The Significance of Modelling Load Diversity in Low Voltage - - PowerPoint PPT Presentation

The Significance of Modelling Load Diversity in Low Voltage Distribution Networks

Euan McGill 29/11/2018

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

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

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

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

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 kW PTx =

Diversified Distribution

Generalized Case

• 3 phase radial feeder
• n ICPs per phase
• Uniformly spaced
• Total Feeder impedance
• f Z

Voltage Drop Equations -

Uniform Load Distribution

• 𝑊

𝑒𝑠𝑝𝑞 𝑣𝑜𝑗

= 𝑊

𝑒𝑠𝑝𝑞𝐵 𝑣𝑜𝑗

𝑊

𝑒𝑠𝑝𝑞𝐶 𝑣𝑜𝑗

𝑊

𝑒𝑠𝑝𝑞𝐷 𝑣𝑜𝑗

= 𝑆𝑓 𝐹𝑃𝑀%𝑣𝑜𝑗 ∙ 𝐽𝑣𝑜𝑗 ∙ 𝑎 𝑆𝑓 𝐹𝑃𝑀%𝑣𝑜𝑗 ∙ 𝐽𝑣𝑜𝑗 ∙ 𝑎 𝑆𝑓 𝐹𝑃𝑀%𝑣𝑜𝑗 ∙ 𝐽𝑣𝑜𝑗 ∙ 𝑎

• 𝐹𝑃𝑀%𝐵 = 𝐹𝑃𝑀%𝐶 = 𝐹𝑃𝑀%𝐷 = 𝐹𝑃𝑀%𝑣𝑜𝑗
• 𝐽𝐵 = 𝐽𝐶 = 𝐽𝐷 =

𝐽𝑢𝑝𝑢𝑏𝑚 3

= 𝐽𝑣𝑜𝑗

• 𝑊

𝑒𝑠𝑝𝑞𝐵 𝑣𝑜𝑗

= 𝑊

𝑒𝑠𝑝𝑞𝐶 𝑣𝑜𝑗

= 𝑊

𝑒𝑠𝑝𝑞𝐷 𝑣𝑜𝑗

= 𝑊

𝑒𝑠𝑝𝑞

• 𝑊

𝑒𝑠𝑝𝑞 𝑒𝑗𝑤

= 𝑊

𝑒𝑠𝑝𝑞𝐵 𝑒𝑗𝑤

𝑊

𝑒𝑠𝑝𝑞𝐶 𝑒𝑗𝑤

𝑊

𝑒𝑠𝑝𝑞𝐷 𝑒𝑗𝑤

= 𝑆𝑓 𝐹𝑃𝑀%𝐵 ∙ 𝐽𝐵 ∙ 𝑎 𝑆𝑓 𝐹𝑃𝑀%𝐶 ∙ 𝐽𝐶 ∙ 𝑎 𝑆𝑓 𝐹𝑃𝑀%𝐷 ∙ 𝐽𝐷 ∙ 𝑎

• 𝐹𝑃𝑀%𝐵 ≠ 𝐹𝑃𝑀%𝐶 ≠ 𝐹𝑃𝑀%𝐷 ≠ 𝐹𝑃𝑀%𝑣𝑜𝑗
• 𝐽𝐵 ≠ 𝐽𝐶 ≠ 𝐽𝐷 ≠

𝐽𝑈𝑝𝑢𝑏𝑚 3

= 𝐽𝑣𝑜𝑗

• 𝑊

𝑒𝑠𝑝𝑞𝐵 𝑒𝑗𝑤

≠ 𝑊

𝑒𝑠𝑝𝑞𝐶 𝑒𝑗𝑤

≠ 𝑊

𝑒𝑠𝑝𝑞𝐷 𝑒𝑗𝑤

Voltage Drop Equations –

Diversified loads

Longitudinal & Across Phase Diversity Scaling Factors

• 𝐿෩

∅ =

𝐿෩

∅𝐵

𝐿෩

∅𝐶

𝐿෩

∅𝐷

= ൗ

𝐹𝑃𝑀%𝐵 𝐹𝑃𝑀%𝑣𝑜𝑗

ൗ

𝐹𝑃𝑀%𝐶 𝐹𝑃𝑀%𝑣𝑜𝑗

ൗ

𝐹𝑃𝑀%𝐷 𝐹𝑃𝑀%𝑣𝑜𝑗

• 𝑊

𝑒𝑠𝑝𝑞 𝑣𝑜𝑗

= 𝑊

𝑒𝑠𝑝𝑞𝐵 𝑣𝑜𝑗

𝑊

𝑒𝑠𝑝𝑞𝐶 𝑣𝑜𝑗

𝑊

𝑒𝑠𝑝𝑞𝐷 𝑣𝑜𝑗

= 𝑆𝑓 𝐹𝑃𝑀%𝑣𝑜𝑗 ∙ 𝐽𝑣𝑜𝑗 ∙ 𝑎 𝑆𝑓 𝐹𝑃𝑀%𝑣𝑜𝑗 ∙ 𝐽𝑣𝑜𝑗 ∙ 𝑎 𝑆𝑓 𝐹𝑃𝑀%𝑣𝑜𝑗 ∙ 𝐽𝑣𝑜𝑗 ∙ 𝑎

• 𝑊

𝑒𝑠𝑝𝑞 𝑒𝑗𝑤

= 𝑊

𝑒𝑠𝑝𝑞𝐵 𝑒𝑗𝑤

𝑊

𝑒𝑠𝑝𝑞𝐶 𝑒𝑗𝑤

𝑊

𝑒𝑠𝑝𝑞𝐷 𝑒𝑗𝑤

= 𝑆𝑓 𝐹𝑃𝑀%𝐵 ∙ 𝐽𝐵 ∙ 𝑎 𝑆𝑓 𝐹𝑃𝑀%𝐶 ∙ 𝐽𝐶 ∙ 𝑎 𝑆𝑓 𝐹𝑃𝑀%𝐷 ∙ 𝐽𝐷 ∙ 𝑎

• 𝐿∅ =

𝐿∅𝐵 𝐿∅𝐶 𝐿∅𝐷 = ൗ

𝐽𝐵 𝐽𝑣𝑜𝑗

ൗ

𝐽𝐶 𝐽𝑣𝑜𝑗

ൗ

𝐽𝐷 𝐽𝑣𝑜𝑗

Longitudinal Diversity Factor Across Phase Diversity Factor Uniform Voltage Drop Equations Diversified Voltage Drop Equations

Diversity Scaling Factor Definition

• 𝑊

𝑒𝑠𝑝𝑞 𝑒𝑗𝑤

= 𝑊

𝑒𝑠𝑝𝑞𝐵 𝑒𝑗𝑤

𝑊

𝑒𝑠𝑝𝑞𝐶 𝑒𝑗𝑤

𝑊

𝑒𝑠𝑝𝑞𝐷 𝑒𝑗𝑤

= 𝐿∅𝐵 ∙ 𝐿෩

∅𝐵 ∙ 𝑊 𝑒𝑠𝑝𝑞𝐵 𝑣𝑜𝑗

𝐿∅𝐶 ∙ 𝐿෩

∅𝐶 ∙ 𝑊 𝑒𝑠𝑝𝑞𝐶 𝑣𝑜𝑗

𝐿∅𝐷 ∙ 𝐿෩

∅𝐷 ∙ 𝑊 𝑒𝑠𝑝𝑞𝐷 𝑣𝑜𝑗

• 𝐿 =

𝐿

𝐵

𝐿𝐶 𝐿𝐷 = 𝐿∅𝐵 ∙ 𝐿෩

∅𝐵

𝐿∅𝐶 ∙ 𝐿෩

∅𝐶

𝐿∅𝐷 ∙ 𝐿෩

∅𝐷

• 𝑊

𝑒𝑠𝑝𝑞 𝑒𝑗𝑤

= 𝑊

𝑒𝑠𝑝𝑞𝐵 𝑒𝑗𝑤

𝑊

𝑒𝑠𝑝𝑞𝐶 𝑒𝑗𝑤

𝑊

𝑒𝑠𝑝𝑞𝐷 𝑒𝑗𝑤

= 𝐿

𝐵 ∙ 𝑊 𝑒𝑠𝑝𝑞𝐵 𝑣𝑜𝑗

𝐿𝐶 ∙ 𝑊

𝑒𝑠𝑝𝑞𝐶 𝑣𝑜𝑗

𝐿𝐷 ∙ 𝑊

𝑒𝑠𝑝𝑞𝐷 𝑣𝑜𝑗

• Unique Combined Diversity Scaling

Factor for each phase

• K>1 means uniform load distribution

underestimates true voltage drop

• K<1 means uniform load distribution
• verestimates true voltage drop
• Varies with time
• Distribution of [K] can be obtained by

analyzing smart meter data

Monte Carlo Method

Monte Carlo Method

Monte Carlo Method

Results

95th Percentile of Kmax During Peak Load Periods Vs Number of ICPs

Results

5th Percentile of Kmin During Low Load Periods Vs Number of ICPs

Convergence of Results

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.

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

Thank you to our industry members of the Power Engineering Excellence Trust 21

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
• f network assets

After Diversity Maximum Demand

𝐵𝐸𝑁𝐸 = 1 𝑂 ෍

𝑜=1 𝑂

𝑄

𝑜 = 𝐵𝑔𝑢𝑓𝑠 𝐸𝑗𝑤𝑓𝑠𝑡𝑗𝑢𝑧 𝑁𝑏𝑦𝑗𝑛𝑣𝑛 𝐸𝑓𝑛𝑏𝑜𝑒 𝑞𝑓𝑠 𝑑𝑣𝑡𝑢𝑝𝑛𝑓𝑠

𝑂 = 𝑂𝑣𝑛𝑐𝑓𝑠 𝑝𝑔 𝑑𝑣𝑡𝑢𝑝𝑛𝑓𝑠𝑡 𝑗𝑜 𝑏 𝑜𝑓𝑢𝑥𝑝𝑠𝑙 𝑄

𝑜 = 𝐸𝑓𝑛𝑏𝑜𝑒 𝑝𝑔 𝑢ℎ𝑓 𝑜𝑢ℎ 𝑑𝑣𝑡𝑢𝑝𝑛𝑓𝑠 𝑏𝑢 𝑢ℎ𝑓 𝑢𝑗𝑛𝑓 𝑝𝑔 𝑜𝑓𝑢𝑥𝑝𝑠𝑙 𝑞𝑓𝑏𝑙 𝑒𝑓𝑛𝑏𝑜𝑒

• This type of load diversity is described within this work as Temporal Diversity

Temporal Diversity in Smart Meter Data

Impact Of Network Aggregation Scale On ADMD Per Customer

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.

Equivalent End Of Line (EOL) Load Model

Detailed Voltage Drop Model Equivalent EOL load model

Equivalent End Of Line Load Model –

Uniform Spacing & Uniform Loading

4 ICP Example Feeder

Case ICP Spacing Load distribution 1 Uniform Uniform 2 Uniform Non-Uniform

Impact Of Longitudinal Diversity On EOL%

Detailed Voltage Drop Model Equivalent EOL load model

Case 1 Case 2

~25% increase in voltage drop

Impact Of Across Phase Diversity On Voltage Drop

• 𝐹𝑃𝑀%𝐵 = 𝐹𝑃𝑀%𝐶 = 𝐹𝑃𝑀%𝐷 = 𝐹𝑃𝑀%∅
• 𝐽

𝐵 ≠ 𝐽𝐶 ≠ 𝐽𝐷 ≠ 𝐽𝑈𝑝𝑢𝑏𝑚 3

= 𝐽𝑣𝑜𝑗

• 𝑊

𝑒𝑠𝑝𝑞𝐵 ≠ 𝑊 𝑒𝑠𝑝𝑞𝐶 ≠ 𝑊 𝑒𝑠𝑝𝑞𝐷

• 𝐽

𝐵 = 𝐽𝐶 = 𝐽𝐷 = 𝐽𝑈𝑝𝑢𝑏𝑚 3

= 𝐽𝑣𝑜𝑗

• 𝑊

𝑒𝑠𝑝𝑞𝐵 = 𝑊 𝑒𝑠𝑝𝑞𝐶 = 𝑊 𝑒𝑠𝑝𝑞𝐷 = 𝑊 𝑒𝑠𝑝𝑞𝑣𝑜𝑗

Uniform load Distribution Diversified loads

Smart Meter Dataset Analysis

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,

• r Number
• f ICPs?

Yes No

Day of year