Optimization of Control Strategies VERSI - (Jos_351 Luis)

8/13/2019 Optimization of Control Strategies VERSI - (Jos_351 Luis)

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Paper accepted for publication in Renewable Energy (http://www.sciencedirect.com/science/journal/09601481)

DOI: 10.1016/j.renene.2006.04.013

Optimization of Control Strategies for Stand-Alone RenewableEnergy Systems with Hydrogen Storage

Rodolfo Dufo-Lpez1, Jos L. Bernal-Agustn1,*, Javier Contreras2

1 Electrical Engineering Department University of Zaragoza. Calle Mara de Luna, 3. E-50018 Zaragoza (Spain).

2Applied Mechanics and Project Engineering Department University of Castilla La Mancha. Campus Universitario s/n. 13071 Ciudad Real (Spain).

Abstract

This paper presents a novel strategy, optimized by genetic algorithms, to control stand-alone hybrid renewable electrical

systems with hydrogen storage. The strategy optimizes the control of the hybrid system minimizing the total cost throughout

its lifetime. The optimized hybrid system can be composed of renewable sources (wind, PV and hydro), batteries, fuel cell,

AC generator, and electrolyzer. If the renewable sources produce more energy than the one required by the loads, the spare

energy can be used either to charge the batteries or to produce H 2 in the electrolyzer. The control strategy optimizes how the

spare energy is used. If the amount of energy demanded by the loads is higher than the one produced by the renewable

sources, the control strategy determines the most economical way to meet the energy deficit. The optimization of the various

system control parameters is done using Genetic Algorithms. This paper explains the strategy developed and shows its

application to a PV-Diesel-battery-hydrogen system.

Keywords:Hybrid Systems, Control Strategies, Genetic Algorithms.

1. Introduction

The electric generation hybrid systems are usually more reliable and lest costly than the systems than use a

single source of energy [1].

When designing a hybrid system both the sizing of the elements and the most adequate control strategy must be

obtained. Obtaining a good control strategy is essential, since the performance of a PV-hydrogen system can be

significantly affected by relatively small changes made in the control strategy [2]. However, to design a hybrid

system is a complicated task. The mathematical design problem (sizing and control) involves a significant

number of variables [3]. That is why classic design techniques are not able to obtain good results, being

necessary to apply other techniques which allow obtaining satisfactory results. In other design problems with a

high number of variables, heuristic techniques have been successfully applied [4]. One of the most commonlyused heuristic techniques is based on Genetic Algorithms [5]. Genetic Algorithms present the advantage of

having low computational requirements obtaining good solutions in reasonable time.

As mentioned before, a very important aspect when designing a hybrid system is the determination of the most

adequate control strategy. Numerous studies have developed control strategies applicable to hybrid systems. In

[6] several control strategies for PV-Diesel systems including batteries are described. Likewise, the HOMER

optimization model [7] uses relatively simple strategies based on the ones studied by Barley et al. [6] and it is

able to obtain an optimal design of a hybrid system by selecting the most appropriate strategy. The program

*Corresponding author. Tel.: +34 976 76 19 21; fax: +34 976 76 22 26.

E-mail:[email protected] (R. Dufo-Lpez). [email protected] (J.L. Bernal-Agustn). [email protected] (J. Contreras)


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HYDROGEMS [8], compatible with TRNSYS [9], simulates hydrogen-based hybrid systems, although it is not

an optimization program. Another program applied to hydrogen-based hybrid systems, Hybrid2 [10, 11],

outperforms HOMER and generates many control strategies; nevertheless it is a simulation program, not an

optimization tool. These hybrid systems, which include renewable energy sources and hydrogen, have also been

studied by many researchers [12-17]. In [18] highly complex systems including renewable sources, ACgenerators and fuel cells are analyzed. In another work [19] the optimization of stand alone renewable-based

hydrogen generation systems through control strategies is dealt with. Another author [2] describes control

strategies of PV-hydrogen based hybrid systems (photovoltaic generator, batteries, electrolyzer and fuel cell)

based on the on/off-switching of the electrolyzer and the fuel cell, depending on the value of the SOC(State of

Charge) of the batteries. In addition, [20] analyzes a renewable energy system, including hydrogen, as a long-

term energy storage source, with a battery bank as a short-term energy storage, where the energy management is

controlled through the SOCof the batteries.

In [21] the economic evaluation of a hybrid wind/photovoltaic/hydrogen generation systems is studied and

compared to a traditional hybrid energy system with battery storage, showing a clear economic advantage of the

traditional wind/PV/battery system over the wind/PV/hydrogen system. However, this situation may change in

the near future due to the decrease in the cost of fuel cells and electrolyzers.

In [22] a method to optimize the design and dispatch of wind-diesel systems with hydrogen storage is presented.

This paper originates from a previous work by the authors [23] in which the HOGA (Hybrid Optimization by

Genetic Algorithms) program is introduced. In this previous paper both the configuration of a PV-Diesel system

with AC loads and the control strategy are optimized using Genetic Algorithms. The control strategies in HOGA

are the same as the ones used in HOMER. In this new paper several improvements are introduced. First, the

electric energy demand can be either AC or DC, allowing for hydrogen demand as well. It is also possible to use

two different methods to estimate the lifetime of the batteries: either Average of full equivalent cycles (used by

the HOMER program) or Rainflow [24]. Moreover, it is possible to apply two different mathematical models

to the battery operation: KiBaM model [25] or Ah model [26]. In addition, the efficiency of the inverter

variable as a function of the output power is analyzed. Other features of the design tool include the possibility to

deal with different types of energy sources (hydro, wind, PV, fuel cells and Diesel generators) and different

types of energy storage (batteries and electrolyzers with hydrogen tanks). Finally, it is also remarkable the novel

control strategy developed and optimized by Genetic Algorithms.

In this paper we describe a new control strategy where the associated operating costs of every element are

specified, as well as the control variables used by the strategy. Additionally, we present an example in which a

control strategy for a PV-Diesel-battery-hydrogen system with AC, DC and hydrogen demands is optimized.

2. Control strategy of the hybrid system

The hybrid system that will be used to explain the control strategy described in this paper is shown in Fig. 1. It

can be observed that the hybrid system can include PV panels, wind turbines, batteries, charge regulator, hydro

turbine, AC generator (Diesel, but also any type of generator can be modeled), battery charger (AC/DC

converter), inverter (DC/AC converter), fuel cell, H2tank and electrolyzer. The fuel cell can be either fed by the

H2previously produced by the electrolyzer or by externally purchased H2. Both the wind turbines and the hydro

turbines can be connected to the AC or DC buses.


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Pre_DC

Electrolyzer H2tank

AC Generator

HYDRO

WIND

Pre_AC

D.C.

LoadUDC

UAC

Pload_DC

Batteries

H2Load

Fuel Cell

Pload_AC

BatteryCharger

PV

Inverter

A.C.Load

Charge

Regulator

Fig. 1. Control strategy of the hybrid system

Hourly intervals are considered for the design strategy calculations, where all the involved variables are assumed

to be constant throughout these intervals.

Two genetic algorithms, main and secondary, are used in the design process. The main one searches for possible

component configurations of the hybrid system (i.e. the power and features of each element), whereas the

secondary one searches for the best strategy for each of the configurations found by the main algorithm. Both

algorithms work jointly to find the optimal configuration of the components and the best control strategy. A

previous paper [23] describes both algorithms in detail. The difference between the previous paper and the one

presented here is due to the improvement in the mathematical models and the new control strategy developed.

Both algorithms are described in section 4.

The objective function to minimize in the optimization process is the total Net Present Cost (NPC) of the system.

TheNPCrepresents the investment costs plus the discounted present values of all future costs during the lifetime

of the system. To calculate the NPCof the system we simulate it throughout its lifetime, obtaining the energy

produced and consumed by the components, their own lifetimes, the number of times in which the components

must be replaced, the operating and maintenance costs, the fuel costs, etc.As a basic control rule, the energy produced by renewable sources must be preferentially used to feed the loads.

For every hour, if the renewable sources (PV, wind and hydro) produce more energy than is demanded, the

surplus power (Pcharge) can be used to charge the batteries or to produce H2 in the electrolyzer. This process is

called CHARGE. Pcharge is the total converted spare power on the DC side (spare DC power plus spare AC

power, the latter one multiplied by the AC/DC converter efficiency), since both the batteries and the electrolyzer

are on the DC side. The decision whether the spare energy is used to charge the batteries or to produce H 2in the

electrolyzer depends on the value of Pcharge, as shown in section 3.

If, on the contrary, the renewable sources are unable to provide for all the energy demand, the load that has not

been met, Pdischarge, should be produced either by the batteries or the AC generator or the fuel cell. This process is

called DISCHARGE. During the DISCHARGEprocess the costs of providing the required energy (using the


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batteries, the AC generator and the fuel cell) must be evaluated. The system will produce the energy that is less

costly, as explained in section 3.

There are 12 control variables of the hybrid system and all of them are optimized by the secondary genetic

algorithm: Pmin_gen, Pmin_FC, SOCmin, Pcritical_gen, SOCstp_gen, Pcritical_FC, SOCstp_FC,H2TANKstp, Plim_charge, P1gen, P1FC,

and P2. All these variables are simultaneously optimized by the secondary algorithm. The value determined bythis algorithm is denoted by the subindex _opt.

In the following subsections the first 8 control variables are described, and also how to determine the control

strategy from them. The last 4 variables are described in section 3.

2.1. Minimum AC generator power

The minimum power of an AC generator is generally set to the minimum value recommended by the

manufacturer, Pmin_gen, below which it cannot work. Besides, the specific consumption (/kWh) for low powers is

always much higher than for high powers. This means that it may be possible for an optimal minimum power to

exist with a higher value (as compared to the one recommended by the manufacturer) and below which the

generator should not work, due to its high specific consumption. Due to this, the design tool presented in this

paper searches for the optimal value of Pmin_gen, named Pmin_gen_opt, which is between Pmin_gen and the nominal

power of the generator.

2.2. Minimum fuel cell power

Fuel cells have a very low minimum power, Pmin_FC, and a very low consumption at zero power; some of them

have no consumption under no-load conditions. However, the program is also able to optimize the value of

Pmin_FC, named Pmin_FC_opt, which ranges between Pmin_FCand the nominal power of the fuel cell.

2.3. Minimum battery SOC

The batteries have a minimum State of Charge recommended by the manufacturer, SOCmin (%), below which

they should not work. If we use the Rainflow battery life model, it is possible that the optimal SOCis higher

than the one recommended by the manufacturer, since the number of cycles depends on the depth of the

discharge, and, therefore, on the percentage of the discharge of the batteries. The program optimizes the value of

SOCmin, named SOCmin _opt, which is between SOCminand SOCmax(100% of the SOC).

2.4. Critical power, SOCsetpoint and H2tank setpoint

2.4.1 AC generator

Due to the aforementioned feature of an AC generator, its high specific consumption at low power, it may be

interesting for it to produce more than the demanded power when the power that must be supplied by the AC

generator has a low value (lower than the critical power limit, Pcritical_gen). That extra power could be used to

charge the batteries up to the SOCvalue, named SOCstp_gen(batteries SOCsetpoint for the AC generator), or to

produce H2in the electrolyzer to fill the H2tank up to the value named H2TANKstp(setpoint for the amount of H2

stored in the tank, measured in kg).


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The program optimizes the value of Pcritical_gen, named Pcritical_gen_opt, which ranges between 0 and the maximum

value of the hourly power consumed by the demand, Pmax_load. The program also optimizes the value of

SOCstp_gen, named SOCstp_gen_opt, which ranges between SOCminand SOCmax. Similarly, the value of H2TANKstp,

namedH2TANKstp_opt, which ranges between 0 and the maximum capacity of the H2tank,H2TANKmax_size(kg), is

optimized.The control strategy related to these variables is as follows:

If the power that the generator must supply (Pdemand) is below Pcritical_gen_opt, then the generator works at nominal

power, PN_gen, meeting the demand Pdemand, where the spare power, Pspare= PN_gen Pdemand, is used as follows:

If (PsparePlim_charge), then the Psparepower is used to charge the batteries up to the SOCstp_gen_optstate, and, if

there is extra power, it is used to generate H2in the electrolyzer up to theH2TANKstp_opttank level. Plim_charge

is the power below which it is more economical to store energy in the batteries than in the H 2 tank. It is

defined in section 3.2.

If (Pspare> Plim_charge), then the Psparepower is used to generate H2in the electrolyzer up to theH2TANKstp_opt

level, and, if there is extra power, it is used to charge the batteries up to the SOCstp_gen_optlevel.

If, after using the spare energy to charge the batteries up to the SOCstp_gen_opt level and to generate H2 in the

electrolyzer (whatever the order is), there still exists some extra energy, then the generator will not work at

nominal power, but at a power at which the energy is not wasted, considering its minimum value, Pmin_gen_opt.

2.4.2 Fuel cell

Analogously to the generator case, the program optimizes the value of Pcritical_FC, named Pcritical_FC_opt, ranging

between 0 and Pmax_load. If the power that must be supplied by the fuel cell is lower than Pcritical_FC_opt, then the

fuel cell works at nominal power meeting the demand, and the spare energy is used to charge the batteries.

The program also optimizes the value of SOCstp_FC(batteries SOC setpoint for the fuel cell), named SOCstp_FC_opt,ranging between SOCminand SOCmax.

If, after trying to use the spare energy to charge the batteries, there is still extra energy, the fuel cell does not

work at nominal power, but at a power without spare energy, considering the Pmin_FC_opt value.

3. CHARGE and DISCHARGE processes

3.1. State definition: CHARGE or DISCHARGE

Fig. 2 shows whether the system is in CHARGE (the renewable sources produce more energy than what is

demanded) or in DISCHARGE (the renewable sources produce less energy than what is demanded) for eachhour, as well as the way to calculate the values of Pchargeor Pdischargeas a function of the AC load, the H2load, the

DC load and the energy produced by the renewable sources.

In each hour, the H2load (for external consumption) is initially met by the H2stored in the tank. If the H2stored

is not enough, the remaining H2, named H2_rest (kg), must be produced in the electrolyzer. This H2_rest (kg)

produced in the electrolyzer is comparable to the DC load, denoted by PH2_rest_conv_DC(W):

PH2_rest_conv_DC =H2_rest 1000/ Elyz (1)

where Elyz (kg H2/kWhinput) is the amount of H2produced for each kWh of electrical energy consumed in the

electrolyzer. This PH2_rest_ conv_DCload behaves as a DC load.


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Fig. 2. Flowchart of the CHARGE and DISCHARGE processes

We denote by Pre_DC to the power produced by the renewable sources that are in the DC bus and Pre_AC to the

power produced by the renewable sources that are in the AC bus. Likewise, we denote by Pload_DC to the power

consumed by the loads in the DC bus (including PH2_rest_ conv_DC) and Pload_AC to the power consumed by the loads

in the AC bus. We can enumerate these variables that appear in Fig. 2 as follows:

AC/DCis the efficiency of the battery charger (AC/DC converter)

cosis the power factor of the AC loads

Sis the apparent power at the inverter output (VA):

S= (Pload_AC- Pre_AC)/ cos (2)


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inv (S) is the inverter efficiency

Sinv is the nominal apparent power of the inverter (VA). Although the inverter can withstand relatively big

overloads, it cannot do so for long periods. Since we use hourly intervals, we assume that the efficiency of the

inverter can reach as much as Sinv.

inv(Sinv) is the efficiency of the inverter at its apparent nominal power

Pinv_max is the maximum active power that can be produced by the inverter:

Pinv_max= Sinvcos/ inv(Sinv) (3)

3.2. CHARGE process

In the case of having spare energy for a 1 hour period (Pcharge> 0), this energy is used to charge the batteries

and/or to produce hydrogen in the electrolyzer (which is stored in the hydrogen tank).

Depending on which of the two devices has the lowest cost of cycling energy (i.e. the operating and maintenancecost for 1 hour, including the depreciation and replacement costs), either the batteries are charged as much as

possible with the spare energy or the electrolyzer works at its highest possible power.

3.2.1 Cost of cycling energy through the batteries

The cost of cycling the energy corresponding to a certain power P (kW) through the batteries during 1 hour,

Ccycling_bat (), including the energy lost, can be calculated as:

1000

global_batcycles_eqDCbat_pN

battcycling_ba

NUNC

CPC =

(4)

whereCbat() is the battery bank acquisition cost, CN(Ah) is the nominal capacity of the battery, Nbat_p is the

number of batteries in parallel, UDC(V) is the DC bus voltage and Ncycles_eqis the average of a battery lifetime in

equivalent full cycles. We have assumed that the batteries can cycle a certain amount of energy that, divided by

its nominal capacity, gives the average lifetime in equivalent full cycles. Finally, global_bat is the overall

efficiency of the batteries (roundtrip efficiency). In Ccycling_batwe do not consider the O&M costs of the batteries;

we consider that they are fixed during the year, therefore, they do not depend on the performance of the batteries.

3.2.2 Cost of cycling energy through the electrolyzer

The cost of cycling the energy corresponding to a certain power P (kW) during 1 hour, where the energy is

stored as H2in the tank, later becoming fuel cell energy, is ():

Elyz FCO&M_Elyz O&M_FC

Elyz FC

cycling_Elyz -FC

Elyz FC

+ + +

=

C CC C

Life LifeC

(5)

where Ccycling_Elyz-FC, unlike Ccycling_bat, does not depend on the power (since the electrolyzer and the fuel cell

lifetimes,LifeElyzand LifeFC(h), respectively, have been considered as not dependent on the power), as well as


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CO&M_Elyzand CO&M_FC, the O&M costs of the electrolyzer and the fuel cell (/h), respectively. CElyzand CFC ()

are the electrolyzer and fuel cell acquisition costs, respectively.

We denote by FC(kWhoutput/kgH2) the amount of electrical energy output for each kg of H2consumed in the fuel

cell. We assume that FC = 1/(AFC +BFC).

AFC and BFC are coefficients of the fuel cell consumption equation, ConsFC (kgH2/h); they can be modeled

similarly to the ones in a Diesel (or oil) generator consumption equation:

ConsFC=BFCPN_FC +AFCP (6)

where P(kW) is the power supplied by the fuel cell at a certain time, PN_FC(kW) is the nominal power of the

fuel cell, andAFCandBFC(kgH2/kWh) are the coefficients of the consumption curve.

The value of the FCexpression is only valid at the fuel cell nominal power. Nevertheless, since BFC is approx. 0

for fuel cells, the error is minimal.

We have not included the H2tank costs, since we have considered both the lifetime and the O&M costs as fixed,

therefore, they do not depend on the performance of the electrolyzer and the fuel cell.

3.2.3 Charge power limit

Fig. 3 depicts the cost of cycling energy () of the batteries and the electrolyzers as a function of the spare

energy Pcharge. It can be observed that, for low values of Pcharge,it is optimal to use the spare energy produced by

the renewable sources to charge the batteries as much as possible; if there is still more energy, then the spare

energy can also produce hydrogen in the electrolyzer.

This phenomenon takes place up to a certain power, Plim_charge, from which it is cheaper to cycle through the

electrolyzer and the fuel cell. This power is obtained from equating Ccycling_batto Ccycling_Elyz-FC:

Elyz FCO&M_Elyz O&M_FC

Elyz FC

lim_chargebat Elyz FC

N bat_p DC cycles_eq global_bat

1000

+ + +

=

C CC C

Life LifeP

C

C N U N

(7)

BatteriesCost ofcyclingenergy()

P(kW)Plim_Charge

Electrolyzer-Fuel Cell

Fig. 3. Cost of cycling energy


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3.2.4 CHARGE strategy optimization

The strategy to optimize the CHARGE process is as follows:

1) If PchargePlim_chargethen the batteries are charged as much as possible, and, if there is still spare energy,

it is used to produce H2in the electrolyzer.

2) If Pcharge> Plim_chargethen the hydrogen is produced in the electrolyzer at full power, and, if there is still

spare energy, it is used to charge the batteries.

If the electrolyzer has a minimum power, Pmin_Elyz, then Plim_charge= max(Plim_charge,Pmin_Elyz).

In the calculation of Plim_chargeit is necessary to take into account:

Although we have already included the proportional replacement cost of the elements in theCcycling_batand

Ccycling_Elyz_FC expressions, the lifetime of the system is not necessarily a multiple of the lifetime of the

components, therefore changing the real value of Plim_charge.

Ccycling_bat depends on the number of equivalent cycles. If the batteries lifetime is modeled using the

Rainflow method, then the calculation is not going to be exact, since it is not possible to know beforehand

the cycled energy through the year.

The expression FC = 1/(AFC +BFC) is only valid at the fuel cell nominal power.

These inaccuracies can cause the value of Plim_charge not to be optimal. The program searches for the optimal

value of Plim_charge, named Plim_charge opt, which ranges between 0 and 2Plim_charge.

3.3 DISCHARGE process

In the case of lack of energy during 1 hour (Pdischarge> 0), the energy is obtained either from the batteries or fromthe AC generator, or from the fuel cell. The selection of the element supplying that energy depends on the

associated costs, described as follows.

3.3.1 Cost of supplying energy with the batteries

The average cost of supplying a certain P (kW) power with the batteries for 1 hour can be calculated, in ,

through the equation:

bat


P_bat

inv DC DC

1000

(1 )

= +

P C

C N U N C

Factor Factor

(8)

where FactorDCis the average annual value of the hourly ratio of the DC consumption vs. total consumption:

36524load_DC

DC

1 load_DC load_AC

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=

=+

i i

i

i

PFactor

P P (9)

FactorDCexpresses the average value of the energy demanded by the DC loads weighted by the overall demand.

It is necessary to quantify this value because the batteries, when supplying DC power do not show external

losses, whereas, when supplying the AC power, it is necessary to consider the inverter losses.


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Notice that, although the inverter efficiency is variable, it is necessary to use its average value to obtain the costs

of supplying the energy and the values of P1and P2(defined later). Hence, invis the efficiency of the inverter

for the average AC load (apparent power), SAC_average, where:

36524

load_ACAC_average

1

/ cos 36524=

= i

i

PS (10)

3.3.2 Cost of supplying energy with the AC generator

The average cost of supplying a certain P(kW) power with the AC generator for 1 hour is, in :

gen fuelP_gen O&M_gen N_gen fuel

gen AC/DC DC DC

fuelfixed_gen

AC/DC DC DC

Pr

(1 )

(1 )

C A PC C B P Pr

Life Factor Factor

A Pr PC

Factor Factor

= + + + =+

= ++

(11)

where Prfuel is the fuel price (/l), A and B and are the coefficients of the consumption curve (l/kWh) [27],

CO&M_genis the O&M cost of the generator (/h), Cgenis the acquisition cost of the AC generator (),Lifegenis the

estimated lifetime of the AC generator (h) and Cfixed_gen() is the operating fixed cost of the Diesel generator.

3.3.3 Cost of supplying energy with the fuel cell

The average cost of supplying power with a fuel cell depends on whether it is fed by the H2produced by the

electrolyzer, and stored in the tank, or it is fed by externally purchased H2.

If the fuel cell uses the H2previously produced by the electrolyzer, then the cost is fixed.

FCP_FC O&M_FC fixed_FC

FC

= + =C

C C CLife

(12)

If the fuel cell uses externally purchased H2(in this case there is no electrolyzer in the hybrid system), then

the cost depends on the power:

FC H2P_FC fixed_FC FC N_FC H2

inv DC DC

(1 )= + +

+

A P PrC C B P Pr

Factor Factor (13)

where PrH2(/kg) is the cost of the externally purchased hydrogen.

3.3.4 DISCHARGE optimization

Fig. 4 shows the cost of supplying energy as a function of the power.

It is observed that, for powers between 0 and a certain value P1, the batteries are the optimal components needed

to supply the power, since they have zero cost at P = 0. It may also be possible that there exists a value of P1

from which it is more economical to supply the power with another component (the AC generator or the fuel

cell). This value of P1is the minimum of the two values resulting from the intersection of the cost function of

supplying energy with batteries and the cost function of supplying energy with other components AC generator

and fuel cell (see Fig. 4).


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Cost()

Fuel Cell

Fuel Cell

BatteriesAC Generator

AC GeneratorBatteries

Cost()

Pdischarge Pdischarge

B) FUEL CELL CONSUMING EXTERNAL H2

P1= P1genP2P2 P1= P1gen

P1FC P1FC

A) FUEL CELL CONSUMING H2FROM ELECTROLYZER

Fig. 4. Cost of supplying energy in the DISCHARGE process

We denote by P1gento the power at which CP_bat= CP_gen(intersection point of the cost of supplying energy with

the batteries and the cost of supplying energy with the AC generator), and by P1FCto the power at which CP_bat=

CP_FC (intersection point of the cost of supplying energy with the batteries and the cost of supplying energy with

the fuel cell).

If the value of P1gen is negative (intersection in the third quadrant), this implies that it is always cheaper to supply

energy with the batteries instead of with the generator. In this case, we make P1gen= , instead of choosing a

negative value, in order to select a coherent value of P1when we make that P1= min (P1gen, P1FC). In the case

of P1FCbeing negative, then we also make P1FC= .

It may be possible that both P1gen and P1FChave negative values, then P1gen= P1FC= , and the transfer of

energy from the batteries is always more economical.

The value of P1is the minimum between P1genand P1FC.

It may be also possible that a value P2exists at which the energy produced by the component supplying power

starting from P1is not the cheapest. This value of P2is obtained by making CP_FC= CP_gen. Meaning that, if P1 =

P1gen, and P2has a non-infinite positive value for which CP_FC= CP_gen, then, if Pdischargeis higher than P2,it is

cheaper to supply with the fuel cell instead of using the AC generator.

Consequently, the strategy that optimizes the DISCHARGE process is described as follows:

1) If Pdischarge< P1then the energy is supplied by the batteries

2) If P1PdischargeP2then the energy is supplied by the component with the lowest value of P1(either

the AC generator or the fuel cell).

3) If Pdischarge> P2then the energy is provided by the component with the highest value of P1(either the

AC generator or the fuel cell).

4) Once the component to supply the required energy, Pdischarge, is selected, we have to consider whether it

is able to provide all the energy needed; if not, the remaining power, named Prest, is provided by the

component that can produce it at the lowest possible cost.

5) If the second component necessary to supply the energy is not available, then the third one is used to

supply the remaining energy.


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Note that, when the components supply energy, they also take into account the values of Pmin_gen, Pmin_FC,

SOCmin, Pcritical_gen, SOCstp_gen, Pcritical_FC, SOCstp_FCandH2TANKstpas defined in sections 2.1 to 2.4.

If P2< P1, steps 2 and 3 become just one step: For powers where P1Pdischarge, the energy is provided by the

component with the lowest value of P1(either the AC generator or the fuel cell).

3.3.5 P1 calculation

P1genis obtained by factoring out Pfrom the CP_bat= CP_genequation:

fixed_gen

gen

bat

N bat_p DC cycles_eq global_bat fuel

inv DC DC AC/DC DC DC

1000

(1 ) (1 )

=

+ +

CP1

C

C N U N A Pr

Factor Factor Factor Factor

(14)

P1FCis obtained by factoring out Pfrom the CP_bat= CP_FCequation:

- If the fuel cell consumes H2previously produced by the electrolyzer:

[ ]fixed_FC inv DC DCFC

bat


(1 )

1000

+=

C Factor Factor P1

C

C N U N

(15)

- If the fuel cell consumes externally purchased H2(there is no electrolyzer in the system):

( )[ ]fixed_FC FC N_FC H2 inv DC DCFC bat

FC H2


(1 )

1000

+ +

=

C B P Pr Factor Factor

P1 C A PrC N U N

(16)

P1= min (P1gen, P1FC) (17)

3.3.6 P2 calculation

We obtain it from equating CP_gen= CP_FC.

- If the fuel cell consumes H2previously produced by the electrolyzer:

fixed_FC fixed_gen AC/DC DC DC

fuel

( ) (1 )

+ =

C C Factor Factor

P2 A Pr

(18)

- If the fuel cell consumes externally purchased H2 (there is no electrolyzer in the system):

fixed_FC FC N_FC H2 fixed_gen

fuel FC H2

AC/DC DC DC inv DC DC

(1 ) (1 )

+ =

+ +

C B P Pr C P2

A Pr A Pr

Factor Factor Factor Factor

(19)

In the calculation of P1and P2it is necessary to take into account the same inaccuracies as in the calculation of

Plim_charge(see section 3.2.4); moreover, the inverter efficiency is variable, so we consider the average power, inv,

in this case.


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These inaccuracies may cause the calculated values of P1gen, P1FCand P2are not optimal. To take into account

these approximations and inaccuracies, the program searches for the optimal values of these variables, named

P1gen_opt, P1FC_optand P2opt, which are between 0 and 2 times the calculated values.

3.3.7 DISCHARGE control strategy examples

Fig. 4 shows the cost functions of the different elements in two cases. In case A, a fuel cell consumes the

hydrogen previously produced by the electrolyzer and in case B the fuel cell consumes the hydrogen produced

externally (i.e. purchased, with no electrolyzer in the system). In both examples, if Pdischarge < P1, then it is better

to supply the energy with the batteries. If the batteries are not able to supply all the Pdischarge power, then the

remaining power, Prest= Pdischarge Pbat, is provided by the AC generator if Prest< P2, and, if not, by the fuel cell.

If P1Pdischarge P2, then it is better to supply the energy with the AC generator. If the generator is not able to

supply all the Pdischargepower, the remaining power, Prest= Pdischarge Pgen, is provided by the batteries if Prest P2then, it is better to supply the energy with the fuel cell. If the fuel cell is not able to supply all the

Pdischargepower, then the remaining power, Prest= Pdischarge PFC, is supplied by the batteries if Prest< P1gen, and, if

not, by the AC generator.

4. Developed Genetic Algorithm

Genetic Algorithms simulate, through a computer program, the phenomena of reproduction, selection, crossing

and mutation that can be observed in nature, being able to solve optimization problems that are difficult to

approach with other techniques. Possible solutions to a particular problem are considered individuals of a

species. In the design problem presented in this paper the species are the configuration and control of a

hybrid system. An individual is a combination of the variables (genes) that we wish to optimize (in our case

the variables, or genes, are the components of the hybrid system and the variables of the control system

strategy).

An individual can be defined by a vector whose components represent the parameters of the system using an

integer code. The genetic algorithm searches for possible designs modifying the integer values of the vectors.

Individuals cross over to give birth to a new offspring in the next generation. The higher the fitness of the

individual, the higher the probability to cross over is. With the new generations, the algorithm finds better

individuals whose fitness functions are closer to the optimal values. Some individuals experiment mutations that

make them change some genes, which can expedite the convergence of the algorithm to the optimal value.

The size of the population (number of individuals), the number of generations (iterations), and the crossing and

mutation rates, are parameters of the Genetic Algorithm. The reader is referred to [5, 28], where the basic

principles of Genetic Algorithms can be found.

In a previous work [23] the characteristics of the developed Genetic Algorithm are described in detail. In this

section we will show, briefly, the changes and improvements that have been done.

The design program is made up of two Genetic Algorithms, the main one and the secondary one, described next.

4.1 Main algorithm

This Genetic Algorithm searches for configurations of PV panels, wind generators, hydro turbine, batteries, AC

generator, fuel cell, electrolyzer and inverter that minimize the cost of the system. This is the general case, if all


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these elements are selected. However, the user can decide whether the system contains all these elements or only

some of them.

The codification of the variables used by the main algorithm is done through a vector made up of 11 integers:

| a| b| c| d| e|f | g | h | i | j | k |

where,

ais the number of PV panels in parallel

bis the type of PV panel

cis the number of wind turbines

dis the type of wind turbine

eis the type of hydro turbine

fis the number of batteries in parallel

gis the type of battery

his the type of AC generator

iis the type of fuel cell

jis the type of electrolyzer

kis the type of inverter

Regarding the inverter, it can be forced to supply the maximum power demanded by the AC load, which is an

option of the design tool. In this case, the inverter selected will be the one with the lowest power whose output is

higher than the AC load maximum. If this option is not used, the type of inverter will be a variable to be

optimized, being possible that an inverter whose output is bigger than the maximum AC consumption is not

needed; in this case, higher powers will be supplied by the AC generator.

The charge regulator, the battery charger and the H2 tank do not take part in the combination of components

optimized by the main algorithm. This is so because, for each possible combination calculated by the main

algorithm, the optimal size of these components is determined once the secondary algorithm obtains the best

control strategy.

The main algorithm simultaneously uses a population of Nm vectors, such as the one aforementioned. The

number of generations isNgen_main_max.

The main algorithm obtains the optimal configuration of the elements minimizing the NPC. The NPCmust be

calculated for each combination, represented by one of theNmvectors which constitute the population.

The fitness function of the ith combination of the main algorithm is assigned according to its rank in thepopulation (rank #1 for the best individual, considering the objective function, and rank #Nm for the worst

solution):

mMAIN

m

( 1)

[( 1) ]i

j

N ifitness

N j

+ =

+ j = 1..Nm (20)

4.2 Secondary algorithm

The Genetic Algorithm obtains, for each configuration provided by the main algorithm, the control strategy that

minimizes the NPC. The secondary algorithm is evaluated for each individual of the main algorithm, trying to

find its best control.


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YES

Evaluation of the control strategy foreach of the Nm vectors of the mainalgorithm. The secondary algorithmis executedNmtimes.

i=1.Nm

Each of the Nmvectors ofthe main algorithm has itsbest control.Sort by NPC the Nm

solutions obtained.

Random generation of Nmvectors from the main algorithm

Ngen_main = 1

Ngen_main


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5. Computational results

A system located in Zaragoza, Spain, has been optimized. As previously mentioned, the program optimizes both

the configuration of the physical components and their control strategy. Nevertheless, if there is a system with its

physical components fixed, for example, a real system that is already installed, the program can optimize the

control strategy. The latter case is the one presented here, since we are mainly interested in showing the strategy

optimization in this paper.

The system whose control will be optimized is a PV-Diesel-battery-hydrogen system with AC, DC and H 2

simultaneous load. We believe this is the first time that a control system with Diesel generator, batteries and fuel

cell is achieved. We have chosen this configuration because every control variable is considered. Although it is

not very common that a Diesel generator and a fuel cell co-exist, the acquisition costs, the O&M of the different

elements and the weather variables may make this configuration optimal in some cases.

The studied system is made up of the following elements:

6,600 WpPV generator:15x4 PV panels of 110 Wpat 12V, with a total acquisition cost of 48,720 , 25years estimated lifetime, and an annual O&M cost of 40 /year.

48,000 Wh battery bank: 4x5 batteries of 200 Ah at 12V, with a total acquisition cost of 22,600 , KiBaM

model (Manwell and McGowan, 1993), estimated lifetime according to Rainflow, battery cycle life as

shown in Fig. 6, 40% minimum SOC, 80% roundtrip efficiency, and an annual O&M cost of 50 /year.

5 kVA inverter, an acquisition cost of 3,600 , 10 years expected lifetime, and a variable efficiency with

an apparent power as shown in Fig. 7.

7 kVA Diesel AC generator, acquisition cost of 3,640 , O&M cost of 0.2 /h, expected lifetime of 7,000

h, minimum power recommended by the manufacturer of 30% of the nominal power (2,100 W), gas-oil

cost of 0.8 /l, consumption parameters:A= 0.246 l/kWh,B= 0.08145 l/kWh [27].

1 kW fuel cell, acquisition cost of 4,000 , O&M cost of 0.2 /h, 30,000 h expected lifetime, consumption

parameters:AFC= 0.06 l/kWh,BFC= 0 (FC= 16.66 kWh/kgH2for the nominal power, corresponding to

50% of the H2Lower Heating Value), 6% minimum power (60W).

0

1000

2000

3000

4000

5000

60007000

8000

9000

10 20 30 40 50 60 70 80 90

DOD(%)

Cycles to Failure

Fig. 6. Battery cycle life (cycles to failure) vs. Depth of Discharge (DOD)


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0

10

20

30

40

50

60

70

80

90

100

0 20 40 60 80 100Output Power (%)

Efficiency (%)

Fig. 7. Inverter efficiency

1 kW electrolyzer, acquisition cost of 3,200 , O&M cost of 0.2 /h, 30000 h expected lifetime, Eyz=0.02157 kgH2/kWh (corresponding to 85% of the Higher Heating Value of H2).

0.1 kg H2tank, with an acquisition cost of 150 , O&M cost 10 /year, 25 years expected lifetime.

70A charge regulator, with a cost of 125 , 10 years lifetime.

Battery charger with a cost of 100 , 10 years lifetime and 90% efficiency.

The system has a 48V DC voltage and a 230V AC voltage. AC loads (40.9 kWh in one day), DC loads (a fixed

300 W value, providing a total of 7.2 kWh in one day), and H 2loads (0.05 kg in one day) are present. Fig. 8

presents the hourly distribution of the AC and DC loads, and Fig. 9 shows the H2loads. Note that we consider

that every day has the same loads.

The total acquisition costs of the different elements of the system make a total of 86,435 , including assembly

costs of 300 . The electrolyzer and fuel cell costs are lower than the current ones in Spain, assuming that they

will go down in the near future.

01000

2000

3000

4000

5000

6000

7000

8000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24Hour

AC+DC Load PV gen. Gen. AC Charge bat.Disch. Bat. Fuel Cell Electrolyzer Pmin_gen_opt

Energy (Wh)

Fig. 8. Simulation of January 24th


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0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Hour

H2 (kg)

H2load H2tank Electrolyzer

Fuel Cell H2TANKstp_opt

Fig. 9. Simulation of the consumption and H2accumulation for January 24th

The irradiation in the city of Zaragoza is shown in Table 1. The effective interest rate considered is 2%. The

maximum unmet load allowed is 0%.

The parameter values, without strategy optimization, recommended by the manufacturers and also calculated are

as follows: Plim_charge= 1,732 W; P1gen= 4,265 W; P1FC= 699 W; P2= (i.e. the generator and fuel cell curves

do not intersect); Pmin_gen = 2100 W; SOCmin = 40%; Pcritical_gen = 0 W, SOCstp_gen = 40%; Pmin_FC = 60 W;

Pcritical_FC= 0 W; SOCstp_FC= 40%,H2TANKstp= 0 kg.

The DISCHARGE parameters are represented in Fig. 10. For these parameter values calculated without strategy

optimization, the systemNPCwould be 285,575 . The fuel, O&M, and replacement costs are 199,140 .

Table 1

Average daily irradiation

Month Jan. Feb. Mar. Apr. May June July Aug. Sep. Oct. Nov. Dec.

Wh/m2 2108 2688 4150 4931 6318 6941 6644 5593 4830 3456 2555 2138

Fuel cell

H2from Electrolyzer.

BatteriesAC Generator

Cost ()

PdischargeP1genP1FC

Fig. 10. DISCHARGE parameters before optimization


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15000

20000

25000

30000

35000

40000

45000

50000

1 2 3 4 5 6 7 8 9 10 11 121314 1516 1718 19 20 2122 2324

Hour

SOC SOCmax SOCmin_opt SOCstp_gen_opt SOCstp_FC_opt

Energy (Wh)

Fig. 11. Simulation of the battery SOCfor January 24th

Using the main algorithm makes no sense in this case, since the physical components are fixed. The calculation

of the optimal strategy has been done with the following parameters of the secondary algorithm: Number of

generations = 30, population = 300,000, crossover rate = 0.7, and mutation rate = 0.01.

When the strategy optimization is finished, the results obtained for the control parameters are:

Plim_charge_opt= 2,772 W; P1gen_opt= 1,279 W; P1FC_opt= 1,118 W; P2opt= 1,365; Pmin_gen_opt= 4550 W (65% of the

nominal power); SOCmin_opt = 40%; Pcritical_gen_opt = 2730 W, SOCstp_gen_opt = 82%; Pmin_FC_opt = 1000 W;

Pcritical_FC_opt= 455 W; SOCstp_FC_opt= 94%,H2TANKstp_opt= 0.093 kg.

The system NPC for the optimized control strategy is 254,521 , this being the minimum value found by the

program. The operation, fuel and replacement costs are 168,086 .

It can be observed that the optimization of the control variables by Genetic Algorithms has allowed us to find the

configuration with the minimalNPC.

Fig. 8, 9 and 11 show the simulation results for one particular day, January 24 th.

The number of cases evaluated is 9106, with a simulation time of 27h 46 (90 cases per second). Considering

that there are 12 control variables, and that each variable can have 10 different values (10% precision), the total

number of possible cases is 1012, taking a time of 352.3 years to solve if the cases are evaluated using an

enumerative technique (without using Genetic Algorithms).

6. Conclusions

We have developed a novel control strategy, optimized through Genetic Algorithms, for the control of stand-

alone renewable energy hybrid systems with hydrogen storage. The energy sources of the hybrid system can be

of the renewable type (wind, PV, hydro), as well as AC generators and fuel cells. The loads can be AC, DC

and/or H2.

The strategy proposed optimizes the control of the hybrid system, obtaining values of different variables that

make the total Net Present Cost of the system minimal.


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We have explained the control strategy in detail, and we have also illustrated it with a representative example

using a PV-Diesel-batteries-hydrogen system, where the need to optimize the different control parameters to get

the lowestNPCpossible can be seen. Genetic Algorithms perfectly fulfill this mission.

Acknowledgment

This work has been supported by IBERCAJA and the University of Zaragoza under the program Proyectos de

Investigacin IBERCAJA. Research Project: IBE2005-TEC-04.

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[1] Muselli M, Notton G, Louche A. Design of hybrid-photovoltaic power generator, with optimization of

energy management. Sol Energy 1999;65(3):143-57.

[2] Ulleberg . The importance of control strategies in PV-hydrogen systems. Sol Energy 2004;76(1-3):323-9.

[3] Seeling-Hochmuth GC. A combined optimisation concept for the design and operation strategy of hybrid-

PV energy systems. Sol Energy 1997;61(2):77-87.

[4] Michalewicz Z, Fogel DB. How to solve it: modern heuristics, 2nd ed. Berlin: Springer; 2004.

[5] Goldberg DE. Genetic algorithms in search, optimization and machine learning. New York: Addison-

Wesley; 1989.

[6] Barley CD, Winn CB, Flowers L, Green HJ. Optimal control of remote hybrid power systems, Part I:

simplified model. In: Proceedings of wind power 95, Washington DC; 1995.

[7] Hybrid Optimization Model for Electric Renewables (HOMER). Website:

www.nrel.gov/international/homer.

[8] Ulleberg . Stand-alone power systems for the future: optimal design, operation & control of solar-

hydrogen energy systems. PhD. Norwegian University of Science and Technology, Trondheim: Department

of Thermal Energy and Hydropower; 1998.

[9] Fiscal A, Thornton J, Klein SA, Beckman WA. Developments to the TRNSYS simulation program. Journal

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[10] Manwell J, Rogers A, Hayman G, Avelar C, McGowan J. Hybrid2a hybrid system simulation model:

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[11] Mills A., Al-Hallaj S. Simulation of hydrogen-based hybrid Systems using Hybrid2. International Journal

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[12] Dienhart H, Siegel A. Hydrogen storage in isolated electrical energy systems with photovoltaic and wind

energy. International Journal of Hydrogen Energy 1994;19(1):61-6.

[13] Kauranen PS, Lund PD, Vanhanen JP. Development of a self-sufficient solar-hydrogen energy system.

International Journal of Hydrogen Energy 1994;19(1):99-106.


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[14] Hollumer P, Joubert JM, Lachal B, Yvon K. Evaluation of a 5 kWp photovoltaic hydrogen production and

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2000;25(2):97-109.

[15] Agbossou K, Kolhe M, Hamelin J. Performance of a stand-alone renewable energy system based on energy

storage as hydrogen. IEEE Trans on Energy Conversion 2004;19(3):633-40.

[16] Santarelli M, Cal M, Macagno S. Design and analysis of stand-alone hydrogen energy systems with

different renewable sources. International Journal of Hydrogen Energy 2004;29(15):1571-86.

[17] Shakyaa BD, Aye L, Musgrave P. Technical feasibility and financial analysis of hybrid windphotovoltaic

system with hydrogen storage for Cooma. International Journal of Hydrogen Energy 2005;30(1):9-20.

[18] Cotrell J, Pratt W. Modeling the feasibility of using fuel cells and hydrogen internal combustion engines in

remote renewable energy systems. In: Proceedings of wind power 03, Austin, Texas; 2003.

[19] Vosen SR, Keller JO. Hybrid energy storage systems for stand-alone electric power systems: optimization

of systems performance and cost through control strategies. International Journal of Hydrogen Energy

1999;24(12):1139-56.

[20] Kolhe M, Agbossou K, Kelouwani S, Anouar A, Fournier M, Hamelin J, Bose TK. Long-term performance

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List of Symbols:

a Number of PV panels in parallel

A Coefficient of the AC generator consumption equation [l/kWh]

AFC Coefficient of the fuel cell consumption equation [kgH2/kWh]

b Type of PV panel

B Coefficient of the AC generator consumption equation [l/kWh]

BFC Coefficient of the fuel cell consumption equation [kgH2/kWh]

c Number of wind turbines

Cbat Battery bank acquisition cost []

CElyz Acquisition cost of the electrolyzer []

Ccycling_bat Cost of cycling the energy corresponding to a power P(kW) through the batteries during 1 hour []

Ccycling_Elyz-FC Cost of cycling the energy corresponding to a power P (kW) through the electrolyzer and the fuel cell

during 1 hour []

CFC Acquisition cost of the fuel cell []

Cfixed_gen Operating fixed cost of the Diesel generator []CN Nominal capacity of the battery [Ah]

ConsFC Consumption of the fuel cell [kgH2/h]

cos Power factor of the AC loads

CO&M_Elyz Operation and maintenance cost of the electrolyzer [/h]

CO&M_FC Operation and maintenance cost of the fuel cell [/h]

CO&M_gen Operation and maintenance cost of the AC generator [/h]

CP_FC Average cost of supplying a certain P(kW) power with the fuel cell for 1 hour []

CP_gen Average cost of supplying a certain P(kW) power with the AC generator for 1 hour []

d Type of wind turbine

DOD Depth of discharge of the battery [% of CN]

e Type of hydro turbine

f Number of batteries in parallel

FactorDC Average annual value of the hourly ratio of the DC consumption vs. total consumption

fitnessmain_i Fitness of the ith combination of the main algorithm

fitnesssec_i Fitness of the ith combination of the secondary algorithm

g Type of battery

h Type of AC generator

H2_rest H2load (for external consumption) that cannot be initially met by the H2stored in the tank [kg]

H2TANKstp Setpoint for the amount of H2stored in the tank [kg]H2TANKstp_opt Setpoint for the amount of H2stored in the tank, value optimized by the program [kg]

i Type of fuel cell

j Type of electrolyzer

k Type of inverter

kgH2 kilograms of hydrogen

LifeElyz Electrolyzer lifetime [h]

LifeFC Fuel cell lifetime [h]

Lifegen AC generator lifetime [h]

Nbat_p Number of batteries in parallel

Ncycles_eq Average of a battery lifetime in equivalent full cycles

Ngen_main_max Number of generations of the main algorithm


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Ngen_sec_max Number of generations of the secondary algorithm

Nm Population of the main algorithm

Nsec Population of the secondary algorithm

NPC Total Net Present Cost of the system (investment costs plus the discounted present values of all future costs

during the lifetime of the system) []

Pcharge Total converted spare power produced by renewable sources on the DC side (spare DC power plus spare

AC power multiplied by the AC/DC converter efficiency) [W]

Pcritical_FC Fuel cell critical power limit. When the demanded power is lower than this value, the fuel cell works at

nominal power, using the extra power to charge the batteries up to the SOCstp_FC_opt [W]

Pcritical_FC_opt Fuel cell critical power limit, value optimized by the program [W]

Pcritical_gen AC generator critical power limit. When the demanded power is lower than this value, the AC generator

works at nominal power, using the extra power to charge the batteries up to the SOCstp_gen_opt state or to

produce H2in the electrolyzer up to theH2TANKstp_opttank level [W]

Pcritical_gen_opt AC generator critical power limit, value optimized by the program [W]

Pdemand Power that must be supplied by the AC generator (or by the fuel cell) [W]Pdischarge Load not met by the renewable sources [W]

PFC Power supplied by the fuel cell [W]

Pgen Power supplied by the AC generator [W]

PH2_rest_conv_DC DC Power consumed by the electrolyzer to supply the hydrogen load (for external consumption) that cannot

be initially met by the H2stored in the tank (H2_rest) [W]

Pinv_max Maximum active power that can be produced by the inverter [W]

Pload_AC Power consumed by the loads in the AC bus [W]

Pload_DC Power consumed by the loads in the DC bus (including PH2_rest_ conv_DC) [W]

Plim_charge Power below which it is more economical to store energy in the batteries than in the H2tank [W]

Plim_charge_opt Power below which it is more economical to store energy in the batteries than in the H2 tank, value

optimized by the program [W]

Pmax_load Maximum value of the hourly power consumed by the demand [W]

Pmin_Elyz Electrolyzer minimum power [W]

Pmin_FC Minimum power of the fuel cell recommended by the manufacturer [W]

Pmin_FC_opt Minimum power of the fuel cell optimized by the program [W]

Pmin_gen Minimum power of the AC generator recommended by the manufacturer [W]

Pmin_gen_opt Minimum power of the AC generator optimized by the program [W]

PN_FC Fuel cell nominal power [W]

PN_gen AC generator nominal power [W]

Prest Remaining power than cannot be supplied by either the batteries or the AC generator or the fuel cell [W]

Pre_AC Power produced by the renewable sources that are in the AC bus [W]

Pre_DC Power produced by the renewable sources that are in the DC bus [W]

Prfuel Fuel price for the AC generator [/l]

PrH2 Hydrogen price (if it is externally purchased) [/kg]

Pspare Difference between the nominal power of the AC generator and the total power demanded by the load [W]

P1 Minimum value between P1genand P1FC[W]

P1FC Intersection point of the cost of supplying energy with the batteries and the cost of supplying energy with

the fuel cell [W]

P1FC_opt P1FCvalue optimized by the program [W]


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P1gen Intersection point of the cost of supplying energy with the batteries and the cost of supplying energy with

the AC generator [W]

P1gen_opt P1genoptimized by the program [W]

P2 Intersection point of the cost of supplying energy with the fuel cell and the cost of supplying energy with

the AC generator [W]

P2opt P2optimized by the program [W]

SOC State of Charge of the battery, defined here as a percentage of the nominal capacity of the battery [% of CN]

SOCmax Maximum State of Charge of the battery [100 % of CN]

SOCmin Minimum State of Charge of the battery recommended by the manufacturer [% of CN]

SOCmin_opt Minimum State of Charge of the battery optimized by the program [% of CN]

SOCstp_FC Batteries SOC setpoint for the fuel cell [% of CN]

SOCstp_FC_opt Batteries SOC setpoint for the fuel cell, value optimized by the program [% of CN]

SOCstp_gen Batteries SOC setpoint for the AC generator [% of CN]

SOCstp_gen_opt Batteries SOC setpoint for the AC generator, value optimized by the program [% of CN]

S Apparent power at the inverter output [VA]SAC_average Average AC load (apparent power) [VA]

Sinv Nominal apparent power of the inverter [VA]

UAC AC bus voltage [V]

UDC DC bus voltage [V]

AC/DC Efficiency of the battery charger (AC/DC converter)

Elyz Amount of H2produced for each kWh of electrical energy consumed in the electrolyzer [kgH2/kWhinput].

FC Amount of electrical energy output for each kg of H2consumed in the fuel cell [kWhoutput/kgH2]

global_bat Overall efficiency of the batteries (roundtrip efficiency)

inv Inverter efficiency for the average AC load (SAC_average)

inv (S) Inverter efficiency

inv(Sinv) Efficiency of the inverter at its apparent nominal power

Documents

Optimization of Control Strategies VERSI - (Jos_351 Luis)