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Vasilis ZoisCS @ USC
Profit – Optimal & Stability Aware Load Curtailment in Smart Grids
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Dynamic and sophisticated demand control– Direct control over household appliances
Curtailment Reasons– Reactive Curtailment» Loss of power generation» Renewable sources don’t work at full capacity
– Proactive» Maximize profits» Reduced power consumption overweigh customer
compensation Customer Satisfaction
– Discounted plan Valuation Function– Plan connected to customer load elasticity
Introduction
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Dynamic pricing– Direct control achieved by monetary incentives
Cost & valuation functions– Convex cost functions– Concave valuation functions
Optimal Curtailment– Component failure as subject of attack– Quantify severity by the amount of the curtailed power
Frequency stability– Locally measured frequency– Centralized approach» Physical constraints» Low computational cost
Previous Work
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Physical power systems model– Graph G= (V,E)» Vertices Buses that generate or consume power» Edges Transmission line i with capacity ci
– Power flow model» Voltage at each bus is fixed
Cost model of power supply– with marginal cost – As power production increases cost increases rapidly
Valuation model of provided power– with marginal cost – Single valuation function for aggregated customer in bus
i– Law of diminishing marginal returns
Model Analysis
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1. =0
Optimization problem hardness– Power grid normal operation» Phase difference » and
– Theorem 1:If the supply cost functions are convex and the valuation
functions are concave, then both reactive and proactive load curtailment problems are convex after linearization.
Optimization Framework
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Reactive curtailment– Fixed amount of supply reduction– Match the supply loss while minimizing
compensation Proactive curtailment– Supply reduction» Savings outweigh curtailment costs
Curtailment problems
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Curtailment Period– Fixed (e.g 15 minutes)– Optimization at the beginning– Cost savings and profits for one period
Comparison of valuation functions– Linear vs concave
Effect of line capacity in optimization
Experiments Overview
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Concave function– Line capacities limit load shedding on specific
busses Linear function– Same curtailment for different capacities
Comparison– Better distribution of curtailment with concave
function
Reactive curtailment experiments
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Setup– Cost functions – Variable α and β
Load Shedding– Supply reduction on each bus changes– Total supply reduction decreases
Proactive curtailment experiments
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Proactive curtailment experiments (2) Capacity effect
– Profits always increase in contrast to power supply Comparison
– Higher profit than in reactive curtailment by optimizing supply reduction
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Additional constraints– Limit curtailed load on each bus– Preserved convexity of optimization problem
Effect of limits– Reduced profits– Limited power reduction» Limit is not reached
Curtailment limits
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Fast response– Critical in reactive curtailment– Primary control within 5- 30s
Experiments– 14,57 or 118 bus systems– Average time from 100 iterations
Computational Cost
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Thank you! Questions?
https://publish.illinois.edu/incentive-pricing/publications/
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