presented by: kerry mcbee co-authors: kelly bloch, jason ... · co-authors: kelly bloch, jason...

IEEE 2011 Electrical Power and Energy Conference

Presented by: Kerry McBee Co-authors: Kelly Bloch, Jason Sexauer


‣ Statement of Problem and Purpose

‣ Derivation of Binomial Distribution

‣ Applications – Planning for transformer replacements

– Proactive vs. Reactive replacement optimization

– Effectiveness of Demand Side Management on EV


[1] EPRI Study: Environmental Assessment of Plug-In Hybrid Electric Vehicles


‣ Electric Vehicles pose a risk to the electric distribution system, especially at high penetrations

– Unless deterred, load is likely to be peak coincident, accelerating the need for capacity projects

– Decreased life of equipment (transformers, conductors, etc...)

– Outages due to blown fuses

– Low Voltage due to overloaded transformer and conductor


‣ Study risks and possible mitigations related to EV effects on,

– Secondary conductors

– Distribution transformer

– Laterals

– Feeder main

– Substation transformer bank


Transformer Analysis

• Which and how many transformers are suscep8ble to excessive loading based on – Exis8ng peak demand – Number of customers connected to transformer – Average EV charger demand

– EV or PHEV penetra8on


‣ Binomial Distribution – Measure number of successes from a series of trials.

‣ If I flip a coin 5 times, what are the chances of seeing 3 heads?

P[X = k] is the probability of k successes in n trials, each with a probability of success p.


‣ For each transformer, a binomial trial is set up – What is the probability of k electric vehicle being connected to a

transformer with n households?

‣ We are interested in cases when k electric vehicles push transformer loading above acceptable limits

where... ‧ SR = Acceptable limit of transformer loading ‧ SP = Currently existing peak demand on transformer ‧ SC = Demand of an electric vehicle charger


‣ Use cumulative form of binomial to find all values of nEV which cause an overload for nmax customers on a transformer

‣ Describes the probability of an overload occurring due to electric vehicle chargers


‣ Events in the sample space must be independent and have consistent probability

– P[A|B] = P[A], ie. the knowledge of A occurring tells nothing about B

– The choice of one customer to connect an EV does not affect his neighbor's choice to do so

– Neglects effects of “Keeping up with Joneses” – Work around: Using spatial information to refine the event probability


‣ Events must be binary (ie, succeed or fail) – Their must exist exactly two events who are mutually exclusive and make up the full sample space and whose probabilities are complementary.

– Limits the ability to consider multiple charging technologies ‧ Used weighted average demand for multi-charger scenarios ‧ High loss of fidelity, especially for marginal cases, but gives

rough ball-park estimates


‣ Households will buy at most one electric vehicle

‣ Electric vehicle chargers are coincident with peak demand

‣ Acceptable loading is 180% of nameplate rating

‣ Two types of chargers – Class I: 1.2 kW peak demand

– Class II: 3.8 kW peak demand


‣ 15 scenarios were analyzed – Charger class (Class I, Class II, and mixes of both)

– EV penetration rate (p) =(10%, 20%, and 30%)

‣ Determine the expected number of transformers to have to replace for a given penetration

‣ Useful for budgetary and supply chain purposes


‣ 40,800 25 kVA transformers in Denver Metro ‣ 946 have existing overloads ‣ Expected replacements due to EV range from 643

to over 5,000 depending on scenario assumptions


‣ What is the optimal failure probability at which to proactively replace? – Proactive Replacement: Expend capital to upgrade transformer,

however retain old transformer at salvage value. Possibly upgrade transformers that will never overload.

– Reactive Replacement: Upgrade transformer only once a failure has occurred. May forfeit salvage value and decrease reliability.


‣ Approach – Find np and nr for various proactive replacement rates

– Optimization Formulization

– where... ‧ P[Fi] = expected value for the ith

transformer’s RV ‧ nt = # transformers in population ‧ np = # proactive replacements ‧ nr = # reactive replacements ‧ Cr = Cost of reactive replacement ‧ Cp = Value realized from proactive

replacement Proactive Reactive


‣ Results – Optimal proactive replacement is more strongly correlated with

salvage rate than scenario aggressiveness

– The more aggressive the scenario, the less transformers cost per unit

– Proactive replacement becomes viable above 5% salvage rate


‣ Unless motivated otherwise, customers will most likely charge an EV during peak demand. ‣ Implementation of a Demand Side Management

(DSM) system targeted at EV may help reduce their impacts. ‣ At what sort of EV penetration is DSM useful?

What sort of participation rate is needed for DSM to be effective?


‣ Approach – Create analysis as before

– Introduce a second binomial trial which tests each overload condition for how many customers need to curtail their load to avoid overload

– Apply Law of Total Probability to determine how much less likely an overload is due to DSM

– Add to probability determined in step 1 (ie, the probability that there is no overload due to capacity) to find total probability that transformer will not overload


‣ Example – 15% EV Penetration Rate; 10% DSM Participation Rate – 5 households connected to a transformer with capacity for 1 EV – DSM has increased the probability of being OK from 83% to 86%


‣ General Equation – Let

– Then

– With this, find

with k successes in n trials with probability p.

probability mass function (PMF) cumulative density function (CDF)


‣ Results – Expected Value of Overloaded Transformers

– Even at only moderate EV penetration levels, DSM becomes effective at mitigating transformer overloads.


‣ Binomial can be applied to determine transformer overloading probabilities ‣ Provide budgetary numbers ‣ Approximate optimal transformer replacement

strategy (proactive vs. reactive) ‣ Study effectiveness of DSM on EV loads

presented by: kerry mcbee co-authors: kelly bloch, jason ... · co-authors: kelly bloch, jason...

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