On Using Storage and Genset for Mitigating Power Grid Failures
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1 1 / 27 On Using Storage and Genset for Mitigating Power Grid Failures Sahil Singla ISS4E lab University of Waterloo Collaborators: S. Keshav, Y. Ghiassi-Farrokhfal
2 1 / 27 Outline Introduction Background Unreliable grid Off-grid Conclusions
3 1 / 27 Outline Introduction Background Unreliable grid Off-grid Conclusions
4 Power outages Developing countries: * Large demand-supply gap * Two-to-four hours daily outage is common 1 1 Tongia et al., India Power Supply Position Centre for Study of Science, Technology, and Policy CSTEP, Aug / 27
5 Power outages Developing countries: * Large demand-supply gap * Two-to-four hours daily outage is common 1 Developed countries: * Storms, lightning strikes, equipment failures * Eg. Sandy 1 Tongia et al., India Power Supply Position Centre for Study of Science, Technology, and Policy CSTEP, Aug / 27
6 3 / 27 Diesel generator A residential neighbourhood augments grid power Usually from a diesel generator (genset)
7 3 / 27 Diesel generator A residential neighbourhood augments grid power Usually from a diesel generator (genset) High carbon footprint!
8 4 / 27 Storage battery
9 4 / 27 Storage battery What if the battery goes empty during an outage?
10 4 / 27 Storage battery What if the battery goes empty during an outage? Storage is expensive!
11 5 / 27 Battery-genset hybrid system Use battery to meet demand If battery goes empty, turn on genset Both benefits
12 6 / 27 Goals We wish to study: (a) Minimum battery size to eliminate the use of genset
13 6 / 27 Goals We wish to study: (a) Minimum battery size to eliminate the use of genset (b) Trade-off between battery size and carbon footprint
14 6 / 27 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
15 6 / 27 Outline Introduction Background Unreliable grid Off-grid Conclusions
16 7 / 27 Factors 10 x Battery level in Wh Power outage duration in hours Figure: Battery trajectories
17 7 / 27 Factors Battery level in Wh 10 x Power outage duration in hours Figure: Battery trajectories Battery size Charging rate Demand during outage Outage duration Inter-outage duration
18 Related Work Mostly empirical * Both sizing and scheduling 2 Wang et al., A Stochastic Power Network Calculus for Integrating Renewable Energy Sources into the Power Grid. IEEE JSAC 8 / 27
19 Related Work Mostly empirical * Both sizing and scheduling Analytical work usually assumes stationarity of demand 2 Wang et al., A Stochastic Power Network Calculus for Integrating Renewable Energy Sources into the Power Grid. IEEE JSAC 8 / 27
20 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 2 Wang et al., A Stochastic Power Network Calculus for Integrating Renewable Energy Sources into the Power Grid. IEEE JSAC 8 / 27
21 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 not model grid unreliability 2 Wang et al., A Stochastic Power Network Calculus for Integrating Renewable Energy Sources into the Power Grid. IEEE JSAC 8 / 27
22 9 / 27 Notation Discrete time model
23 9 / 27 Notation Discrete time model a(t) is arrival in time slot t A(s, t) is arrival in time s to t
24 9 / 27 Notation Discrete time model a(t) is arrival in time slot t A(s, t) is arrival in time s to t Name Description B Battery storage capacity C Battery charging rate x(t) Grid availability 0 or 1 d(t) Power demand b(t) Battery state of charge b d (t) Battery deficit charge = B b(t) l(t) Amount of loss of power
25 Background Analogy between loss of packet and loss of power 3 Buff b(t) a(t) C C d(t) B B 3 Ardakanian et al., On the use of teletraffic theory in power distribution systems. In Proceedings of e-energy 10 / 27
26 Background Analogy between loss of packet and loss of power 3 Buff b(t) a(t) C C d(t) B B Pr{b(t) 0} = Pr{b d (t) B} = Pr{Buffer B} = Pr{l(t) > 0} 3 Ardakanian et al., On the use of teletraffic theory in power distribution systems. In Proceedings of e-energy 10 / 27
27 11 / 27 Stochastic demand Choices for demand model: Constant average demand E[d(t)]
28 11 / 27 Stochastic demand Choices for demand model: Constant average demand E[d(t)] Markov model * Most results assume stationarity
29 11 / 27 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
30 12 / 27 Stochastic Network Calculus Example: Design a door * Model human heights
31 12 / 27 Stochastic Network Calculus Example: Design a door * Model human heights Pr{height 6ft} = p 0
32 12 / 27 Stochastic Network Calculus Example: Design a door * Model human heights Pr{height 6ft} = p 0 Pr{height > 6ft + σ} (1 p 0 )e λσ = ε g (σ)
33 12 / 27 Stochastic Network Calculus Example: Design a door * Model human heights Pr{height 6ft} = p 0 Pr{height > 6ft + σ} (1 p 0 )e λσ = ε g (σ) Interested in modeling cumulative demand
34 12 / 27 Stochastic Network Calculus Example: Design a door * Model human heights Pr{height 6ft} = p 0 Pr{height > 6ft + σ} (1 p 0 )e λσ = ε g (σ) Interested in modeling cumulative demand * Statistical sample path envelope { } Pr sup{a(s, t) G(t s)} > σ s t ε g (σ)
35 12 / 27 Outline Introduction Background Unreliable grid Off-grid Conclusions
36 13 / 27 Modeling Transformation and effective demand
37 13 / 27 Modeling Transformation and effective demand d e (t) = [d(t) + C](1 x(t)) = [d(t) + C]x c (t)
38 Sizing in absence of genset Using an amendment of Wang et al. 4 Pr{l(t) > 0} min (Pr{x c (t) > 0}, ε g ( B sup(g(τ) Cτ) τ 0 )) 4 Wang et al., A Stochastic Power Network Calculus for Integrating Renewable Energy Sources into the Power Grid. IEEE JSAC 14 / 27
39 Sizing in absence of genset Using an amendment of Wang et al. 4 Pr{l(t) > 0} min (Pr{x c (t) > 0}, ε g ( B sup(g(τ) Cτ) τ 0 )) Goal is to size battery such that probability of loss of power is at most ɛ, 4 Wang et al., A Stochastic Power Network Calculus for Integrating Renewable Energy Sources into the Power Grid. IEEE JSAC 14 / 27
40 Sizing in absence of genset Using an amendment of Wang et al. 4 Pr{l(t) > 0} min (Pr{x c (t) > 0}, ε g ( B sup(g(τ) Cτ) τ 0 )) Goal is to size battery such that probability of loss of power is at most ɛ, thus ( )) (Pr{x c (t) > 0}, ε g min = B ( B sup(g(τ) Cτ) τ 0 ) sup(g(τ) Cτ) + ε 1 g (ɛ ) τ 0 ɛ I (Pr{x c (t)=1}>ɛ ) 4 Wang et al., A Stochastic Power Network Calculus for Integrating Renewable Energy Sources into the Power Grid. IEEE JSAC 14 / 27
41 15 / 27 Sizing in presence of genset Reduce carbon footprint For large gensets carbon emission t l(t) Scheduling becomes trivial (we ll come back later)
42 16 / 27 Sizing in presence of genset (contd.) Goal is to estimate expected total loss (carbon emission)
43 16 / 27 Sizing in presence of genset (contd.) Goal is to estimate expected total loss (carbon emission) Under some assumptions: [ T ] ( T E l(t) min E [ d(t)x c (t) ], t=1 t=1 Pr{max ( [D e (s, t) C(t s) B] + ) > 0}. T t=1 ) E[d(t)]
44 17 / 27 Data set 4500 Irish homes Randomly selected 100 homes Two-state on-off Markov model for outage λ ON OFF µ
45 18 / 27 Data Fitting Use data set to compute best parameters: Envelope G = σ + ρt
46 18 / 27 Data Fitting Use data set to compute best parameters: Envelope G = σ + ρt Exponential distribution to model ε g fails
47 18 / 27 Data Fitting Use data set to compute best parameters: Envelope G = σ + ρt Exponential distribution to model ε g fails Weibull distribution to model ε g
48 18 / 27 Data Fitting Use data set to compute best parameters: Envelope G = σ + ρt Exponential distribution to model ε g fails Weibull distribution to model ε g Hyper-exponential distribution to model ε g
49 19 / 27 Results (absence of genset) Battery size B in Wh 8 x ε = 2.7*10 4 Dataset quantile Ideal D e model Weibull dist. Hyper exp dist Logarithm of target power loss probability log ε 10
50 20 / 27 Results (presence of genset) Average carbon emission in a week in Wh 12 x I (B=0) II (B<C) III (B>C) Battery less bound Our bound Ideal D e model Dataset quantile Battery size in Wh x 10 5
51 20 / 27 Outline Introduction Background Unreliable grid Off-grid Conclusions
52 21 / 27 Motivation Off-grid industry using genset: how to improve efficiency?
53 21 / 27 Motivation Off-grid industry using genset: how to improve efficiency? For small gensets, rate of fuel consumption k 1 G + k 2 d(t)
54 21 / 27 Motivation Off-grid industry using genset: how to improve efficiency? For small gensets, rate of fuel consumption k 1 G + k 2 d(t) Storage battery can help!
55 22 / 27 Problems (a) Given a genset size, how to size battery and schedule power? (b) How to jointly size battery and genset?
56 22 / 27 Problems (a) Given a genset size, how to size battery and schedule power? (b) How to jointly size battery and genset? We talk only about the former in this presentation
57 23 / 27 Battery usage Theorem: Problem same as minimizing genset operation time
58 23 / 27 Battery usage Theorem: Problem same as minimizing genset operation time Offline optimal given by a mixed IP
59 23 / 27 Battery usage Theorem: Problem same as minimizing genset operation time Offline optimal given by a mixed IP General offline problem NP-hard
60 23 / 27 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
61 23 / 27 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 ratio k 1 G C + k 2 k 1 + k 2
62 24 / 27 Savings Before: T k 1 GT + k 2 d(t) t=1
63 24 / 27 Savings Before: T k 1 GT + k 2 d(t) t=1 After (under some assumptions): k 1 GT 1 C 1 C + 1 E[d(t)] T + k 2 d(t) t=1
64 24 / 27 Savings Before: T k 1 GT + k 2 d(t) t=1 After (under some assumptions): k 1 GT 1 C 1 C + 1 E[d(t)] T + k 2 d(t) t=1 Beyond a small value, independent of battery size!
65 25 / 27 Result
66 25 / 27 Outline Introduction Background Unreliable grid Off-grid Conclusions
67 26 / 27 Summary Power grid unreliable or absent * Genset has high carbon footprint
68 26 / 27 Summary Power grid unreliable or absent * Genset has high carbon footprint Storage battery expensive * Reduce the size
69 26 / 27 Summary Power grid unreliable or absent * Genset has high carbon footprint Storage battery expensive * Reduce the size Minimum battery size required to avoid genset
70 26 / 27 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
71 26 / 27 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
72 27 / 27 Limitations & Future Work Past predicts future Battery model: size and charging rate independent Lack of data from developing countries Technical assumptions
73 Appendix 27 / 27
74 27 / 27 Results (absence of genset) 2.5 x Battery size B in Wh ε = 2.7*10 4 Dataset quantile MSM bound Kesidis bound Hyper exp dist Logarithm of target power loss probability log 10 ε
75 27 / 27 Three modes Three modes of battery-genset hybrid system operation: 1. Demand met by battery only 2. Demand met by genset only 3. Demand simultaneously met by battery and genset
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