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Presenter: qinghua shen

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### Transport-Based Load Modeling and Sliding Mode Control of Plug-In Electric Vehicles for Robust Renewable Power Tracking

Presenter: qinghua shen

BBCR SmartGrid

content Plug-In Electric Vehicles for Robust Renewable Power Tracking

- Intro to PEV
- Control-Oriented PEV Load Model
- PEV model Simulations
- Control Part
- Conclusions

BBCR SmartGrid

Intro Plug-In Electric Vehicles for Robust Renewable Power Tracking

- 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 SmartGrid

Intro Plug-In Electric Vehicles for Robust Renewable Power Tracking

- 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 SmartGrid

Control-Oriented PEV load Model Plug-In Electric Vehicles for Robust Renewable Power Tracking

- 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 SmartGrid

Control-Oriented PEV load Model Plug-In Electric Vehicles for Robust Renewable Power Tracking

- 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: Pmax
- Instantaneous charging power
Pmax u(t)

- For a small control volume of length of dx, the flux of roads entering the segment:

BBCR SmartGrid

Control-Oriented PEV load Model Plug-In Electric Vehicles for Robust Renewable Power Tracking

- 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 SmartGrid

Control-Oriented PEV load Model Plug-In Electric Vehicles for Robust Renewable Power Tracking

- 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 SmartGrid

Control-Oriented PEV load Model Plug-In Electric Vehicles for Robust Renewable Power Tracking

- 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 SmartGrid

PEV Load Model Simulations Plug-In Electric Vehicles for Robust Renewable Power Tracking

- 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 SmartGrid

PEV Load Model Simulations Plug-In Electric Vehicles for Robust Renewable Power Tracking

- 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

- fout(t) denote output flow at the last discretization segment governed by the dynamics of PEVs
- W(t) is

BBCR SmartGrid

PEV Load Model Simulations Plug-In Electric Vehicles for Robust Renewable Power Tracking

- Monte Carlo and State Space Model simulations
- Use u(t) = 0.5 and u(t) = 0.1 for Pmax = 2KW

BBCR SmartGrid

Control part Plug-In Electric Vehicles for Robust Renewable Power Tracking

- Objectives:
- Derive a control law for the charging rate u(t), such that stabilizes the imbalance between the power supply Pdes(t) and demand PT(t), represented by a measurable error signal
e(t) = Pdes(t) - PT(t)

- Derive a control law for the charging rate u(t), such that stabilizes the imbalance between the power supply Pdes(t) and demand PT(t), represented by a measurable error signal
- Control design
- Lyapunov stability conditions
- A positive-definite Lyapunov candidate function V(t) = 0.5e2(t)
- V(t+1) – V(t): design u(t) such that this term is negative

- Lyapunov stability conditions
- Key assumptions:
- power trajectory remains inside the trackable domain of the PEV load

BBCR SmartGrid

Control part Plug-In Electric Vehicles for Robust Renewable Power Tracking

- 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

- Following control law results in the convergence of the tracking error defined by e(t) to zero

BBCR SmartGrid

An example: wind power tracking Plug-In Electric Vehicles for Robust Renewable 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 SmartGrid

An example: wind power tracking Plug-In Electric Vehicles for Robust Renewable Power Tracking

BBCR SmartGrid

conclusion Plug-In Electric Vehicles for Robust Renewable Power Tracking

- 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 SmartGrid

Thank you! Plug-In Electric Vehicles for Robust Renewable Power Tracking

BBCR SmartGrid

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