The document discusses research into optimizing the size and placement of battery storage systems in high voltage grids to better integrate renewable energy sources. The research aims to increase grid stability while reducing costs by using batteries to store excess renewable energy and supply power when renewable output is low. Linear programming is used to model the transmission grid and determine the optimal battery deployment to minimize generation and curtailment costs subject to operational constraints. Test cases on modified IEEE networks show storage can significantly reduce renewable curtailment and relieve transmission line congestion.

1. Laura Fiorini
Sassari, 26/05/2016
The integration of storage in HV-grids:
optimal use of renewable sources
Distributed Systems Group

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Introduction
Renewable Energy Sources (RES) has been encouraged significantly in order to fulfil the 2020
targets (e.g. reduction in greenhouse gas emission, improve the EU's energy efficiency and increase the
share of renewable energy)
Growing amount of variable and non-programmable energy
TSOs’ role more complex and challenging: secure and reliable electrical system.

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Research question
What is the optimal size and siting of storage systems
to increase the equilibrium of the system,
while reducing the operation costs?
SOURCE: http://www.toshiba.co.jp/sis/en

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Transmission grid as a graph
Generation plants
Loads
Batteries
Transmission lines
Sources
Sinks
Sources/
sinks
Edges
𝑃𝑠,𝑚𝑖𝑛 𝑃𝑠,𝑚𝑎𝑥 𝑃𝑟,𝑎𝑣
𝑐 𝑠
𝑙 𝑡,%
𝑆𝑜𝐶 𝑏,𝑚𝑖𝑛 𝑆𝑜𝐶 𝑏,𝑚𝑎𝑥 𝑆𝑜𝐶 𝑏,𝑗
𝑐ℎ 𝑏,𝑗 𝑑𝑖𝑠 𝑏,𝑗 𝜂 𝑐ℎ 𝜂 𝑑𝑖𝑠
𝑤 𝑢, 𝑣 𝑐 𝑢, 𝑣
Bus bars Inner nodes Flow conservation

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Objective function
𝑚𝑖𝑛
𝑗=0
95
𝑝∈𝑃
𝑐 𝑝 ∙ 𝑃𝑝,𝑗 +
𝑟∈𝑅
𝑐 𝑟 ∙ 𝑃𝑟,𝑗 + 𝑐𝑢𝑟𝑡_𝑐𝑜𝑠𝑡 ∙
𝑟∈𝑅
𝑃𝑟,𝑗,𝑎𝑣 − 𝑃𝑟,𝑗
Marginal costs
Equivalent marginal cost
of energy curtailment
(300 €/MWh)
96 time steps per
day Curtailed energy
subject to several linear constraints

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Implementation
• Software in Java SE 7 and GNU Math Prog
• Linear programming problem (simplex method)
• CPU Intel® CoreTMi5-2430M
• 2.40 GHz
• 8 Gb of RAM
• Ubuntu 14.04 LTS 64 bit.

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Metrics
• Most stressed lines
𝑈𝑡𝑖𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝐼𝑛𝑑𝑒𝑥 𝑈(𝑒) 𝑗 =
𝑓 𝑒,𝑗
𝑐 𝑒
∙ 100
𝐹𝑙𝑜𝑤 𝑏𝑎𝑠𝑒𝑑 𝐶𝑒𝑛𝑡𝑟𝑎𝑙𝑖𝑡𝑦 𝐼𝑛𝑑𝑒𝑥 𝐶 𝑓(𝑒) 𝑗 =
𝑓 𝑒,𝑗
𝑓 𝑡𝑜𝑡,𝑗
∙ 100
• Curtailment
𝐶𝑢𝑟𝑡𝑎𝑖𝑙𝑒𝑑 𝑒𝑛𝑒𝑟𝑔𝑦 0.25 𝑗=0
95
𝑟∈𝑅(𝑃𝑟,𝑗,𝑎𝑣 − 𝑃𝑟,𝑗)
• Batteries’ exploitation
𝑇𝑖𝑚𝑒 𝑠𝑡𝑒𝑝𝑠 𝑆𝑜𝐶 𝑏,𝑗 > 𝑆𝑜𝐶 𝑏,𝑚𝑖𝑛
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑜𝑓 𝑚𝑎𝑥𝑖𝑚𝑢𝑚 𝑒𝑛𝑒𝑟𝑔𝑦 𝑠𝑡𝑜𝑟𝑒𝑑 𝑆𝑜𝐶 𝑎𝑣
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑜𝑓 𝑚𝑎𝑥 𝑝𝑜𝑤𝑒𝑟 𝑖𝑛𝑗𝑒𝑐𝑡𝑒𝑑/𝑒𝑥𝑡𝑟𝑎𝑐𝑡𝑒𝑑 𝑐ℎ 𝑎𝑣

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Test case: modified version of IEEE-RTS 96
Solar-PV farms
• 44÷55MW
• Load buses
Wind farms
• 170÷400 MW
• Middle of longer lines
Renewable plants:
Total capacity up to 74% of
winter global demand
-25% edges’ capacity

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Load demand curves and renewable profiles
4000
5000
6000
7000
8000
9000
10000
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92
Loaddemand(MW)
Time (h/4)
18th January
18th April
18th July
17th October
8652 MW
9716 MW 9866 MW
8559 MW
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Power(p.u)
Time (h)
Solar-PV production
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0.80
0.90
1.00
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
Power(p.u)
Time (h)
Wind production

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Sizing and siting of batteries
Line’s capacity
MW
SoCb,max
MWh
chb,max
MW
K
h
#
131 131 19 6.89 4
375 375 75 6.89 6
TOTAL 2774 412 10
Energy Intensive
Random WindRanking

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Curtailment
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92
Power(MW)
Time (h/4)
Curtailed power Renewable production Total load demand Traditional production
• Without batteries

12. -800
-300
200
700
1200
1700
0
2000
4000
6000
8000
10000
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92
Power(MW)
Power(MW)
Time (h/4)
Curtailed power
Batteries' flows
Load curve
Adjusted
renewable
production
Distributed Systems Group
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Curtailment
• With batteries
No batteries Random Ranking Wind
40%
Total (MWh) 16 867.4 12 252.5 12 252.5 12 252.5
Reduction % -27.36 -27.36 -27.36
66%
Total (MWh) 52 408 40 945.5 40 966 41 003.1
Reduction % -21.87 -21.83 -21.76

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Centrality analysis
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
1 11 21 31 41 51 61 71 81 91 101 111 121
Averagecentralityindex(%)
Number of lines
40% No storage 40% Random
131-137
155-161
107-133
132-133
Linear trend
4/150 lines carry a
significant part of the global
flow (around 16%)

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Lines congestions
-600
-500
-400
-300
-200
-100
0
100
200
300
400
500
0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92
Power(MW)
Time (h/4)
batteries' flows Power flow without storage Power flow with storage

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Batteries utilization
Type 40% 66%
h/4 SoCav chav h/4 SoCav chav
MWh % MW MWh % MW
131/19 107 71.5 54.5 16.7 245 97.8 74.7 19.0
375/56 81 203.6 54.3 51.5 233 265.3 70.8 56.0
• Batteries utilization increases with percentage of RES installed in terms of time steps and stored
energy
• Energy capacity is rarely fully exploited

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Conclusions
• Introduction of energy-intensive batteries allows the grid to store energy when the renewable
availability is excessive, and use it at a later time to reduce the supply from conventional plants.
• Different policies of siting have no significant influence on the batteries’ performance.
• Introduction of storage appears to considerably reduce the congestion of a critical corridor, with
possible economical benefits.

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Storage and deregulated electricity market
Source: UCTE
PRODUCERS
Max profit
CONSUMERS
Variable demand
TSO
reliability

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New Research Question
What is the optimal size and siting of storage systems
to increase the reliability of the system?

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Simulation: 3 timelines
1. Forecasting operation
- Day-ahead market’s results define the unit commitment for each hour of the following day
- Expected renewable production is subtracted from the hourly load. The remaining load must
be met by the thermoelectric plants
2. Normal operation
- Actual generators’ state, wind speed, cloudiness and load forecasting error are drawn by MC
technic
- If spinning reserve is enough, the dispatching is very similar to the scheduled one
3. Emergency operation
- The balance is met by using the modulation power of the units in operation
- Fast generators are shut down (or turn on) if production is still too high (or too low)
- Batteries are put in service by TSO
- As last resorts, load is curtailed (or the excessive renewable energy)

20. Laura Fiorini
University of Groningen
Thank you
The integration of storage in HV-grids: optimal use of renewable sources
Distributed Systems Group

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Linear constraints…
• ∀𝑝 ∈ 𝑃 𝑃𝑝,𝑚𝑖𝑛 ≤ 𝑃𝑝,𝑗 ≤ 𝑃𝑝,𝑚𝑎𝑥
• ∀𝑟 ∈ 𝑅 0 ≤ 𝑃𝑟,𝑗 ≤ 𝑃𝑟,𝑗,𝑎𝑣 ≤ 𝑃𝑟,𝑚𝑎𝑥
• ∀ 𝑢, 𝑣 ∈ 𝐸 − 𝑐 𝑢, 𝑣 ≤ 𝑓 𝑢, 𝑣 ≤ 𝑐 𝑢, 𝑣
• ∀𝑡 ∈ 𝑇 𝑣∈Γ(𝑡) 𝑓(𝑢, 𝑡) 𝑗 = 𝑙 𝑡,𝑗
• ∀𝑛 ∈ 𝑁 𝑢,𝑛 ∈𝐸 𝑓 𝑢, 𝑛 𝑗 = 𝑛,𝑧 ∈𝐸 𝑓 𝑛, 𝑧 𝑗
• 𝑝∈𝑃 𝑃𝑝,𝑗 + 𝑟∈𝑅 𝑃𝑟,𝑗 + 𝑏∈𝐵 𝑓(𝑏, 𝑛) 𝑗 = 𝑡∈𝑇 𝑙 𝑡,𝑗
Transmission lines capacity
Fulfillment of power demand
Flow conservation
Balance between supply and
demand
Upper and lower power generation
limits

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…Linear constraints
• ∀𝑏 ∈ 𝐵 𝑖𝑓 𝑓 𝑏, 𝑛 > 0
𝑓(𝑏, 𝑛) 𝑗
𝜂 𝑑𝑖𝑠
≤ 𝑚𝑖𝑛 𝑐ℎ 𝑏,𝑚𝑎𝑥 ,
𝑆𝑜𝐶 𝑏,𝑗−1 − 𝑆𝑜𝐶 𝑏,𝑚𝑖𝑛
Δ𝑗
• ∀𝑏 ∈ 𝐵 𝑖𝑓 𝑓 𝑏, 𝑛 < 0
𝑓(𝑏, 𝑛) 𝑗 𝜂 𝑐ℎ ≤ 𝑚𝑖𝑛 𝑐ℎ 𝑏,𝑚𝑎𝑥 ,
𝑆𝑜𝐶 𝑏,𝑚𝑎𝑥−𝑆𝑜𝐶 𝑏,𝑗−1
Δ𝑗
• ∀𝑏 ∈ 𝐵 𝑆𝑜𝐶 𝑏,𝑚𝑖𝑛 ≤ 𝑆𝑜𝐶 𝑏,𝑗 ≤ 𝑆𝑜𝐶 𝑏,𝑚𝑎𝑥
• ∀𝑣 ∈ 𝑉s
−𝜋
2
≤ 𝜃 𝑣,𝑗 ≤
𝜋
2
• 𝜃𝑠,𝑗 = 0 s: slack node
Batteries’ state of charge
Power and energy flows
Phase angle constraints

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Centrality analysis (2)
3
3.5
4
4.5
5
5.5
10% 20% 30% 40% 50% 66% 74%
Averagecentralityindex(%)
RES installed capacity
131-137 155-161 107-113
2.6
2.7
2.8
2.9
3
3.1
3.2
30% 40% 50% 66% 74%
Averagecentralityindex(%)
RES installed capacity
152-173 128-172