Distributed Control of Electric Vehicle Charging

Omid Ardakanian, Catherine Rosenberg, S. Keshav

EV market is growing rapidly

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Electric Vehicles – Challenges & Opportunities

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spatial & temporal uncertainties

EV charging load is significant

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Electric Vehicles – Challenges & Opportunities

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spatial & temporal uncertainties

impact on the distribution network

EV charging load is significant

Lopes, J.A.P.; Soares, F.J.; Almeida, P.M.R., "Integration of Electric Vehicles in the Electric Power System," Proceedings of the IEEE , vol.99, no.1, pp.168,183, Jan. 2011

Impacts on the Grid • Branch and transformer congestion

– accelerates degradation of power apparatus

– leads to overheating (risk of explosion)

– may trigger the protection system

• Voltage swings at distant buses – affects the grid reliability

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Electric Vehicles – Challenges & Opportunities

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spatial & temporal uncertainties

scheduling & control

impact on the distribution network

EV charging load is significant

State of the Art Approach: Scheduling

• Scheduling solutions typically solve a power flow problem

• They rely on

– an accurate model of the distribution network

– prediction of the home loads

– prediction of arrivals and departures of EVs

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Our Approach is…

To adapt the charging rate of EV chargers to the available capacity of the distribution network in real-time using the same tricks as TCP congestion control

Real-time control is feasible in the smart grid

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Smart Grid Enables Real-time Control

• Pervasive measurement

• Broadband communication

• Increased intelligence

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MCC nodes

Smart chargers

Every line/transformer has a setpoint

We are inspired by the success of TCP congestion control

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efficiency

fairness

scalability

stability

robustness

responsiveness

Optimal Control

A single snapshot optimization problem:

max𝑟𝑎𝑡𝑒 log 𝑟𝑎𝑡𝑒𝑠𝑠∈𝒮

subject to

0 ≤ 𝑟𝑎𝑡𝑒𝑠 ≤ 𝑚𝑎𝑥𝑟𝑎𝑡𝑒𝑠 ∀𝑠 ∈ 𝒮

𝐸𝑉 𝑙𝑜𝑎𝑑𝑙 + ℎ𝑜𝑚𝑒 𝑙𝑜𝑎𝑑𝑙 ≤ 𝑠𝑒𝑡𝑝𝑜𝑖𝑛𝑡𝑙 ∀𝑙 ∈ ℒ

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Similar to [Low99], [Kelly98]

utility of s

Optimal Control

A single snapshot optimization problem:

max𝑟𝑎𝑡𝑒 log 𝑟𝑎𝑡𝑒𝑠𝑠∈𝒮

subject to

0 ≤ 𝑟𝑎𝑡𝑒𝑠 ≤ 𝑚𝑎𝑥𝑟𝑎𝑡𝑒𝑠 ∀𝑠 ∈ 𝒮

𝐸𝑉 𝑙𝑜𝑎𝑑𝑙 + ℎ𝑜𝑚𝑒 𝑙𝑜𝑎𝑑𝑙 ≤ 𝑠𝑒𝑡𝑝𝑜𝑖𝑛𝑡𝑙 ∀𝑙 ∈ ℒ

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Similar to [Low99], [Kelly98]

Optimal Control

A single snapshot optimization problem:

max𝑟𝑎𝑡𝑒 log 𝑟𝑎𝑡𝑒𝑠𝑠∈𝒮

subject to

0 ≤ 𝑟𝑎𝑡𝑒𝑠 ≤ 𝑚𝑎𝑥𝑟𝑎𝑡𝑒𝑠 ∀𝑠 ∈ 𝒮

𝐸𝑉 𝑙𝑜𝑎𝑑𝑙 + ℎ𝑜𝑚𝑒 𝑙𝑜𝑎𝑑𝑙 ≤ 𝑠𝑒𝑡𝑝𝑜𝑖𝑛𝑡𝑙 ∀𝑙 ∈ ℒ

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Similar to [Low99], [Kelly98]

𝑙

𝑠𝑢𝑏𝑡𝑟𝑒𝑒(𝑙)

Optimal Control

Consider a series of snapshots

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1 2 3 4

(measured by an MCC node)

line

/tra

nsf

orm

er

load

ing

Distributed Control vs. Centralized Control

Pros:

• No single point of failure

• Scalability

• Charging rates do not change drastically – the stepsize bounds the change

Cons:

• Convergence time

• Communication overhead

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Dual Decomposition & Control Rules

• Two phases are repeated in every iteration of the algorithm

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Master Problem (solved at MCC nodes)

Subproblem 1 (solved at EV charger 1)

Subproblem n (solved at EV charger n)

𝑝𝑟𝑖𝑐𝑒𝑠 𝑝𝑟𝑖𝑐𝑒𝑠

…

Lagrangian multipliers

Dual Decomposition & Control Rules

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MCC nodes solve master problem

Smart chargers solve subproblems

Dual Decomposition & Control Rules

1. MCC nodes update congestion prices and send them to downstream EV chargers

𝑝𝑟𝑖𝑐𝑒𝑙 ← max {𝑝𝑟𝑖𝑐𝑒𝑙 − 𝑠𝑡𝑒𝑝𝑠𝑖𝑧𝑒 × (𝑠𝑒𝑡𝑝𝑜𝑖𝑛𝑡𝑙 − 𝑙𝑜𝑎𝑑𝑙), 0}

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Master Problem (solved at MCC nodes)

Subproblem 1 (solved at EV charger 1)

Subproblem n (solved at EV charger n)

𝑝𝑟𝑖𝑐𝑒𝑠 𝑝𝑟𝑖𝑐𝑒𝑠

…

Lagrangian multipliers

Dual Decomposition & Control Rules

2. New rates are obtained from solving subproblems using new congestion prices

𝑟𝑎𝑡𝑒𝑠← min1

𝑝𝑎𝑡ℎ 𝑝𝑟𝑖𝑐𝑒𝑠, 𝑚𝑎𝑥𝑟𝑎𝑡𝑒𝑠

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Master Problem (solved at MCC nodes)

Subproblem 1 (solved at EV charger 1)

Subproblem n (solved at EV charger n)

… 𝑟𝑎𝑡𝑒1

𝐸𝑉 𝑙𝑜𝑎𝑑𝑙

𝑟𝑎𝑡𝑒𝑛

Measurement/Control Timescale

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t = 0 iteration 1

MCC node decreases congestion price

line

/tra

nsf

orm

er

load

ing

Measurement/Control Timescale

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t = delay iteration 1

Downstream chargers increase their rate

line

/tra

nsf

orm

er

load

ing

Measurement/Control Timescale

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t = Tc

iteration 2

MCC node increases congestion price

line

/tra

nsf

orm

er

load

ing

Measurement/Control Timescale

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t = Tc+delay iteration 2

Downstream chargers decrease their rate

line

/tra

nsf

orm

er

load

ing

Stability

• Control is stable for 𝑠𝑡𝑒𝑝𝑠𝑖𝑧𝑒 ≤ 𝑠𝑡𝑒𝑝𝑠𝑖𝑧𝑒∗, 𝑇𝑐 ≥ 𝑑𝑒𝑙𝑎𝑦

• The rate of convergence depends on both 𝑠𝑡𝑒𝑝𝑠𝑖𝑧𝑒, 𝑇𝑐

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under-damped

over-damped

Simulation

IEEE 13-bus test feeder

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Operation Modes of the Algorithm

• Normal operation mode

• Emergency response mode

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change in home load

change in home load

Conclusions

• Controlling the EV charging load reduces the need for over-provisioning

• Pervasive measurement and broadband communication in a distribution network motivate real-time control of elastic loads

• Using explicit congestion notification, the EV charging load can be controlled in real-time

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Guidelines for Setting Control Parameters

• 𝑇𝑐 must be as small as possible

– But in practice 𝑇𝑐 ≫ 𝑑𝑒𝑙𝑎𝑦

• 𝑠𝑡𝑒𝑝𝑠𝑖𝑧𝑒 must be as large as possible

– 𝑠𝑡𝑒𝑝𝑠𝑖𝑧𝑒 = 𝑠𝑡𝑒𝑝𝑠𝑖𝑧𝑒∗

• 𝑠𝑒𝑡𝑝𝑜𝑖𝑛𝑡 can be chosen such that overshoots do not cause line or transformer overloading

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