---
title: 2019_Optimal Scheduling of Energy Storage System for Peak Reduction Using a Prediction Interval
tags:  #機械学習  
author: [小平　大輔](https://convert.docswell.com/user/daisuke-kodaira)
site: [Docswell](https://www.docswell.com/)
thumbnail: https://bcdn.docswell.com/page/ZP7R3N4LE9.jpg?width=480
description: Control of Smart Grid and Renewable Energy Systems - CSGRES 2019
published: March 31, 22
canonical: https://convert.docswell.com/s/daisuke-kodaira/5XGWRZ-2022-03-31-093247
---
# Page. 1

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1
Optimal Scheduling of Energy
Storage System for Peak Reduction
Using a Prediction Interval
Daisuke Kodaira
e-mail: daisuke.kodaira03@gmail.com


# Page. 2

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2
Peak shaving using Energy Storage System (ESS)
Demand
[MW]
Objective:
• Peak shaving on distribution network (22.9kV) by ESSs
[hour]
0
6
12
18
24


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3
System configuration
• Two Energy Storage Systems (batteries) are installed in the field
• The ESSs are controlled by remote. The schedule is determined by the network
operator 24 hours ahead
Substation to
ESS1: 5.8 km
ESS1 to ESS2:
9.5 km
Load
22.9 kV
ESS2 to end of
line: 7.4 km
PV
ESS1
PCS: 0.75 MW
Battery: 1.5 MWh
Network operator controls
ESSs by remote
ESS2
PCS: 1 MW
Battery: 2 MWh


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4


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The steps of peak shaving
Evaluation
Load
Prediction
• Load Prediction
- How much is the peak tomorrow?
- When will the peak comes tomorrow?
• ESS scheduling
- What is the best schedule of ESSs?
ESS Scheduling
• Evaluation
- How much we shaved the peak?


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6
Load Prediction - problem
The prediction is not always reliable….
Load on feeder
MW
Observed Load
“Prediction tells us
we don’t need to
operate ESS for peak”
Line capacity
10
Predicted
Load
6
0
1 2 3
････
23 hour
Now
ESS cannot reduce the peak appropriately
in case the prediction has huge error


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Load Prediction - solution
The concept of probability is necessary to evaluate the risk
Prediction Interval (PI)
Line capacity
“Prediction tells us
the load falls into gray zone
with 95% probability”
Prediction with PI is proposed by many existing studies
➢ How can we utilize the PI for ESS control?


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8
From Load Prediction to ESS operation
Probability
Load [MW]
0
5
3
8
････
4
Probability
Load [MW]
5
8
10
11
14
････


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ESS optimized schedule – objective function
t ~ t+1
am0:00 ~ am1:00
Probability
Probability
95% PI
Upper
boundary
Lower
boundary
95% PI
MW
1
4
5
6
10
MW
𝐵𝑙𝑜𝑤𝑒𝑟 (𝑡, 𝑛)
𝐵𝑢𝑝𝑝𝑒𝑟 (𝑡, 𝑛)
24
𝒂𝒓𝒈 𝒎𝒊𝒏 𝛼 𝐵𝑢𝑝𝑝𝑒𝑟 𝑡, 𝑛 − 𝐸𝑆𝑆𝑜𝑢𝑡(𝑡), 𝑡 = 1. . 24, 𝑛 = 1 … . 𝑁
𝐸𝑆𝑆𝑜𝑢𝑡(𝑡)
𝑤ℎ𝑒𝑟𝑒
2
+
𝛽
෍
(𝐸𝑆𝑆𝑜𝑢𝑡
𝑡
)
∞
𝑡=1
𝑁: 𝑡ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑜𝑏𝑠𝑒𝑟𝑣𝑎𝑡𝑖𝑜𝑛 𝑝𝑜𝑖𝑛𝑡𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑛𝑒𝑡𝑤𝑜𝑟𝑘
𝑡: 𝑡ℎ𝑒 𝑡𝑖𝑚𝑒 𝑖𝑛 𝑎 𝑑𝑎𝑦 𝑖𝑛 𝑎 ℎ𝑜𝑢𝑟𝑙𝑦 𝑏𝑎𝑠𝑖𝑠
𝐸𝑆𝑆𝑜𝑢𝑡 𝑡 : 𝑡ℎ𝑒 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝐸𝑆𝑆 𝑜𝑢𝑡𝑝𝑢𝑡 𝑜𝑟 𝑖𝑛𝑝𝑢𝑡 [𝑀𝑊]


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Simulation result for one day
Predicted PI
Adjusted PI
SOC ESS#1
SOC ESS#2
Discharging
Charging


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Simulation result for one day
7
Without ESS
with ESS
6
Predicted upper boundary
Load [MW]
5
4
3
2
Peak1
Peak3
Peak2
1
0
0:00
3:00
6:00
9:00
12:00
15:00
18:00
21:00
24:00
0:00
Peak reduction: 5.58 MW -&gt; 5.56 MW….too small?


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Simulation result for one year
Reduction
Reduction
Deterministic Prediction
Deterministic
prediction
Prediction interval
(Confidence Interval)
Deterministic Prediction
without error
(ideal operation)
Prediction
Interval
Median of
reduction [MW]
-0.43
(-7.2%)
-0.58
(-9.9%)
-0.81
(-12.1%)
Average of
reduction [MW]
-0.47
(-6.8%)
-0.61
(-9.1%)
-0.76
(-11.8%)
Highest peak
in a year [MW]
10.05 -&gt; 9.97
(-0.8%)
10.05 -&gt; 9.42
(-6.2%)
10.05-&gt; 8.91
(-11.3%)


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# Page. 14

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How can we build Prediction Intervals (PIs)?
Now, Let’s assume we are ESS operator. We have to select the
one of the prediction algorithm and boundaries. How can we
chose one of them?
My algorithm tell the boundary
containing 100% data set.
But the width is wider.
My algorithm tells the boundary
containing 90% data set.
The width is smaller.


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15
Various PIs example
Past Load and PIs
Chebyshev
Confidence Interval
Window
Each PI has another boundaries. Window shows the most optimistic
one and Chebyshev shows the most pessimistic one


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Construction of PIs
• Window
Pick the 5% and 95% data in ascending data as the boundaries.
1 2 3 4 5 6 7 8 9 10
𝑙𝑜𝑤𝑒𝑟 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 = 10 ∗ 0.05 → 1
𝑢𝑝𝑝𝑒𝑟 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 = 10 ∗ 0.95 → 10
• Confidence Interval
The data is assumed to follow the normal distribution, calculate 95% CI
𝑙𝑜𝑤𝑒𝑟 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 = 𝜇 − 2𝜎
𝑢𝑝𝑝𝑒𝑟 𝑏𝑜𝑢𝑛𝑑𝑎𝑟𝑦 = 𝜇 + 2𝜎
• Chebyshev
Chebyshev’s inequality ensure the certain percentage of data lays in
certain range
1
𝑃 𝑥 − 𝜇 ≥ 𝑘𝜎 ≤ 2
𝑘


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Construction of PIs - Chebyshev
• Chebyshev’s inequality
Chebyshev’s inequality ensure the certain probability as the sample
lays in certain range
1
𝑃 𝑋 ≥ 𝜇 + 𝑘𝜎 ≤ 2 (𝑋 ≥ 𝜇)
𝑘
When extracting one sample from a certain
random variable 𝑋, the probability that it is
1
greater than 𝜇 + 2𝜎 is 2 or less.
2
𝑃 𝑋 ≤ 𝜇 − 𝑘𝜎 ≤
1
(𝑋 &lt; 𝜇)
𝑘2


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Load Prediction result
(a) Sample-based
(b) Confidence-interval-based
(c) Chebyshev-based


