Energy Storage

Energy Storage
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The exercises explore price arbitrage with a battery storage system for day-ahead market optimization. Additionally, it delves into calculating battery capacity for an isolated PV-supplied facility to ensure energy security during cloudy days.

  • Energy Storage
  • Battery System
  • Market Optimization
  • PV System
  • Energy Efficiency

Uploaded on Mar 11, 2025 | 0 Views


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  1. Energy Storage 1. Exercises Dr.sc. Mirna Gr ani Prof. Hrvoje Pand i mirna.grzanic@fer.hr hrvoje.pandzic@fer.hr 1

  2. 1. Price arbitrage with a battery storage system 1 MW / 2 MWh battery storage system performs day-ahead market arbitrage. If the storage is full at the beginning of the day and its charging efficiency is 95% (battery can exchange maximum of 1 MW with the grid), what is the highest profit it can reach during the day with market prices shown in Table. 2 Energy storage

  3. Results 209.99 EUR 209.39 EUR charging/ dischargi ng charging/discha rging rging state of charge charge charging/discha state of state of charge hour hour price price market profit 0 1 1 -1 -1 1 -1 1 -1 1 0.8 1 -0.11 -1 0 0 0 1 1 -0.11 -1 -1 1 1 market profit 0 1 1 -1 -1 1 -1 1 -1 1 0.8 1 -0.11 -1 0 0 0 1 1 -0.11 -1 -1 1 hour price market profit 1 2 3 4 5 6 7 8 9 9 44 47 52 39 35 50 43 54 49 62 52 42 42 37 50 51 49 59 64 55 48 44 60 67 67 0 0 2 1 0 0 0 0 1 2 3 4 5 6 7 8 44 47 52 39 35 50 43 54 49 62 52 42 42 37 50 51 49 59 64 55 48 44 60 2 1 1 2 3 4 5 6 7 8 9 44 47 52 39 35 50 43 54 49 62 52 42 42 37 50 51 49 59 64 55 48 44 60 67 0 2 0 0 -1 -1 -1 47 52 -39 -35 50 -43 54 -49 62 41.6 -42 -4.42 -37 -37 -1 47 52 -39 -35 50 -43 54 -49 62 41.6 -42 -4.42 -0.9 -1 0.95 0.95 -0.95 0.95 1.1 0.1 1.05 0.9 42.3 52 -39 -35 47.5 -43 54 -49 62 49.4 -42 -4.42 -37 1 0.95 0.95 0.95 0.95 1.9 0.9 1.85 0.85 1.8 0.8 0.8 0.95 0.95 1.9 0.9 1.85 0.85 1.8 -1 -1 2 -1 -1 0.95 1.05 0.95 0.95 -1 1 -1 1 2 1 -1 -1 -1 0.95 0.95 0.95 1.95 0.95 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 24 -1 -1 10 11 12 13 14 15 16 17 18 19 20 21 22 23 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 -1 -0.8 0.95 0.1 0.95 0.95 0 0 -0.95 0.95 0.1 0.95 0 0.95 -0.8 0.95 0.1 0.95 1.05 1.05 0.95 1.05 1 0.95 -0.11 2 2 2 2 1 0 0 2 2 2 2 1 0 -1 0 0 0 1 1 2 2 2 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1 -1 59 64 64 -1 -1 59 64 -1 59 0.1 0.95 0.95 0.95 0.1 1.05 1.05 -5.79 -48 -44 -44 0.1 0.95 0.95 0.1 1.05 -0.11 -5.79 -48 -44 0.1 0.95 0.1 -5.79 -48 -1 -1 1 1 2 1 0 0 2 1 0 2 1 -1 -1 -1 60 67 67 -1 -1 60 67 -1 60 Energy storage 1 3

  4. 2. Energy Storage in an isolated PV-supplied facility Independent photo-voltaic system consists of PV modules, battery and load. Load consists of 5 energy saving light bulbs working on DC current and voltage of 12 V. Three light bulbs have power of 7 W, while two have power of 11 W. Light bulbs are on 6 hours per day. Efficiency of the battery discharging is 1 = 0.8, efficiency of the charging controller 2 = 0.92, and efficiency of the PV system 3 = 0.85. Calculate capacity of the battery which could secure the necessary energy in case of 5 consecutive cloudy days during which battery would be the only source. 4 Energy storage

  5. Results ??=1 ???= 3 7 + 2 11 = 43 ?,??? 6 ???? ??=1 ??? Energy discharged from battery in 1 hour: =43 ? ? = 43 ? ??? ??=1 ??? = 53.75 ? 0.8 Energy discharged from battery in 6 hours in 5 days: ??=30 ???? = 53.75 ? 30 = 1612.5 ? Battery capacity: ? =??=30 ???? ? 12 ? ??? ??? =1612.5 ? = 134.375 Ah 5 Energy storage

  6. 3. Storage in an isolated wind-supplied facility An isolated telecommunication plant has a constant load of 2.5 kW. It is powered by a wind turbine, whose normalized production is given in Table. a) What is the minimum installed capacity of the wind turbine to supply the load at all times? How much wind energy is curtailed? b) What installed power and capacity of the battery storage are needed in order to avoid wind curtailment? Battery efficiency is 100% and the battery is empty in the beginning. What amount of installed wind power capacity is needed in that case? 6 Energy storage

  7. Results 0.2 0.3 0.4 0.5 0.4 0.2 0.2 0.2 0.4 0.3 0.5 0.7 0.6 0.3 0.3 0.3 0.2 0.1 0.1 0.1 0.4 0.6 0.6 0.7 Hour 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 normalized real production 5 7.5 10 12.5 10 5 5 5 10 7.5 12.5 17.5 15 7.5 7.5 7.5 5 2.5 2.5 2.5 10 15 15 17.5 load 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 Curtailment 2.5 5 7.5 10 7.5 2.5 2.5 2.5 7.5 5 10 15 12.5 5 5 5 2.5 0 0 0 7.5 12.5 12.5 15 a) What is the minimum installed capacity of the wind turbine to supply the load at all times? How much wind energy is curtailed? 0.1 ?????= ????? ?????=2.5 ?? = 25 ?? 0.1 ????????????= 155 ?? 155 7 Energy storage

  8. Results Hour normalized real production load 1 2 3 4 5 6 7 8 9 0.2 0.3 0.4 0.5 0.4 0.2 0.2 0.2 0.4 0.3 0.5 0.7 0.6 0.3 0.3 0.3 0.2 0.1 0.1 0.1 0.4 0.6 0.6 0.7 2.5 3.75 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 b) ??????+ ?????= ??????+ ??? 5 6.25 Battery is empty in t=1, no discharing 5 2.5 2.5 2.5 5 0.2 ?????= ????? 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 3.75 6.25 8.75 7.5 3.75 3.75 3.75 2.5 1.25 1.25 1.25 ?????????=????? =2.5 0.2= 12.5 ?? ????? 0.2 5 7.5 7.5 8.75 8

  9. Results b) ??????+ ?????= ??????+ ??? Hour normalized real productionload 1 2 3 4 5 6 7 8 9 0.2 0.3 0.4 0.5 0.4 0.2 0.2 0.2 0.4 0.3 0.5 0.7 0.6 0.3 0.3 0.3 0.2 0.1 0.1 0.1 0.4 0.6 0.6 0.7 2.5 3.75 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 5 Battery must be able to charge the maximum wind surplus: 0.7 12.5 = 2.5 + ??? ???? = 0.7 12.5 2.5 = 6.25 ?? 6.25 5 2.5 2.5 2.5 ? 5 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 3.75 6.25 8.75 7.5 3.75 3.75 3.75 2.5 1.25 1.25 1.25 5 7.5 7.5 8.75 9

  10. Results real productionload 2.5 3.75 Excess wind Battery storage Hour normalized SOC 1 2 3 4 5 6 7 8 9 0.2 0.3 0.4 0.5 0.4 0.2 0.2 0.2 0.4 0.3 0.5 0.7 0.6 0.3 0.3 0.3 0.2 0.1 0.1 0.1 0.4 0.6 0.6 0.7 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 0 0 0 1.25 2.5 3.75 2.5 1.25 2.5 3.75 2.5 1.25 3.75 7.5 10 10 10 10 12.5 13.75 17.5 23.75 28.75 5 6.25 5 2.5 2.5 2.5 0 0 0 0 0 0 Battery capacity: ??????= 47.5 ?? 5 2.5 1.25 3.75 6.25 2.5 1.25 3.75 6.25 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 3.75 6.25 8.75 7.5 3.75 3.75 3.75 2.5 1.25 1.25 1.25 5 5 1.25 1.25 1.25 1.25 1.25 1.25 30 31.25 32.5 32.5 31.25 0 0 -1.25 -1.25 -1.25 2.5 -1.25 -1.25 -1.25 2.5 30 28.75 31.25 36.25 41.25 47.5 5 7.5 7.5 8.75 5 5 5 5 6.25 6.25 10

  11. 4. Electricity costs Electricity price for a household is 0,4655 kn/kWh in the high tariff (7-22 h) and 0,2280 kn/kWh in the low tariff (22-7 h). Overall network fees are 0,35 kn/kWh in the high tariff and 0,17 kn/kWh in the low tariff. What are the electricity costs for this household on this specific day? Hour Load (kW) Hour Load (kW) Hour Load (kW) 1 0,5 9 1,5 17 2,3 2 0,5 10 1,0 18 3,5 3 0,6 11 1,0 19 3,1 4 0,7 12 0,4 20 2,8 5 0,5 13 1,0 21 2,5 6 0,5 14 1,5 22 1,7 7 0,9 15 1,6 23 0,9 8 1,5 16 1,8 24 0,5 11 Energy storage

  12. Hour Load (kW) Price energy Price network charges Total cost 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0.5 0.5 0.6 0.7 0.5 0.5 0.9 1.5 1.5 0.228 0.228 0.228 0.228 0.228 0.228 0.228 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.228 0.228 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.17 0.17 0.199 0.199 0.2388 0.2786 0.199 0.199 0.3582 1.22325 1.22325 0.8155 0.8155 0.3262 0.8155 1.22325 1.3048 1.4679 1.87565 2.85425 2.52805 2.2834 2.03875 1.38635 0.3582 0.199 1 1 0.4 1 1.5 1.6 1.8 2.3 3.5 3.1 2.8 2.5 1.7 0.9 0.5 24.4104

  13. 5. Electricity costs What are the electricity costs if the house has solar panels whose output is given in the table as well? The supplier is required to purchase the excess electricity from this household at 90% of the price it charges. Hour Load (kW) PV (kW) Hour Load (kW) PV (kW) Hour Load (kW) PV (kW) 1 0,5 0 9 1,5 0,7 17 2,3 1,8 2 0,5 0 10 1,0 0,9 18 3,5 1,3 3 0,6 0 11 1,0 1,1 19 3,1 0,5 4 0,7 0 12 0,4 1,5 20 2,8 0 5 0,5 0 13 1,0 2,5 21 2,5 0 6 0,5 0 14 1,5 2,7 22 1,7 0 7 0,9 0 15 1,6 2,6 23 0,9 0 8 1,5 0,5 16 1,8 2,0 24 0,5 0 13 Energy storage

  14. Price network charges Net load (kW) Hour Load (kW) Price energy Total cost PV (kW) Cost 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 0 0 0 0 0 0 0.5 0.5 0.6 0.7 0.5 0.5 0.9 1.5 1.5 0.228 0.228 0.228 0.228 0.228 0.228 0.228 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.4655 0.228 0.228 0.17 0.17 0.17 0.17 0.17 0.17 0.17 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.35 0.17 0.17 0.199 0.199 0.2388 0.2786 0.199 0.199 0.3582 1.22325 1.22325 0.8155 0.8155 0.3262 0.8155 1.22325 1.3048 1.4679 1.87565 2.85425 2.52805 2.2834 2.03875 1.38635 0.3582 0.199 0.5 0.5 0.6 0.7 0.5 0.5 0.9 0.199 0.199 0.2388 0.2786 0.199 0.199 0.3582 0.8155 0.6524 0.08155 -0.0419 -0.46085 -0.62843 -0.50274 -0.41895 -0.08379 0.40775 1.7941 2.1203 2.2834 2.03875 1.38635 0.3582 0.199 0.5 0.7 0.9 1.1 1.5 2.5 2.7 2.6 2 1.8 1.3 0.5 0 0 0 0 0 1 0.8 0.1 -0.1 -1.1 -1.5 -1.2 -1 -0.2 0.5 2.2 2.6 2.8 2.5 1.7 0.9 0.5 1 1 0.4 1 1.5 1.6 1.8 2.3 3.5 3.1 2.8 2.5 1.7 0.9 0.5 ???? = ??.?? ?? 14 Energy storage

  15. 6. Profitability of investment If we assume that the household installed photo-voltaic system with 3kWp and we can approximate the same daily consumption and production profile for the entire year, what is the period of the return in the investment? The price for PV system is 1400 /kW. 15 Energy storage

  16. Results ???? ??? ??? ?? = 24,41 ?? ???? ??? ?? = 11,67 ?? ????? ??????? = 12,74 ?? ?????? ??????? = 4650,10 ?? ?????????? ???? = 1400 /kW 7.5 3?? = = 31 500 ?? ?????????? ???? ?????? ???????= ?????? ?? ?????????? = 31500 4650,10= 6,77 ????? = 16 Energy storage

  17. 7. Optimal Microgrid Operation The expected non-dispatchable loading during a 6-hour period and PV production is given in the table. The microgrid also comprises of two dispatchable units and a controllable load. The first dispatchable unit has rated power 100 kW and operating costs 0,030 /kWh, while the second unit has rated power 120 kW and operating costs 0,050 /kWh. Controllable load has rated power 25 kW in each hour. Determine the operation costs in the following cases: 1. Controllable load is fixed in each hour. 2. Controllable load is HVAC (120% retrieval factor) and it is possible to reduce up to 20% of consumption in each hour, a total of 20 kWh during 6 hours. 3. Controllable load cannot be controlled, but a battery is included in the microgrid; charging efficiency is 0.9, maximum state of charge is 30 kWh and battery is empty at the beginning. Hour Load PV 1 80 kW 30 kW 2 160 kW 10 kW 3 220 kW 30 kW 4 90 kW 20 kW 5 200 kW 10 kW 6 180 kW 30 kW 17 Energy storage

  18. Results Load kW PV kW Contollable load kW To be supplied First unit up to 100 kW Second unit up to 120 kW 1. Hour 1 2 3 4 5 6 80 160 220 90 200 180 30 10 30 20 10 30 25 25 25 25 25 25 75 175 215 95 215 175 75 100 100 95 100 100 0 75 115 0 115 75 ???? = 570 0.03 + 380 0.05 = 36.10 18 Energy storage

  19. Results 2. Load kW Contollable load kW First unit up to 100 kW Second unit up to 120 kW Hour PV kW To be supplied 1 2 3 4 5 6 80 160 220 90 200 180 30 10 30 20 10 30 25 25 25 25 25 25 75 175 215 95 215 175 75 100 100 95 100 100 0 75 115 0 115 75 Load kW Controllable load kW 30 25+5*4*1.2=49 10 30 20 10 30 First unit up to 100 kW Second unit up to 120 kW Hour PV kW To be supplied 75+24=99 1 2 3 4 5 6 80 99 0 160 220 90 200 180 25-5=20 25-5=20 170 210 95 210 170 100 100 95 100 100 70 110 25 0 25-5=20 25-5=20 110 70 ???? = 594 0.03 + 360 0.05 = 35.82 19 Energy storage

  20. Results 3. Load kW Contollable load kW First unit up to 100 kW Second unit up to 120 kW Hour PV kW To be supplied 1 2 3 4 5 6 80 160 220 90 200 180 30 10 30 20 10 30 25 25 25 25 25 25 75 175 215 95 215 175 75 100 100 95 100 100 0 75 115 0 115 75 First unit up to 100 kW Second unit up to 120 kW Load kW PV kW Contollable load kW To be supplied Pbat After battery Hour SOC 1 2 3 4 5 6 80 30 160 10 220 30 90 20 200 10 180 30 25 25 25 25 25 25 75 175 -22.5 215 95 215 175 25 22.5 100 100 100 100 100 100 100 0 0 152.5 215 100 210.5 175 52.5 115 0 5 4.5 0 -4.5 0 0 110.5 0 75 ???? = 600 0.03 + 353 0.05 = 35.65 20 Energy storage

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