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The Significance of Modelling Load Diversity in Low Voltage
Distribution Networks
Euan McGill
29/11/2018
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Presentation Contents
• Load Modelling Simplifications in LV Network Simulations
• Statistical Analysis on Smart Meter Load Data
• Hypothesized Impacts Of Load Modelling Simplifications On
Voltage
• Statistical Framework For Quantifying The Significance Of
Uniform Vs Diversified Load Distribution Within LV Network
Analysis
• Conclusions & Future work
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Load Modelling Within Existing Research
GREEN Grid 3
• Transformer load uniformly distributed among all downstream
premises
• When Transformer load is high all houses are heavily
loaded
• When Transformer load is low all houses are lightly loaded
• Is this behavior representative of reality?
Representative Urban type LV network
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Load Diversity In Smart Meter Data Set
GREEN Grid
Distribution of ICP level loads during annual peak load
period
Mean 2.4 kW
P5 0.2 kW
P50 2.2 kW
P95 5.8 kW
Statistical Summary
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Longitudinal Diversity
PTx = 5 kW
ΦA
1 kW
1 kW
1 kW
1 kW
1 kW
PTx = 5 kW
ΦA
0.5 kW
0.25 kW
0.25 kW
1.5 kW
2.5 kW
Uniform Distribution
Diversified Distribution
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Across Phases Diversity
Uniform Distribution ΦA
1 kW
1 kW 1 kW
ΦA ΦB
ΦB
ΦC
ΦC
PTx =
1 kW
1 kW 1 kW
ΦA
0.5 kW
1 kW 1.5 kW
ΦA ΦB
ΦB
ΦC
ΦC
0.5 kW
1.5 kW 1 kWPTx =
Diversified Distribution
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Generalized Case
• 3 phase radial feeder
• n ICPs per phase
• Uniformly spaced
• Total Feeder impedance of Z
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Voltage Drop Equations -Uniform Load Distribution
• 𝑉𝑑𝑟𝑜𝑝𝑢𝑛𝑖 =
𝑉𝑑𝑟𝑜𝑝𝐴𝑢𝑛𝑖
𝑉𝑑𝑟𝑜𝑝𝐵𝑢𝑛𝑖
𝑉𝑑𝑟𝑜𝑝𝐶𝑢𝑛𝑖
=
𝑅𝑒 𝐸𝑂𝐿%𝑢𝑛𝑖 ∙ 𝐼𝑢𝑛𝑖 ∙ 𝑍
𝑅𝑒 𝐸𝑂𝐿%𝑢𝑛𝑖 ∙ 𝐼𝑢𝑛𝑖 ∙ 𝑍
𝑅𝑒 𝐸𝑂𝐿%𝑢𝑛𝑖 ∙ 𝐼𝑢𝑛𝑖 ∙ 𝑍
• 𝐸𝑂𝐿%𝐴 = 𝐸𝑂𝐿%𝐵 = 𝐸𝑂𝐿%𝐶 = 𝐸𝑂𝐿%𝑢𝑛𝑖
• 𝐼𝐴 = 𝐼𝐵 = 𝐼𝐶 =𝐼𝑡𝑜𝑡𝑎𝑙
3= 𝐼𝑢𝑛𝑖
• 𝑉𝑑𝑟𝑜𝑝𝐴𝑢𝑛𝑖 = 𝑉𝑑𝑟𝑜𝑝𝐵
𝑢𝑛𝑖 = 𝑉𝑑𝑟𝑜𝑝𝐶𝑢𝑛𝑖 = 𝑉𝑑𝑟𝑜𝑝
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• 𝑉𝑑𝑟𝑜𝑝𝑑𝑖𝑣 =
𝑉𝑑𝑟𝑜𝑝𝐴𝑑𝑖𝑣
𝑉𝑑𝑟𝑜𝑝𝐵𝑑𝑖𝑣
𝑉𝑑𝑟𝑜𝑝𝐶𝑑𝑖𝑣
=
𝑅𝑒 𝐸𝑂𝐿%𝐴 ∙ 𝐼𝐴 ∙ 𝑍
𝑅𝑒 𝐸𝑂𝐿%𝐵 ∙ 𝐼𝐵 ∙ 𝑍
𝑅𝑒 𝐸𝑂𝐿%𝐶 ∙ 𝐼𝐶 ∙ 𝑍
• 𝐸𝑂𝐿%𝐴 ≠ 𝐸𝑂𝐿%𝐵 ≠ 𝐸𝑂𝐿%𝐶 ≠ 𝐸𝑂𝐿%𝑢𝑛𝑖
• 𝐼𝐴 ≠ 𝐼𝐵 ≠ 𝐼𝐶 ≠𝐼𝑇𝑜𝑡𝑎𝑙
3= 𝐼𝑢𝑛𝑖
• 𝑉𝑑𝑟𝑜𝑝𝐴𝑑𝑖𝑣 ≠ 𝑉𝑑𝑟𝑜𝑝𝐵
𝑑𝑖𝑣 ≠ 𝑉𝑑𝑟𝑜𝑝𝐶𝑑𝑖𝑣
Voltage Drop Equations –Diversified loads
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Longitudinal & Across Phase Diversity Scaling Factors
• 𝐾෩∅ =
𝐾෩∅𝐴𝐾෩∅𝐵𝐾෩∅𝐶
=
ൗ𝐸𝑂𝐿%𝐴
𝐸𝑂𝐿%𝑢𝑛𝑖
ൗ𝐸𝑂𝐿%𝐵
𝐸𝑂𝐿%𝑢𝑛𝑖
ൗ𝐸𝑂𝐿%𝐶
𝐸𝑂𝐿%𝑢𝑛𝑖
• 𝑉𝑑𝑟𝑜𝑝𝑢𝑛𝑖 =
𝑉𝑑𝑟𝑜𝑝𝐴𝑢𝑛𝑖
𝑉𝑑𝑟𝑜𝑝𝐵𝑢𝑛𝑖
𝑉𝑑𝑟𝑜𝑝𝐶𝑢𝑛𝑖
=
𝑅𝑒 𝐸𝑂𝐿%𝑢𝑛𝑖 ∙ 𝐼𝑢𝑛𝑖 ∙ 𝑍
𝑅𝑒 𝐸𝑂𝐿%𝑢𝑛𝑖 ∙ 𝐼𝑢𝑛𝑖 ∙ 𝑍
𝑅𝑒 𝐸𝑂𝐿%𝑢𝑛𝑖 ∙ 𝐼𝑢𝑛𝑖 ∙ 𝑍
• 𝑉𝑑𝑟𝑜𝑝𝑑𝑖𝑣 =
𝑉𝑑𝑟𝑜𝑝𝐴𝑑𝑖𝑣
𝑉𝑑𝑟𝑜𝑝𝐵𝑑𝑖𝑣
𝑉𝑑𝑟𝑜𝑝𝐶𝑑𝑖𝑣
=
𝑅𝑒 𝐸𝑂𝐿%𝐴 ∙ 𝐼𝐴 ∙ 𝑍
𝑅𝑒 𝐸𝑂𝐿%𝐵 ∙ 𝐼𝐵 ∙ 𝑍
𝑅𝑒 𝐸𝑂𝐿%𝐶 ∙ 𝐼𝐶 ∙ 𝑍
• 𝐾∅ =
𝐾∅𝐴𝐾∅𝐵𝐾∅𝐶
=
ൗ𝐼𝐴 𝐼𝑢𝑛𝑖
ൗ𝐼𝐵 𝐼𝑢𝑛𝑖
ൗ𝐼𝐶 𝐼𝑢𝑛𝑖
Longitudinal Diversity Factor Across Phase Diversity Factor
Uniform Voltage Drop Equations Diversified Voltage Drop
Equations
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Diversity Scaling Factor Definition
• 𝑉𝑑𝑟𝑜𝑝𝑑𝑖𝑣 =
𝑉𝑑𝑟𝑜𝑝𝐴𝑑𝑖𝑣
𝑉𝑑𝑟𝑜𝑝𝐵𝑑𝑖𝑣
𝑉𝑑𝑟𝑜𝑝𝐶𝑑𝑖𝑣
=
𝐾∅𝐴 ∙ 𝐾෩∅𝐴 ∙ 𝑉𝑑𝑟𝑜𝑝𝐴𝑢𝑛𝑖
𝐾∅𝐵 ∙ 𝐾෩∅𝐵 ∙ 𝑉𝑑𝑟𝑜𝑝𝐵𝑢𝑛𝑖
𝐾∅𝐶 ∙ 𝐾෩∅𝐶 ∙ 𝑉𝑑𝑟𝑜𝑝𝐶𝑢𝑛𝑖
• 𝐾 =
𝐾𝐴𝐾𝐵𝐾𝐶
=
𝐾∅𝐴 ∙ 𝐾෩∅𝐴𝐾∅𝐵 ∙ 𝐾෩∅𝐵𝐾∅𝐶 ∙ 𝐾෩∅𝐶
• 𝑉𝑑𝑟𝑜𝑝𝑑𝑖𝑣 =
𝑉𝑑𝑟𝑜𝑝𝐴𝑑𝑖𝑣
𝑉𝑑𝑟𝑜𝑝𝐵𝑑𝑖𝑣
𝑉𝑑𝑟𝑜𝑝𝐶𝑑𝑖𝑣
=
𝐾𝐴 ∙ 𝑉𝑑𝑟𝑜𝑝𝐴𝑢𝑛𝑖
𝐾𝐵 ∙ 𝑉𝑑𝑟𝑜𝑝𝐵𝑢𝑛𝑖
𝐾𝐶 ∙ 𝑉𝑑𝑟𝑜𝑝𝐶𝑢𝑛𝑖
• Unique Combined Diversity Scaling Factor for each phase
• K>1 means uniform load distribution underestimates true
voltage drop
• K
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Monte Carlo Method
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Monte Carlo Method
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Monte Carlo Method
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Results
95th Percentile of Kmax During Peak Load Periods Vs Number of
ICPs
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Results
5th Percentile of Kmin During Low Load Periods Vs Number of
ICPs
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Convergence of Results
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Conclusions & Future Work
• LV network simulations which assume uniform load distribution
can result in erroneous voltage drop calculations.
• Longitudinal and Across Phase Diversity Scaling Factors were
defined to relate the voltage drop equations for the uniform and
diversified cases
• Results have demonstrated significant underestimations of
voltage drop during high load periods where networks typically
operate around the lower statutory limit for steady state
voltage.
• On the contrary overestimations of voltage drop during low
load periods where networks typically operate around the upper
statutory limit for steady state voltage are also possible.
• Impact studies for future scenarios which fail to capture the
non-uniformity of ICP level loads may consequently mask over
potential steady state voltage violations.
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Conclusions & Future Work
• In the future, locational clustering of Electric Vehicles and
Photovoltaics may result in increased Longitudinal and Across Phase
diversity, worsening the extent of the problem described here.
• Future work will look to:
– Assess the impacts of emerging technologies on Longitudinal
and Across Phase diversity
– Assess the impacts within real life network topologies (i.e.
not purely radial)
– Assess the impacts on neutral voltage rise
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Thank you to our industry members of the Power Engineering
Excellence Trust 21
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Load Diversity Definition
• Load Diversity describes the coincidence of peak loading among
individual consumers
• Unlikely that the daily peak demands of individual consumers
will coincide
• Load diversity is used in planning in order to curb the total
capacity requirements of network assets
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After Diversity Maximum Demand
𝐴𝐷𝑀𝐷 =1
𝑁
𝑛=1
𝑁
𝑃𝑛 = 𝐴𝑓𝑡𝑒𝑟 𝐷𝑖𝑣𝑒𝑟𝑠𝑖𝑡𝑦 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝐷𝑒𝑚𝑎𝑛𝑑 𝑝𝑒𝑟 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟
𝑁 = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟𝑠 𝑖𝑛 𝑎 𝑛𝑒𝑡𝑤𝑜𝑟𝑘
𝑃𝑛 = 𝐷𝑒𝑚𝑎𝑛𝑑 𝑜𝑓 𝑡ℎ𝑒 𝑛𝑡ℎ 𝑐𝑢𝑠𝑡𝑜𝑚𝑒𝑟 𝑎𝑡 𝑡ℎ𝑒 𝑡𝑖𝑚𝑒 𝑜𝑓 𝑛𝑒𝑡𝑤𝑜𝑟𝑘 𝑝𝑒𝑎𝑘
𝑑𝑒𝑚𝑎𝑛𝑑
• This type of load diversity is described within this work as
Temporal Diversity
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Temporal Diversity in Smart Meter Data
Impact Of Network Aggregation Scale On ADMD Per Customer
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Research Incentives
• In New Zealand the penetration of disruptive technologies such
as EV’s and residential PV is increasing.
• These technologies may significantly alter the load profiles
of individual consumers.
• The net consequences of which will impact steady state
voltages in low voltage networks.
• To quantify these impacts within load flow simulations a
representative load modelling approach for future scenarios is
required.
• It is hypothesized that the emergence of these technologies
will increase load diversity in low voltage networks.
• The significance of accounting for load diversity within LV
network modelling thus needs to be investigated.
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Equivalent End Of Line (EOL) Load Model
Detailed Voltage Drop Model Equivalent EOL load model
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Equivalent End Of Line Load Model –Uniform Spacing & Uniform
Loading
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4 ICP Example Feeder
Case ICP Spacing Load distribution
1 Uniform Uniform
2 Uniform Non-Uniform
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Impact Of Longitudinal Diversity On EOL%
Detailed Voltage Drop Model Equivalent EOL load model
Case 1
Case 2
~25% increase in voltage drop
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Impact Of Across Phase Diversity On Voltage Drop
• 𝐸𝑂𝐿%𝐴 = 𝐸𝑂𝐿%𝐵 = 𝐸𝑂𝐿%𝐶 = 𝐸𝑂𝐿%∅
• 𝐼𝐴 ≠ 𝐼𝐵 ≠ 𝐼𝐶 ≠𝐼𝑇𝑜𝑡𝑎𝑙
3= 𝐼𝑢𝑛𝑖
• 𝑉𝑑𝑟𝑜𝑝𝐴 ≠ 𝑉𝑑𝑟𝑜𝑝𝐵 ≠ 𝑉𝑑𝑟𝑜𝑝𝐶
• 𝐼𝐴 = 𝐼𝐵 = 𝐼𝐶 =𝐼𝑇𝑜𝑡𝑎𝑙
3= 𝐼𝑢𝑛𝑖
• 𝑉𝑑𝑟𝑜𝑝𝐴 = 𝑉𝑑𝑟𝑜𝑝𝐵 = 𝑉𝑑𝑟𝑜𝑝𝐶 = 𝑉𝑑𝑟𝑜𝑝𝑢𝑛𝑖
Uniform load
Distribution
Diversified loads
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Smart Meter Dataset Analysis
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Smart Meter Data Set
Randomly Sample the Required
Number of Smart Meters
Number of ICPS
Calculate Diversity Factors for Current
Time Interval
Assign Each SM to a Network ICP
Output Diversity Factors Data for Current Interval
More Monte Carlo
Iterations?
Yes
No
End
Time of Day
Change Time of Day, Day of Year, or Number
of ICPs?
Yes
No
Day of year
