Transcript Security Constrained Economic Dispatch Resmi Surendran

Security Constrained
Economic Dispatch
Resmi
Surendran
January 21, 2010
Outline



Overview of the SCED
Texas two step
SCED optimization
Security Constrained Economic Dispatch
• SCED evaluates Energy Offer Curves to produce a least cost
dispatch of On-Line Resources while respecting transmission
and generation constraints.
– Manages the transmission system reliability and security
– Operates within the physical constraints of the system
– Meets the power balance while maintaining system reliability at
minimum cost
• SCED is executed:
– Every 5 minutes (at a minimum)
– May be initiated more often by an ERCOT operator or other
ERCOT systems
Components
Different
components of the
RT system
SCED – Input /Output
• SCED Inputs:
– Energy Offer Curves
– Output Schedule
– Mitigated offer cap /floor curves
– Telemetry
– Resource limits
– Network constraints flow and limit
– Competitive constraints
• SCED outputs:
• LMPs
• Resource-Specific Base Points
Energy Offer Curve
$/MWH
Real Price Curve
Piecewise Linear (ERCOT)
Stepwise Approximation
Pmin
Pmax
MW
Proxy Energy Offer Curve: Resource without Full Offer Range
QSE-submitted Energy Offer Curves are extended from 0MW to infinity;
1000.00 $/MWh
999.99 $/MWh
Energy Offer
Price
($/MWh)
HSL
LSL
0
Quantity (MW)
-249.99 $/MWh
-250.00 $/MWh
Epsilon
Proxy Energy Offer Curve: Resource with Output Schedule
Proxy energy curves are created for resources with Output Schedules and
no Incremental/Decremental Offer Curves;
Price
($/MWh)
1000.00 $/MWh
999.99 $/MWh
Ooutput
Schedule
LSL
HSL
0
-249.99 $/MWh
Quantity (MW)
-250.00 $/MWh
Epsilon
Proxy Energy Offer Curve: Wind Powered Resource without Offer
Proxy energy curves are also created for wind-powered resources that
have not submitted Energy Offer Curves.
Price
($/MWh)
1000.00 $/MWh
LSL
HSL
0
-249.99 $/MWh
Quantity (MW)
-250.00 $/MWh
Epsilon
Resource Limits
Resource Limits calculated by RLC is used in SCED and LFC
Resource Limits – Change in HDL/LDL
Resource Limits – Change in HDL/LDL
Resource Limits – Change in HDL/LDL
Constraints
• Generated by doing contingency analysis based on
State Estimator results
• Removes constraints that are resolved by SPS and
RAPs
• Constraints are passed to SCED only if approved by
operator in Transmission Constraint Manager (TCM)
• Operator removes constraints that for which there are no
Market solution or which has temporary ction plan
developed due to some outages
• Both competitive and non-competitive constraints are
passed to SCED from TCM.
June, 2009
SCED – The Texas Two Step
SCED optimization executes twice each cycle
• To ensure competition and reduce Market Power
Price
($/MWh)
Constraints are classified beforehand
• Competitive
• Non-Competitive
Original Energy Offer
Curve
Capped Offer
Curve
Reference LMP
Mitigated Offer
Cap curve
Mitigated Offer
Floor
Quantity (MW)
0
Step 1
• Uses the Energy Offer Curves for all On-Line Generation Resources
• Observes the limits of the Competitive Constraints only
• Determines “Reference LMPs“
Step 2
• Observes limits of all Competitive and Non-Competitive Constraints
• The Energy Offer Curve for any on-line Resource is capped at the
greater of the Reference LMP from Step 1 or the Mitigated Offer Cap.
• The Energy Offer Curve for any on-line Resource is bounded at the
lesser of the Reference LMP from Step 1 or the Mitigated Offer Floor.
May 23, 2016
Two-Step SCED-Step 1:
• Uses the Energy Offer Curves for all On-Line
Generation Resources
• Submitted or created by ERCOT
• Only observes the limits of the Competitive
Constraints only
• Determines “Reference LMPs“
Data Processing between SCED Step 1 and Step 2
Price
($/MWh)
Original Energy Offer
Curve
Capped Offer
Curve
Reference LMP
Mitigated Offer
Cap curve
Mitigated Offer
Floor
Quantity (MW)
0
(1)Cap the Energy Offer Curves at the greater of the Reference LMP at the
Resource Node or the Mitigated Offer Cap curve
(2) Bound it at the lesser of the Reference LMP at the Resource Node or the
Mitigated Offer Floor.
Two-Step SCED-Step 2:
• Uses the capped and bounded Energy Offer curve
• Observes limits of all Competitive and Non-Competitive
Constraints
• Creates LMPs, Base Points, Shadow Prices for the
constraints etc
SCED - Two-Step
Initial data processing
SCED Two-step
Outputs
Step 1 (only Competitive
Constraints)
Reference Locational
Marginal Prices (LMPs)
Data processing between
step 1 and step 2
Capped and bounded
energy offer curves
Step 2 (both Competitive
and Non-Competitive
Constraints)
Base Points & final LMPs
Settlement Point Prices (SPP)
SCED Objective
Minimize
Cost of dispatching generation
integral (offer cost * MW dispatched)
+ Penalty for violating Power Balance constraint
sum (Penalty cost * violation amount)
+ Penalty for violating transmission constraint
sum (Penalty cost * violation amount)
SCED Constraints
• Power Balance Constraint
sum (Base Point) + under gen slack – over gen slack
= Generation to be dispatched
• Transmission constraint
sum( Shift Factor * Base Point) – violation slack ≤ limit
• Ramp Limit constraint
LDL ≤ Base Point ≤ HDL
Power Balance Penalty Curve
MW
violation
Violation
<1
Price
$/MWh
200
1≤
Violation
<5
250
5≤
Violation
< 10
300
10 ≤
Violation
< 20
400
20 ≤
Violation
< 30
500
30 ≤
Violation
< 40
1000
40 ≤
Violation
< 50
2250
50 ≤
Violation
< 100000
3001
The SCED under generation Power Balance Penalty Curve will be capped at 2251 until the
HCAP becomes 3000.
Power Balance Penalty
• Power Balance Penalty is the maximum cost paid for one
addition/less MW of generation to meet the load. i.e. It caps
the energy component of the LMP.
• It sets the energy price in case of scarcity
• ERCOT doesn’t have price caps
• SWCAP caps the offers and not the prices
• i.e. with SWCAP at $180 and the Power Balance Penalty
curve up to 3000 the system wide prices could go up to 3000
and higher than 3000 in specific areas if there is congestion
Transmission Constraint Maximum Shadow Prices
Default maximum Shadow Price are assigned to monitored
elements based on voltage level. These could be assigned
higher or lower values based on operational experience.
Base Case:
$5,000/MW
Generic constraints : $5,000/MW
Post Contingency
345 kV:
$4,500/MW
138 kV:
$3,500/MW
69 kV:
$2,800/MW
Shadow Price
 Shadow Price of a constraint is the increase in the objective when
the constraint limit is reduced by 1 MW
 Maximum Shadow Price is set as the coefficient of the slack variable
corresponding to the constraint in the SCED objective function. i.e. it
is the maximum allowed increase in production cost for resolving
1MW of the constraint.
 Objective = Min ( Cost of generation dispatch
+ Sum ( Maximum Shadow Price * Slack variable)
 LMP at any electrical bus is
Energy Component = Shadow price of Power Balance constraint
+
Congestion Component = - sum ( Shift Factor * Shadow Price for
the constraint )
LMP during Congestion
LMP     SF line  SP line
line
Resource moved down for congestion
Offer Pr iceunit[$ / MWh ]
max
Offer Pr iceunit
Lambda
LMP cong
LMP
cong
Punit
min
Offer Pr iceunit
Punit[MW ]
min
Punit
opt
Punit
max
Punit
LMP during Congestion
LMP     SF line  SP line
line
Resource moved up for congestion
Offer Pr iceunit[$ / MWh ]
max
Offer Pr iceunit
LMP
LMP cong
Lambda
cong
Punit
min
Offer Pr iceunit
Punit[MW ]
min
Punit
opt
Punit
max
Punit
Thanks!
Appendix
SCED Mathematical Formulation in Theory
Minimize
Sumseg&unit { Ccost = ½ ∙ aslope ∙ P2unit + Punit∙ bconst + cmincost }
Subject to:
sumseg&unit { Punit } = Pload
sumseg&unit { SFunit/line ∙ Punit } ≤ Limitline
Pmin ≤ sumseg{Punit} ≤ Pmax
- Power balance
- Transmission limits
- Unit limits
Optimality Conditions
Lagrange Function:
L = sumseg&unit { ½ ∙ aslope ∙ P2unit + Punit∙ bconst + cmincost } +
λ ∙ (Pload – sumseg&unit { Punit }) +
sumline {µline ∙ (Limitline – sumseg&unit { SFunit/line ∙ Punit } ) }
Optimality Conditions:
(1)d L /dPunit = aslope ∙ Punit + bconst - λ - sumline {µline ∙ SFunit/line } = 0
(2)sumseg&unit { Punit } = Pload
- Power balance
(3)sumseg&unit { SFunit/line ∙ Punit } + Fslack = Limitline
- Transmission limits
(4) µline ∙ Fslack = 0
- complementary slackness
(5)Pmin ≤ sumseg {Punit }≤ Pmax ;
(6)Fslack ≥ 0
SCED Objective
Objective =
Min { Cost of generation dispatch + Sum ( Max Shadow Price * Slack variable)}
[ EnergyCurve Pr ice
r ,offer, seg ,t
Generation
dispatch cost
* Re sSegDispMW r ,offer,seg ,t
r ,offer, seg
 0.5 * EnergyCurveSloper ,offer,seg ,t * (Re sSegDispMW r ,offer,seg ,t )2 ]
Slack
Variable
Max Shadow
Price
+
Slack
Variable
PenaltyCostENG * ( EnergySlackUpMWt  EnergySlackDnMWt ) +
TranPenaltyCost
c ,t
* TranSlackMWc ,t
c
Max Shadow
Price
Slack
Variable
SCED Constraints
Power Balance Constraints:
 Re sDispMW
r ,t
 EnergySlackUpMWt  EnergySlackDnMWt  Loadt
r
Transmission Network Constraints:
Resource Constraints:
( SPdemand,t )
 SF
r , c,t
* Re sDispMW r ,t
 TranSlackMWc ,t  lim it c ,t
r
( SPc ,t )
0  Re sSegDispMW r ,offer, seg ,t  Re sOfferSegSizer ,offer, seg ,t
Re sDispMW r ,t
  Re sSegDispMW r ,offer, seg ,t
seg
Ramp Rate Constraints (HDL, LDL):
LDL r ,t  Re sDispMW r ,t
 HDL r ,t
Caculate LMP at each bus at target time t
LMPbus,t  SPdemand,t   SFbus,c ,t * SP c ,t
c
• LMPs are used to calculate Settlement Point Prices.
Calculate Settlement Point Price (SPP)
Types of Settlement Points:
– Resource Nodes
– Load Zones
– Hubs
Resource Node SPP
Resource Nodes
• A Resource Node is an Electrical Bus
where a Generation Resource’s
measured output is settled.
The Real-Time Settlement Point Price for a Resource Node Settlement
Point is a Base-Point time-weighted average of the Real-Time LMPs.
RTSPP =  y (RNWF y * RTLMP y)
Where the Resource Node weighting factor is:
RNWFy  [Max (0.001, r B Pr, y ) * TLMPy ] /[  y ( Max (0.001, r B Pr, y ) * TLMPy )]
y
r
- A SCED interval in the 15-minute Settlement Interval.
- A Resource at the Resource Node.
Load Zone
Load Zones
A Load Zone is a group of Electrical Buses, each with a
load, which are assigned to the same zone for
settlement purposes.
• Three types of Load Zones
– Competitive Load Zones
◦ Four congestion zones in effect during the
2003 ERCOT market
– Non-Opt in Entity (NOIE) Load Zones
– DC Tie Load Zones
Load Zone SPP
• A, B, C, and D are all electrical buses
within Load Zone
• Dollar amounts represent LMPs
Total Load = 10 MW
Percentage of load at each bus
A: 2 / 10 = 20%
B: 2 / 10 = 20%
C: 1 / 10 = 10%
D: 5 / 10 = 50%
$4
2 MW
$20
1 MW
$1
2 MW
$10
5 MW
Load-weighted avg. of LMPs at all buses
= (20% * LMPbus A ) + (20% * LMPbus B)
+ (10% * LMPbus C) + (50% * LMPbus D)
= (20% * $4 ) + (20% * $1 )
+ (10% * $20 ) + (50% * $10 )
= $0.80 + $0.20 + $2.00 + $5.00
= $8.00
Calculation of Load Zone Settlement Point Prices
– Load-weighted average of LMPs at all buses assigned to that Zone
– In Real-Time, LMPs will also be time-weighted.
HUBs
Hubs
• Hubs are defined by the Protocols
– Hubs consist of Hub Buses
– Hub Buses consist of one or more electrical buses
within a single substation.
• Hubs are only used for trading purposes
HUB SPP
• The blue boxes represent Hub
Buses within the Hub
• The orange rectangles represent
Electrical buses within the Hub
Buses
First, determine simple averages for all
Hub Buses:
A and D only have one bus:
LMPs
For Hub Bus A = $5
For Hub Bus D = $20
LMPs
Hub Bus B = ($8 + $12) / 2 = $10
Hub Bus C = ($4 + $9 + $2) / 3 = $5
Hub Settlement Point Price
= (LMPA + LMPB + LMPC + LMPD) / 4
= ($5 + $10 + $5 + $20) / 4
= $40 / 4
= $10
LMP = $5
LMP = $8
LMP = $12
LMP = $4
LMP = $20
LMP = $9
LMP = $2
Calculation of Hub Settlement Point
Prices
– Simple average of Hub Bus LMPs
– Hub Bus LMP is the simple average of LMPs at
Electrical Buses within the Hub Bus.
– In Real-Time, LMPs will also be time-weighted.