ARTICLES

 

An Optimal Rural Community PV Microgrid Design Using Mixed Integer Linear Programming and DBS CAN Approach

 

 

Jane Namaganda-Kiyimba^I; Joseph Mutale^II

^IMember, IEEE; Department of Electrical & Electronic Engineering, The University of Manchester, UK, M13 9PL, Manchester, UK (e-mail: jane.namaganda-kiyimba@manchester.ac.uk) and the Department of Electrical and Computer Engineering, Makerere University, Kampala, Uganda
^IISenior Member, IEEE; Department of Electrical & Electronic Engineering, The University of Manchester, UK, M13 9PL, Manchester, UK (e-mail: j.mutale@manchester.ac.uk)

 

 

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ABSTRACT

The deployment of microgrids has been identified as one of the fastest ways of bringing electricity to the large number of people that are currently without electricity access. In developing countries in Africa, most of these people live in rural locations that are not served by the main grid making it necessary to establish community microgrids. These microgrids should be optimally sized so as to meet the electrical needs of the communities cost effectively. This work presents an efficient and robust sizing approach for off-grid PV microgrid systems that has been named as the ComfiGrid Sizing Approach in this research. This approach utilizes "Mixed Integer Linear Programming (MTLP)" to optimally size the PV microgrid. The ComfiGrid optimization algorithm uses hourly load variation, hourly solar irradiance values and hourly ambient temperature to optimally size the system. This approach also uses the "Density Based Spatial Clustering of Applications with Noise (DBSCAN)" algorithm to aggregate load and meteorological data. MATLAB software is used to execute the optimization algorithm. The results show that it is possible to achieve accuracy and a faster convergence to the solution with the proposed approach than that of the iterative method.

Index Terms: Microgrid, Mixed Integer Liner Programming, Reliability, Rural Electrification, Solar Photovoltaics

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I. Introduction

ACCESS to electricity is one of the major factors that contribute to economic growth of communities and countries. With increased level of electrification, people's standards of living are improved and numerous opportunities open up due to the availability of electric power. Developing countries in Africa are faced with the challenge of having to electrify remote rural areas where most of the people live. Extending the main grid to these areas cannot be easily achieved because of the technical and financial difficulties associated with such projects. Microgrids offer a cost effective option for electrifying these remote areas due to their ability to function independently from the main grid and can also be designed to interconnect with the main grid should there be an opportunity for extension of the grid to the remote community. This has led to what are known as community microgrids. According to [1], a microgrid can be defined as a "localized grouping of electricity generation, energy storage, energy control and conversion, energy monitoring and management, and load management tools, capable of operating while connected to the traditional main grid or function independently". Microgrids offer the opportunity to utilize renewable energy resources such as solar photovoltaics (PV), wind, hydro and bio gas reducing dependency on fossil fuels that are harmful to the environment and human health.

Microgrid design consists of several aspects such as generation modelling, load modelling, storage, local network, sizing of the components and determination of the control strategy. One of the critical steps in the design process of PV microgrids is the determination of the sizes of system components. In this research, an efficient and improved approach to PV system sizing is presented. The limitations of the current sizing approaches are discussed in section II of this paper. It should be noted that when sizing PV systems, the main aim of the process should be to obtain a realistic possible optimum combination of the system components. The optimum solution is one that satisfies the load at a given level of reliability while minimizing capital and operational costs [2].

 

II. The Current Typical PV System Sizing Approach

The current typical approach to sizing of PV systems provided by PV manuals such as [3] involves the use of sizing sheets to determine the number and specifications of the components required [4][5][6][7][8][9][10]. The sizing procedure is based on average values of daily load and peak sun hours for the month with least solar irradiance. The assumption is that if the PV system is designed to meet the load demand at this radiation, then it will be sufficient to meet load demand throughout the year.

The battery capacity is determined using (1). The acronyms used in the equations are defined in the Appendix.

The number of PV modules is determined by (2), (3) and (4).

The size of the inverter, controller and the system wiring are determined as defined in [3] [11][12].

A. Merits of the Current Typical PV System Sizing Approach

The above procedure is explained in [3] which presents simple equations that can be used to size solar PV systems. The equations can be scripted in available tools such as Microsoft Excel to further ease computation and replication of the procedure to various locations [13] [6].

B. Shortcomings of the Current Approach to Sizing PV Systems

The current typical PV system sizing procedure does not consider the variation in the load demand and irradiance with time throughout the year. If the load demand consists of consecutive days where the daily load is higher than the average daily load, the battery capacity designed using this simple procedure may be insufficient to meet the desired days of autonomy and therefore the system is undersized. However, if the days of high load demand are relatively spread over time, the simple sizing procedure may oversize the system since the same system reliability could be achieved by designing with a lower daily load [14] [15] [11] [16].

Numerical methods are among the methods proposed in literature to improve the accuracy of PV system sizing . These methods evaluate the load, the PV output energy and battery state of charge for each hour throughout the year. The battery charges when the PV output energy is greater than the load demand current and discharges when the PV output is less than the load demand. If the output from the PV and battery cannot meet the load demand, there is a deficit [11]. A Loss of Load probability (LLP) is used as the measure of the system's reliability. The LLP is defined as the ratio of the total deficit energy to the total load demand over the period of consideration, typically one year. With a predefined LLP based on the user's satisfaction, an optimal configuration of the PV and battery is determined.

Numerical methods yield more reliable and optimum systems. The shortcoming with the numerical method discussed above is that the process of iterating through hourly data leading to long execution times and may sometimes lead to inability to converge to an optimal solution [16]. One way of overcoming this challenge is to reduce the time steps of the iteration without affecting the outliers in the hourly load demand and PV output energy.

This research presents the ComuGrid Sizing approach as a new method for PV system sizing based on the Density Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm and Mixed Integer Linear Programming (MILP) algorithm to determine the sizing of the solar PV system components that will give a minimum Annualized Total Life Cycle Cost (ATLCC) for a predefined desired LLP. The ComuGrid Sizing approach provides a more reliable sizing procedure than the basic sizing method since it considers the variation in the load demand and irradiance throughout the year instead of average values of load and irradiance. It also provides improvement to the numerical method discussed above by reducing the time steps of the iteration. The next sections of the paper will describe DBSCAN clustering algorithm, the MILP algorithm and the optimization process of the proposed sizing approach.

 

III. The Proposed ComuGrid Sizing Approach

In this research a solar PV community microgrid (ComuGrid) whose components are indicated in the block diagram shown in Fig. 1 is presented and optimally sized.

 

 

The steps involved in the sizing of the microgrid components using the proposed approach are described below.

Step1: Input the load and irradiance data

In this step, the hourly load current I_L(t) is determined based on the community's appliance usage and ratings. The specifications of the PV and battery are defined. The hourly irradiance, S(t), and temperature,T(t), of the community's location are also defined.

Step2: Calculate the hourly PV output current

The hourly PV output current I_pv(t) is calculated using (5).

Step 3: Consolidate the Load and Irradiance for consecutive time steps

This step involves consolidation of the load and PV outputs into fewer time steps. Subsection A presents the detailed description of this consolidation process.

Step 4: Determine the range of number of PV modules (PV_mi, PV_max ) and batteries (Bat_min, Bat_max) for the optimization process.

Use the method based on sizing sheets to determine the initial number of PV modules and Batteries. Assume an initially large range where the number of PV modules and batteries range from one to ten times the values obtained using the sizing sheets.

In order to determine the minimum values (PV_min, Bat_min ), consider the month with the least average load and assume that the LLP is larger than the desired LLP for the community. Using the range derived from the basic method above and the optimization procedure described in subsection B, determine the values (PV_min, Bat_min ).

In order to determine the maximum values (PV_max, Bat_max ), consider the month with the highest average load and assume that the LLP is smaller than the desired LLP for the community. Using the range derived from the basic method above and the optimization procedure described in subsection B, determine the values (PV_max, Bat_max ).

Step 5: Use the MILP procedure as described in subsection B to determine the size of system components that give minimum ATLCC for the desired LLP.

A. DBSCAN Clustering Algorithm

The main concept of the DBSCAN algorithm is that all the points within a cluster are such that the distance between them is less than a predefined radius referred to as the eps [17]. This concept is applied to the hourly irradiation and load data as follows: A three dimensional point(t, I_L(t), 7py(_t)), is defined for each hour t where ,I_L(t) is the load demand and I_PV(t) is the Output current of a single PV module at each hour. First, all consecutive points where the PV output is zero are clustered. These correspond to the night hours of each day. The points are consolidated into one time step t where the PV output for the time step is zero and the load is the sum of the respective loads. Thereafter, all consecutive points for which the PV output Ip_V(f) are in a range of m% of each other and the loads I_L(t) are also in a range of m% of each other are clustered and consolidated into one time step. The PV output for the time step is the sum of the respective PV outputs and the load is the sum of the respective loads. This paper has considered a value of m equal to 10%. The consolidation is illustrated in Fig. 2. All the shaded values in the first table on the left are consolidated into one time step resulting into the second table on the right with fewer time steps.

 

 

B. Mixed Integer Linear Programming Approach

The objective of this optimization method is to obtain the optimal design of a system that minimizes the ATLCC while meeting the load demand with a desired LLP that is dependent on the customer's satisfaction.

Optimization Problem

The objective function for the mixed-integer linear programming (MILP) problem is;

minimise ATLCC

subject to the constraints defined by (6) to (32). The ATLCC is defined by (55). The acronyms used in the equations are defined in the Appendix.

The PV System Model

The number of PV modules is within a maximum and minimum range determined above.

The current balance at each time period is given as

Battery Model

The number of batteries is within a maximum and minimum range determined above. It is assumed that initially, the battery is full. Thereafter, in each time period, the battery cannot charge to more than the battery capacity and cannot discharge to less than the minimum allowable battery capacity.

In each time period, the battery shall be either in charging or discharging state as represented by ( 18) [18]

Where Φ_ch(t) and Φdis(t) are binary variables representing charging and discharging modes.

During charging mode (Φ_Ch(t) - 0), the PV system charges the battery. There is no discharge current and deficit current.

When the battery is full, there is a surplus due to excess energy from the PV.

The charge and surplus currents cannot exceed the maximum PV output for each hour

During the discharge mode Φ_dis(t) - 0, the PV system current is insufficient to meet the load demand. The battery supplies the extra current to meet load demand. There is no charge current and surplus current.

If State of Charge (SOC) of the battery falls below DOD, there is a deficit.

The Deficit and Discharge currents cannot exceed the Load current

The energy balance equation for the battery is given by (31) [19]

The LLP is less than or equal to a desired LLP [2]

Controller Specification

The controller is sized using (33) to (35). [2]

Where; SF is a safety factor to ensure that the array can withstand high currents. I_sc is the module short circuit current, Ctrler_v is the voltage rating of the controller and is equal the DC system voltage, Ctrler_Sel is the current rating of the controller selected basing on the voltage rating and current ratings (Ctrler_scc) and Ctrler_LdAmps. The total number of controllers Ctrler_Total is then obtained.

Inverter Sizing and Specification

The inverter is sized using (36) and (37). [2]

Cost Analysis

The capital cost for the PV array and the battery storage is given by (38) and (39) respectively [2].

Maintenance cost of PV modules and Batteries per year is assumed to be 2% of the capital costs [4]. This is presented in (40) and (41) respectively.

The annualized capital and maintenance cost of the PV modules is estimated using (42) [16].

The annualized capital maintenance cost and replacement cost of the batteries is calculated using (43) [16].

Where;

The capital cost for the transformers is calculated using (45).

Maintenance cost of the Transformers per year is given by (46).

The annualized capital and maintenance cost of the transformers is estimated using (47).

The total capital costs for other components are lamped together as 20% of PV cost as given in (48).

The total capital costs for other components aside PV and Batteries are given by (49)

The annualized Capital costs of other components is estimated using (50). [2]

Where;

ndr is the net of discount inflation rate and is given by (51). ir is the real interest rate and fr is the inflation rate [2],

The total life cycle cost is the sum of the respective component costs and is given by (52). [2]

The annualized salvage value of the system is given by (53). [2]

Where;

CC_D is the capital cost of the disposable component and is given by (54). [2]

The annualized total life cycle cost is given by (55). [2]

The levelized cost of energy (LCE) is obtained using (56) below [16].

 

IV. Case Study Using the Comugrid Sizing Approach

The ComuGrid Sizing approach proposed in this research was implemented using MATLAB software and it was used to design a community microgrid for a village in the district of Tororo in eastern Uganda. The location chosen is not connected to the main utility grid. The village considered has 100 households, a maize mill, ladies and men's salons, a primary school and a clinic. The household categories and appliance usage were estimated based on the energy survey conducted by the Uganda Bureau of Statistics and Ministry of Energy and Mineral Development for 2012 [19] as well as the Uganda National household survey for 2016 [20]. The average load demand per day is 485kWh.

The make and model of the PV module chosen for the system is the TT, Auversun, AV275M96NB-5P while the battery chosen is the Concorde Sun Xtender PVX-2580L. These types of battery and PV module were chosen as they have been successfully used in other studies on PV systems such as those in [4]. A depth of discharge of 0.8 was used. The renewables.ninja tool [20] [21] [22] was used to generate the hourly solar data and ambient temperature for the target location. The community microgrid was also sized using the basic sizing method defined in [3] and the results from the two methods were compared. The basic sizing was done using 4 days of autonomy.

The comparison between the basic sizing approach and the ComuGrid approach is shown in Table I.

 

 

The ATLCC and the LCE obtained using the ComuGrid Sizing approach are lower than those obtained using the basic sizing approach. The LLP for the ComuGrid Sizing approach is lower than that for the basic sizing approach.

The performance of the two methods was compared considering the month with highest load. Fig. 3 and Fig. 4 show the sample hourly performance of such a system when sized using the two methods. During this period, The LLP for the system sized using the basic method was 0.44 and the average state of charge was 0.21. This means that the system sized using the basic method was unable to meet the load demand for a period equivalent to 13 days and the battery was operating near minimum DOD for most of the time as shown in Fig. 4. The period of deficit is longer than the 4 days of autonomy used during the sizing. The LLP for the system sized using the proposed ComuGrid MILP based method was 0.05 and the average state of charge was 0.5. This means that the system sized using the proposed ComuGrid MILP based method was unable to meet the load demand for a period equivalent to just 1.5 days.

 

 

The results discussed above show that the ComuGrid Sizing approach yields a better system that is both technically reliable and cost effective as compared to the one achieved using the basic sizing method.

It is however noted that the Levelized Cost of Energy obtained using the ComuGrid approach (£0.42/kWh approximately 2,000/= UGX) is higher than that for the main utility grid, which is 752.5/= UGX [23]. This is due to the cost of storage. When storage is not considered, the price for the electricity is £0.07/kWh (approximately 350/= UGX).

The microgrid was sized using different consolidation values for m = 5%, 10%, 20% and 30% . The results are shown in Table II.

 

 

The results show that the total time steps processed reduce with an increase in m. However the results for the ATLCC, LCE, Number of PV modules and batteries are similar for the different values of m. This is because the consolidation maintains the outlier periods for the irradiance and load demand.

 

V. Conclusion

Many developing countries are aiming to improve the electrification rate of their countries especially in the remote areas that are very costly to connect to the main grid. In this regard there is urgent need for optimum, reliable and cost-effective off-grid electrification projects. These projects should be sustainable and serve the growing needs of the communities for which they are designed. In this paper a community microgrid system has been proposed that uses an improved PV sizing approach taking into consideration hourly load variation together with the hourly variation of solar irradiance and ambient temperature of the area. This is an improvement from the basic sizing approach presented in solar PV design and installation manuals. The results have shown that a system sized using the basic method is unreliable and more expansive than one sized using the proposed ComuGrid sizing approach that utilizes MILP. The main contribution of this paper is that it has provided a method for reducing the hourly load and irradiance data into fewer time steps to aid in faster execution and convergence to the optimal solution. In addition, it has provided a MILP based method and a process on how to derive the search space of the optimization starting from the basic sizing method. Lastly from the results it can be seen that the cost of electricity from off-grid systems incorporating storage is still higher than that supplied by the main grid. This cost can be expected to go down with reduction in prices for battery storage and provision of attractive subsidies for investment in rural electrification systems.

 

References

[1] P. Peng, "Microgrids: A Bright Future," Huawei Commun., no. 63, pp. 6-8,2011.

[2] T. Khatib and W. Elmenreich, Modeling of Photovoltaic Systems Using MATLAB: Simplified Green Codes. Wiley, 2016. '

[3] Solar Energy International, Photovoltaics Design and Installation Manual. New Society Publishers, 2004.

[4] S. K. Sakiliba, A. S. Hassan, J. Wu, and E. Saja, "Assessment of Stand-Alone Residential Solar Photovoltaic Application in Sub-Saharan Africa : A Case Study of Gambia," J. Renew. Energy, vol. 2015, pp. 1-10,2015.         [ Links ]

[5] A. Soufi, A. Chermitti, and N. B. Triki, "Sizing and Optimization of a Livestock Shelters Solar Stand-Alone Power System," Int. J. Comput. Appl.,vol. 71, no. 4,pp. 975-8887,2013.         [ Links ]

[6] A. Abu-jasser, "A stand-alone photovoltaic system, case study: A residence in gaza," J. Appl. Set Environ. Sanit., vol. 5, no. 1, pp. 81-91,2010.         [ Links ]

[7] M. Ishaq and U. H. Ibrahim, "Design Of An Off Grid Photovoltaic System : A Case Study Of Government Technical College, Wudil, Kano State," Int. J. Sci. Technol. fiei., vol. 2, no. 12,2013.         [ Links ]

[8] I. Standards, C. Committee, D. Generation, and E. Storage, IEEE Guide for Array and Battery Sizing in Stand-Alone Photovoltaic (PV) Systems, no. May. 2008.

[9] I. S. C. C. 21, IEEE Recommended Practice for Sizing Lead-Acid Batteries for Photovoltaic (PV) Systems, vol. 2000, no. July. 2000.

[10] U. A. Saleh, Y. S. Haruna, and F. I. Onuigbo, "Design and Procedure for Stand-Alone Photovoltaic Power System for Ozone Monitor Laboratory at Anyigba, North Central Nigeria," Int. J. Eng. Sci. Innov. Technol, vol. 4, no. 6, pp. 41-52, 2015.         [ Links ]

[11] K. Bataineh and D. Dalalah, "Optimal Configuration for Design of Stand-Alone PV System," vol. 2012, no. May, pp. 139-147,2012.

[12] A. K. Shukla, K. Sudhakar, and P. Baredar, "Design, simulation and economic analysis of standalone roof top solar PV system in India," Sol. Energy, vol. 136, no. July, pp. 437-449,2016.         [ Links ]

[13] C. Oko, E.. Diemuodeke, E.. Omunakwe, and E. Nnamdi, "Design and Economic Analysis of a Photovoltaic System: A Case Study," Int. J. Renew. Energy Dev., vol. 1, no. 3, pp. 65-73,2012.         [ Links ]

[14] H. Louie and P. Dauenhauer, "Effects of load estimation error on small-scale off-grid photovoltaic system design, cost and reliability," Energy Sustain. Dev., vol. 34, pp. 30-43,2016.         [ Links ]

[15] H. A. Kazem, T. Khatib, and K. Sopian, "Sizing of a standalone photovoltaic/battery system at minimum cost for remote housing electrification in Sohar, Oman," Energy Build., vol. 61, no. June, pp. 108-115,2013.         [ Links ]

[16] I. A. Ibrahim, T. Khatib, and A. Mohamed, "Optimal sizing of a standalone photovoltaic system for remote housing electrification using numerical algorithm and improved system models," Energy, vol. 126, pp. 392-403,2017.         [ Links ]

[17] D. Birant and A. Kut, "ST-DBSCAN: An algorithm for clustering spatial-temporal data," DataKnowl. Eng., vol. 60, no. 1, pp. 208221,2007.         [ Links ]

[18] T. Khatib, A. Mohamed, and K. Sopian, "A review of photovoltaic systems size optimization techniques," Renew. Sustain. Energy Rev., vol. 22, pp. 454-465,2013.         [ Links ]

[19] A. Malheiro, P. M. Castro, R. M. Lima, and A. Estanqueiro, "Integrated sizing and scheduling of wind/PV/diesel/battery isolated systems," Renew. Energy, vol. 83, pp. 646-657,2015.         [ Links ]

[20] S. Pfenninger, "Dealing with multiple decades of hourly wind and PV time series in energy models: A comparison of methods to reduce time resolution and the planning implications of inter-annual variability,"Appl. Energy, vol. 197, pp. 1-13,2017.         [ Links ]

[21] S. Pfenninger and I. Staffell, "Long-term patterns of European PV output using 30 years of validated hourly reanalysis and satellite data," Energy, vol. 114, pp. 1251-1265,2016.         [ Links ]

[22] "Renewables.ninja." [Online]. Available: https://www.renewables.ninja/. [Accessed: 01-Mar-2018].

[23] UMEME, "UMEME." [Online]. Available: https://www.umeme.co.ug/tariffs. [Accessed: 30-Mar-2020].

 

 

 

Jane Namaganda-Kiyimba is a Member of the IEEE. She obtained a BSc degree in Electrical Engineering (First Class Honors) from Makerere University, Uganda in 2007. She obtained an MTech degree in Power and Energy Systems from the National Institute of Technology Karnataka, Surathkal India in 2011. She is currently pursuing a PhD in Electrical and Electronics Engineering at The University of Manchester, UK.

She is an Assistant Lecturer in the Department of Electrical and Computer Engineering at Makerere University and has previously worked as a Network Planning Engineer for Warid Telecom Uganda, now Airtel and Uganda Telecom.

Mrs. Namaganda-Kiyimba is a member of the IET, UK.

 

 

Joseph Mutale is a Senior Member of the IEEE. He obtained a BEng degree in Electrical Machines and Power Systems from The University of Zambia in 1981. He studied for a postgraduate diploma in Electric Power Distribution Systems at the Norwegian Institute of Technology between 1983 and 1984. His MSc in Electric Power Transmission and Distribution and PhD in Power System Economics were obtained from UMIST, which is now part of The University of Manchester, in 1987 and 2000 respectively. He joined The University of Manchester in 2002 and is currently a Professor of Sustainable Energy and Electric Power Systems. Previously, he spent over 15 years in the electric utility industry. This included a wide range of technical posts at Copperbelt Power Company, now Copperbelt Energy Corporation and ZESCO, the Zambian National Utility.

Prof. Mutale is a Chartered Engineer, Fellow of the IET and Past Chair of the IEEE Working Group on Sustainable Energy Systems for Developing Communities.

 

 

Appendix

Symbols and Acronyms

ATLCC Annualized Total Life Cycle Cost

Alpha PV panel temperature coefficient

Bat Total number of Batteries

Bat_CeffBattery Charging Efficiency

Bat_deffBattery Discharging Efficiency

Bat_AHAH rating of one Battery

Bat_capBattery Storage Capacity (AH)

Bat_maxMaximum Number of Batteries

B^atmax_par Maximum number of Batteries in Parallel

Bat_minMinimum Number of Batteries

Batpar Number of Batteries in Parallel

Bat_serNumber of Batteries in Series

C_BatCost of Battery

C_BataAnnualized capital maintenance cost

and replacement cost of the batteries CC_BatCapital Cost of Batteries

CC_CWTotal capital costs for other components

CC_Dcapital cost of the disposable components

CC₀c Total capital costs for other components aside PV and Batteries

CCoca Annualized Capital costs of other components

CCpv Capital Cost of PV modules

CC_TRCapital Cost of transformers

Cpv Cost of one PV module

Cpva Annualized capital and maintenance cost of the PV modules

CS_aAnnualized salvage value of the system

C_TRaAnnualized capital and maintenance cost of the transformers

C_Tr Cost of one transformer

Ctrler_LdAmps Maximum DC Load Amps that controller must handle

Ctrler_sccController short circuit current

Ctrler_Sei Controller current rating

Ctrler_TotalNumber of Charge Controllers in operation during the system lifetime

Ctrler_vVoltage rating of the controller

DBSCAN "Density Based Spatial Clustering of Applications with Noise "

Desired_LLP Desired Loss of Load Probability

DOD Depth ofDischarge for the Battery

D_autDays of Autonomy

E_TOTTotal energy consumed by the load from the system per year

fr Inflation Rate

I_ch (t) Battery Charge Current at time (t)

'def(t) Deficit Current at time (t)

I_dis (t) Battery Discharge Current at time (t)

I_lnvInverter current rating

I_mpPeak Amps per module at STC

I_L(t) Load demand current at time (t)

I_PV(_t) Output current of a single PV module at time (t)

IPV(t) Total output current of the PV array at time (t)

I_scPV Module Short Circuit Current

IsurOD Surplus Current at time (t)

ir Real Interest Rate

L_BatLifetime of the Battery

L_PVPV system Lifetime

L_sMicrogrid System Lifetime

L_TRLifetime of the transformer

LCC Sum of annualized capital, annualized maintenance and annualized replacement costs

LCE Levelized cost of energy

LLP Loss of Load Probability

M A large number

ndr Net of discount inflation rate

Max_DCACMaximum Continuous Direct Current of the controller

MCC_BatMaintenance cost of batteries

MCCpv Maintenance cost of PV modules

MCC_TRMaintenance cost of transformers

MILP "MixedInteger Linear Programming"

N_TRNumber of transformers

P_cTotal Connected AC Power

PSH Peak sun hours per day

PV Number of PV Modules

PV_maxMaximum Number of PV Modules

PVmax_par Maximum Number of PVModules in Parallel

PV_minMinimum Number of PV Modules

PV_par Number ofPV Modules in Parallel

PV_ser Number ofPV Modules in Series

S(t) Solar Radiation(W/m²) at time (t)

SF safety factor

SOC(t) Battery State of Charge

STC Standard Test Conditions

T(t) Ambient Temp (°C)at time (t)

Vdc DC System voltage

V_mpNominal Module Voltage (Voltage at MPP under STC)

Y_BatNumber of times ofBattery Replacement

Z Average Daily Load (Amp-Hour per Day)

cp_ch (t) Binary variable for charging mode

cp_chsurBinary variable for the discharge/deficit mode

(Pais (t) Binary variable for discharging mode

cp_disdefBinary variable for the charge/surplus mode

ribat Battery Efficiency