Stochastic Storage Valuation Considering Aging Processes ...€¦ · Stochastic Storage Valuation...

Stochastic Storage Valuation Considering

Aging Processes (Lithium-Ion)

Benjamin Böcker, Andreas Dietrich, Christoph Weber

Session MB-43: Energy Storage and Renewables

Stream: Stochastic Models in Renewably Generated Electricity

28th European Conference on Operational Research, Poznan, Poland, 7/4/2016

• Future energy systems:

– High share of renewables (dominated by highly fluctuating wind and pv infeed)

– Political and social objective of a withdrawal from conventional (fossile based) power plants

challenge to match electricity demand and supply

Increasing need of flexibility options

Storage as one important group of technologies

• Valuating storage highly depends on

7/4/201628th European Conference on Operational Research, Poznan, Poland

Motivation

2

Motivation 1 2 3 4 5

– Stochastic / Uncertainty

▪ prices fluctuations (e.g. energy and reserve markets)

▪ PV fluctuations (e.g. private households)

▪ Regulatory framework

– Technical characteristics

▪ Limitation in storage volume and capacity

▪ Reversible and irreversible losses / aging

• Adequate Valuation makes it necessary to considering both

– Stochastic / Uncertainty and Technical characteristics

Using Least-Square Monte Carlo Method

– Stochastics of infeed and/or prices can take into account

– Advantage of considering the non-linearity of aging (calendrical and cyclical)


Motivation

3

Motivation 1 2 3 4 5


Agenda

4

1. Motivation

2. Simplified Aging Model

3. Least-Square Monte Carlo Approach

4. Application: Spot Market

5. Conclusion

Stochastic Storage Valuation Considering Aging Processes (Lithium-Ion) 1 2 3 4 5


Calendrical Aging – Database

5

Simplified Aging Model 1 2 3 4 5

Normalized capacity vs. timeCalendar life time (one year calendar life time at 50°C corresponds to approximately 5.6 years at 25°C)

Quelle: Ecker, Nieto, Käbitz, Schmalstieg, Blanke, Warnecke, Sauer; Calendar and cycle life study of Li(NiMnCo)O2-based 18650 lithiumion batteries; Journal of Power Sources, 2013

Quelle: Saft, 2014


Calendrical Aging – Overview Lithium-Ion

6


𝑐𝑖𝑛𝑣,𝑉𝑆 = 1000€

𝑘𝑊ℎ


Cyclical Aging – Database

7



Cyclical Aging – Overview Lithium-Ion

8



𝑘𝑊ℎ𝑐𝑖𝑛𝑣,𝑉𝑆 = 1000€

𝑘𝑊ℎ


Aging of a Lithium-Ion Battery (calendrical and cyclical aging)

9



𝑘𝑊ℎ


Agenda

10

1. Motivation




5. Conclusion


• Originally for valuating American options [Longstaff, Schwartz, 2001]

– optimal exercise (single option – sell)

– one-time

– N price-paths

• Adjusted algorithm for storage valuation [Felix, Weber, 2008], [Boogert, De Jong,2005, 2006]

– optimal operation (multiple options – charging/discharging) – limited by the storage level (volume)

(one-dimensional grid of storage states)

– multiple-time

• Considering storage aging / state of health (SOH) – [Böcker, Dietrich, Weber, 2016]

– optimal operation (multiple options – charging/discharging) – limited by the storage level (volume) and SOH

(two-dimensional grid of storage states)


Demarcation to existing Applications

11

Least-Square Monte Carlo Approach 1 2 3 4 5

• Fixed grid of

– States: State of Charge (SOC) and State of Health (SOH)

– Paths: Prices and/or Infeed (stochastic simulation)

– Options: all possible storage operation (delta SOC)

• Backward simulation (start at T>estimated life time)

• Objective:

– Calculate value of the storage (at all states) over the time

– Derive of target costs


Method – Overview

12


Storage Level


Method – Algorithm

13


SO

C

SOH

1. Step: Determination Continuation Value

discounting each Value(t+1,…)

0

-1

-2

+1

+2

2. Step: Estimate 𝐶𝑉 considering all paths

regression of CV for each state on all paths

4. Step: Select most efficient options

highest value (each state and path)

3. Step: value determination including all options

cash flow (varies between options) plus affiliated 𝐶𝑉

t+1t

𝑉(𝑡 + 1, 𝑠𝑡𝑎𝑡𝑒𝑠, 𝑝𝑎𝑡ℎ𝑠)𝐶𝑉(𝑡, 𝑠𝑡𝑎𝑡𝑒𝑠, 𝑝𝑎𝑡ℎ𝑠)𝐶𝑉 (𝑡, 𝑠𝑡𝑎𝑡𝑒𝑠, 𝑝𝑎𝑡ℎ𝑠)

𝑉𝑂(𝑡, 𝑠𝑡𝑎𝑡𝑒𝑠, 𝑝𝑎𝑡ℎ𝑠, 𝑜𝑝𝑡𝑖𝑜𝑛𝑠)

𝑉(𝑡, 𝑠𝑡𝑎𝑡𝑒𝑠, 𝑝𝑎𝑡ℎ𝑠)

• Implementation in MATLAB

• Based on pre-calculated array of possible options (considering limitations of storage states)

and related changes in the storage states SOC and SOH

More efficient through avoid catching invalid options (charging and discharging rates) within the loop

• Using matrix-operations as far as possible

• Additional:

– Using developed storage aging model

– Implantation of inverter efficiency curve


Method – Implementation

14



Agenda

15

1. Motivation




5. Conclusion


• Stationary Battery:

– Power of 1MW

– Volume of 5MWh

– Cell efficiency of 0.98

– Total efficiency between and 0.57 and 0.88

– ~7.000 Full-Cycles

– EOL 0.7 (EOsL 0.4)

– Interest rate 5.7 %

• Generating revenues on Spot-Market (no Reserve)


Main Specifications of the Lithium-Ion Battery

16

Application: Spot Market 1 2 3 4 5

• Spot-Prices (2016 – 2015, hourly, right)

• Installed conv. Capacities (below)

• Number of negative Residual-Load


Price Simulation

17


• 10 State of Charge (SOC)

• 15 Available storage volume (0.4 until 1) and 21 (0 until 1) SOH

• 20 different option for each state (no impossible options)

• Simulation time ~ 1h per year


Implementation in MATLAB

18



Value of the Battery Storage: 2016

19


Continuation Value for a full and new storage

265,5


Analyzing of the Storage Value (left: base, right: double aging after EOL)

20


-10% in maximum valueLife time

• Inverter Costs ~ 30 to 150 T€/MW 30 T€/MW

• Target costs: 265.5𝑇€−1𝑀𝑊∙30

𝑇€

𝑀𝑊

5𝑀𝑊ℎ= 47.1

€

𝑀𝑊ℎ≪ 100

€

𝑀𝑊ℎ

• Seasonality: More revenues during summer


Target Costs Estimation

21



Agenda

22

1. Motivation




5. Conclusion


Method:

• Flexible approach to valuate storage systems with their main characteristics under

uncertainty

• Problem: Life-time simulation for a more realistic valuation

• Further research question:

– How to estimate the value (partly-aged) storage systems without lifetime-simulation?

– Decrease number of simulations (time steps) until reaching “stable” valuation

No efficient investment in Lithium Ion battery systems (action only on spot market)


Summary

23

Conclusion 1 2 3 4 5

Many Thanks

Contact: Benjamin Böcker

E-Mail: [email protected]

Phone.: +49 201/183-7306

mailto:[email protected]

Backup Slides

Contact: Benjamin Böcker

E-Mail: [email protected]

Phone.: +49 201/183-7306

mailto:[email protected]

• Summary: Aging increases with higher SOC

• Combined Model:

1. Relation to SOC (50°C)

2. Adjustment to SAFT Data

Saft: ~10% Aging in 20 years (25°C)


Calendrical Aging – Model Approach

26


a -6,804E-04

b -1,306E-04

c 2,554E-02

SOC

0,0

0,3

0,7

0,9

𝑑𝑉𝑙𝑜𝑠𝑠,𝑐𝑎𝑙 𝑆𝑂𝐶(𝑡) = 𝑎 ∙ 𝑆𝑂𝐶(𝑡) + 𝑏 ∙ 𝑑𝑡

𝑑𝑆𝑂𝐻𝑐𝑎𝑙 𝑙𝑆 𝑡 , ∆𝑙𝑆 𝑡 , 𝑣𝑆 𝑡 =𝑎

𝑣𝑆 𝑡∙ 𝑙𝑆 𝑡 + 0,5∆𝑙𝑆 𝑡 + 𝑏 ∙ 𝑐 ∙ ∆𝑡 ∙ 1 − 𝐸𝑂𝐿

• Cycle test includes calendrical aging

– Adjustment to exclude calendrical aging, extract cyclical aging, assumption:

– Same charge- discharge rates (0.5 C charging, 1 C discharging) time/cyclus = 3 hours

– Uniform aging ( ∅𝑆𝑂𝐶 = 1 − 0,5 ∙ 𝐷𝑂𝐷 )


Cyclical Aging – Model Approach

27


DOD [-] Cycle old [-] ∅ 𝑺𝑶𝑪 [-] 𝑻𝑪𝒚𝒄𝒍𝒆 [h] 𝒅𝑺𝑶𝑯 [-] Cycle new [-]

1 5.000 0,5 15.000 - 0,0250 5.128

0,6 10.000 0,7 18.000 - 0,0387 10.403

0,2 100.000 0,9 60.000 - 0,1581 118.780

0,05 1.000.000 0,975 150.000 - 0,4224 1.731.322

𝑇𝐶𝑦𝑐𝑙𝑒 = 𝐷𝑂𝐷 ∙ 𝐶𝑦𝑐𝑙𝑒𝐷𝑂𝐷 ∙ 3 𝐶𝑦𝑐𝑙𝑒 𝑛𝑒𝑤 =𝐶𝑦𝑐𝑙𝑒 𝑜𝑙𝑑

1 + 𝑑𝑆𝑂𝐻 Cycle aging new

𝑑𝑆𝑂𝐻𝑐𝑦𝑐 𝑙𝑆 𝑡 , ሶ𝑙𝑆 𝑡 , 𝑣𝑆 𝑡 = −1

2𝑎1 −

𝑙𝑆 𝑡 + ሶ𝑙𝑆 𝑡

𝑣𝑆 𝑡

−𝑏

− 1 −𝑙𝑆 𝑡

𝑣𝑆 𝑡

−𝑏

• Estimate continuation value 𝐶𝑉 regression of CV for each state on paths

– Using polynomial fit of the degree of three

• Why using an estimation of the continuation value?

– CV varies depending on the current price/path

– Uncertainty of the true future value of the storage

(primary based on the cash flows)

– No perfect foresight

(Otherwise simultaneous calculation of single optimal

decisions for each path separately)

• Considering uncertainty Using Estimation


Method – Closer Look

2. Step: Estimate Continuation Value

28


27.12.2016 13:00 SOC = 0.44 SOH = 0.64

• Value determination are divided into cash flow (varies between options) and affiliated 𝐶𝑉

• Cash flow or pay-off function highly dependent on application, e.g.:

– revenues on the spot-market

– avoided electricity purchase in private households

• Affiliated 𝐶𝑉

– Each exercise of an option (charging, discharging rates) leads to changes in both storage level and SOH

– Even in the case of fine meshed grids of the states, these changes typically doesn't met the grid exactly

– Multidimensional interpolation (linear) on the 𝐶𝑉-grid


Method – Closer Look

3. Step: Value Determination Including all Options

29


Stochastic Storage Valuation Considering Aging Processes ...€¦ · Stochastic Storage Valuation...

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