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

IEEE 2011 Electrical Power and Energy Conference

‣ 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

IEEE 2011 Electrical Power and Energy Conference

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

IEEE 2011 Electrical Power and Energy Conference

‣ 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

IEEE 2011 Electrical Power and Energy Conference

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

– Secondary conductors

– Distribution transformer

– Laterals

– Feeder main

– Substation transformer bank

IEEE 2011 Electrical Power and Energy Conference

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  

IEEE 2011 Electrical Power and Energy Conference

‣ 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.

IEEE 2011 Electrical Power and Energy Conference

‣ 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

IEEE 2011 Electrical Power and Energy Conference

‣ 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

IEEE 2011 Electrical Power and Energy Conference

‣ 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

IEEE 2011 Electrical Power and Energy Conference

‣ 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

IEEE 2011 Electrical Power and Energy Conference

‣ 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

IEEE 2011 Electrical Power and Energy Conference

‣ 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

IEEE 2011 Electrical Power and Energy Conference

IEEE 2011 Electrical Power and Energy Conference

‣ 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

IEEE 2011 Electrical Power and Energy Conference

IEEE 2011 Electrical Power and Energy Conference

‣ 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.

IEEE 2011 Electrical Power and Energy Conference

‣ 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

IEEE 2011 Electrical Power and Energy Conference

IEEE 2011 Electrical Power and Energy Conference

IEEE 2011 Electrical Power and Energy Conference

IEEE 2011 Electrical Power and Energy Conference

‣ 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

IEEE 2011 Electrical Power and Energy Conference

‣ 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?

IEEE 2011 Electrical Power and Energy Conference

‣ 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

IEEE 2011 Electrical Power and Energy Conference

‣ 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%

IEEE 2011 Electrical Power and Energy Conference

‣ General Equation – Let

– Then

– With this, find    

with k successes in n trials with probability p.

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

IEEE 2011 Electrical Power and Energy Conference

IEEE 2011 Electrical Power and Energy Conference

‣ Results – Expected Value of Overloaded Transformers

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

IEEE 2011 Electrical Power and Energy Conference

‣ 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

IEEE 2011 Electrical Power and Energy Conference