OPTIMAL SCHEDULING OF BATTERY STORAGE WITH GRID TIED PV SYSTEMS FOR TRADE-OFF BETWEEN CONSUMER ENERGY COST AND STORAGE HEALTH Sushil Kumar Bhoi , Manas Ranjan Nayak PII: DOI: Reference:
S0141-9331(20)30433-6 https://doi.org/10.1016/j.micpro.2020.103274 MICPRO 103274
To appear in:
Microprocessors and Microsystems
Received date: Revised date: Accepted date:
23 July 2020 10 September 2020 17 September 2020
Please cite this article as: Sushil Kumar Bhoi , Manas Ranjan Nayak , OPTIMAL SCHEDULING OF BATTERY STORAGE WITH GRID TIED PV SYSTEMS FOR TRADE-OFF BETWEEN CONSUMER ENERGY COST AND STORAGE HEALTH, Microprocessors and Microsystems (2020), doi: https://doi.org/10.1016/j.micpro.2020.103274
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OPTIMAL SCHEDULING OF BATTERY STORAGE WITH GRID TIED PV SYSTEMS FOR TRADE-OFF BETWEEN CONSUMER ENERGY COST AND STORAGE HEALTH Sushil Kumar Bhoi1, Manas Ranjan Nayak*2 1
Department of Electrical Engineering, Government College of Engineering, Bhawanipatna , India . E-mail: [email protected]
Department of Electrical Engineering CAPGS, Biju Patnaik University of Technology, Rourkela, India. E-mail: [email protected]
ABSTRACT With the advent of renewable energy in India has initiated consumers to get energy storage systems to mange solar power variation. To solve intermittency issues from weather related events that occur with residential photovoltaic generation, intelligent power management strategies have been carried outto tune efficacy of the consumer’s renewable energy system while reducing cost. The proposed method decides the state of charge schedule for the battery storage based on a dynamic programming algorithm that minimizes consumer energy cost and maximizes energy storage state of health. The battery state of health was introduced into the model as an ageing coefficient that forces conservative battery behaviour to preserve its lifetime with continued use.Simulation results show a high potential to increase the profitability of a grid connected PV- BESS system using time of use (TOU) tariff. Keywords:Photovoltaic (PV), Battery Energy Storage System, Dynamic Programming, Energy Management, Optimization. 1. INTRODUCTION Renewable energy is clean energy, derived from natural resources that are constantly replenished. Such as sun, rain and wind etc. in recent year, grid connected Renewable Energy Systems (RESS)  have become blooming technology to solve many problems such as demand of high electricity, minimal use of fuel resources and reduction of Co2 emissions . Especially, Photovoltaic (PV) employs solar panels to convert sunlight to electricity. PV systems are widely used in many areas ranging from small to large power station. According to Govt. of India polices, to aid PV development, minimize cost and expansion of PV systems anticipated to continue in future. However, PV systems make grid management difficult to match with the high electricity demand due to its intermittent and irregular nature ;. To solve the aforementioned issue, a storage element is added with the PV systems ;. Eeyer et al. 
presented an integrated system by combining PV system, storage element and grid, can used in several applications. With the increasing popularity of household PV and the availability of lead acid battery energy storage system (BESS), intelligent power management solutions are needed to reduce consumer cost and increase the performance. The span of lead acid battery is reduced due to the capacity generation which occurs each charge or discharge cycle [8-11]. PV systems as a main source of capacity generation cause decline in battery lifetime due to variable depth of discharge (DOD) cycling. Several papers have explained various economic minimization methods for management of power in the system that integrates state of health of battery [12-14]. A paper has been published that hailed primary motivation for this work .The selfconsumption for residential RES has been optimized by using linear programming algorithm in the research. The predetermined schedule of charge/discharge for the battery was the limitations in this paper. The battery power was not determined based on load profiles and solar irradiance by using linear programming algorithm. The power of battery was predetermined for every hour as well. This paper uses dynamic Programming (DP) based on Bellman-Ford algorithm as a optimization algorithm to find the optimal path for the batterycharges in the RES ; . Dynamic programming has many advantages over the enumeration scheme, the chief advantage being a reduction in the dimensionality of the problem. It is one of the refined algorithm design standards and is powerful tool which yields definitive algorithms for various types of optimization problems. The main contributions of this paper are as follows: 1. Power flow management for grid connected PV system with storage which concentrate on optimal scheduling is modelled as a DP process which is tuned to reduce consumer energy cost and improved energy storage simultaneously . 2. A sensitivity analysis has been performed to analyze the impact of various factors including grid price, grid power, feed-in-tariff and cost function of DP optimisation in a selected day of summer and winter.
3. This research also provides insight into strategies used to utilize the energy storage system effectively. The remainder of the paper is outlined as follows: section 2 presents the system modelling. Section 3 explains problem formulation. Section 4 describes DP algorithm. Section 5 provides experimental outcomes. Finally, section 6 summarizes the paper. 2. SYSTEM MODELLING Figure1 shows the general structure of energy management system (EMS) is considered in this paper. It consists of a PV panel, batteries, utility grid, charge controller, power converters and the loads associated with the users. The main function of EMS is to manage the energy flow directions in all components. The BESS is responsible to supply power during discharging and receive power during charging. The system can provide power to get power in case of demandin order to ensure power system reliability.
ACDC DC-DC Converter Converter
Loads PGrid (t) > 0
Pb(t ) < 0
DC- AC Converter Pb(t ) > 0
PGrid (t ) < 0
Figure 1:System Modelling 2.1. Modelling The PV panel power can be determined based on the area and efficiency of the PV panel in relation to solar radiation considering de-rating because of dirt, temperature, DC cable loss and manufacturer’s output tolerance .
P (t ) A pvg p N p f m f d f c inv pv IR (t ) (1)
Where IR (t ) is the global horizontal irradiance (GHI) at hour t in W/m2 . The hourly GHI data for the selected day of summer & winter in 2019 at Bhubaneswar, India isgathered from Indian Meteorological Department as shown in figure 2.
Figure 2: MeanHourly Solar Irradianceina Summer and Winter Day The de-rating due to temperature is calculated by
f c [1 Tcoeff (Tmo Tr )] (2) The module temperature
is given by:
Tmo Ta (
NOCT 20 800
) IR (t ) (3)
The AC output power at AC bus bar is given by: PPV (t ) P(t ) in in _ sb
Table 1 provides the PV system specifications. Table 1: PV System Specifications Parameters
Area of PV Panel ( A)
De-rating factor for manufacturer’s tolerance ( f m )
De-rating factor due to dirt ( f d )
Cable loss between inverter and the panel ( inv pv )
PV generator reference efficiency ( pvg )
Efficiency of perfect maximum power point tracking ( p )
Inverter efficiency ( in )
AC cable loss ( inv sb )
Nominal Operating Cell temperature (NOCT )
Ambient temperature (T a )
Temperature coefficient (Tcoeff )
Reference temperature (Tr )
2.2. Modellingof BESS The instantaneous power of the battery ( Pb ) is expressed as: Pb (t ) Vb t I b t (5)
The voltage and current of the batteries depends upon the value of the change in state of charge ( SOC ), between node j and node k. Here, node j represents the SOC of the battery at time ( t t ) and node k represents the SOC of the system at time t. The voltage for a RollsSurette Flooded Deeep Cycle S-550 6V Lead Acid Battery during charge and discharge is calculated by (6) and (7) based on the linear interpolation of the results of an experiment . Vb t 6.75 1.2 SOC t Nb t , I b 0 (6) Vb t 6.295 1.02 1 SOC t Nb t , I b 0 (7)
Where N b t is the number of batteries connected in series, and SOC (t ) is the SOC of the system at node k. The battery current ( I b ) is calculated using coulomb-counting method.
Where change in charge ( Q ) can be defined as the difference between reference capacity at node k and reference capacity at node j. Q C t C t t C xk C x j (9)
The Batteries State of Health (SOH) is calculated by SOH t
Cr t (10) Cr ,nom t
Where C r,nom t is the nominal capacity taken from the data sheet of manufacturer . In this model, battery performance deteriorates with every discharge of battery as given in  and . Capacity of reference losses are considered to be linear based on the battery discharge by  and . At every t , if the value for SOC is less than zero, then the battery is in discharging mode, the new value for reference capacity, C r t , is obtained by (11) from the losses of capacity of reference, C r t , calculated with (12). Cr t Cr t t Cr t (11)
Cr t Cr ,nom t Z SOC t t SOC t
Table 2 lists the parameters of lead acid battery. Table 2: Description of Lead Acid Battery Name of the Parameter Nominal voltage of one battery Float voltage of one battery Number of batteries ( N b ) in series
Specification 6 Volt 6.75 Volt 4
Capacity of the total battery storage (C ) Minimum SOC ( SOC Step in SOC ( SOC )
) / Maximum SOC ( SOC
Minimum change in SOC (SOC (SOC max ) Starting value of SOC Ageing coefficient (Z ) Battery initial cost (BiC )
400 Ah max
20%/ 90% 1%
) / Maximum change in SOC
-70% / 70% 50% 0.00031 9125 Rs./kWh
The value of Z has been taken from the results of an experiment performed at INES institute . 2.3. Modeling of Load The hourly load profile data was collected based on the electricity consumption of residential utility customer for the selected day of summer & winter in 2019 at Bhubaneswar, India as shown in figure 3. The average, maximum and minimum load demands in summer are 1.224 kW, 1.604 kW and 0.784kW respectively. The average, maximum and minimum load demands in summer are 1.031 kW, 1.501 kW and 0.707kW respectively.
Figure 3:HourlyProfile of Load inSummerand Winter Day 2.4. Modeling of Grid The power management decides the required power to be generated to fulfill the demand and to store energy in the battery. It there is low or no power from natural resources, the system depends on the grid. If there is excessive power, the system provides the power to the power grid. In case of power sell to the grid: PGrid t PL t PPV t
Pb t ,
PGrid 0 (13)
In case of power purchased from the grid: PGrid t PL t PPV t
Pb t ,
PGrid 0 (14)
max The maximum grid power ( PGrid ) and grid penalty factor (GPF ) are 1.4 kW and 10 respectively
Electricity Grid Price ( EGP ) and Feed-In Tariff ( FIT ) during Peak hour and Off-peak hour of the day in summer and winter are given in table 3. Table 3: FIT and EGP during Peak Hour and Off-Peak Hour of the Day Type of electricity Season price Tier 1 Summer (Fixed & price) Winter
Summer Tier 2 (Time of use price) Winter
Hour of the day
EGP in Rs./kWh
FIT in Rs./kWh
Off-Peak hour&Peak hour [ For all hours in a day]
Off-Peak hour [1, 2, 3, 4, 5, 6, 7, 8, 9 ,10 ,23 , 24] Peak hour [11, 12, 13, 14 , 15, 16 ,17, 18, 19, 20, 21, 22] Off-Peak hour [1, 2, 3 ,4 ,5 ,6 ,11 ,12 ,13 ,14, 15, 16, 21, 22 ,23]
Peak hour [7, 8, 9, 10, 17, 18, 19 ,20]
3. PROBLEM FORMULATION The minimization function considers the power purchased or sold from the grid attime t, and the cost to substitute the system’s storage incorporating the constraint. The other name of cost to replace the system’s storage in ageing cost of the battery. 3.1. Objective Function The system cost function can be expressed as: Min CF Min
C t C t (15) t t0
Where CF is the cash flow for the 24 - hour period, C R t is the cash earned and C P t is the cash spent. Every value of CF is taken for every time step, t , as given in (16). CF t CR t CP t (16)
The cash spent and cash earned are calculated:
CP t PGrid t EGP t BrC t , CR t PGrid t FIT t ,
PGrid t 0 (17) PGrid t 0 (18)
Where EGP and FIT are the electricity grid price and the feed-in-tariff for energy purchased by the grid from the PV system. The ageing cost for the battery, BrC , is determined by: BrC x j , xk , t BiC
SOH x j , xk , t 1 SOH min
Where BiC is the initial cost for the battery bank of the system.Based on the iterative procedure of the Bellman - Ford algorithm, SOH x j , x k , t , change in state of health, follows the similar notation as SOC ,change in state of charge. The variation in health state can be computed by using Equation (20). SOH x j , xk , t SOH x j t t SOH xk (20)
3.2. System Operating Constraints The system operating constraints are expressed as: PGrid t PL t PPV t
Pb t (21)
SOC min SOC t SOC max min b
Pb t P
SOH t SOH min (24) max (25) PGrid t PGrid
SOC min SOC t SOC max (26)
Constraint (21) defines the power conservation law of physics, constraints (22) – (24) & (26) prevents the battery from collapsing due to excess charging and large depth of battery discharge and limit deterioration of battery and in constraint (25) the value of PGrid t must not be max greater than PGrid otherwise grid penalty is used in the calculation of cash purchased cost.
4. APPLICATION OF DYNAMIC PROGRAMMING (DP) ALGORITHM The goal of the tuning based control methods is to tune the outcome of the power components by reducing objective function typically represented by the cash earned and the cash spent for the renewable energy systems.DP is a type of metaheuristic algorithms, due to its ease of
solution.Thefundamental principles to DP are based closely on the work of Bellman and Kalaba
. Each time step consists of 71 states which are defined by using SOC value and set to 0.01. Based on the one hour time steps, this system consist of 24 steps, over 24-hour period. In this system, both the terminal and initial SOC is set to 0.5 p.u.. SOC
Figure 4: SOC Space of Batteries and All Possible Trajectories from Initial Node to Terminal Node Figure 4 illustrates an example of SOC space of batteries and all possible trajectories from initial node to terminal node. All possible trajectories exists between SOC min and SOC max . At each time step, the move between two states corresponds to SOC . The power balance
equation, eq. (21) determines PGrid x j , x k , t for the system based on Pb x j , x k , t , PL t and PPV t for each SOC . The load profiles and solar radiation data was predetermined. Based on
SOH x j , xk , t , the battery replacement cost is calculated. Grid power PGrid t , determines whether or not the grid penalty factor should be applied when CF and edge weight is calculated.
Finally, CF is calculated using PGrid x j , x k , t and BrC x j , xk , t . The DPoptimizes the path from initial state of change to final state of change by spotting low cash flow needed to touch final state of change in a day. Y.Riffonneau DP iterative process in the flowchart has been utilized for optimal power management . 5. SIMULATION AND RESULT ANALYSIS
This section presents simulation results of the proposed system. The designed system has one string of 20 PV modules connected in series to total power of 3.082KW. The power converter of 24V has been used in grid tied storage system with the battery bank. The battery band consisted of 6v batteries in a string of 4, totalling 24v with maximum capacity of 400Ah. The optimal power flow management presented in this paper is based on the two differing load profiles and corresponding solar irradiance datasets for summer and winter seasons at Bhubaneswar. All simulations have been done by using MATLAB for Tier 1 (fixed) price and Tier 2 (variable) price as given in Table4and follows the multistage decision DP method. The numerical outcomes show the optimal path from initial SOC to final SOC, battery voltage and battery current for two different seasons. Table 4 summarizes the final cost function for DP algorithm in summer and winter power management. Table 4:Objective Function (Cash Flow) for Tier 1 & 2 Price Season
Cash flow (CF) in Rs. Cash flow (CF) in Rs. for Tier 1 fixed price for Tier 2 TOU price Summer - 2.89 - 24.67 (Utility grid has to pay to the customer ) (Utility grid has to pay to the customer ) – Gains to customer – Gains to customer Winter 36.67 21.08 (Customer has to pay to the utility grid ) (Customer has to pay to the utility grid ) In the table 4,the cash flow (CF) for Tier 2 TOUpriceare compared with the Tier 1 fixed price in summer and winter. The Cash flow (CF) forTier 2 TOU pricegives a better value than Tier 1 during summer and winter. Table 4 shows the system cost function plays significant role in higher PV generation. The active power variation of the various components on a typical day of summer and winter for Tier 1 & Tier 2 electricity price are shown in figures 5, 6, 7, & 8.
Figure 5:Change of Active Power for PV/Grid/BESS/Load in a Summer Day for Tier 1 Price
Figure 6: Change of Active Power for PV/Grid/Battery /Load in a Winter Day for Tier 1 Price
Figure7: Change of Active Power for PV/Grid/Battery /Load in a SummerDay for Tier 2 Price
Figure8: Change of Active Power for PV/Grid/Battery /Load in a Winter Day for Tier 2 Price In figures 5, 6, 7, & 8, the positive and negative power of battery represents the charging and discharging condition of battery respectively. Positive and negative power of grid represents the consumption of power by load / battery and feed-in power to gridrespectively. The loadrepresents the consumption of power by the customer.
Figure 9:SOC Schedule of Battery in Summer and Winter Day for Tier 1 Price Figure 9 shows SOC schedule of Battery in summer and winter day for Tier 1price.Duringasummer day, the battery has been discharged from 12.00 AM to 8.00 AM to offset the load. From 8.00 AM to 4.00 PM, the battery has been charged with solar power as much as possible because it is considered to be economical operation. Peak load from 4.00 PM to 11.00 PM drive the battery to discharge until it returns to terminal SOC of 50%. The battery remains in rest condition from 11.00 PM to 12.00 PM. Duringawinter day in figure 9, the battery remains in rest condition from 12.00 AM to 10.00 AM. The battery has been charged from 10.00 AM to 4.00 PM with solar power as much as possible because it is considered to be economical operation over the 24-hour period. The battery has been discharged from 4.00 PM to 11.00 PM to offset the load. The battery has been discharged until it returns to terminal SOC of 50%. The battery remains in rest condition from 11.00 PM to 12.00 AM. In both summer and winter days,the electricity grid price and feed in tariff are equal. Hence the battery can be charge during peak hour and discharge during off peak hour.
Figure 10: SOC Schedule of Battery in Summer and Winter Day for Tier 2 Price Figure 10 shows SOC schedule of Battery in summer and winter day for Tier 2price. During a summer day, the battery has been discharged from 12.00 AM to 2.00 AM then the battery has been charged from 2.00 AM to 4.00 AM with grid power as much as possible because it is considered to be economical operation over the 24-hour period for the user to purchase power from the grid between 2.00 AM and 4.00 AM to charge the battery than it is to max pay the penalty factor, GPF, when grid power goes above PGrid .Thus, the charged battery was max discharged from 4.00 AM to 7.00 AM to keep the power purchased from exceeding PGrid .Then
the battery has been chargedfrom 7.00 AM to 4.00 PM with solar power as much as possible. Peak load from 4.00 PM to 10.00 PM drive the battery to discharge until it returns to terminal SOC of 50%. The battery remains in rest condition from 10.00 PM to 12.00 PM because the grid supplies power to offset the load. During a winter day in figure10, the battery has been charged from 12.00 AM to 6.00 AM with grid power as much as possible because it is considered to be economical operation. Then, the charged battery was discharged from 6.00 AM to 10.00 AM to keep the power max purchased from exceeding PGrid . The battery has been charged from 10.00 AM to 4.00 PM with
PV power. The battery was discharged from 4.00 PM to 10.00 PM to offset the load. The battery start charging from 10.00 PM to 12.00 AM until it returns to terminal SOC of 50%.
In both summer and winter days, during off peak load hour, the electricity grid price and feed in tariff both are less than the peak load hour price. Hence the battery charged during off peak load hour and discharged during peak load hour. Figure 11 & 12 show current flow, and voltage of the Battery in summer and winter day for Tier 1 & 2 price.
Figure 11: Current of the Battery in Summer and Winter Day for Tier 1 & 2 Price
Figure 12: Voltage of the Battery in Summer and Winter Day for Tier 1 & 2 Price
6. CONCLUSION This paper has presented a novel method to optimize the system economics. The proposed system uses DP algorithm for optimization. It includes energy storage state of health and unique system constraints. The integration of grid connected PV-BESS unit has the advantages of demand charge management, renewable energy time shift, and capacity farming.The cost saving is observed to be increased by using the proposed method. The proposed system considers the fix &TOU tariff, and defines SOC for each hour of a day in summer and winter season in order to minimise the objective function. Performance of the proposed system is analyzed by varying several factors. The experiment is conducted by using real time GHI data and temperature data of Bhubaneswar, India. The outcomes ensure the technical and economical benefits of using PV panels along with BESS in India. The testing platform can be used for future research in modeling household renewable system with energy storage components. by comparing power management optimization techniques, testing a wide variety of irradiance and load profiles, performing long-term system analyses and softening economic constraints in lieu of prolonged component lifetimes.
Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Sushil Kumar Bhoi , received the M.Tech degree from Veer Surendra Sai University of Technology, Burla, Odisha in Electrical Engineering. He is currently an assistant professor at Govt. College of Engineering, Bhawanipatna. His research interests are Renewable Energy, Energy Storage System, Optimization techniques and Microgrid.
Manas Ranjan Nayak, received Ph.D degree from Electrical Engineering Department of Siksha ‘O’ Anusandhan University, Bhubaneswar. He is currently an associate professor at CAPGS, Biju Patnaik University of Technology, Rourkela, Odisha. His research interests are Renewable Energy, Energy Storage System, Electric Vehicle, and its integration in distribution system, Power system planning, Optimization techniques.