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Stochastic optimization of distributed
energy resources in smart grids
Joao Soares, Zita Vale GECAD / IPP – Polytechnic of Porto
1
Paper No: 15PESGM2908
Outline
• Introduction • Energy Resource Management • Uncertainty in ERM • ERM considering uncertainty • Case study
– Smart distribution network– scenario for year 2040
2
Introduction 3
Wind Power
Solar Power
Energy Storage
Electric Vehicles
Utility Grid
Demand Response
Loads
The network can be islanded from the Utility Grid
Market
VPP
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Energy Resource Management
Resource Management
(day-ahead, hour-ahead, real-time)
Resource Forecasting Island Mode Capability
Demand Response Self-healing Capability
Energy Resource Management • Market transactions • Contracts with suppliers • Generation • Demand Response • Storage • Electric vehicle • Power Flow
Real Time data acquisition Loads monitoring Generation monitoring Storage levels
Self-healing Capability
Direct Load Control
Resource Forecasting
Market Day-ahead scheduling
Hour-ahead scheduling
Real-time scheduling
24h
1h
……
Island Mode Capability
Demand Response
Uncertainty in ERM • Why considering uncertainty in ERM?
Forecast errors
– Wind (wind variation, weather conditions) – Solar PV (irradiation, clouds, etc.) – Load demand (user’s behavior, buildings, etc.) – EVs (user’s behavior, charging patterns, location)
5
Wind and Solar Scenarios • The forecasting error varies with the geographical location,
weather conditions and time horizon; • The wind scenarios are independent with solar scenarios:
– Assuming the errors follow a normal distribution – Wind and Solar: Monte Carlo simulations can generate a
set scenarios; – Scenario reduction techniques (e.g. clustering)
6
Pinson, Pierre, et al. "From probabilistic forecasts to statistical scenarios of short-term wind power production." Wind energy 12.1 (2009): 51-62. Su, Wencong, Jianhui Wang, and Jaehyung Roh. "Stochastic energy scheduling in microgrids with intermittent renewable energy resources." Smart Grid, IEEE Transactions on 5.4 (2014): 1876-1883. Botterud, Audun, et al. "Use of wind power forecasting in operational decisions." Argonne National Laboratory (2011).
Wind and Solar Scenarios 7
Botterud, Audun, et al. "Use of wind power forecasting in operational decisions." Argonne National Laboratory (2011).
Electric Vehicles uncertainty
• Why is uncertainty present?
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– Location in the grid, e.g. network bus, network zone
– Energy demand
– Users’ behavior but diferent from regular load
– When, where and how much?
Electric Vehicles uncertainty
• Challenge: Reliable user’s behavior data
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• Possible approach: cloud-based information
• Near future?
Cloud-based Information 10
Cloud-based Information 11
Data Parameters Description of data structure
Type of data Data class Size per record Vehicle’s ID Identification of EV int32 4 bytes
Location GPS location (latitude
and longitude and timestamp)
Double 3x8 bytes
Battery status Battery capacity; SOC level int32 2x4 bytes
Connected to outlet Connected (0/1); Outlet ID if available Binary and int32 1 + 4 bytes
Charged energy Charged energy; Start and end timestamp int32 and Double 4 + 2x8 bytes
Charge rate Charging power int32 4 bytes
Trip consumptions Energy consumption in the trip; Start and end
timestamp int32 and Double 4 + 2x8 bytes
• Table shows a very simple data scheme for the information that could be transmitted between the EVs and the cloud
• How much data will be stored?
Cloud-based Information 12
• Data creation (estimation per year)
0
0
1
5
25
125
625
3.125
10k 100k 500k 10m
Tera
byte
s (T
B)
Number of EVs
Cloud data impact (annually)
5 min 1 min 15 s
1600 TB
80 TB
• Data creation (estimation per year)
Cloud-based Information 13
• How can this concept be useful?
• …for stochastic scenarios generation
• So to motivate further research…
Stochastic Scenario Generation 14
• The day-ahead scenarios can provide information about the EVs’ locations for the next day, considering the information contained in the cloud (historic data);
• The hour-ahead scenarios takes into account the actual EVs’ location, and uses the historical data with similar last-hours pattern to generate a set of possible scenarios for the next hour.
Monte Carlo Simulation • Values must be filtered (e.g. vehicles’ locations) and according
to rules: – Weekends/weekdays – Time horizon (day-ahead, hour-ahead) – Holidays – Special Events (football day, music festival, etc.) – Traffic conditions
• To reduce computational burden, the historical data may be shrinked: – For example: 4 periods, each period representing 6 hours; – The reduced data is an important aspect of the methodology efficient use; – A matrix is built with the historical connections to the grid (for instance
outlet/network bus) of a given EV.
15
Tree combination 16
1 - Scenarios can be generated using forecast errors 2- Combination (load, wind, EVs) to obtain the final probability 3- Scenario reduction (just a small set of representative scenarios)
Pinson, Pierre, et al. "From probabilistic forecasts to statistical scenarios of short-term wind power production." Wind energy 12.1 (2009): 51-62. Su, Wencong, Jianhui Wang, and Jaehyung Roh. "Stochastic energy scheduling in microgrids with intermittent renewable energy resources." Smart Grid, IEEE Transactions on 5.4 (2014): 1876-1883.
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ForecastLoad L t Load L t Load L t
ForecastDG DG t GCP DG t DG DG t DG DG t
ForecastTrip EV t Trip EV t Trip EV t
P P P
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ωω ω
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Uncertainty modeling in ERM 17
Consumption Forecast errors: Normal distribution function
Only uncertainty in travel forecast considered in this
formulation Distributed generation
EVs trip
Generation curtailed power
Forecast Scenario
generation index ω representing each considered scenario
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Energy Resources Management
• Objective function
18
Generation curtailed power
Vehicles charge
Distributed generation External suppliers
Vehicles discharge
Non-supplied demand
Minimize the operation cost
Probability of scenario ω
scenario
Uncertainty
Energy Resources Management • Constraints:
– Power balance – Voltage limits – Line thermal limits – Resource limits
• DG units • External suppliers • EVs • …
19
Energy Resources Management • Constraints for each scenario :
– Network power active power balance at bus i in period t
– Network power reactive power balance at bus i in period t
20
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NNi i i
Di t Load L t NSD L t Ch EV tL EV
G V V V G B P P
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ω ω ω ω ω ω ω
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= =
=
− − = −
= +
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= − ∀ ∈ ∀ ∈ ∀ ∈
∑
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𝜔𝜔
Energy Resources Management • Constraints:
– Voltage magnitude and angle at bus i in period t
– Line thermal limits at line k in period t
21
( ) { } { } { }, 1, , ; 1, , ; 1, ,i iMin Max Bi tV V V N t T i Nωω ω≤ ≤ ∀ ∈ ∀ ∈ ∀ ∈
( ) { } { }, 1,..., ; 1,...,i iMin Max Bi t t T i Nωθ θ θ≤ ≤ ∀ ∈ ∀ ∈
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N t T i N
ω ω ω ω
ω ω ω ω
ωω
× × − + × ≤
× × − + × ≤ ∀ ∈ ∀ ∈ ∀ ∈
Energy Resources Management • Constraints:
– Active and reactive generation limit for the DG unit in period t
– Active and reactive generation limit for the external supplier SP in period t
– Reactive demand power for the load L in period t
22
( ) ( ) ( ) ( ) ( ) { } { }, , , , , , , , , , 1,..., ; 1,..., DGMin DG t DG DG t DG DG t Max DG t DG DG tP X P P X t T DG Nω ω ω ω ω× ≤ ≤ × ∀ ∈ ∀ ∈
( ) ( ) ( ) ( ) ( ) { } { }, , , , , , , , , , 1,..., ; 1,..., DGMin DG t DG DG t DG DG t Max DG t DG DG tQ X Q Q X t T DG Nω ω ω ω ω× ≤ ≤ × ∀ ∈ ∀ ∈
{ } { }( , ) ( , ) ; 1,..., ; 1,...,SP SP t SPMax SP t SPP P t T SP N≤ ∀ ∈ ∀ ∈
{ } { }( , ) ( , ) ; 1,..., ; 1,...,SP SP t SPMax SP t SPQ Q t T SP N≤ ∀ ∈ ∀ ∈
( ) { } { }( , ) ( , ) ( , ) ( , ) ( , ) tan 1,..., ; 1,...,Load L t Load L t Red L t Cut L t NSD L t LQ P P P P t T L Nϕ= − − − × ∀ ∈ ∀ ∈
Energy Resources Management • Constraints:
– Energy stored at the end of period t for each EV
– Minimum and maximum stored energy in the electric vehicle V in period t
23
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Stored EV t Stored EV t Trip EV t c EV Ch EV t Dch EV td EV
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≤ ≤
∀ ∈ ∀ ∈ ∀ ∈
Energy Resources Management • Constraints:
– Charge and discharge processes are not simultaneous in the
electric vehicle V in period t
– Charge and discharge limits of the electric vehicle V in period t
24
( ) ( )
{ } { } { }, , , , 1
1, , ; 1, , ; 1, ,Ch EV t Dch EV t
EV
X X
N t T EV Nω ω
ωω
+ ≤
∀ ∈ ∀ ∈ ∀ ∈
{ } { }( , , ) ( , ) ( , , ) 1,..., ; 1,...,Ch V t ChLimit V t Ch V t VP P X t T V Nω ω≤ × ∀ ∈ ∀ ∈
{ } { }( , , ) ( , ) ( , , ) 1,..., ; 1,...,Dch V t DchLimit V t Dch V t VP P X t T V Nω ω≤ × ∀ ∈ ∀ ∈
Case study
• Goal: operation cost minimization • 33-bus distribution network – scenario for year 2040 • High DER penetration
– 66 DG units – 218 consumers – 1000 electric vehicles
• 10 external suppliers
25
Case study - Forecast 26
Production and consumption
Energy trips of EVs
Several scenarios were based on the deviations on these forecast resources:
• 5% consumers demand • 15% renewable DGs
• 10% EVs trip
Case study - Results
• Energy resource scheduling results
• Scheduled power for the external suppliers
27
Deterministic approach Stochastic approach Cost (m.u.) 6979.31 7069.82 +1.3%
External suppliers represent around 49% of the necessary energy
consumption in the grid
Case study - Results • Energy resource scheduling results – stochastic approach
28
Production
Consumption
Computational burden
29
Deterministic (1 scenario) Stochastic approach 33-bus 1000 EVs 6 hours 1 week
180-bus 6000 EVs 2 weeks ???
• The execution time refers to full AC model using GAMS (MINLP)
• The DC model is much faster because it is linear but not considers losses
• Centralized scheme is hard to solve
• EVs treated individually are the problem in ERM (it may be aggregated)
• Decentralized scheme is an alternative
• Metaheuristics can reduce the 1 scenario problem to seconds to minutes
• The need for metaheuristics in stochastic optimization is important
Stochastic optimization of distributed
energy resources in smart grids
Joao Soares, Zita Vale GECAD / IPP – Polytechnic of Porto
30
Paper No: 15PESGM2908
• Following the same cloud-based approach
• Cloud data can be used to obtain users’ charging/driving behavior
• It can be assumed to follow a normal distribution with mean and standard deviation for every period.
31
Energy demand
