slide1 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Vasilis Zois CS @ USC PowerPoint Presentation
Download Presentation
Vasilis Zois CS @ USC

Loading in 2 Seconds...

play fullscreen
1 / 13

Vasilis Zois CS @ USC - PowerPoint PPT Presentation


  • 143 Views
  • Uploaded on

Profit – Optimal & Stability Aware Load Curtailment in Smart Grids. Vasilis Zois CS @ USC. Introduction. Dynamic and s ophisticated demand control Direct control over household appliances Curtailment Reasons Reactive Curtailment Loss of power generation

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Vasilis Zois CS @ USC' - fell


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide2
Introduction
  • 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
slide3
Previous Work
  • 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
slide4
Model Analysis
  • 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
slide5
Optimization Framework
    • =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.

slide6
Curtailment problems
  • Reactive curtailment
    • Fixed amount of supply reduction
    • Match the supply loss while minimizing compensation
  • Proactive curtailment
    • Supply reduction
      • Savings outweigh curtailment costs
slide7
Experiments Overview
  • 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
slide8
Reactive curtailment experiments
  • 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
slide9
Proactive curtailment experiments
  • Setup
    • Cost functions
    • Variable α and β
  • Load Shedding
    • Supply reduction on each bus changes
    • Total supply reduction decreases
slide10
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
slide11
Curtailment limits
  • 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
slide12
Computational Cost
  • Fast response
    • Critical in reactive curtailment
    • Primary control within 5- 30s
  • Experiments
    • 14,57 or 118 bus systems
    • Average time from 100 iterations
slide13

Thank you!

Questions?

https://publish.illinois.edu/incentive-pricing/publications/