Optimal Control for Battery Storage UsingNonlinear Models

Di Wu, Patrick Balducci, Alasdair Crawford,Vilayanur Viswanathan, and Michael Kintner-Meyer

Pacific Northwest National Laboratory

October 12, 2017

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Outline

Outline

1 Introduction

2 Optimal charging control using linear and nonlinear models

3 Case study

4 Conclusion and future work

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Introduction

Background

Grid applications:Energy arbitrageBalancing serviceCapacity valueDistribution system upgrade deferralOutage mitigation

Customer-side applications:Energy charge reductionDemand charge reduction

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Introduction

Motivation

Optimal control is desired in order to best utilize the limitedpower and energy capacity of BSSLook-ahead optimization is required to capture interdependentoperation over timeFixed power rating and constant round-trip or one-wayefficiencies are used in existing optimal scheduling methods

I inaccurate economic assessment resultsI infeasible operating schedule

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Optimal charging control using linear and nonlinear models

Optimal scheduling with linear battery model

P1 : maxpk,pbatt

k,sk,∆sk

K∑k=1

λkpk

subject to:Charging/discharging limit: −p−

max ≤ pk ≤ p+max, ∀k = 1 , · · · ,K

Rate change of energy in batt.: pbattk =

{pk/η

+ if pk ≥ 0pkη

− if pk < 0, ∀k = 1 , · · · ,K

SOC change: ∆sk = pbattk ∆T/Emax, ∀k = 1 , · · · ,K

Dynamics of SOC: sk = sk−1 −∆sk, ∀k = 1 , · · · ,KSOC limits: Sk ≤ sk ≤ Sk, ∀k = 1 , · · · ,K

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Optimal charging control using linear and nonlinear models

Limitations with existing linear battery model

[−pmin, pmax]: incapable to model varying charging/dischargingrangeEmax: inaccurate to represent energy capacityη+, η+: difficult to estimate overall efficiency and inaccurate tocapture actual losses

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Optimal charging control using linear and nonlinear models

Varying power capability and SOC change rate

0 0.2 0.4 0.6 0.8 1−1

−0.5

0

0.5

1

1.5

SOC

Ch

an

ge

of

SO

C p

er

ho

ur

charging 600 kW

charging 500 kW

charging 400 kW

charging 200 kW

discharging 800 kW

discharging 520 kW

discharging 400 kW

1 MW/3.2 MWh vanadium redox BSS

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Optimal charging control using linear and nonlinear models

Varying power capability and SOC change rate (cont.)

0 0.2 0.4 0.6 0.8 1

−0.2

−0.1

0

0.1

0.2

0.3

SOC

Ch

an

ge

of

SO

C p

er

10

0 k

W p

er

ho

ur

charging 600 kW

charging 500 kW

charging 400 kW

charging 200 kW

discharging 800 kW

discharging 520 kW

discharging 400 kW

1 MW/3.2 MWh vanadium redox BSS

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Optimal charging control using linear and nonlinear models

Optimal scheduling with nonlinear battery model

P2 : maxpk,sk,∆sk

K∑k=1

λkpk

subject to:Charging/discharging limit: pk ∈ Psk

, ∀k = 1 , · · · ,KSOC change: ∆sk = f(pk, sk), ∀k = 1 , · · · ,K

Dynamics of SOC: sk = sk−1 −∆sk, ∀k = 1 , · · · ,KSOC limits: Sk ≤ sk ≤ Sk, ∀k = 1 , · · · ,K

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Case study

Assumptions and inputs

BSS: 1 MW/3.2 MWh vanadium redox BSS at Turnersubstation in Pullman in Washington State.Applications: energy arbitrage and energy imbalance reductionPrice: The Mid-Columbia prices from 2011 to 2015

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Case study

Economic performance comparison results

2011 2012 2013 2014 20150

5

10

15

20

25

30

35

40

45

$000

Opt. P1 using constant eff. & power

Opt. P2 using nonlinear model

2 MW/6.4 MWh

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Case study

Varying round-trip efficiency

0 0.2 0.4 0.6 0.8 10.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

SOC

RT

E

η(s) = rch(s)rdisch(s)

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Case study

BSS power and SOC

01/06/15−06:00 12:00 18:00 01/07−00:00 06:00 12:00 18:00 01/08−00:00

20

25

30

01/06/15−06:00 12:00 18:00 01/07−00:00 06:00 12:00 18:00 01/08−00:00−2

−1

0

1

2

3

Existing method P1

Proposed method P2

01/06/15−06:00 12:00 18:00 01/07−00:00 06:00 12:00 18:00 01/08−00:00

0

0.2

0.4

0.6

0.8

1

Price ($/MWh)

Power (MW)

SOC

Dis

char

ging

Cha

rgin

g

Fig. 5. Charging/discharging operation and SOC in sample days.

of 60% underestimates the efficiency of BSS for manypossible operation and leaves BSS as standby for manytime period when arbitrage could be profitable.

To better see this, energy prices, charging/dischargingoperation, and SOC from both methods are plotted fortwo days of 2015 in Fig. 5. The hours at the beginningand end of the sample period are corresponding to veryhigh and low prices, respectively. Both methods gener-ate similar battery discharging and charging operation atthe beginning and end of the sample period, becausethe price difference is big enough compared with RTEand energy arbitrage using BSS is profitable. However,existing method P1 outputs some infeasible operation.For example, the BSS is discharged at 2 MW from 7 to9 a.m. and the SOC decreases from 100% to 20%. Infact, the BSS can only be discharged at this full poweroutput within a very limited SOC range. For the otherhours, existing method P1 leaves BSS as standby most ofthe time, because using a constant RTE of 60%, pricedifference is not big enough to recover 40% losses inenergy arbitrage. On the other hand, the proposed methodP2 with nonlinear model is capable to accurately explorethe BSS operating space at different operating power andSOC, takes into account the varying losses, finds profitable

operation, and operates BSS at higher efficiency region tomaximize the benefits from energy arbitrage.

V. CONCLUSION AND FUTURE WORK

This paper presents a novel nonlinear battery model andoptimal control for evaluation and operational schedulingof BSS. Compared with existing methods, the proposedmethod can better capture varying charging/dischargingefficiency and charging/discharging power capability, andtherefore can generate more realistic and optimal operationof BSS for grid applications. The case study using acommercial BSS shows that being incapable of incorpo-rating accurate nonlinear models in optimal schedulingcould results in significant errors in benefits assessment,and even infeasible operation in operational planning. Infuture work, we plan to apply the proposed method withnonlinear BSS model for other grid applications, andevaluate the benefits.

REFERENCES

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[9] J. Neubauer and M. Simpson, “Deployment of behind-the-meterenergy storage for demand charge reduction,” National RenewableEnergy Laboratory, Tech. Rep. NREL/TP-5400-63162, Jan. 2015.

[10] D. Wu, M. Kintner-Meyer, T. Yang, and P. Balducci, “Analyticalsizing methods for behind-the-meter battery storage,” J. EnergyStorage, vol. 12, pp. 297–304, Aug. 2017.

[11] Washington State Department of Commerce, Clean Energy Fund.[Online]. Available: http://classic.commerce.wa.gov/Programs/Energy/Office/Pages/Clean-Energy-Fund-1.aspx

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Conclusion and future work

Conclusion and future work

Conclusion:Nonlinear BSS model better captures varying charging/discharging powercapability and efficiencies.Optimal scheduling without accurate nonlinear BSS model could result insignificant errors in benefits assessment, and even infeasible operation.

Future work:Apply the proposed method with nonlinear model for other grid and/orcustomer-side applications.

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Q & A

Thank you! Questions?

Di Wudi.wu@pnnl.gov

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