An LP Formulation for Inter-Island
Trading of Regulation Services
EPOC, September 2008
E Grant Read
University of Canterbury
and
EGR Consulting Ltd
Disclaimer
This presentation relates to a draft formulation that may be
subject to revision
The views expressed are solely those of the author, and not
necessarily shared by Concept Consulting, the Electricity
Commission, or the System Operator
No opinion is expressed or implied as to whether this, or any
other formulation, should be implemented in New Zealand.
University of Canterbury
EGR Consulting Ltd
Outline
Ancillary service co- optimisation
Why is regulation different?
Issues to be accounted for
Simplifying assumptions
The mathematics of implementing regulation
Potential gains from inter-island trading
LP formulation for regulation trading
University of Canterbury
EGR Consulting Ltd
Ancillary service co-optimisation
The New Zealand electricity market pioneered cooptimisation of energy and ancillary services
Two contingency (raise) response services traded,
separately, for each AC island system
This was generalised in Australia
Six contingency (raise/lower) response services in a multiregional AC system
Plus “frequency keeping” (or “regulation”)
Plus (recently) limited modelling of constraints on HVDC
link to Tasmania
University of Canterbury
EGR Consulting Ltd
Why is regulation different?
Regulation (or “Frequency Keeping”) is:
About continuous response to essentially symmetric fluctuations in the
generation/load balance (maintaining constant frequency)
Not about occasional response to large asymmetric contingencies
(ie unit/link failure)
Regulation is not coordinated by providers responding
independently to a rapid frequency drop in an AC system
If shared between several providers, it is coordinated by:


Calculating and apportioning the required adjustment, and
Communicating this via “Automatic Generation Control” (AGC)
This calculated response can :
Take account of requirements in each AC island sub-system
Allow inter-island trading or sharing
University of Canterbury
EGR Consulting Ltd
Issues to be accounted for
Participant offers
Assumed to have the same form as for current ancillary services
(other markets use a different form)
Unit freeboard capacity
Providers must be able to swing production both up and down
AGC range limits
Units can only be controlled within limits of AGC equipment
Ramp rate limits
Providers must be able to swing production at an acceptable rate
Joint ramping restrictions
That rate may be limited by ramping for other purposes
HVDC freeboard capacity
Nett impact of two island swings can not breach constraints
University of Canterbury
EGR Consulting Ltd
Simplifying assumptions
We will ignore:
AGC implementation issues
No group dispatch
Intra-interval re-dispatch
Ramping limits
AGC range limits
Losses
We will assume:
Simple HVDC limits
A symmetric up/down regulation service
Constant participation factors in each dispatch interval
University of Canterbury
EGR Consulting Ltd
Implementing Regulation
PID feedback control algorithm calculates aggregate
island response requirement:
Proportional to current frequency deviation, and/or
Integral of recent frequency deviations, and/or
Differential of frequency deviation
Unit participation factors (PF) must allow for:
Proportional sharing of regulation duties within each island
Inter-island sharing of duties so as not to violate HVDC
limits
These do not appear directly in the LP formulation, but
yield useful insights
University of Canterbury
EGR Consulting Ltd
Participation Factors
Requirement for symmetric linear/proportional response is
actually quite restrictive
Response for each unit is a proportional share of aggregate island
response, RESPi, given by:
RESPS  PFSS  REQS  PFsn  REQN
So nett increase in South-North transfer must be:
SWINGSN  RESPS  REQS
 ( PFSS  1)  REQS  PFsn  REQN
And remember, this must be symmetric, irrespective of the direction
of HVDC transfer for energy purposes.
University of Canterbury
EGR Consulting Ltd
Response Requirements?
SI Response Requirement
NI Response
Requirement
MAX
Swing Implications of Island Requirements
Down
ZERO
MAX
Up
MAX
Down
ZERO
MAX
Up
University of Canterbury
EGR Consulting Ltd
BIG QUESTION?
Is inter-island trading of regulation supposed to
deliver gains from:
Regulation sharing, or
Regulation transfer?
They are both valuable, but
They are not the same, and
We can not use the same HVDC capacity for both
University of Canterbury
EGR Consulting Ltd
Base Case: No trading
Aggregate response in each island equals aggregate requirement
in that island:
PFSS  1
PFSN  0
PFNS  0 PFNN  1
In other words:
Each island meets its own requirement
There is no change to South-North transfer
And the market must clear:
.
MarketQuantityi  MAXReqi
University of Canterbury
for i  S , N
EGR Consulting Ltd
Limiting Case: Sharing only
With no nett transfer of regulation service, the market must still
clear :
MarketQuantityi  MAXReqi for i  S , N
But we can use HVDC swing capacity to share actual response
PFSS  ( 2MAXReq S -Hreg)/ 2MAXReq S
PFSN  Hreg/ 2MAXReq N
PFNS  Hreg/ 2MAXReq S
PFNN  ( 2MAXReq N  Hreg)/ 2MAXReq N
This keeps HVDC swing to:
ZERO when both island requirements move up/down together
HReg when island requirements move in opposite directions
University of Canterbury
EGR Consulting Ltd
Limiting Case: Transfer only
If nett transfer of regulation is allowed, ignoring benefits from
sharing, the market can clear :
MarketQuantityS  MarketQuantityN  MAXReq S  MAXReq N
If we use all the HVDC swing capacity, HReg, for (say) South to
North regulation transfer, we get:
PFSS  1
PFSN  Hreg/Req N
PFNS  0
PFNN  (MAXReq N  Hreg)/MAXR eq N
In other words, there is no reciprocal sharing, but:
SI meets all its own requirement, plus as much as possible of the NI
requirement, given HVDC swing capacity
NI ignores SI requirement, just meeting residual NI requirement
University of Canterbury
EGR Consulting Ltd
Trade-off
The above formulae can be generalised to allow
simultaneous sharing and transfer, but:
HReg must be allocated between transfer and sharing
 HReg ≤ Hcap…
the HVDC freeboard

Gains may be made by using AGC to develop a
competitive market within each island, but further:
Transfer reduces market purchase costs by allowing
purchase from the cheaper island, while
Sharing brings operational benefits by reducing probability
of extreme island responses
...although this only reduces market purchase costs if
island requirements are reduced to reflect this
University of Canterbury
EGR Consulting Ltd
NOTE
None of this depends on the underlying direction of
HVDC energy transfer
So, at any time we may have (for example):
Energy being traded from North to South, with
Regulation being traded from South to North
In real time, this means that:
Regulation service will be delivered from South to North,
By varying the fundamental North-South energy flow
(In principle this could involve reversing HVDC flow direction,
but we do not allow this because there is a “no-go” zone around zero
HVDC flow)
University of Canterbury
EGR Consulting Ltd
HVDC limits: HReg feasible region
Regulation
(HReg)
(Limit imposed by possible upswing
for regulation purposes)
Flow+Reg < JointMAX
Flow-Reg >JointMIN
(Limit imposed by possible
downswing for regulation purposes)
(Absolute limit on
acceptable up/downswing
for regulation purposes)
REGMAX
HVDC freeboard (HCAP)
JointMIN
JointMAX
Energy Flow
HVDC energy flow
LP may set Hreg <Hcap to avoid counter-productive excess “sharing”
LP formulation for regulation trading
(if sharing does not reduce requirements)
SI regulation
purchase
(SReg)
National
requirement
SN transfer limit
(no sharing)
SReq
+HCap
Balance point
(no transfer, only sharing)
SReq
SReq
-HCap
NS transfer limit
(no sharing)
NReq
-HCap
NReq
NReq
+HCap
NI regulation
purchase
(NReg)
.. and if sharing does reduce requirements
Balance point moves in to reflect gains from sharing spare
swing capacity not used by trading
SReg
SN limit
SReq
+ HCap
Balance
line
SReq
NS limit
SReq
- HCap
NReq
-HCap
NReq
NReq
+ HCap
NReg
Conclusion
This formulation should allow symmetrical inter-island trading of
regulation service
Constraints also developed to deal with ramping issues etc
Some issues to be resolved wrt interaction with SPD ramp limits, 5 minute (re-)
dispatch, HVDC state modelling, etc
An issue arises as to whether “sharing” should reduce national
requirements
The optimal solution does not necessarily use all available HVDC
swing capacity
Implementation is only possible if some form of AGC is actually
implemented
The costs and benefits have not been quantified (by me)
University of Canterbury
EGR Consulting Ltd