On Using Storage and Genset for Mitigating Power Grid Failures

Introduction Background Unreliable grid Off-grid Conclusions

On Using Storage and Genset forMitigating Power Grid Failures

Sahil SinglaISS4E lab

University of Waterloo

Collaborators: S. Keshav, Y. Ghiassi-Farrokhfal

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Outline

Introduction

Background

Unreliable grid

Off-grid

Conclusions

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Outline

Introduction

Background

Unreliable grid

Off-grid

Conclusions

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Power outages

• Developing countries:* Large demand-supply gap* Two-to-four hours daily outage

is common1

• Developed countries:* Storms, lightning strikes,

equipment failures* Eg. Sandy

1Tongia et al., India Power Supply Position 2010. Centre for Study ofScience, Technology, and Policy CSTEP, Aug 2010

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Power outages

• Developing countries:* Large demand-supply gap* Two-to-four hours daily outage

is common1

• Developed countries:* Storms, lightning strikes,

equipment failures* Eg. Sandy

1Tongia et al., India Power Supply Position 2010. Centre for Study ofScience, Technology, and Policy CSTEP, Aug 2010

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Diesel generator

• A residential neighbourhood augments grid power

• Usually from a diesel generator (genset)

• High carbon footprint!

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Diesel generator

• A residential neighbourhood augments grid power

• Usually from a diesel generator (genset)

• High carbon footprint!

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Storage battery

• What if the battery goes empty during an outage?• Storage is expensive!

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Storage battery

• What if the battery goes empty during an outage?

• Storage is expensive!

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Storage battery

• What if the battery goes empty during an outage?• Storage is expensive!

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Battery-genset hybrid system

• Use battery to meet demand

• If battery goes empty, turn on genset

• Both benefits

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Goals

We wish to study:

(a) Minimum battery size to eliminate the use of genset

(b) Trade-off between battery size and carbon footprint

(c) Scheduling power between battery and genset

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Goals

We wish to study:




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Goals

We wish to study:




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Outline

Introduction

Background

Unreliable grid

Off-grid

Conclusions

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Factors

0 2 4 6 8 10 12

2

4

6

8

10x 10

5

Power outage duration in hours

Battery

level in

Wh

Figure: Battery trajectories

• Battery size

• Charging rate

• Demand duringoutage

• Outage duration

• Inter-outageduration

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Factors

0 2 4 6 8 10 12

2

4

6

8

10x 10

5

Power outage duration in hours

Battery

level in

Wh

Figure: Battery trajectories

• Battery size

• Charging rate

• Demand duringoutage

• Outage duration

• Inter-outageduration

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Related Work

• Mostly empirical* Both sizing and scheduling

• Analytical work usually assumes stationarity of demand

• No analytical work on battery sizing vs carbon trade-off

• Wang et al.2 do battery sizing for renewables – do notmodel grid unreliability

2Wang et al., A Stochastic Power Network Calculus for IntegratingRenewable Energy Sources into the Power Grid. IEEE JSAC

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Related Work






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Related Work






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Related Work






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Notation

• Discrete time model

• a(t) is arrival in time slot t

• A(s, t) is arrival in time s to t

Name DescriptionB Battery storage capacityC Battery charging rate

x(t) Grid availability 0 or 1d(t) Power demandb(t) Battery state of chargebd(t) Battery deficit charge = B − b(t)l(t) Amount of loss of power

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Notation






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Notation






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Background

• Analogy between loss of packet and loss of power3

B

Buffa(t) C

B

b(t)C d(t)

Pr{b(t) ≤ 0} = Pr{bd(t) ≥ B}= Pr{Buffer ≥ B} = Pr{l(t) > 0}

3Ardakanian et al., On the use of teletraffic theory in power distributionsystems. In Proceedings of e-Energy

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Background

• Analogy between loss of packet and loss of power3

B

Buffa(t) C

B

b(t)C d(t)

Pr{b(t) ≤ 0} = Pr{bd(t) ≥ B}= Pr{Buffer ≥ B} = Pr{l(t) > 0}

3Ardakanian et al., On the use of teletraffic theory in power distributionsystems. In Proceedings of e-Energy

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Stochastic demand

Choices for demand model:

• Constant average demand E [d(t)]

• Markov model* Most results assume stationarity

• Network calculus* Worst case analysis

• Stochastic network calculus

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Stochastic demand


• Constant average demand E [d(t)]• Markov model

* Most results assume stationarity



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Stochastic demand


• Constant average demand E [d(t)]• Markov model

* Most results assume stationarity



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Stochastic Network Calculus

• Example: Design a door* Model human heights

Pr{height ≤ 6ft} = p0Pr{height > 6ft + σ} ≤ (1− p0)e−λσ = εg(σ)

• Interested in modeling cumulative demand* Statistical sample path envelope

Pr

{sups≤t{A(s, t)− G(t − s)} > σ

}≤ εg(σ)

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Pr{height ≤ 6ft} = p0

Pr{height > 6ft + σ} ≤ (1− p0)e−λσ = εg(σ)


Pr


}≤ εg(σ)

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Pr


}≤ εg(σ)

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• Interested in modeling cumulative demand

* Statistical sample path envelope

Pr


}≤ εg(σ)

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Pr


}≤ εg(σ)

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Outline

Introduction

Background

Unreliable grid

Off-grid

Conclusions

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Modeling

• Transformation and effective demand

de(t) = [d(t) + C](1− x(t))= [d(t) + C]xc(t)

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Modeling

• Transformation and effective demand

de(t) = [d(t) + C](1− x(t))= [d(t) + C]xc(t)

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Sizing in absence of genset

Using an amendment of Wang et al.4

Pr{l(t) > 0} ≤ min

(Pr{xc(t) > 0}, εg

(B − sup

τ≥0(G(τ)− Cτ)

))

• Goal is to size battery such that probability of loss of poweris at most ε∗, thus

min

(Pr{xc(t) > 0}, εg

(B − sup

τ≥0(G(τ)− Cτ)

))≤ ε∗

=⇒ B ≥

(supτ≥0

(G(τ)− Cτ) + εg−1 (ε∗)

)I(Pr{xc(t)=1}>ε∗)


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Pr{l(t) > 0} ≤ min

(Pr{xc(t) > 0}, εg

(B − sup

τ≥0(G(τ)− Cτ)

))

• Goal is to size battery such that probability of loss of poweris at most ε∗,

thus

min

(Pr{xc(t) > 0}, εg

(B − sup

τ≥0(G(τ)− Cτ)

))≤ ε∗

=⇒ B ≥

(supτ≥0

(G(τ)− Cτ) + εg−1 (ε∗)

)I(Pr{xc(t)=1}>ε∗)


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Pr{l(t) > 0} ≤ min

(Pr{xc(t) > 0}, εg

(B − sup

τ≥0(G(τ)− Cτ)

))

• Goal is to size battery such that probability of loss of poweris at most ε∗, thus

min

(Pr{xc(t) > 0}, εg

(B − sup

τ≥0(G(τ)− Cτ)

))≤ ε∗

=⇒ B ≥

(supτ≥0

(G(τ)− Cτ) + εg−1 (ε∗)

)I(Pr{xc(t)=1}>ε∗)


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Sizing in presence of genset

• Reduce carbon footprint

• For large gensets

carbon emission ∼∑

t

l(t)

• Scheduling becomes trivial (we’ll come back later)

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Sizing in presence of genset (contd.)

• Goal is to estimate expected total loss (carbon emission)

• Under some assumptions:

E

[T∑

t=1

l(t)

]≈ min

( T∑t=1

E[d(t)xc(t)

],

Pr{max([De(s, t)− C(t − s)− B]+

)> 0}.

T∑t=1

E [d(t)])

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Sizing in presence of genset (contd.)

• Goal is to estimate expected total loss (carbon emission)

• Under some assumptions:

E

[T∑

t=1

l(t)

]≈ min

( T∑t=1

E[d(t)xc(t)

],

Pr{max([De(s, t)− C(t − s)− B]+

)> 0}.

T∑t=1

E [d(t)])

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Data set

• 4500 Irish homes

• Randomly selected 100 homes

• Two-state on-off Markov model for outage

ON OFF

λ

µ

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Data Fitting

Use data set to compute ‘best’ parameters:

• Envelope G = σ + ρt

• Exponential distribution to model εg fails

• Weibull distribution to model εg

• Hyper-exponential distribution to model εg

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Data Fitting






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Data Fitting






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Data Fitting






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Results (absence of genset)

−4 −3.5 −3 −2.5 −20

1

2

3

4

5

6

7

8x 10

5

Logarithm of target power loss probability log10

ε∗

Battery

siz

e B

∗ in W

h

Dataset quantile

Ideal De model

Weibull dist.

Hyper−exp dist.

ε∗ =

2.7

*10

−4

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Results (presence of genset)

0 1 2 3 4 5

x 105

2

4

6

8

10

12x 10

5

Battery size in Wh

Avera

ge c

arb

on e

mis

sio

n in a

week in W

h

Our bound

Ideal De model

Dataset quantile

Battery−less bound

III (B

>C

)

II (

B<

C)

I (B

=0)

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Outline

Introduction

Background

Unreliable grid

Off-grid

Conclusions

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Motivation

• Off-grid industry using genset: how to improve efficiency?

• For small gensets, rate of fuel consumption

k1G + k2d(t)

• Storage battery can help!

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Motivation



k1G + k2d(t)


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Motivation



k1G + k2d(t)


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Problems

(a) Given a genset size, how to size battery and schedulepower?

(b) How to jointly size battery and genset?

We talk only about the former in this presentation

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Problems

(a) Given a genset size, how to size battery and schedulepower?

(b) How to jointly size battery and genset?

We talk only about the former in this presentation

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Battery usage

Theorem: Problem same as minimizing genset operation time

• Offline optimal given by a mixed IP

• General offline problem NP-hard

• Online Alternate scheduling

• Competitive ratiok1

GC + k2

k1 + k2

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Battery usage






GC + k2

k1 + k2

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Battery usage






GC + k2

k1 + k2

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Battery usage






GC + k2

k1 + k2

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Battery usage






GC + k2

k1 + k2

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Savings

• Before:

k1GT + k2

T∑t=1

d(t)

• After (under some assumptions):

k1GT1C

1C + 1

E [d(t)]

+ k2

T∑t=1

d(t)

Beyond a small value, independent of battery size!

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Savings

• Before:

k1GT + k2

T∑t=1

d(t)


k1GT1C

1C + 1

E [d(t)]

+ k2

T∑t=1

d(t)


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Savings

• Before:

k1GT + k2

T∑t=1

d(t)


k1GT1C

1C + 1

E [d(t)]

+ k2

T∑t=1

d(t)


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Result

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Outline

Introduction

Background

Unreliable grid

Off-grid

Conclusions

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Summary

• Power grid unreliable or absent* Genset has high carbon footprint

• Storage battery expensive* Reduce the size

• Minimum battery size required to avoid genset

• Trade-off between battery size and genset carbon footprint

• Power scheduling to improve genset efficiency

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Summary






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Summary






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Summary






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Summary






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Limitations & Future Work

• Past predicts future

• Battery model: size and charging rate independent

• Lack of data from developing countries

• Technical assumptions

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Appendix

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Results (absence of genset)

−4 −3.5 −3 −2.5 −20

0.5

1

1.5

2

2.5x 10

6

Logarithm of target power loss probability log10

ε∗

Battery

siz

e B

∗ in W

h

Dataset quantile

MSM bound

Kesidis bound

Hyper−exp dist.

ε∗ =

2.7

*10

−4

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Three modes

Three modes of battery-genset hybrid system operation:

1. Demand met by battery only2. Demand met by genset only3. Demand simultaneously met by battery and genset

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Documents

On Using Storage and Genset for Mitigating Power Grid Failures