Transport-Based Load Modeling and Sliding Mode Control of Plug-In Electric Vehicles for Robust Renewable Power Tracking. Presenter: qinghua shen. content. Intro to PEV Control-Oriented PEV Load Model PEV model Simulations Control Part Conclusions. Intro.

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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

Intro to PEV

Control-Oriented PEV Load Model

PEV model Simulations

Control Part

Conclusions

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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 gridâ€™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.

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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

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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.

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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: Pmax

Instantaneous charging power

Pmax u(t)

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

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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

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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

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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

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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.

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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

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

W(t) is

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PEV Load Model Simulations

Monte Carlo and State Space Model simulations

Use u(t) = 0.5 and u(t) = 0.1 for Pmax = 2KW

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Control part

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)

Control design

Lyapunov stability conditions

A positive-definite Lyapunov candidate function V(t) = 0.5e2(t)

V(t+1) â€“ V(t): design u(t) such that this term is negative

Key assumptions:

power trajectory remains inside the trackable domain of the PEV load

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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

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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

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An example: wind power tracking

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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