Smart Grids EE 772 Department of Electrical Engineering Indian Institute of Technology Bombay, India October 5, 2018
Sizing and operation of Battery Storage Devices Smart Grids 2 / 31
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 Smart Grids 3 / 31
Imbalance caused by base-load generation scheme PR ( t + ( n − 1) · N D ) + PS ( t + ( n − 1) · N D ) = PB ( n, t ); 1 � t � N D , 1 � n � N Y 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. Smart Grids 4 / 31
Segregate datasets with different Frequency components Smart Grids 5 / 31
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 Smart Grids 6 / 31
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’. Smart Grids 7 / 31
Scheduling objective function The Objective Function: 2 � P K { P K min d ( t ) − d ( t ) } � �� � � �� � 1 � t � N D Total RE-BSD dispatch Average of total RE-BSD dispatch Smart Grids 8 / 31
Constraints for Scheduling objective The constraints: G K ( t ) − P K g ( t ) − P K d ( t ) = 0 P K g ( t ) Λ( t ) = | (P K g ( t )) | + ǫ � � b ( t ) − P K g ( t ) � � P K b ( t ) − η ch · P K P K g ( t ) · (1 + Λ( t )) + · (1 − Λ( t )) = 0 η dch � P K k h b ( t ) = 0 1 � t � N D Smart Grids 9 / 31
Constrains related to the battery, two battery model � T Total energy contained: Q K ( t ) = C 0 + k h t =1 P K b ( t ) where, 1 � T � N D C 0 is the initial charge stored within the battery Smart Grids 10 / 31
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 ‘+’: + = max { Q K } − C 0 C K ∆SOC Capacity of battery ‘-’: − = C 0 − min { Q K } C K ∆SOC Smart Grids 11 / 31
Determining Life of Batteries Two methods to determine the life are compared: (i) Depth of Discharge based method, (ii) Throughput method ◦ Throughput of the battery is defined as, � Υ = k h | P b ( t ) | t ◦ Intra- and Inter-day depth of discharge (DOD) may not remain constant ◦ Rated throughput can be defined as, Y = F · C ◦ Therefore, DOD based Life of battery calculation will be tedious ◦ Simplistically, F can be defined to be ◦ Life of the battery in this method can number of cycles at standard operating be calculated as, condition. 1 Life batt = � m i =1 N i /CF i Smart Grids 12 / 31
Throughput of the battery: � T K = k h � � � P K b ( t ) � t Rating of the Converter: P K = max �� � �� � P K g ( t ) Smart Grids 13 / 31
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. Smart Grids 14 / 31
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 − 3 σ < X < µ + 3 σ } = 0 . 99730 = ⇒ events with |X − µ | > 3 σ are virtually impossible Selection of σ in sizing is upto the discretion of the planner. 1 What if the samples does not follow normal distribution? Smart Grids 15 / 31
Calculation of statistical sizing C = C + + C − C − ′ SOC avg = C + + C − + ǫ Average SOC may not reside at 50% capacity. Smart Grids 16 / 31
The C-Rate adjustment ‘1C-rate’ of the battery is the required constant current output from batteries to discharge it within one hour C rate = | P b ( t ) | ; ∀ t C Increasing capacity rating decreases C-rate Increasing current-drawn has a negative effect on life Statistically calculated C-rate ( R ): �� � � P K b ( t ) � � R = µ ( R K ) + 3 · σ ( R K ) R = ; � � C � � If, R > R lim , to improve the life of batteries, modify calculation of batteries to: C ′ = C · R R lim Smart Grids 17 / 31
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. Smart Grids 18 / 31
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