Transport-Based Load Modeling and Sliding Mode Control

of Plug-In Electric Vehicles for Robust Renewable Power

Tracking

Presenter: qinghua shen

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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 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.

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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 powerPmax 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) – 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

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Thank you!

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