presented by: kerry mcbee co-authors: kelly bloch, jason ... · co-authors: kelly bloch, jason...
TRANSCRIPT
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IEEE 2011 Electrical Power and Energy Conference
Presented by: Kerry McBee Co-authors: Kelly Bloch, Jason Sexauer
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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
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IEEE 2011 Electrical Power and Energy Conference
[1] EPRI Study: Environmental Assessment of Plug-In Hybrid Electric Vehicles
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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
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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IEEE 2011 Electrical Power and Energy Conference
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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
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IEEE 2011 Electrical Power and Energy Conference
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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.
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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
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IEEE 2011 Electrical Power and Energy Conference
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IEEE 2011 Electrical Power and Energy Conference
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IEEE 2011 Electrical Power and Energy Conference
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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
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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?
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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
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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%
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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)
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IEEE 2011 Electrical Power and Energy Conference
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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.
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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
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IEEE 2011 Electrical Power and Energy Conference