Smart Grids EE 772 Department of Electrical Engineering Indian - - PowerPoint PPT Presentation

Smart Grids

EE 772

Department of Electrical Engineering Indian Institute of Technology Bombay, India

October 5, 2018

Sizing and operation of Battery Storage Devices

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Background

• With storage devices, renewable energy generators can behave as con-

stant generation base-load plant, or, renewable energy forecast uncer- tainty can be mitigated

• Sizing is mostly carried out considering probable scenarios, one of the

possible choice can be the use of historical dataset

• Multiple types of storage devices for bulk energy storage in conjunction

is well established:

low-frequency component to be associated with finite cycle batteries Large life-cycle battery to be used in conjunction with high-frequency component Battery mix will be cost-effective

• Typically, DFT-IDFT and the cut-off frequency segregates high and low

frequency components within a dataset

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Imbalance caused by base-load generation scheme

PR (t + (n − 1) · ND) + PS (t + (n − 1) · ND) = PB(n, t); 1 t ND, 1 n NY

Injection from the batteries should cancel out the variability within the stor- age device. Therefore, injection from the batteries should be 180◦ phase apart with zero mean.

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Segregate datasets with different Frequency components

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Segregation of frequency components in the forecast error dataset

Bitaraf et al., Sizing Energy Storage to Mitigate Wind Power Forecast Error Impacts by Signal Processing Techniques

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Minimum variability injection scheme

Objective: We want to contain all the daily variabilities within the batteries for both high and low frequency components for a given cut-off frequency. Challenge: (i) If the sizing of storage devices is given injection from RE-BSD can not be constant. (ii) With asymmetric charging and discharging characteristics, the average injection won’t simply be the daily sample average. Solution: The objective is to ‘minimize the squared sum of injection of variability into the grid’.

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Scheduling objective function

The Objective Function: min

• 1tND

   PK

d (t) Total RE-BSD dispatch

− {PK

d (t)}

• Average of total RE-BSD dispatch

  

2

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Constraints for Scheduling objective

The constraints:

GK(t) − PK

g (t) − PK d (t) = 0

Λ(t) = PK

g (t)

|(PK

g (t))| + ǫ

• PK

b (t) − ηch · PK g (t)

• · (1 + Λ(t)) +
• PK

b (t) − PK g (t)

ηdch

• · (1 − Λ(t)) = 0

kh

• 1tND

PK

b (t) = 0 Smart Grids 9 / 31

Constrains related to the battery, two battery model

Total energy contained: QK(t) = C0 + kh T

t=1 PK b (t)

where, 1 T ND C0 is the initial charge stored within the battery

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Constrains related to the battery, two battery model

To ensure complete utilization of the batteries for the complete historical data set, while maintaining desired depth of discharge difference. This ensures preservation of the life of the battery. Capacity of battery ‘+’: CK

+ = max{QK} − C0

∆SOC Capacity of battery ‘-’: CK

− = C0 − min{QK}

∆SOC

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Determining Life of Batteries

Two methods to determine the life are compared: (i) Depth of Discharge based method, (ii) Throughput method

• Intra- and Inter-day depth of discharge

(DOD) may not remain constant

• Therefore, DOD based Life of battery

calculation will be tedious

• Life of the battery in this method can

be calculated as, Lifebatt = 1 m

i=1 Ni/CFi

• Throughput of the battery is defined

as, Υ = kh

• t

|Pb(t)|

• Rated throughput can be defined as,

Y = F · C

• Simplistically, F can be defined to be

number of cycles at standard operating condition.

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Throughput of the battery: TK = kh

• t
• PK

b (t)

• Rating of the Converter:

PK = max

• PK

g (t)

• Smart Grids

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Random sampling

Challenge: We can calculate capacity ratings, throughput of batteries and power rating of the converter

• 1. for all possible days
• 2. sought the help of random sampling and use finitely many samples

Benefit of random sampling:

• 1. Sample mean = Population mean
• 2. Sample variance is a function of Population standard deviation
• 3. Random sampling will help in reduced computational burdens with

moderate accuracy.

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Calculation of statistical sizing

If the capacity ratings, throughput of batteries and power rating of the converter calculated based on randomly sampled days follows normal distribution 1 C+ = µ(C+) + 3 · σ(C+) C− = µ(C−) + 3 · σ(C−) P = µ(P) + 3 · σ(P) T = µ(T) + 3 · σ(T) P{µ − 3σ < X < µ + 3σ} = 0.99730 = ⇒ events with |X − µ| > 3σ are virtually impossible Selection of σ in sizing is upto the discretion of the planner.

1What if the samples does not follow normal distribution? Smart Grids 15 / 31

Calculation of statistical sizing

C = C+ + C− SOC

′

avg =

C− C+ + C− + ǫ Average SOC may not reside at 50% capacity.

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The C-Rate adjustment

‘1C-rate’ of the battery is the required constant current output from batteries to discharge it within one hour Crate = |Pb(t)| C ; ∀t Increasing capacity rating decreases C-rate Increasing current-drawn has a negative effect on life Statistically calculated C-rate (R): R =

• PK

b (t)

C

• ;

R = µ(RK) + 3 · σ(RK) If, R > Rlim, to improve the life of batteries, modify calculation of batteries to: C′ = C · R Rlim

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Optimal cut-off frequency

The prime goal: Find the optimal cut-off frequency, that minimizes the annualized sum of the cost of battery and PE-converter. Challenge: Calculation of sizing of batteries and PE-Converters at each cut-off frequency is computationally intensive. Solution: Statistically select finite number of cut-off frequencies to evaluate the total cost. Based on these ‘costly’ samples generate a probability distribution of the cut-off frequencies so as to enable random selection of new cut-off frequencies where probability of selection of cut-off frequency near the existing optima is the highest.

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