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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/