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Methods and Processes for Hydro-thermalScheduling
Prof. Olav Bjarte FossoDept of Electrical Power EngineeringNorwegian University of Science and Technology (NTNU)
Hydro Power in Norway
• Electricity: ~ 100% hydro power• Largest in Europe, nr 6 in the
world• 30% of hydro power cap. In
European Union (50 % of storage)• Installed capacity : ~ 29000 MW• Generation average,: ~ 125 TWh• Consumption: ~ 124 TWh• Average inflow +- 20 %
4
Real-world problems characterized by
• Large physical models (Geographical and time horizon)• Non-linear and non-convex with many local optimums
– Final solution may depend on the starting point– Global optimal solution never guaranteed
• Binary variables complicates the solution process and mayin some parts of the complete problem be important
• User-experience and ”non-mathematical” constraints (rule-based and state dependent) may be important
• Hydro scheduling is no exception regarding these problems
5
Challenges in hydro scheduling
• Cascaded reservoir systems with different storage capacitycouples the decisions between the generation plants
• The storage capacity and variable inflow couples thedecisons over time– Inflow range in Norwegian system: 95 – 140 TWh (Average
load 125 TWh)– Significant storage capacity requires long planning horizons
(Typical up to 5 years)– Other system characteristics dictates the time resolution
• The relative size of the hydro system compared to thethermal system call for different co-ordination principles(Peak shaving – similar size – hydro-dominated)
• Multi state• Typical more than 1000 different storages in an fundamental market model
• Very varying storage size ( from about three years to hours)• Stochastic multidimensional
• Inflow, wind, radiation• Correlated in time an space
• Historical observations• Short-term forecast, snow pack information
• Exogenous prices• Multi stage
• Weekly (split into intraweek time step)• Several year long planning horizon
• Transmission constrained• Several thousand nodes
Large scale stochastic dynamic optimization
Multi-area model ofNordic countries
V -S Ø
V -M I
H A L
T e l
Ø -L
G /L
H e l
T ro
N -M I
S -Ø -L
S -L
D Kø s t
E s tla n d
L a tv ia
L ita u e n
P o le nN e d
N o rdS v er ig e
F in
F in la n d
S ydS v er ig e
D Kv e s t
T y s k la n dE F I
Scheduling Hierarchy(Norway – present practice)
Detailed simulation (1 -12 weeks)Verification of plans with
non-linear simulation
Long term scheduling ( 1-5 years)Stochastic models for optimazation
and simulation
Reservoir levelsMarginal water values
Seasonal scheduling (3-18 months)Multi-scenario
Deterministic optimization models
Marginal water valuesReservoir boundaries
Short term scheduling (1-2 weeks)Deterministic optimization models
Plans
9
Methods in use
• SDP (Long-term)– Aggregated– Stochastic
• SDDP (Long / Mid-term)– Detailed– Stochastic
• Scenario-based (Mid-term)– Deterministic
• Deterministic(Short-term)– LP– MIP– DP– Lagrange relaxation
Simulation of markets with storages and weather uncertainty
Storage possibilities Strategy by (SDP/SDDP) Markets and prices
Simulating markets (LP)Stochastic, inflowsolar, wind etc
Supply/demand data
Water value
Simulation
System operation
Storage utilization
Courtesy: Birger Mo, SINTEF
12
Marginal water values calculated for all pointsover the time horizon
20·1 + 28·5 + 30·9 + 35·20 + 40·9 + 60·5 + 70·1
4
2
070
60
1 2Tm7
Tm6
20 Tm128 Tm230 Tm335 Tm440 Tm5
92n-51
94
96
98100
Reservoir [%]
n2,0
n-1
1,51,00,80,5
0,0
0,0
48 49 50 51 52 uke
Iterate over the time horizon (n-52, n)
(1+ 5 + 9 + 20 + 9 + 5 + 1)VV4 = = 37,2 [øre/kWh]
13
Illustration of water values
00
0,8
1,0
Reservoir content [GWh]
week50 100 150 200
1,2
0,6
0,4
0,2
øre/kWh0
1020
3040
Application example – Integration of balancingmarkets
Detailed water course descriptionAbout 300 thermal power plantsTransmission corridors (NTC)
Fundamentalmodel
Denmark, Finland, Norway, SwedenGermany, Netherlands, Belgium
NorthernEurope
2010 – current state of the system2020 – a future state of the system
Systemscenarios
Hydrology (Inflow)TemperatureWind speed
Severalclimatic years
16
Coupling between planning levels
• Different models at different planning levels complicates thecoupling and information flow
• The next level of analysis does not necessarily get input data ofsufficient precision
• Aggregation / disaggregation challenges
• Coupling principles:– Price coupling (individual / aggregated)– Volume coupling
Coupling principleIncremental water values
Shorter-term Longer-term
Reservoirlevel Flexible reservoir drawdown
with possibility to move waterbetween periods
Puts certain requirements on the methods usedin both periods
Short-term hydro power optimization
20
Network formulation – short-term
InflowReservoir content
Discharge
Time intervalls
Reservoirbalances
22
Linear programming
• Linear models are fundamental for most the modeling andsimulation
• The experience shows that most of the physical problemscan be solved by using linear models as building blocks
• Non-linearities can be handles by:– Piece-wise linear segments– Iteration for successive refinement– Integer variable and to check combinations
• Algorithms are available to solve very large problems fast
Coupling principleVolume coupling
Shorter-term Longer-term
Reservoirlevel Specified reservoir
endpoint level
Less requirements to the methods used
Linearization
P
Q
Pmin Pbest
Pmax
Q
Pmin P1
Pmax
Q
Pmin P(n-1)
Pmax
P P
1. iteration 2. iteration n. iteration
Full description Full description Incrementaldescription
Short-term hydro power optimization
Norway - an energy nation…….
3 generations of energy development: Hydro Power, Petroleum, Renewables
0
1000
2000
3000
4000
5000
6000
7000
Meaninflow
Demand
GWh/week
Week
Max.inflow
Min.inflow
Problem:Optimal use of reservoirs with:• stochastic precipitation, inflow, prices• seasonal variations• reservoirs with multiple years storage
Resource – demand profiles
5 1 0 1 5 20 2 5 3 0 35 4 0 4 5 5 0
1
2
3
4
5
6
W e ek n o .
Nor
mal
ised
wee
kly
data
[%]
H yd ro in flow M id tn o rgeH yd ro in flow N o rw a yD e ma n d N o rw a yD e ma n d M id tn o rg eW in d En ergy
Complementarity: Wind Power / Hydro vs. Demand
28
Norwegian hydropower for balancing• The reservoirs are natural lakes
• Multi-year reservoirs• Largest lake stores 8 TWh• Total 84 TWh reservior capacity
• Balancing capacity estimates 2030• 29 GW installed at present• + 10 GW with larger tunnels and
generators• + 20 GW pumped storage• 30 GW total new capacity
• Within todays environmentallimits
• Requires more transmission capacityCourtesy: Birger Mo / CEDREN