photovoltaic system using PSO: Case study for the city of Cujubim, Brazil

Energy 142 (2018) 33e45

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Optimum design of a hybrid diesel-ORC / photovoltaic system using PSO: Case study for the city of Cujubim, Brazil Ana Lisbeth Galindo Noguera*, Luis Sebastian Mendoza Castellanos, Electo Eduardo Silva Lora, Vladimir Rafael Melian Cobas
, Brazil Excellence Group in Thermal Power and Distributed Generation-NEST, Institute of Mechanical Engineering, Federal University of Itajuba

a r t i c l e i n f o

a b s t r a c t

Article history: Received 10 May 2017 Received in revised form 1 September 2017 Accepted 3 October 2017 Available online 4 October 2017

In this work, the optimal design of a hybrid electric power generation system for isolated zones, using Particle Swarm Optimization (PSO) technique, is presented. A study is carried out taking as case of study, ^ nia-Brazil, consisting of photovoltaic panels, a diesel generator, the city of Cujubim, in the state of Rondo batteries and an organic Rankine Cycle, which is used for the heat recovery of the exhaust gases from the diesel generator sets, what is the novelty of this study. Decision variables, involved in the optimal design problem of the hybrid system, are the number of photovoltaic panels, the number of batteries and the nominal power of the diesel generator. Directly connected to the size of the diesel generator, is the nominal power of ORC system, not being a decision variable. All components are modeled and the objective function is the cost of power generation, with system reliability, results of the simulation show that the hybrid system is profitable to supply electric power demand of a selected city. © 2017 Elsevier Ltd. All rights reserved.

Keywords: Hybrid system Photovoltaic system Diesel generator Organic Rankine cycle (ORC) Particle swarm optimization (PSO)

1. Introduction Electric power systems having a renewable sources of primary energy as sun light, are very attractive, especially for energy supply in isolated locations, since they provide coherent, sustainable and clean energy. To increase the reliability of the electricity supply and to have continuity in the service, the hybrid systems present a better option. These systems can be engineered by integration of diesel generators with renewable resources such as photovoltaic solar energy, thus, providing greater system reliability, in addition to maximizing its performance and reducing costs, due to the fact of almost negligible fuel consumption. Use of renewable energy resources in an efficient and economically viable way depends on the correct design and operational strategy of the system; optimization of a hybrid system ensures full utilization of the potential of all system components and optimum conditions in relation to the economic aspects and reliability of the system. Halabi et al. [1] applied HOMER software for optimization of a hybrid PV/diesel/battery system and its performance for two locations; Pulau Banggi Island and Tanjung Labian, Sabah, Malaysia, demonstrating that the presence of

* Corresponding author. E-mail address: [email protected] (A.L. Galindo Noguera). https://doi.org/10.1016/j.energy.2017.10.012 0360-5442/© 2017 Elsevier Ltd. All rights reserved.

renewable energy sources improves the performance of standalone systems and reduces energy storage requirements. Khatib et al. [2] performed the optimization of an FV-diesel system with batteries, taking into account the loss of power probability (LPSP). Optimization algorithm considers the specifications of photovoltaic module and diesel generator, in addition to the battery, in order to close and determine the best economic configuration of the hybrid system. Agarwal [3] used iterative optimization technique to find optimal sizing of hybrid PV-Battery-Diesel system, model considers the life cycle cost and CO2 emissions as the optimization objectives. Authors showed that hybrid system reduces the life cycle cost by 40% and CO2 emissions by 78% when compared with standalone Diesel Generators. Malheiro et al. [4] have addressed the sizing and scheduling of hybrid isolated systems via a mixed-integer linear programming, with a proposed method determining the optimal operation of each individual subsystem and an optimum size of system components based on the minimum levelized cost of energy (LCOE). Tazvinga et al. [5] have used quadratic programming to optimize hybrid photovoltaicedieselebattery energy system, a proposed method determines the optimum energy dispatch of the system based on the minimum fuel consumption costs. Results show that photovoltaicedieselebattery model achieves 73% and 77% fuel savings in winter and 80.5% and 82% fuel savings in summer considered when compared to the case where the diesel generator satisfies the load on its own. Kushida and Abe [6] used

34

A.L. Galindo Noguera et al. / Energy 142 (2018) 33e45

Nomenclature ACS ACC ACO&M AFC Am BH Btil C CAR CBAT Cc CCI CEB CFR CO&M Cpg Crep C1 C2 d DH dn Dtil El f FG FR frep GH gi GSC G0 Gtil h ian IB I0 iter k KT k1 LHVf

Annualized cost $ Annualized capital costs $ Annualized operation and maintenance costs $ Annual fuel costs $ PV panel area m2 Direct horizontal irradiance kWh/m2 Direct tilted irradiance kWh/m2 Battery capacity Ah Annualized replacement costs $ Capital cost of the battery bank $ Fuel price $/L Capital const $ Energy cost of the battery bank $/Ah Capital recovery factor $ Operation and maintenance cost $/h Exhaust gas specific heat kJ/(kg
K) Replacement cost of a component $ Cognitive coefficient Social Coefficient Annual real interest rate Diffuse horizontal irradiance kWh/m2 Day number of the year Diffuse tilted irradiance kWh/m2 Load demand kWh Annual inflation rate Fuel consumption at rated power L/h Fuel consumption at partial load L/h Factor arising Global horizontal irradiance kWh/m2 The best global position Solar constant (1367) W/m2 Extraterrestrial irradiance W/m2 Global tilted irradiance kWh/m2 Specific enthalpy kJ/kg Nominal interest rate Battery current A Solar extraterrestrial irradiance kWh/m2 Number of current iterations Constriction factor Clearness index Anisotropy index Fuel lower heating value kJ/kg

mar mf

Air flow kg/s Working fluid mass flow rate kg/s

mfuel

Specific mass of the fuel kg/s

mg n NB nC Nporj Npv

Mass flow of the exhaust gases kg/s Project lifetime Number of batteries Cycles Number of battery Lifetime of the project Number of photovoltaic panels

·

· ·

linear programming techniques for optimal design of a grid connected PV-diesel hybrid system in Japan, a method proposed determines the most suitable installed capacities, a most practical use, and minimize annual cost. In another approach Lotfit et al. [7] presented the optimal design of a stand-alone hybrid solar-wind- diesel system, using Imperialist

Nrem Nrep NOCT Pi Pc PDm
ax Pload PnG Q

Remaining life of the component Replacement cost Normal Operating Cell Temperature The best individual particle position Critical Discharge Load kW Maximum depth of discharge % Operating power generator kW Rated power diesel generator kW Battery charge Ah

Q

Rate of heat transfer of condenser kW

·

·

cond

Q evap QG r1, r2 S SOC SSF Tamb TC Tcref Tg Tgpp v VC Vec Vg VSC w

Rate of heat transfer of evaporator kW Energy from exhaust gases kW Random number between 0 and 1 Salvage value State of charge % Sinking fund factor Ambient temperature  C Cell temperature  C Reference cell temperature  C Exhaust gas temperature K Exhaust gas temperature at the evaporator outlet K particle velocity Charging voltage V Final charge voltage V Gassing voltage V Overcharge voltage V Inertia weight parameter

Wis Wnet Wp

Turbine isentropic power kW Net power of cycle kW Power consumed by the pump kW

Wt x

Turbine mechanical power generated kW particle position, the vector of decision variables

·

·

Greek symbols Panel efficiency temperature coefficient f Latitude ( ) d Solar declination ( ) qZS Solar zenith angle ( ) qS Angle of incidence ( ) u Hour angle ( ) hC Battery charge efficiency hciclo Cycle efficiency hg PV panels efficiency hgen Electric generator efficiency hiv Power conditioning efficiency his;t Turbine isentropic efficiency hp Pump isentropic efficiency href Reference module efficiency r Reflectivity of the ground rfuel Fuel density kg/m3 t Operating time

bt

Competitive Algorithm (ICA), Particle Swarm Optimization (PSO) and Ant colony optimization. Results showed that (ICA) is faster and more accurate, compared with particle cloud and ant colony algorithms. Perera et al. [8] developed an optimal configuration of Internal Combustion Generator (ICG) systems with renewable energy using Pareto fronts., an analysis considered conflicting objectives

A.L. Galindo Noguera et al. / Energy 142 (2018) 33e45

such as Levelized Energy Cost, initial capital cost, power supply reliability and emission of greenhouse gases; results showed that it is difficult to assure the convergence of the multi objective optimization when more than three objectives are used. Hammed et al. [9] presented an optimum design method of FV-wind-battery hybrid systems using the open-space (PSO) algorithm, being total cost objective function and technical sizing is the constraint, evaluated according to two parameters: energy balance and the reliability of the service. Sharafi e ELMekkawy [10] presented multiobjective optimization of the hybrid system, composed by modules FV, wind turbine, diesel generator, fuel cell, batteries, electrolyzed and hydrogen tank, using the ε-constraint method, which is a non-Pareto-based search technique. This method has been used to minimize-simultaneously- the total cost of the system, unmet load and fuel emission. Tsuanyo et al. [11] presented a method for optimum design and techno-economic analysis of a FV-diesel system using GA (Genetic algorithms), without batteries, considering the Leveled Cost of Electricity. They investigated two cases: identical generators and generators of different sizes, showing that the system with identical generators is more profitable. Maheri [12] developed a multi-objective optimization method using genetic algorithm combined with Monte Carlo simulation for cost and system reliability optimization of a stand-alone wind-PV-diesel system. Borhanazad et al. [13]. Used Multi-Objective Particle Swarm Optimization (MOPSO) to find the best configuration of the hybrid wind/PV system with battery storage and diesel generator. This method has been used to minimize Cost of electricity (COE) and satisfying desired reliability levels based on loss of power supply probability (LPSP). Mohamed et al. [14] compares the use of PSO algorithm and iterative optimization techniques (IOT) to minimize overall cost of a stand-alone hybrid PV/wind/battery/ diesel energy system, showing that PSO algorithm is better for finding the optimal solution and faster than IOT. Several conventional optimization methods have been used for hybrid energy systems. Linear programming model, mixed integer linear programming, iterative techniques are examples of classical algorithms widely in use for optimizing hybrid systems. However, classical algorithms have some drawbacks like rigid iterations, less flexibility, slow convergence speed, needs more computation time [15]. In recent years, new generation optimization approaches such as genetic algorithm (GA) and particle swarm optimization (PSO), were widely used because they required less computation time and had efficient global search solutions [15]. PSO algorithm was suggested as one of the most useful and promising methods for designing the hybrid systems due to the use of global optima to find the best solution [16]. According to the literature, it was verified that several studies have been developed in order to present the optimal configuration of the different hybrid power systems, in terms of economics and reliability. This study complements the studies carried out by other authors, since it aims to take advantage of renewable energy sources at lowest possible cost; however other studies used diesel generator as a complementary source, not considering the use of the energy of the exhaust gases from the generator. In this sense the organic Rankine cycle (ORC) may be appropriate for use and conversion of low and medium temperature residual energy into electric energy. The use of a lower power secondary cycle such as the ORC for the exhaust gas heat recovery of diesel generator would increase the production of electric energy without increasing the fuel consumption, which is a real novelty of this study. In this paper, the optimization of a hybrid system using diesel generator, solar photovoltaic, batteries and an ORC cycle for the exhaust gas heat recovery of the diesel generator sets, to produce additional power, is presented. In designing a hybrid system, the optimum configuration (optimum distribution of power), is

35

determined, depending on the available resources, leading to production of energy of desired quality to feed the autonomous network. To achieve this goal, this study proposes the use of Particle Swarm Optimization using an own computer code, elaborated in Matlab, to be able to evaluate the coupling of ORC technology with a hybrid system.

2. System descriptions Hybrid system consists of a photovoltaic system, a diesel generator set, battery bank, bi-directional inverter, allowing both conversion C.C- A.C for load handling and A.C - D.C conversion for feeding the battery bank by the generator set, as well as an Organic Rankine Cycle, which is used for generator set exhaust gas heat recovery and in this way, increase the global production of electricity. A schematic diagram of the system is shown in Fig. 1; thephotovoltaic source is connected to D.C. using power conditioning units and the ORC-generator set connected to both A.C and D.C bus, through the inverter.

3. Modeling system components For optimization of hybrid system, energy models of the technologies, that comprise system must be defined, in terms of generation with photovoltaic, diesel and ORC generation technologies, as well as in terms of process of loading and unloading battery bank.

3.1. Photovoltaic system For systems integrating photovoltaic modules, a mathematical model of solar resource is necessary, to obtain hourly total solar irradiance (on). For the calculation of solar irradiance on tilted surface, it is necessary to know extraterrestrial irradiance over a horizontal surface, in addition to determining the direct and diffuse component of the irradiance on a horizontal surface, and the direct, diffuse and reflected components on a tilted surface. i. Extraterrestrial irradiance over a horizontal surface and Clearness Index Extraterrestrial irradiance over a horizontal surface G0 is given by Refs. [17, 18],:


 360 $ dn ½cosðfÞcosðdÞsinðuÞ G0 ¼ GSC * 1 þ 0; 033cos 365 þ sinðfÞsinðdÞ

(1)

where GSC is the solar constant (1367 W/m2); dn, is the day number counted from the beginning of the year; f, is the geographic latitude ( ); d, is the solar declination ( ), e u is the true solar time. Angle of true solar time and solar declination are calculated from the equations:

u ¼ ðhour  12hourÞ $ ð15 =hourÞ 

d ¼ 23; 45 * sin 360

284 þ dn 365

(2)

 (3)

Integration of the equation of G0, from the initial time u1 to the final hour u2 allows obtaining the hourly solar extraterrestrial irradiance over a horizontal surface I0 in kWh/m2, according to Equation (4) [18].

36

A.L. Galindo Noguera et al. / Energy 142 (2018) 33e45

Fig. 1. Hybrid system diagram.

I0 ðtÞ ¼

12 $ GCS

p


 360 $ dn 1 þ 0; 033cos 365


 cosðfÞ $ cosðdÞ $ sinðu2  u1 Þ  pðu2  u1 Þ sinðfÞsinðdÞ þ 180

BH ðtÞ ¼ GH ðtÞ  DH ðtÞ

iii. Estimation of the hourly solar irradiance on tilted surface

(4)

Clearness index KT relates the global solar irradiance at Earth's surface (GH) and solar extraterrestrial irradiance (I0) by:

G ðtÞ KT ¼ H Io ðtÞ

(7)

(5)

ii. Estimation of the direct and diffuse components of horizontal irradiance Correlation between the diffuse fraction of horizontal radiation, KD and the clearness index KT, allows to obtain diffuse irradiance value from global irradiance value. For calculation of the hourly diffuse fraction the following expressions are used [19]:

Hourly global solar irradiance on tilted surface (Gtil) is given by Equation (8) [17].

Gtil ðtÞ ¼ Btil ðtÞ þ Dtil ðtÞ þ r * GH ðtÞ *

  1  cosðbÞ 2

(8)

where r is the reflectivity of the ground, that according to Luque e Hegedus [17] values close to 0.2 can be used for sites where reflectivity is unknown. Direct component of the hourly irradiance on the inclined surface Btil is given by Equation (9).

Btil ðtÞ ¼ BH ðtÞ

max½0; cosðqS Þ cosðqZS Þ

(9)

where qZS is solar zenith angle and qS is the angle of incidence. To determine the diffuse irradiance on the soil, we can use the

Se kT < 0; 22 kD ¼

DH ðtÞ ¼ 1  0; 09 * kT GH ðtÞ

Se 0; 22 < kT < 0; 80 kD ¼

DH ðtÞ ¼ 0; 9511  0; 1604kT þ 4; 388k2T  16; 638k3T þ 12; 336k4T GH ðtÞ

(6)

Se 0; 8 > kT kD ¼

DH ðtÞ ¼ 0; 165 GH ðtÞ

Since solar irradiance in the horizontal plane is equal to the sum of the direct components BH and diffuse DH, one can calculate direct irradiance as:

model of Hay and Devies cited in Ref. [17]. This model uses a modulation factor called anisotropy index, k1, defined as:

A.L. Galindo Noguera et al. / Energy 142 (2018) 33e45

k1 ¼

GH ðtÞ  DH ðtÞ I0 ðtÞ

(10)

 
 1 þ cosðbÞ max½0; cosðqS Þ þ k1 Dinc ðtÞ ¼ DH ðtÞ ð1  k1 Þ 2 cosðqZS Þ Finally, having evaluated the three components, hourly global solar irradiance on arbitrarily orientation of an angle b, Gtil , can be calculated using Equation (8). Instantaneous power generated in a photovoltaic system is given by Equation (12) [20e22].

(12)

where Am is stands for the PV panel area (m2): hg is PV panels efficiency given by:

h



hg ðtÞ ¼ href hiv 1  bt * TC ðtÞ  Tcref

i

NOCT  20 Ginc ðtÞ 800

(14)

Where Tamb is ambient temperature and NOCT is the Normal Operating Cell Temperature. 3.2. Diesel generator Energy modeling for a diesel generator consists of a set of regressions elaborated from the information provided by several manufacturers (Cummins, Generac, Scania, Genmac, among others). Data base contains information about commercial generators in the range of 9 kWe to 2800 kWe, which allowed obtaining energy flows as a function of full and partial load. Fuel consumption, exhaust gas temperature and air flow at rated power are given by: 0;945 FG ¼ 0; 395 * PnG

(15)

Tg ¼ 8109 P3nG þ 5105 P2nG  0; 112PnG þ 563; 6

(16)

0;9954 m_ ar ¼ 0; 0021 * PnG

(17)

Where FG is fuel consumption at full load (L/h); PnG is rated power (kW); Tg is exhaust gas temperature ( C) e m_ ar is air flow (kg/ s). Fuel consumption at partial load is determined by:

FR ðtÞ P ðtÞ ¼ 0; 9187 * load þ 0; 0784 FG Pn

(18)

where FR is fuel consumption at partial load (L/h) e Pload is operating power generator (kW); specific mass of fuel in kg/s can be calculated as:

m_ fuel ðtÞ ¼ rfuel *

FR ðtÞ 1 * 1000 3600

(20)

Where QG is the energy from exhaust gases (kW); and LHVf is the fuel lower heating value (43000 kJ/kg). Mass flow of exhaust gases is obtained from energy mass balance of engine, as:

m_ g ðtÞ ¼ m_ fuel ðtÞ þ m_ ar ðtÞ

(21)

With the data of the mass flow and energy from exhaust gases at partial load of the engine it is possible to determine the temperature of these gases, by Equation (22).

Tg ðtÞ ¼

Q_ G ðtÞ þ Tamb ðtÞ m_ g ðtÞ * Cpg ðtÞ

(22)

(13)

where href is the reference module efficiency; hiv is the power conditioning efficiency; ht is the PV panel efficiency temperature coefficient,; Tcref is the reference cell temperature ( C) e TC is the cell temperature ( C), it's calculate as [17]:

TC ðtÞ ¼ Tamb ðtÞ þ

  Pload ðtÞ 2 P ðtÞ  0; 0453 * load Pn Pn

þ 0; 3201 (11)

Ppv ðtÞ ¼ hg * Nm * Am * Gtil ðtÞ

Being, rfuel the fuel density (833 kg/m3).The energy of the exhaust gases can be calculated as:

QG ðtÞ ¼ 0; 0003 * FR ðtÞ * LHVf

Diffuse irradiance on tilted surface obtained as:

37

(19)

3.3. Organic Rankine cycle Fig. 2 shows a scheme of an organic Rankine cycle; to describe the performance of the cycle the mass balance and energy of each components of the thermal system are described. For the thermodynamic analysis of ORC integrated in the heat recovery system of the internal combustion engine, some assumptions are applied to make the problem easer to model: ✓ Cycle operation occurs under permanent regime; ✓ There is no change in potential energy and kinetic energy of the working fluid throughout the cycle; ✓ Evaporator heat losses are not taken into account; ✓ Pressure drops in evaporator and pipes are assumed to be negligible [24]; ✓ Isentropic efficiency of turbine and pump are assumed as hb ¼ 80% and ht ¼ 70% respectively [25]; ✓ Condenser temperature is assumed to be 35  C [26]; ✓ Efficiency of the electric generator is assumed to be 93%.

3.3.1. Evaporator According to Shu et al. [25], Tian et al. [27] and Vaja and Gamborotta [26], it is necessary to ensure a minimum temperature difference of 30 at the pinch point (DTpp, min) to ensure good heat exchanger performance at phase-change. For this work, the heat transfer process can be divided into two stages: preheating and evaporation. To determine the heat that can be recovered as well as the working fluid mass flow rates it is necessary to perform an energy balance in the evaporator from the temperature profile shown in Fig. 3. First energy balance upstream of the pinch point (between 2 and 3), referring to complete fluid vaporization, where Tgpp ¼ T2X þ DTpp;min .; working fluid mass flow rate can be calculated as:

 mg * Cpg * Tg  Tgpp mf ¼ h3  h2x

(23)

Where mf is working fluid mass flow rate (kg/s); Tg is exhaust gases temperature (K); Tgpp is temperature of the exhaust gases at the pinch point and h3 and h2x are enthalpies of the working fluid at outlet and at the pinch point of the evaporator.

38

A.L. Galindo Noguera et al. / Energy 142 (2018) 33e45

Fig. 2. (a) Scheme of an ORC. (b) Temperature-entropy diagram [23]

Where h4s is the enthalpy of the fluid for an isentropic condition at turbine outlet and h3 is fluid enthalpy at turbine inlet. Thus, mechanical power generated by turbine is determined as:

_ t ¼ m_ ðh  h Þ W 3 4 f

(26)

3.3.3. Condenser Heat rejected by the cycle is calculated by:

Q_ con ¼ m_ f ðh4  h1 Þ

(27)

3.3.4. Pump Thermodynamic model of the pump is established according to its isentropic efficiency:

hp ¼

h2S  h1 h2  h1

(28)

Power consumed by the pump is calculated by Equation (14):

Wp ¼ m_ f ðh2  h1 Þ

Fig. 3. Evaporator temperature profile.

Enthalpies of working fluid are obtained as a function of evaporation temperature determined for the ORC. For this, the multiplatform “CoolProp” free software library was used, to provide thermodynamic properties of working fluid [28]. Specific heat ðCpg Þ is estimated from exhaust gases composition and temperature difference. A second energy balance allows determining exhaust gas temperature at evaporator outlet:

Tg;out ¼ Tg;pp  m_ f

h2x  h2 m_ g * C pg

3.3.2. Turbine Turbine performance is established according to isentropic efficiency of equipment, which is defined as:

_ W

h h

Once all the states of the cycle are known, it is possible to calculate net power, through Equation (15):

Wnet ¼ ðWt  Wb Þ $ hgen

(30)

Thermal efficiency of the cycle is calculated as:

hciclo ¼

Wt  Wb Q_

(31)

evap

(24)

If the temperature, Tg;out , previously calculated, is lower than the minimum allowed temperature for exhaust gases, to reduce working fluid mass flow rate is necessary, until satisfies imposed condition ðTg;out > 120  CÞ.

4 his;t ¼ _ t ¼ 3 W is h3  h4;s

(29)

(25)

3.4. Battery modeling To model the behavior of the batteries, model proposed in Ref. [29e33] was used. In this model, three processes are considered: discharge, charge and overcharge. During battery charging or discharging, battery life and efficiency are significantly reduced, so the state of charge (SOC) must be limited to ensure safe battery operation (SOCmin  SOCt  SOCmax).

3.4.1. Discharge voltage

A.L. Galindo Noguera et al. / Energy 142 (2018) 33e45

Ahstore represents ampere-hours stored in the battery and the term 0.95  C considers voltage value from which gasification process begins; denominator considers current injected or extracted in operating time t. This time is inversely proportional to the current intensity variation and is expressed by:

I ðtÞ 4 Vd ðtÞ ¼ ð2; 085  0; 12ð1  SOCðtÞÞÞ  B  C10 1 þ IB ðtÞ1;3 ! 0; 27 þ þ 0; 02 ð1  0; 007DTÞ SOCðtÞ1;5 (32) First term of the equation represents voltage variation with the state of charge (SOC) (electrolytic concentration) and second term variation due to internal resistance, IB represents battery current and DT is the temperature variation, with reference to 25 C. State of charge is given by:

SOCðtÞ ¼ SOC0 þ

Q ðtÞ h CðtÞ C

(33)

Where Q is charge generated or supplied at a given, (Q (t) ¼ IB  t); C (t) is the battery capacity; corresponding expression to battery capacity is established beginning with the discharge current corresponding to C10 rated capacity (10 h regime) and is given by:

CðtÞ ¼ C10

1; 67  0;9 ð1 þ 0; 005 * DTÞ I ðtÞ 1 þ 0; 67 * BI10

(34)

The efficiency of a battery ðhC Þ during discharge is assumed as 100%, however, total amount of useful charge available during discharge is limited by current rate and temperature [34]. 3.4.2. Charging voltage

VC ðtÞ ¼ ð2  0; 16SOCðtÞÞ þ þ

0; 48 ð1  SOCðtÞÞ1;2

IB ðtÞ 6  C10 1 þ IB ðtÞ0;86 !

þ 0; 036 ð1  0; 025DTÞ

(35)

In charging process, the state of charge (SOC) is a function of charge efficiency ðhC Þ, being dependent on the state of charge in an earlier period, current ratio as shown in Equation (36):

hC ðtÞ ¼ 1  exp

20; 73 IB ðtÞ I10

þ 0; 55

!! ðSOCðt  1Þ  1

(36)

t¼

17; 3  1;67 B 1 þ 852 * CI10

(40)

3.5. Operation strategy Among many possible strategies to be implemented in a hybrid diesel generator generation system, three can be highlighted, based on predefined operations proposed by Barley and Winn [35]. Strategy called “cyclic charge”, fix diesel generator is automatically triggered when the battery reaches a certain minimum voltage level, determined by its maximum discharge depth; strategy called “load following strategy”, consists in using the diesel only to comply with the load, while battery is recharged only by the photovoltaic system and “frugal discharge strategy”, is based on critical load, where if the net load is higher than the critical load, it is economical to run the diesel generator set. Fig. 4 illustrates the flowchart of the operation strategy employed, based on direct comparison between electricity production costs of a diesel-ORC system and discharging batteries costs; from this comparison a reference value, a critical discharge load (Pc), is obtained. If the difference between the energy demanded by the load and energy generated by renewable sources is less than Pc, it is cheaper to use the batteries. Otherwise, even if there is still energy in the batteries, when energy to be dispatched to the load is higher than Pc value, diesel-ORC system is used. Critical Discharge Load (Pc) can be obtained by the equivalence of the cost of generating energy whit the generator and the cost of drawing energy out of the batteries, such as:

Pc ¼

ð0:030968 * Cc * PnG þ CO&M Þ * hinv CEB  0; 3628 * Cc

(41)

Equation (41) is adapted from Lopez [36], where, Cc is fuel price [$/L]; PnG is diesel generator output power [kW]; CO&M is diesel generator's hourly operation and maintenance cost [$/h]; and CEB refers to energy cost of battery bank and can be calculated as::

CEB ¼

CBAT CB * PDm
ax * nc

(42)

Where, CBAT is capital cost of battery bank [$]; CB is nominal capacity of battery bank (Ah); PDm
ax is maximum depth of discharge [%] and nc is number of full cycles of battery.

3.4.3. Overcharge voltage

    Ahstore  0; 95C VSC ðtÞ ¼ Vg þ Vec  Vg 1  exp IB ðtÞt   ð1  0; 002DTÞ

39

4. System optimization

(37)

where Vec is final charge voltage and Vg is gassing voltage, given by:


 I ð1  002 * DTÞ Vec ¼ 2; 45 þ 2; 011 * ln 1 þ B C10

(38)


 I ð1  002 * DTÞ Vg ¼ 2; 24 þ 1; 97 * ln 1 þ B C10

(39)

4.1. Particle swarm optimization algorithm (PSO) PSO is a technique based on populations called swarm, formed by particles where each particle represents a possible solution of the problem; particles move around in a multidimensional search space, during flight. Each particle, according to its own experience and the experience of neighboring particles, adapt its position. However PSO tries to find optimal solution by moving particles and evaluating fitness of new position [37]. Considering that a position of a particle i at time t can be represented by xi (t) and its velocity as vi(t), position and velocity

40

A.L. Galindo Noguera et al. / Energy 142 (2018) 33e45

Fig. 4. Flowchart of Operation strategy.

vectors are stored during processing of algorithm at a time t and used to update the population at time t þ 1. To update current particle swan, PSO uses the information of best position obtained by the particle until a moment defined by Pi(t) and the best position found by particle neighborhood, until a moment defined by gi(t). In order to search for better velocity and position, in next iteration, velocity and position of each particle may be obtained by using current velocity and position as expressed by the following equation [38]:

∅ ¼ C1 þ C2 ;

(44) ∅>4

(45)

Where k is constriction factor, w is inertia weight parameter, C1 is cognitive coefficient, C2 is social coefficient and r1, r2 are random number between 1, 0 [10, 38]. A commonly used approach to increase PSO performance, promoting a balance between global and local search, consists of starting w with a high value and decreasing it during the execution of PSO, as shown in Equation (46) [38, 39].

 w¼



wmax  wmin ðitermax  iterÞ þ wmin itermax

 C2 ¼

 C1f  C1i iter þ C1i itermax

(47)

 C2f  C2i iter þ C2i itermax

(48)

(43)

xid ðt þ 1Þ ¼ xid ðtÞ þ vid ðt þ 1Þ 2 k ¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

;

2  ∅  ∅2  4∅

 C1 ¼

Where C1i is initial cognitive coefficient, C1f is final cognitive coefficient, C2i is initial social coefficient and C2f is final social.

vid ðt þ 1Þ ¼ k½w * vid ðtÞ þ C1 * r1 * ðPid ðtÞ  xid ðtÞÞ þ C2 * r2 * ðgid ðtÞ  xid ðtÞÞ

maximum step size that a particle can give in a single interaction. C1 and C2 on acceleration coefficient can be expressed by Refs. [38, 40].

(46)

Where iter number of current iterations and itermax is maximum number of iterations. Normally, parameter w can be changed between 0.4 and 0.9. [38]. The acceleration coefficients C1 and C2 exert an influence on

4.2. Objective function and constraints Optimum combination of the hybrid system aims to minimize the cost of generation during the simulated period, which is one year, and to guarantee a system reliability; considered project horizon was 20 years.

4.2.1. Objective function Optimization problem is defined as:

minimizarFðXÞ ¼ GC

(49)

Decision variable vector of optimization problem is given as.



X ¼ Npv NB PnG

(50)

Where Npv is number of photovoltaic panels; NB number of batteries and PnG is diesel generator power. Economic assessment takes into account capital costs, operation and maintenance costs, fuel costs and replacement costs on a yearly base [37, 41].yearly system cost calculated by:

A.L. Galindo Noguera et al. / Energy 142 (2018) 33e45

ACS ¼

X

ACCj þ CARj þ ACO&Mj þ AFC

(51)

j

Where, j is component indicator; ACCj annualized capital costs, ACO&Mj the annualized operation and maintenance costs, CARj annualized replacement costs and AFC the annual fuel costs.The Annualized capital cost is calculated as:

ACC ¼ CCI * CRFði; nÞ

(52)

CCI is capital cost, CFR (i, n) is capital recovery factor calculated by.

CRFði; nÞ ¼

d * ð1 þ dÞn ð1 þ dÞn  1

(53)

Where n is project lifetime and d is annual real interest rate by:

d¼

ian  f 1þf

(54)

Annualized replacement cost of system components is given by.

  CAR ¼ Crep frep SSF d; Ncomp  SSSF d; Nproy

(55)

Where Crep is replacement cost of a component; frep is a factor arising; S is a salvage value; SSF is sinking fund factor, factor arising is given by:

 8 > < CRF d; Nproj ; frep CRF d; Nrep > : 0;

Nporj > 0

(56)

Nrep ¼ 0

Nporj is project lifetime and Nrep is replacement cost duration entire lifetime, salvage value (S) is given by:

S ¼ Cremp *

Nrem Ncomp

(57)

Where Nrem , remaining life of component at end of project lifetime. SSF is sinking fund factor, given by:

SSFðd; nÞ ¼

d ð1 þ dÞn  1

P LPSðtÞ LPSP ¼ P EL ðtÞ

ACS El

(66) where LPS(t) is loss of power supply during hour t, EL(t) is load demand, kWh; EPV(t) and EG(t)) are total energy produced by PV and diesel-ORC, respectively; EB (t-1) is energy stored in battery during hour t-1; EBmin is minimum charge quantity of battery bank and hinv is inverter efficiency. Charge/discharge energy of battery bank is subject to the following constraint:

SOCmin  SOCðtÞ  SOCmax

5. Case study ^nia State, Simulations were performed for Cujubim city, in Rondo located at 09 21046 “latitude South and 62 350 07” longitude West. Data from hourly irradiation on horizontal surface (kWh/m2) and temperature, were available through the National Institute of Meteorology (INMET) [42]. Fig. 6a shows variation of hourly irradiance on horizontal and inclined surfaces for one year (8760 h), Fig. 6b and c shows the temperature variation and electric demand respectively. Table 1 lists data used in case study, most of which are provided by manufacturers. Hybrid system was simulated by a routine developed in Matlab, to find the best configuration of photovoltaic modules, batteries,

(58)

(59)

4.2.2. Restrictions To ensure system reliability, loss of power supply probability (LPSP) is used in the optimization problem, to penalize objective function; fitness function is formed by objective function of Equation (49) plus those terms that penalize particles that do not satisfy problem established value for LPSP and it is expressed as:

(64)

Where k is penalty parameter whose purpose is to increase objective function value of the infeasible individuals ðLPSPobj  LPSPn Þ in the problem, to satisfy desired LPSP minimizing generation cost (GC). LPSP is defined as a ratio of all energy deficits to total load demand, during a considered period and is given by:

(67)

Fig. 5 shows a flowchart of optimization process, input data required for optimization of hybrid system are: initial investment costs, replacement costs, operation and maintenance costs of all system components, as well as project life, service life and technical specifications of system components, in addition to them, time data of solar irradiation, temperature and place load demand in one year, are necessary.

Where El is load demand in kWh in one year period (Dt ¼ 8.760 h).

  minimizarFðXÞ ¼ GC þ k * LPSPobj  LPSPn

(65)

LPSðtÞ ¼ EL ðtÞ  ðEG ðtÞ þ ðEPV ðtÞ þ EB ðt  1Þ  EBmin Þhinv Þ

Generation cost (GC) is calculated by.

GC ¼

41

Fig. 5. Flowchart of the optimization process.

42

A.L. Galindo Noguera et al. / Energy 142 (2018) 33e45

Fig. 6. (a) Solar Irradiance, (b) temperature and (c) Load demand.

Table 2 PSO parameters.

Table 1 Parameters for simulation [43e49]. Analysis Horizon Tax rate Inflation Fuel price Efficiency of inverter PV power rating Photovoltaic investment price Operation and maintenance costs Efficiency of PV system Temperature Coefficient Nominal reference temperature Normal panel cell operating temperature PV Panel area PV Life Span Inverter life span Diesel Generator Diesel Generator Price Operation and maintenance cost Diesel generator life span ORC ORC investment price ORC life span Battery capacity rating Battery price Replacement Cost Battery voltage rating Battery open circuit voltage Minimum charge state (SOCmin) Maximum charge state (SOCmax) Initial charge state (SOC)

20 years 14.25% a.a 9.321 % 1.05 $/L 93% 260 W 1.72 $/Wp 1% of investment 16.16% 0.34%/ C 25  C 45 C 1.6085 m2 25 years 10 years 846e1250 kW $ 95746e574000 3% of investment 20000 hours Depends on the diesel generators 5477e8646 $/kW 20 years 200 Ah $ 380 unit $ 380 12 V 14.4 V 70% 98% 98%

diesel generator and ORC cycle. In this simulation, parameters of PSO algorithm are presented in Table 2 5.1. Result of optimum system design For optimal design of hybrid system (Diesel-ORC-FV-Batteries), six generator units, 3 generators of 1250 kW and 3 of 846 kW, were used for a total of 6288 kW; simulation results indicate that best

Parameter

Value

Particles number Maximum number of iterations Minimum Acceleration Constant Maximum Acceleration Constant Minimum inertia weight parameter Maximum inertia weight parameter Dimension of the problem Initial Population

30 60 0.5 2.05 0.4 0.9 3 Random

system configuration, shown in Table 3, results in a generation cost of $ 0.301/kWh. Loss of power supply probability (LPSP) was 0.028%, which is less than 1% established in optimization problem, so load demand is supplied in 99.972% of the time; renewable resource (photovoltaic) contribution share to the supply system is quite significant, 57.91%. Battery bank size proposed by the algorithm results in a small amount of batteries, equivalent to an autonomy of approximately 1 h, because battery bank is playing a primarily operational role by allowing diesel generators to operate at an optimum loading point. Fig. 7 shows a convergence curve of PSO algorithm, being possible to observe that best generation cost variation is small, especially when number of iterations increases; in this case, objective function (generation cost) did not present any variation, from iteration 28. To evaluate feasibility of proposed hybrid system, a simulation of a system was performed, where diesel generator is only source of electricity generation; system has 8 generating units: 4 generators of 1250 kW, 3 of 846 kW and one of 1050 kW. Results indicate a generation cost of $ 0.487/kWh., indication of a percentage reduction of 38.15% by use of the proposed hybrid system presents a in relation to average generation cost of a pure diesel system, being feasible its implementation.

A.L. Galindo Noguera et al. / Energy 142 (2018) 33e45

43

Table 3 Result of system simulation and optimization . LPSP desired

PV number

Battery number

Diesel Generator (kW)

ORC (kW)

GC $/kWh

LPSP (%)

FR (%)

1%

59064

4540

6288

722.66

0.301

0.028

57.91

Fig. 7. Convergence curve of the PSO algorithm.

5.2. System simulation during a period of one year Table 4 show energy generated by a hybrid diesel-ORC/ photovoltaic system and a diesel system in a period of one year, showing also hours of operation of each generating unit, as well as fuel consumption by generator set. In Table 4 it can be seen that use of a hybrid system will allow a reduction of 51.11% of fuel consumption in relation to a diesel system, because using a ORC means an increase of 10.86% of energy generated, complemented with reduced number of generating units and shorter operating times of each one. A relatively recent assessment, frequently found in literature, is the reduction in fuel consumption in internal combustion engines when combined in a hybrid system with PV solar energy utilization. Tsuanyo et al. [11]. reports optimization in such a system, obtaining, as a consequence, a reduction of the specific fuel consumption between 23 and 29%. Greater reduction in specific fuel consumption reported in this paper, results from additional utilization of the ORC. So, it can be

Fig. 8. Daily variation of load demand, photovoltaic power production, Diesel-ORC energy generation and Batteries production.

Table 4 Simulation results of one year period. Parameter

Hybrid system

Diesel system

Load demand (MWh/yr) Energy production by PV (MWh/yr) Energy production by Diesel-ORC (MWh/yr) Energy production by Diesel (MWh/yr) Diesel operation time (h) a UG-01 (1250 kW) UG-02 (1250 kW) UG-03 (846 kW) UG-04 (846 kW) UG-05 (846 kW) UG-06 (1250 kW) UG-07 (1250 kW) UG-08 (1050 kW) Fuel consumption (L/yr)

37567 28408 20644 ——

37567 —— —— 38424

5823 5771 4125 1361 200 61 0 0 5098300

8760 8729 8760 6007 2829 2143 100 1378 10429628

a

UG ¼ Generating unit.

Fig. 9. Mode of operation of diesel generators and power generated by the ORC cycle.

concluded that engineering a hybrid Diesel-ORC/photovoltaic system is an effective technical and economic option to be applied in geographic isolated areas.

44

A.L. Galindo Noguera et al. / Energy 142 (2018) 33e45

fuel consumption. A possibility to use this modeling to design and evaluate such systems for electrification of similar isolated communities, was a validated possibility. Use of organic Rankine cycle for exhaust gas heat recovery from diesel generator sets considering R245fa as the cycle working fluid, give an increase of 10.86% energy generated, without increase fuel consumption. Methodology developed for optimum design of hybrid diesel/ Organic Rankin Cycle system/photovoltaic and batteries system demonstrated to be adequate and especially useful in situations when it is necessary to dimension a system in an optimal and robust way, showing also a possible configuration of hybrid systems that can be one viable solutions to electrification problems in remote regions away from national electric network. Acknowledgments Fig. 10. Energy production for each component of the system.

5.3. Daily system performance Fig. 8 shows energy balance of the system for one day. It can be observed that generation of photovoltaic system totally supplies the energy demanded by load in the period from 9am to 4pm. In the period between 16: 00 and 17:00 h the photovoltaic system, together with battery bank supply total energy load demand, between 21:00 h and 22:00 h, the diesel-ORC system plus batteries provides the necessary energy to supply the charge. Fig. 9 shows mode and profile of diesel generators and ORC operation. In Fig. 9, it can be seen that of six (6) diesel generating units available at the plant, four (4) units are used, which together with the ORC cycle provide all energy demanded by load in that period. During operating time, units 1, 2 and 3 operate at nominal power and unit 4 operates at a load factor of 70%, while operating in this range the motors have lower specific fuel consumption and higher efficiency. From the figure it is also observed that the power generated by the ORC cycle increases when the units 3 and 4 start to operate. 5.4. Monthly system performance As shown in Fig. 10, electric energy production of diesel generators 1, 2 and 3 is almost constant throughout the year; diesel generator 4 presented highest production in September and October, while diesel generators 5 and 6 have an almost imperceptible production, photovoltaic system has greater production of electricity compared with diesel-ORC system. 6. Conclusions An optimization model has been successfully developed for a diesel/Organic Rankin Cycle system/photovoltaic and batteries, for electrification of isolated communities, as in case of Cujubim city in ^ nia State in Brazil. A system was engineered considering an Rondo optimum combination (lower cost of energy generated) of available energy resources and load to be supplied throughout the year, with a reasonable level of reliability, using meta-heuristic optimization techniques like the PSO algorithm. Generation cost is objective function to be minimized and a technical constrain in loss of power supply probability, obtained results indicate that implementation of an optimized Diesel-ORCphotovoltaic-battery hybrid system is able to reduce generation cost by approximately 38.15% in comparison with generation cost of a diesel system. To employ alternative sources of generation allows reducing participation of conventional energy systems with smaller

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