1. Transport-Based Load Modeling and Sliding Mode Control of Plug-In Electric Vehicles for Robust Renewable Power Tracking Presenter: qinghua shen BBCR SmartGrid0

2. content Intro to PEV Control-Oriented PEV Load Model PEV model Simulations Control Part Conclusions BBCR SmartGrid1

3. Intro What is PEV: plug-in electric vehicles PEV on grid – On the negative side, PEVs represent an additional grid load that may overstretch the power grid, especially in localities with high levels of PEV adoption. – On the positive side, the ability to potentially control PEVs as a dispatch- able load group can improve grid’s stability and reliability by enabling the grid to both reduce stress during peak hours and accommodate renewable generation to a greater extent To achieve these benefits: – grid needs: i) the ability to communicate with its PEV loads, and ii) the ability to control them in a stable and robust manner based on this communication. BBCR SmartGrid2

4. Intro One solution for reliable grid: – Demand-side power management(direct load control) – Challenging due to uncertainties on both the demand (# of active PEV) and generation sides(renewable power), and difficult to measure Focus of this paper – A model of the demand/load(validated of real data ) – A control method BBCR SmartGrid3

5. Control-Oriented PEV load Model Basic idea: – The aggregate PEV power demand at a given time depends on the number of PEVs connected to the grid and their charging power. – A universal control signal u(t), [0,1] to scale the charging power. – Determining the number of PEVs connected to the grid at a given time can be challenging in practice, particularly under variable-rate charging conditions. BBCR SmartGrid4

6. Control-Oriented PEV load Model Goal:aggregate PEV power demand – X: storage level – Concentration of PEVs: Q(x,t) – Entering/exiting PEV: w(x,t) – Maximum charging power of individual PEV: P max – Instantaneous charging power P max u(t) – For a small control volume of length of dx, the flux of roads entering the segment: BBCR SmartGrid5

7. Control-Oriented PEV load Model The rate of increase of load concentration inside the control volume is given by the difference between the total entering and exiting fluxed divided by the length of the control volume, as BBCR SmartGrid6

8. Control-Oriented PEV load Model Merging (1) into (2), obtain the governing PDE of the dynamics of PEVs as Also define the boundaries The aggregate charging power of PEVs can be obtained through integrating the concentration of PEVs over the full energy storage range, and multiplying by the instantaneous charging power of PEVs BBCR SmartGrid7

9. Control-Oriented PEV load Model State space representation – Discretized for numerical simulations and control design – Discretizing the storage interval into K equal segments of length – Finite difference Where and Thus, the aggregate power can be represented as BBCR SmartGrid8

10. PEV Load Model Simulations Monte Carlo Model: National household Travel Survey – First trip departure times – Last trip arrival times – Trip length For each trip, calculate – Energy consumption rate: trip length/daily trip energy demand Adopt the end of travel charging strategy: 3 conditions – Battery charge reaches the daily trip demand – Battery reaches maximum charge level – PEV leaves the grid Assume energy consumption rate and effective battery size of PEVs are distributed normally: 4 mi/kWh and 7 kWh. BBCR SmartGrid9

11. PEV Load Model Simulations State-Space disturbance model – How to get W(t) Entering/exiting PEV? – Let f in (t) denote the total PEV flow into the grid can be obtained use last trip arrival time distribution – f out (t) denote output flow at the last discretization segment governed by the dynamics of PEVs – W(t) is BBCR SmartGrid10

12. PEV Load Model Simulations Monte Carlo and State Space Model simulations – Use u(t) = 0.5 and u(t) = 0.1 for P max = 2KW BBCR SmartGrid11

13. Control part Objectives: – Derive a control law for the charging rate u(t), such that stabilizes the imbalance between the power supply P des (t) and demand P T (t), represented by a measurable error signal e(t) = P des (t) - P T (t) Control design – Lyapunov stability conditions A positive-definite Lyapunov candidate function V(t) = 0.5e 2 (t) V(t+1) – V(t): design u(t) such that this term is negative Key assumptions: – power trajectory remains inside the trackable domain of the PEV load BBCR SmartGrid12

14. Control part Control Law designed: – Following control law results in the convergence of the tracking error defined by e(t) to zero Where the control gain satisfies a robustness condition given by – Remark: u(t) bounded between 0 and 1 under the law BBCR SmartGrid13

15. An example: wind power tracking Setup – Wind date from National Renewable Energy Lab, a 10.5 MW wind plant – Use the Monte Carlo model with 1000PEVs – 24 hours simulation – The wind power is calculated as about 57.5MWh, corresponds to the daily energy demand of nearly 12150 PEVs – Examine the track performance BBCR SmartGrid14

16. An example: wind power tracking BBCR SmartGrid 15

17. conclusion A modeling and control framework for the robust renewable power tracking using PEVs A PDE model with the consideration of control variables and validated through real data A control law derived from Lyapunov stability conditions Limitations – U(t): homogeneous, location ignorance – Control objective: from power system point of view BBCR SmartGrid16

18. Thank you! BBCR SmartGrid17