A Novel Method for Optimal Calculation of Stand-Alone Renewable

Energy Systems

VAN DUC PHAN, QUANG SY VU, HUU SON LE, VAN BINH NGUYEN

Faculty of Automotive Engineering

School of Engineering and Technology

Van Lang University

Ho Chi Minh City

VIETNAM

Abstract: - Nowadays, the development and use of clean energy sources are receiving strong attention all over

the world. However, the current methods used to calculate the design of these systems have proved

unconvincing when the optimization is performed by "soft" optimization, and there are certain defects. In this

paper, a new method for more robust optimization of independent renewable energy systems is proposed, in

which the essential elements of the system such as energy characteristics are obtained in the reality of

renewable energy generators or weather changes over time of the year are also considered to solve the problem

of optimizing the energy system more efficiently, meet the demand for efficient energy use and optimize

consumer investment costs.

Key-Words: Renewable energy generator, Stand-alone system, Linear programming problem, Battery, Simplex-

method.

Received: April 25, 2021. Revised: February 12, 2022. Accepted: March 13, 2022. Published: April 18, 2022.

1 Introduction

Currently, the use of independent renewable

energy systems is gaining wide attention because of

its undeniable advantages, such as reducing carbon

emissions, environmental pollution, climate change,

etc. This system can be found everywhere, such as

power supply systems for remote areas, islands

where the power grid is difficult to reach [1, 2]. In

the transportation sector, they are used to build

electric charging stations using renewable energy to

charge electric vehicles, or in other fields [3-6], etc.

There are many studies on optimizing these systems,

but most of them are only done with "soft"

optimization, i.e., systems that are optimized using

control methods. based on previously selected

system parameters [4-10]. The selection of

installation parameters of these systems is mostly

based on estimation because no specific calculation

method is effective. That prompted us to find a more

effective method in calculating the optimal design

of the installation parameters of the independent

energy system and this is also the main content of

the paper.

In most of the research related to independent

energy systems, we found [3,5-10] the authors gave

different optimization methods, but most of them

are soft optimization methods. The authors [3]

performed a cost optimization calculation of the

energy storage portion used in the stand-alone

system. This has not shown the ability of the whole

system to work effectively. The authors [5-11] have

proposed optimal methods controlled by

optimization algorithms or by combining different

sources. However, in these articles, there is no

mention of determining any installation parameters

for the equipment used in the system. Soft

optimization based on predetermined system

parameters is just about finding the best

performance of this system. Some other authors [9]

mentioned the combined use of different energy

sources but also did not give convincing calculation

methods. In the work [10], some guidelines have

been given for selecting lead-acid batteries for use

in independent systems, and of course, a convincing

calculation method has not been provided. All of

this creates a defect in the overall optimization of

the renewable energy system. In practice, it is not

easy to determine the optimal system parameters.

For an independent renewable energy system, this

becomes even more difficult, because it is not

possible to accurately determine the consumption

characteristics of the load or the energy

characteristics obtained in practice from renewable

energy generators, which are highly dependent on

weather conditions, and this is also the reason why it

is difficult to find an efficient calculation method.

All the studies mentioned above on optimization

of the systems are based on partial optimization

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(hard) or optimal control (soft). This is not

convincing, to achieve complete optimization, all

parameters of the system must be included in the

specific calculation.

A thoroughly optimized energy system must

include the optimization of installed equipment, and

then incorporate intelligent control methods. In this

paper, the authors present a more specific and

detailed optimal calculation method used in the

calculation and design of an independent renewable

energy system, which compensates for the defect

mentioned above. This method fully represents the

calculation of the installed capacity of the storage

devices and of the generators under a given load

which is assumed to be predetermined. In practice,

this assumption can be fully realized when the load

graph can be built based on past energy

consumption and future plans. In addition to

calculating the installed capacity of the renewable

energy generators, in this method, the captured

energy characteristics of the wind and solar

generators are included. These characteristics were

obtained by the author from the electrical

engineering laboratory of the Peter the Great St.

Petersburg Polytechnic University and were used in

the work [12]. This allows the optimal calculation of

the system and the response to the energy

consumption needs of the load more realistically

and more suitable for different geographical areas.

The optimal calculation of the investment cost of the

system depends on many factors such as the

manufacturer, the size of the system, etc. therefore

the authors did not include it in this paper. However,

this is completely possible based on the optimal

installation parameters of the system.

The stand-alone system used to illustrate the

proposed method consists of wind and solar

generators, UPS, and consumer loads. To be more

general, the consumed load consists of two parts, the

fixed component is the important loads, and the

variable component is the loads that can change the

time of using electricity such as charging other

equipment. For a simple problem description, the

power loss on the device is considered negligible.

This system is related to a project to study the

possibility of installing a renewable energy system

to replace gas turbine generators.

The results illustrating the proposed method

shown in Figures 1-12 are extracted from countless

relationships showing the system's ability to work in

four seasons of the year. As can be seen easily in the

next section, the system description function

consists of 4 main variables (installed capacities of

renewable energy generators and UPS capacity)

which include a multitude of ingredient variables.

For a graphical representation, some results are

illustrated by specific parameters (installed capacity

of wind and solar generators). From the results

obtained, it is possible to accurately determine the

optimal values of the devices used in the system.

Combining this result with optimal control methods

will allow the optimization of the energy system to

be more thorough and rigorous.

2 Problem Formulation

The difficulties encountered in solving the energy

problem as mentioned above are the nonlinearity of

the energy problem. In this section, the linearization

of the nonlinear energy problem and solving them

by the linear programming method are presented in

detail. The mathematical model of the problem

- For batteries:

sto min sto sto max

()P P t P  

(1)

sto min sto sto max

()W W t W

(2)

here

 

sto

– total instant power of the batteries and

 

sto

– total instant capacity of the batteries;

sto min

;

sto max

;

sto min

and

sto max

– limits of power and

energy of the batteries to its safety assurance.

sto sto sto

( ) ( ) (0)

W t P t dt W



It should be noted that the maximum

storage/converter capacity should be taken

according to the charge/discharge limit of the. These

limits are valid for each type of battery used [11-

17].

sto ( ) 0Pt

if at time t, the battery discharges

electricity, and

sto ( ) 0Pt

if at time t, the battery

charges.

sto (0) 0W

sto sto

( ) ( )

W t P t dt

(3)

Limits of actual energy characteristics of

generators:

solar solar max

0 ( )P t P

(4)

wind wind max

0 ( )P t P

(5)

where

solar max

and

wind max

– installed power of wind

turbines and solar panels;

 

solar

and

 

wind

–

actual power of wind turbines and solar panels.

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load ()Pt

- The load instantaneous power

consumption, consists of two components, as

mentioned above

const ()Pt

var ()Pt

load const var

( ) ( ) ( )P t P t P t

(6)

Here

const ()Pt

- Important load components;

var ()Pt

load element that can shift the moment of

consumption.

The energy power consumption

load

from

0t

tT

, here T - simulation interval, we have [16]:

load load const var const var

0 0 0

( ) ( ) ( )

T T T

W P t dt P t dt P t dt W W    

  

(7)

Equation of power balance [18]

solar wind sto load

( ) ( ) ( ) ( )P t P t P t P t  

var solar wind sto const

( ) ( ) ( ) ( ) ( )P t P t P t P t P t    

(8)

Solving nonlinear equations with a variety of

conditions as mentioned above by the analytic

method has many difficulties, so we bring the above

problem to a linear form.

We examine the column vectors

sto

solar

wind

var

whose elements are values corresponding to

the quantities

sto ()Pt

solar ()Pt

wind ()Pt

var ()Pt

, at

discrete times.

:{ 0; ; }

k k k N

t t t t h t T



   

, here h

– Observed steps in the simulation process. To make

it simpler to write quantities, we notation

sto, sto ()

P P t

solar, solar ()

P P t

wind, wind ()

P P t

var, var ()

P P t

. We have

sto sto,1 sto,2 sto,

, , , t

P P P





;

solar solar,1 solar,2 solar,

, , , t

P P P





;

wind wind,1 wind,2 wind,

, , , t

P P P





;

var var,1 var,2 var,

, , , t

P P P





The amount of energy consumed can change the

time of use.

var var var, var 1 load const

()

TNt

W P t dt P h h B W W



       



1P

Here 1 – Unit vectors have corresponding

dimensions. If

sto (0)W

sto ()WT

sto,N

, we got:

sto sto sto sto,1 2 sto,

(0) tN

W W h W B W      1P

sto 2 sto, sto (0)

h B W W    1P

(8) in matrix form:

 

const,1

var

const,2

sto 3

solar

const,

wind N





   





EEEE B

here E – the unit matrix. Finally, we have:

var 1

sto 2

solar

wind 3



    



   





   

   



   



   





   



1 0 0 0

0 1 0 0 AX B

0 0 0 0

E E E E

(10)

Here 0 – zeros vector has a corresponding size.

For (3)

sto,n sto sto, sto max

0 (0) ; 1,

W W P h W n N



    



Its matrix form

 

sto,1

sto,2

sto sto max sto

sto,

1 0 0

1 1 0

(0) (0)

1 1 1 N

W h W W





     





sto sto max sto

sto

(0) (0)W W W



     1 S P 1

, from here

 

sto max sto

sto

(0)





 





 

 

var

sto sto max sto

solar sto

wind

(0)



   



   





   

   



   





   

   



S1 CX D

. (11)

For clarity, we re-enumerate the conditions in

the form of inequality as follows,

var load

sto min sto sto max

solar solar max

wind wind max

0 ( )

()

0 ( )

P t P

P P t P

P t P





  











And, in matrix form

var load

sto sto max

sto min

solar solar max

wind wind max



   



   

 

    





   

 

   

 



   

. (12)

The investment cost of the system can be

calculated according to the installed capacities

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solar max

wind max

sto max

of the devices, so it

can be optimized when the installed capacity of the

devices is optimized, i.e. the objective function will

be installed capacities to reach a minimum.

 

solar wind var sto

solar max

wind max

, , , sto max

sto max

min













P P P

(13)

This is a multi-objective optimization problem,

so in solving this problem, the multi-objective

optimization methods are chosen.

Problem (13) with conditions in the form of

equality (10), inequalities (11), and limits (12)

related to the linear programming problem, and to

solve this type of problem, we apply simple

methods. (Simplex method) [18-20]. The total

number of variables when simulating the system

within a year can be up to dozens, hundreds of

thousands of variables [15-16].

3 Problem Solution

The system simulations operate for a year with

variable model functions, i.e., they are not that they

fluctuate in a range that reflects the uncertainty of

the actual energy consumption as well as the actual

energy of the generators.

The obtained result is the ability (Prob %) to

meet electricity consumption demand according to

four installation parameters (

solar max

wind max

sto max

). They are the main parameters of the

independent power system and have been described

in mathematical equations, and participate in the

optimization process as mentioned in the

introduction part. For an intuitive look, some results

are graphically depicted relative to the values of the

generators.

The obtained results (Figures 1 to 12) have

shown the reasonableness of the proposed method.

When installed capacity/power is large, the system

completely meets the energy consumption demand.

This is very practical because when the installed

capacity/power of the storage energy system is

larger, more energy is stored, so they can

completely always meet the electricity demand. In

contrast, when they are small, the response is

markedly reduced.

Figures 1 to 12 show the probability that the

system can function perfectly, being able to meet

the requirements of the load consumption

corresponding to the installed power level of the

generating sources. Figures 1 to 3 show the system's

response capacity in spring, figure 4 to 6 - summer,

figure 7 to 9 - fall and figure 10 to 12 – winter.

From the results illustrated in Figures 1 to 12,

the installed capacity levels of the system can be

selected and from there a specific investment cost

can be calculated.

For example, in Figure 1, when the installed

capacity of the generator

solar

= 3 kW,

wind

= 4 kW,

at the power level of the battery is 3.5 kW and its

capacity is 4kW.h, the system works almost

perfectly (~96,7%) in spring, ie the sources supply

enough for consumption needs. When the installed

power of the generators is the same, but the installed

power and (or) capacity of the storage system are

reduced, the system cannot meet the consumption

demand at a certain time. Because when the weather

is bad and the installed power and (or) capacity of

the battery is too low, it will not meet the electricity

demand.

Figures 1 to 12 show the system working

probabilities corresponding to the four seasons of

the year. The choice of the installed capacity of the

equipment must satisfy the consumption over the

seasons. For example, when

solar

= 3 kW,

wind

= 4

kW (Figures 1, 4, 7, 10), at the power level of the

battery of 3 kW and its capacity is 4 kW.h, the

system works almost perfectly (~94.6%) in summer

(Figure 4), but does not meet consumer demand (the

probability less than 90%) in other seasons (Figures

1, 7, 10).

Fig. 1: Potential system performance in spring,

when Psolar = 3 kW; Pwind = 4 kW.

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Fig. 2: Potential system performance in spring,

when Psolar = 4 kW; Pwind = 3 kW.

Fig. 3: Potential system performance in spring,

when Psolar = 4 kW; Pwind = 3 kW.

Fig. 4: Potential system performance in summer,

when Psolar = 3 kW; Pwind = 4 kW.

Fig. 5: Potential system performance in the summer,

when Psolar = 4 kW; Pwind = 3 kW.

Fig. 6: Potential system performance in the summer,

when Psolar = 4 kW; Pwind = 4 kW.

Fig. 7: Potential system performance in fall, when

Psolar = 3 kW; Pwind = 4 kW.

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Fig. 8: Potential system performance in fall, when

Psolar = 4 kW; Pwind = 3 kW.

Fig. 9: Potential system performance in fall, when

Psolar = 4 kW; Pwind = 4 kW.

Figure 10: Potential system performance in the

winter, when Psolar = 3 kW; Pwind = 4 kW.

Fig. 11: Potential system performance in winter,

when Psolar = 4 kW; Pwind = 3 kW.

Fig. 12: Potential system performance in winter,

when Psolar = 4 kW; Pwind = 4 kW.

The level of response to the energy consumption

demand corresponding to the different installed

power levels is clearly shown in Figures 1 to 12.

From these graphs, it is not difficult to choose the

optimal system values.

Clearly, the results obtained above (Figures 1 to

12) have shown the perfect working level of the

system relative to the input parameters that are the

installed powers of the stand-alone system. When

the installation parameters of the system are

optimized, it is not difficult to deduce that the cost

of the system can also be optimized.

4 Conclusion

In this paper, the optimal installed capacity

calculation has been solved by bringing the

nonlinear problem to a linear form. This method is

more convincing in calculating the design of the

energy system independently than estimating

installed capacity combined with optimal control in

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many previous studies. The simulation of the

proposed method is performed on an independent

renewable energy system. The results of the

simulation showed clearly the installed capacities of

the devices so that the energy system meets demand.

Obviously from the graphs (Figures 1 to 12),

choosing the optimal installation tool and inferred

that the optimization of investment costs can be

done easily. For example, for this system, when the

installed capacity of wind power generator Pwind = 4

kW, solar power generator Psolar = 3 kW, battery Psto

= 3.5 kW, and the capacity of battery Wsto = 4 kW.h,

the system always ensures the adequate power

supply.

In the mathematical model of the problem in the

previous section, including descriptive functions for

energy sources, the charge/discharge, the capacity of

the storage unit, and the consumed loads are the

basic components of an independent energy system.

Therefore, this method can be used in general for all

independent energy systems using renewable energy

generators with different electricity consumption

requirements. This method required accurate load

chart and weather characteristics where the system

is installed. This can be considered a difficulty of

the proposed method, especially for localities that

have not yet completed the above information

systems (including forecasting of energy

consumption and weather).

The proposed method has eliminated the

difficult calculation and replaced the estimation of

the system's design parameters by calculating

specific optimization. It allows the optimal

calculation of installed capacities more precisely

and specifically. This not only has great technical

significance but also has special implications for

transporting equipment to remote areas because the

optimal calculation of the system components can

be derived from the optimal calculation of the

installed capacity

In addition, the life cycle of energy storage units

is relatively short compared to other devices in the

system and the substances used in their manufacture

are also very harmful to the environment. So the

optimization of installed capacity for this part also

has great significance for environmental protection.

References:

[1] Bassam, N.E. “Renewable energy for rural

communities”, Renewable Energy, Vol.24,

pp.401-408.

[2] Riesch, G. (1997). “European rural and other

off-grid electrifications”, Solar Energy

Materials and Solar Cells, Vol.47, pp.265-

269, 2001.

[3] T. Dragičević, H. Pandžić, D. Škrlec, I. Kuzle,

J. M. Guerrero and D. S. Kirschen, "Capacity

Optimization of Renewable Energy Sources

and Battery Storage in an Autonomous

Telecommunication Facility," in IEEE

Transactions on Sustainable Energy, vol. 5,

no. 4, pp. 1367-1378, Oct. 2014.

[4] T. Mai et al., "Renewable Electricity Futures

for the United States," in IEEE Transactions

on Sustainable Energy, vol. 5, no. 2, pp. 372-

378, April 2014.

[5] Tran, V.H. and Coupechoux, M.. Cost-

constrained Viterbi Algorithm for Resource

Allocation in Solar Base Stations. IEEE

Transactions on Wireless Communications, 1-

15,2017.

[6] Priyono, W., Wijaya, D.F., Firmansyah, E.

(2018). Study and Simulation of a Hybrid

Stand-alone PV System for Rural

Telecommunications System. 2018 3rd

International Conference on Information

Technology, Information Systems and

Electrical Engineering (ICITISEE),

Yogyakarta, Indonesia., 418-422, 2018.

[7] Mirshekarpour, B. and Davari, S.A. (2016).

Efficiency Optimization and Power

Management in a Stand-Alone Photovoltaic

(PV) Water Pumping System. 7th Power

Electronics, Drive Systems & Technologies

Conference (PEDSTC 2016), 427-433.

Tehran, Iran, 2016.

[8] J. Han, C. Choi, W. Park, I. Lee, and S. Kim,

"Smart home energy management system

including renewable energy based on ZigBee

and PLC," in IEEE Transactions on Consumer

Electronics, vol. 60, no. 2, pp. 198-202, May

2014.

[9] B. Zhou et al., "Optimal Scheduling of

Biogas–Solar–Wind Renewable Portfolio for

Multicarrier Energy Supplies," in IEEE

Transactions on Power Systems, vol. 33, no.

6, pp. 6229-6239, Nov. 2018.

[10] Guide, I.. IEEE Guide for Selecting,

Charging, Testing, and Evaluating Lead-Acid

Batteries Used in Stand-Alone Photovoltaic

(PV) Systems. IEEE, 2014

[11] L. Maharjan, S. Inoue, H. Akagi, and J.

Asakura, "State-of-charge (SOC)-balancing

control of a battery energy storage system

based on a cascade PWM converter," IEEE

Trans. Power Electron., vol. 24, no. 6, pp.

1628-1636, Jun. 2009.

WSEAS TRANSACTIONS on SYSTEMS and CONTROL

DOI: 10.37394/23203.2022.17. 18

Van Duc Phan, Quang Sy Vu,

Huu Son Le, Van Binh Nguyen

E-ISSN: 2224-2856

165

Volume 17, 2022

[12] Korovkin N.V., V.Q. Sy 2018. Оптимизация

энергопотребления на основе

использования накопителя энергии,

Известия НТЦ Единой энергетической

системы. SPB, Russia

[13] Vazquez, S., Lukic, S. M., Galvan, E.,

Franquelo, L. G. & Carrasco, J. M.. Energy

storage systems for transport and grid

applications. IEEE Transactions on Industrial

Electronics, 3881-3895, 2010,

[14] Ribeiro, P. F., Johnson, B. K., Crow, M. L.,

Arsoy, A. & Liu, Y.. Energy storage systems

for advanced power applications. Proceedings

of the, 1744-1756, 2001.

[15] Valentin, A.. “Energy Storage Technologies:

The Past and the Present”. Proceedings of the

IEEE, 1777 – 1794, 2014.

[16] Phu Tran Tin, Quang Sy Vu, Duy Hung Ha,

Minh Tran, 2020. “Energy Cost Savings

Based On The Uninterruptible Power Supply

(UPS)”, International Journal of Electrical and

Computer Engineering (IJECE), vol10 no 4,

p. 4237-4243, 2020.

[17] H. Zhang, “A battery storage device for

distributed hybrid-powered smart grid system

and control method thereof,” European Patent

2645522 A1, Oct. 2, 2013.

[18] Демирчян, К., Нейман, Л. & Коровкин, Н..

Теоретические основы электротехники.

С.П.Б: Питер, 2009.

[19] Schrijver, A, “Theory of Linear and Integer

Programming,” New York: John Wiley &

sons, 1998.

[20] Stone, R.E. and Tovey, C.A, “Erratum: The

simplex and projective scaling algorithms as

iteratively reweighted least-squares methods,”

SIAM Review, pp. 220–237, 1991.

[21] J. Yao, H. Li, Y. Liao, and Z. Chen, “An

improved control strategy of limiting the DC-

link voltage fluctuation for a doubly-fed

induction wind generator,” IEEE Trans.

Power Electron., vol. 23, no. 3, pp. 1205–

1213, May 2008.

[22] A. Timbus, M. Liserre, R. Teodorescu, P.

Rodriguez, and F. Blaabjerg, “Evaluation of

current controllers for distributed power

generation systems,” IEEE Trans. Power

Electron., vol. 24, no. 3, pp. 654–664, Mar.

2009.

[23] Y. W. Li and C. N. Kao, “An accurate power

control strategy for power-electronics-

interfaced distributed generation units

operating in a low-voltage multibus

microgrid,” IEEE Trans. Power Electron., vol.

24, no. 12, pp. 2977–2988, Dec. 2009.

[24] I. Park, et al, “Nanoscale Patterning and

Electronics on Flexible Substrate by Direct

Nanoimprinting of MetallicNanoparticles,”

Advanced Materials, vol. 20, pp. 489 – 496,

2008.

[25] A.V. Boicea, G. Chicco, and P. Mancarella,

“Optimal operation at partial load of a 30 kW

natural gas microturbine cluster,” Buletinul

Stiintific al Universitatii Politehnica

Bucuresti, Seria C, vol. 73, no. 1, pp. 211–

222, Mar. 2011. S. Shepard, “Vehicle to Grid

Frequency Regulation Revenue Will Surpass

$190 Million Annually by 2022,” Boulder,

CO, USA: Navigant Res., Oct. 2013.

[26] K. Yang and A. Walid, “Outage-storage

tradeoff in frequency regulation for smart grid

with renewables,” IEEE Trans. Smart Grid,

vol. 4, no. 1, pp. 245–252, Mar. 2013.

[27] S. Thakare, K. Priya, C. Ghosh, and S.

Bandyopadhyay, “Optimization of

photovoltaic-thermal based cogeneration

system through water replenishment profile,”

Solar Energy, vol. 133, pp. 512-523, Aug.

2016.

[28] M.Prakash, A.Sarkar, and J.Sarkar, et al.,

“Proposal and design of a new biomass based

syngas production system integrated with

combined heat and power generation,”

Energy, vol. 133, no. 15, pp. 986-997, Aug.

2017.

[29] I. Duggal and B. Venkatesh, “Short-term

scheduling of thermal generators and battery

storage with depth of discharge-based cost

model,” IEEE Trans. Power Syst., vol. 30, no.

4, pp. 2110-2118, Jul. 2015.

[30] H. Hahn, B. Krautkremer, and K. Hartmann,

et al., “Review of concepts for a demand-

driven biogas supply for flexible power

generation,” Renew. Sustain. Energy Rev.,

vol. 29, pp. 383-393, Jan. 2014.

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WSEAS TRANSACTIONS on SYSTEMS and CONTROL

DOI: 10.37394/23203.2022.17. 18

Van Duc Phan, Quang Sy Vu,

Huu Son Le, Van Binh Nguyen

E-ISSN: 2224-2856

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Volume 17, 2022