR2Award ≥0

s)  MPC & LPC Constraint for every modeled Controllable Load Resource i=1,2,3…Ncl: (Shadow price = θicl)

MPCi-LPCi-MWiRegDnAward-MWiRegUpAward-MWiPFRAward-MWiCR1Award-MWiSR1Award ≥0

t)  AS Offer MW constraint for every Controllable Load Resource i=1,2,3…Ncl: (Shadow price = θicl-ASup,θicl-ASdn respectively)

ASOfferMWi-MWiRegUpAward-MWiPFRAward-MWiCR1Award-MWiSR1Award ≥0

ASOfferMWi-MWiRegDnAward ≥0

u)  HSL & LSL Constraint for every “Quick/Fast” Resource qualified for FRRS-Up and FFR1 and partly modeled as Generation Resource i=1,2,3…Nfg: (Shadow price = θifg)

HSLi-LSLi-MWiFRRSUpAward-MWiFFR1Award ≥0

v)  AS Offer MW constraint for every “Quick/Fast” Resource qualified for FRRS-Up and FFR1 and partly modeled as Generation Resource i=1,2,3…Nfg: (Shadow price = θifg-AS)

ASOfferMWi-MWiFRRSUpAward-MWiFFR1Award ≥0

w)  MPC & LPC Constraint for every “Quick/Fast” Resource qualified for FRRS-Up, FRRS-Dn and FFR1 and partly modeled as Controllable Load Resource i=1,2,3…Nfcl: (Shadow price = θifcl)

MPCi-LPCi-MWiFRRSDnAward-MWiFRRSUpAward-MWiFFR1Award ≥0

x)  AS Offer MW constraint for every “Quick/Fast” Resource qualified for FRRS-Up and FFR1 and partly modeled as Controllable Load Resource i=1,2,3…Nfcl: (Shadow price = θifcl-ASup,θifcl-ASdn respectively)

ASOfferMWi-MWiFRRSUpAward-MWiFFR1Award ≥0

ASOfferMWi-MWiFRRSDnAward ≥0

Pricing Analysis By Applying KKT optimality conditions:

The objective and constraints are combined to form the Lagrange function:

L=Objective- iShadowpricei×Constrainti

At optimal solution ∇L=0 (KKT optimality condition)

i.e. the partial derivative of L with respect to each award MWiEnergyBidAward,MWiEnergyOfferAward,MWiRegUpAward, etc will equate to zero at the optimal solution.

Taking the partial derivative of L with respect to each award MWiEnergyBidAward,MWiEnergyOfferAward,MWiRegUpAward, etc. results in:

∇LMW=0= -i=1NebCiEnergyBid×∆MWiEnergyBidAward+i=1NgCiEnergyOffer×∆MWiEnergyOfferAward+i=1Ng+NclCiRegUpOffer×∆MWiRegUpAward+i=1Nfg+NfclCiFRRSUpOffer×∆MWiFRRSUpAward+i=1Ng+NclCiRegDnOffer×∆MWiRegDnAward+i=1NfclCiFRRSDnOffer×∆MWiFRRSDnAward+i=1Ng+NclCiPFROffer×∆MWiPFRAward+i=1Ng+NclCiCR1Offer×∆MWiCR1Award+i=1Ng+NclCiSR1Offer×∆MWiSR1Award+i=1Nbl+Nfg+NfclCiFFR1Offer×∆MWiFFR1Award+i=1NblCiFFR2Offer×∆MWiFFR2Award+i=1NblCiCR2Offer×∆MWiCR2Award+i=1NblCiSR2Offer×∆MWiSR2Award- λi=1Ng∆MWiEnergyOfferAward-i=1Neb∆MWiEnergyBidAward-αi=1Ng+Ncl∆MWiRegUpAward+i=1Nfg+Nfcl∆MWiFRRSUpAward -βi=1Ng+Ncl∆MWiRegDnAward+i=1Nfcl∆MWiFRRSDnAward-γi=1Ng+Ncl∆MWiCR1Award+i=1Nbl∆MWiCR2Award-δi=1Ng+Ncl∆MWiSR1Award+i=1Nbl∆MWiSR2Award -ϕi=1Ng+Ncl∆MWiPFRAward+R×i=1Nbl+Nfg+Nfcl∆MWiFFR1Award+i=1Nbl∆MWiFFR2Award+ωFRRSUpi=1Nfg+Nfcl∆MWiFRRSUpAward+ωFRRSDni=1Nfcl∆MWiFRRSDnAward-ωCR1i=1Ng+Ncl∆MWiCR1Award-ωSR1i=1Ng+Ncl∆MWiSR1Award+ωFFRi=1Nbl+Nfg+Nfcl∆MWiFFR1Award+i=1Nbl∆MWiFFR2Award+ωFFR1i=1Nbl+Nfg+Nfcl∆MWiFFR1Award+i=1Nebθieb∆MWiEnergyBidAward-i=1NgθiLSL∆MWiEnergyOfferAward-∆MWiRegDnAward+i=1NgθiHSL∆MWiEnergyOfferAward+∆MWiRegUpAward+∆MWiPFRAward+∆MWiCR1Award+∆MWiSR1Award+i=1Ngθig-ASup∆MWiRegUpAward+∆MWiPFRAward+∆MWiCR1Award+∆MWiSR1Award+i=1Ngθig-ASdn∆MWiRegDnAward+i=1Nblθibl∆MWiFFR1Award or FFR2Award or CR2Award or SR2Award+i=1Nblθibl-AS∆MWiFFR1Award or FFR2Award or CR2Award or SR2Award+i=1Nclθicl∆MWiRegDnAward+∆MWiRegUpAward+∆MWiPFRAward+∆MWiCR1Award+∆MWiSR1Award+i=1Nclθicl-ASup∆MWiRegUpAward+∆MWiPFRAward+∆MWiCR1Award+∆MWiSR1Award+i=1Nclθicl-ASdn∆MWiRegDnAward+i=1Nfgθifg∆MWiFRRSUpAward+∆MWiFFR1Award+i=1Nfgθifg-AS∆MWiFRRSUpAward+∆MWiFFR1Award+i=1Nfclθifcl∆MWiFRRSDnAward+∆MWiFRRSUpAward+∆MWiFFR1Award+i=1Nfclθifcl-ASup∆MWiFRRSUpAward+∆MWiFFR1Award+i=1Nfclθifcl-ASdn∆MWiFRRSDnAward

Rearranging the terms by ∆MWiEnergyBidAward, ∆MWiEnergyOfferAward,∆MWiRegUpAward, etc. we get:

a)  For each energy bid i=1,2,3,…Neb, the following equation holds true

CiEnergyBid= λ-θieb

b)  For each energy offer from modeled Generation Resource i=1,2,3,…Ng, the following equation holds true

CiEnergyOffer=λ-θiHSL+θiLSL

c)  For each RegUp offer from modeled Generation Resource i=1,2,3,…Ng, the following equation holds true

CiRegUpOffer= α-θiHSL-θig-ASup

d)  For each RegDn offer from modeled Generation Resource i=1,2,3,…Ng, the following equation holds true

CiRegDnOffer= β-θiLSL-θig-ASdn

e)  For each PFR offer from modeled Generation Resource i=1,2,3,…Ng, the following equation holds true

CiPFROffer= ϕ-θiHSL-θig-ASup

f)  For each CR1 offer from modeled Generation Resource i=1,2,3,…Ng, the following equation holds true

CiCR1Offer= γ+ωCR1-θiHSL-θig-ASup

g)  For each SR1 offer from modeled Generation Resource i=1,2,3,…Ng, the following equation holds true

CiSR1Offer= δ+ωSR1-θiHSL-θig-ASup

h)  For each FFR1 offer from modeled “blocky” Load Resource i=1,2,3,…Nbl, the following equation holds true

CiFFR1Offer= Rϕ-ωFFR-ωFFR1-θibl-θibl-AS

i)  For each FFR2 offer from modeled “blocky” Load Resource i=1,2,3,…Nbl, the following equation holds true

CiFFR2Offer= Rϕ-ωFFR-θibl-θibl-AS

j)  For each CR2 offer from modeled “blocky” Load Resource i=1,2,3,…Nbl, the following equation holds true

CiCR2Offer= γ-θibl-θibl-AS

k)  For each SR2 offer from modeled “blocky” Load Resource i=1,2,3,…Nbl, the following equation holds true

CiSR2Offer= δ-θibl-θibl-AS

l)  For each RegUp offer from modeled Controllable Load Resource i=1,2,3,…Ncl, the following equation holds true

CiRegUpOffer= α-θicl-θicl-ASup

m)  For each RegDn offer from modeled Controllable Load Resource i=1,2,3,…Ncl, the following equation holds true

CiRegDnOffer= β-θicl-θicl-ASdn

n)  For each PFR offer from modeled Controllable Load Resource i=1,2,3,…Ncl, the following equation holds true

CiPFROffer= ϕ-θicl-θicl-ASup

o)  For each CR1 offer from modeled Controllable Load Resource i=1,2,3,…Ncl, the following equation holds true

CiCR1Offer= γ+ωCR1-θicl-θicl-ASup

p)  For each SR1 offer from modeled Controllable Load Resource i=1,2,3,…Ncl, the following equation holds true

CiSR1Offer= δ+ωSR1-θicl-θicl-ASup

q)  For each FRRS-Up offer from “Quick/Fast” Resource partly modeled as Generation Resource i=1,2,3,…Nfg, the following equation holds true

CiFRRSUpOffer= α-ωFRRSUp-θifg-θifg-AS

r)  For each FFR1 offer from “Quick/Fast” Resource partly modeled as Generation Resource i=1,2,3,…Nfg, the following equation holds true

CiFFR1Offer= Rϕ-ωFFR-ωFFR1-θifg-θifg-AS

s)  For each FRRS-Up offer from “Quick/Fast” Resource partly modeled as Load Resource i=1,2,3,…Nfcl, the following equation holds true

CiFRRSUpOffer= α-ωFRRSUp-θifcl-θifcl-ASup

t)  For each FRRS-Dn offer from “Quick/Fast” Resource partly modeled as Load Resource i=1,2,3,…Nfcl, the following equation holds true

CiFRRSDnOffer= β-ωFRRSDn-θifcl-θifcl-ASdn

u)  For each FFR1 offer from “Quick/Fast” Resource partly modeled as Load Resource i=1,2,3,…Nfcl, the following equation holds true

CiFFR1Offer= Rϕ-ωFFR-ωFFR1-θifcl-θifcl-ASup

MCPC for proposed Future Ancillary Service

MCPC for a given AS is computed after the DAM optimization is complete. MCPCs are a linear combination of Shadow Prices of constraints. In the current Nodal Market, the MCPCs are setup to be the Shadow Price of a single constraint (procurement constraint of the respective AS).

1. In the current ERCOT market, all demand (load) is bought at the Load Zone (except for Wholesale Load). Load Resources cannot submit Resource Specific (locational) demand bids (bid to buy energy). Load Resources can only submit Resource specific Offers to sell Ancillary Services.
2. Hence, the Load Resource Limit Constraints do not have an energy consumed portion between their lower and upper limits.
3. Generation Resources, however, can submit Resource specific Offers to sell energy and Ancillary Services.
4. Due to the above two features of our market design, in the DAM optimization:
5. For Generation Resources, the energy and AS co-optimization process allocates the offered MW capacity (constrained between LSL and HSL) between energy and Ancillary Services taking into account opportunity costs for energy and Ancillary Services. i.e. the prices (LMP-energy and MCPC-AS) incorporate opportunity costs
6. For Load Resources, as there is no energy component (demand), the energy and AS co-optimization process only allocates the offered MW capacity considering only AS offer(s)
7. If AS offers from Load Resources were cleared against the AS requirement from Load Resources, as there is no consideration of energy, then the corresponding AS MCPC will be determined solely by the marginal AS Offer from Load Resources – there is no opportunity cost for energy incorporated.

In the current ERCOT Nodal Market,

1. Load Resources are allowed to offer into any and all AS products.
2. AS Offers from Load Resources are cleared together with AS Offers from Generation Resources and thus,
3. The resultant MCPC reflects any opportunity costs for energy and other Ancillary Services. This decision was there even in the Zonal Market for RRS and seems to reflect a policy decision made by the stakeholders.
4. The equivalency ratio between MW offered for AS from Load Resources and MW offered for the same AS from Generation Resources is one (RAS = 1).

For the proposed future Ancillary Service product set, the same concepts (policy decisions) have been carried forth based on discussion at the FAST meetings,

1. PFR and FFR procurement is governed primarily by the constraint that incorporates the equivalency ratio R between PFR and FFR
2. This is similar to the way RRS is currently cleared if we consider R=1
3. Due to the equivalency ratio R, the MCPCRRS-LR for FFFR must reflect this ratio. Note: if in the current RRS, if there was a decision to incorporate the ratio R (which comes from reliability studies), then the MCPC for RRS from Load Resources must be R*MCPCRRS-Gen
4. Similarly for CR (CR1&CR2) and SR (SR1&SR2), the CR and SR Offers from Generation Resource and Load Resource are cleared together to meet the total CR and SR requirement respectively. This is done to allow for substitution between the AS offers from Generation and Load Resources.

AS Product / MCPC / Comments
PFR / ϕ / Shadow Price of the PFR+FFR1+FFR2 procurement constraint
FFR1 / Minimum R×ϕ,VOLL / R (equivalencing ratio of PFR to FFR) multiplied by the Shadow price of the PFR_FFR1+FFR2 procurement constraint. This FFR2 MCPC is capped at VOLL
FFR2 / Minimum R×ϕ,VOLL / R (equivalencing ratio of PFR to FFR) multiplied by the Shadow price of the PFR+FFR1+FFR2 procurement constraint. This FFR1 MCPC is capped at VOLL