A stochastic power network calculus for integrating renewable energy sources into the power grid Presenter: qinghua shen Wang, Kai, et al. "A stochastic power network calculus for integrating renewable energy sources into the power grid." Selected Areas in Communications, IEEE Journal on 30.6 (2012):

content Intro Formulation Power system modelling Performance metrics Case study Conclusions 2

1. Intro Motivation use environmentally friendly sources adopt storage to match uncertain supply and demand (island) improve reliability of the system 3

1. Intro Motivation  Why network calculus The ability of the stochastic network calculus to model broad classes of queueing scenarios and capture statistical multiplexing gain  Why extend Decoupled arrival and service process Specific performance metrics: Fraction of Time that energy is not-served (FTNS) waste of power supply (WPS) (drop rate) 4

2. Formulation Problem description Island: only renewable sources for supply Storage has limited capacity C Np: PV panels, Nw wind turbines Objectives: reliability provisioning in terms of FTNS 5

2. Formulation Network Calculus  was designed to facilitate stochastic performance analysis (tail performance analysis with multiplexing)  Envelop process to characterize arrival process  Queue characterization: 6

3. Power system modelling Energy storage: discrete – Charged: – Discharged: – Differences from queue Departure is not a function of the arrival and current queue 7

3. Power system modelling Energy demand and supply – Upper curve: – Lower curve: – Similar for supply – Upper curve: similar to queue – Lower curve: needed for energy storage – Tightness: tradeoff between shapes of curves and bounding function 8

4. Performance metrics Transform to non-recursive – recursive – Non-recursive: – Compare to previous work Finite buffer length 9

4. Performance metrics How to present metrics recursive form Loss of power supply: Fraction Time of no service: Waste of power supply (WPS) 10

4. Performance metrics How to present metrics non recursive form Loss of power supply: Fraction Time of no service: Waste of power supply (WPS): 11

4. Performance metrics Bound expression Loss of power supply: Intuition: upper of demand - lower of supply Waste of power supply (WPS): Intuition: upper of supply – lower of demand 12

4. Performance metrics More benefits to come! Multiplexing: For N source with Similar results for upper bound Something is missing! (hao) 13

5. A case study Santa Catalina Island 14

5. A case study Model fitting – Linear function with rate equal to long term mean rate – exponential functions for the bounding functions 15

5. A case study Model fitting – Linear function with rate equal to long term mean rate – exponential functions for the bounding functions 16

5. A case study Model fitting – Linear function with rate equal to long term mean rate – exponential functions for the bounding functions 17

5. A case study Numerical results – Impacts of PV panels, wind and season 18

6. Conclusion Issues: demand and supply for an island – Only renewable energy – Storage aided – Reliability Good point – New type of “queue” – Finite buffer analysis Insufficient – Does this really matter (finite queue, decoupled?) My view – Not average tail but instantaneous tail(New fitting) – How will renewable energy impacts the market? 19