Sizing Algorithm for a PV-battery-H2-hybrid System Employing Particle Swarm Optimization

Available online at www.sciencedirect.com

ScienceDirect Energy Procedia 73 (2015) 154 – 162

9th International Renewable Energy Storage Conference, IRES 2015

Sizing algorithm for a PV-battery-H2-hybrid system employing particle swarm optimization Martin Paulitschke*, Thilo Bocklisch, Michael Böttiger Chemnitz University of Technology, Department of Power Systems and High-Voltage Engineering Reichenhainer Str. 70, 09126 Chemnitz

Abstract Thepaper presents a new concept for the optimal design of autonomous energy supply systems based on a photovoltaic plant, a battery and a hydrogen storage path (PV-battery-H2-hybrid system) with the focus on the optimal sizing of therated power and the capacity of all system components. For this purpose a multi-criteria objective function (combining installation and operating costsas well as componentlifetime) and multiple constrains (e.g. security of supply) are considered. The basic characteristics and the complexity of the resulting solutionspace of the optimization problem are described as a function of the sizing and energy management parameters. For the minimization of the objective function a particle swarm algorithm was employed. The paper presents the implementation of the algorithm and simulation results for an example hybrid system configuration. The behaviour of the particle swarm is investigated for different scenarios. Results demonstrate excellent computational speed and accuracy compared to other optimization methods. © by by Elsevier Ltd.Ltd. This is an open access article under the CC BY-NC-ND license © 2015 2015The TheAuthors. Authors.Published Published Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of EUROSOLAR - The European Association for Renewable Energy. Peer-review under responsibility of EUROSOLAR - The European Association for Renewable Energy Keywords:autonomous energy supply system; PV; battery; hydrogen; storage; sizing; particle swarm; optimization

1. Introduction Previous investigations have demonstrated a great potential for decentralized and autonomous energy supply systems and mini grids especially on islands and for off-grid electrification in developing countries [1]. So far, these systems oftentimes still involve some type of fossil fuel. Due to limited access, increasing fuel prices, future

* Corresponding author. Tel.: +49 371 531 39395; fax: +49 371 531 839395. E-mail address: [email protected]

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of EUROSOLAR - The European Association for Renewable Energy doi:10.1016/j.egypro.2015.07.664

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shortage of fossil fuels and unacceptable CO2-emissions, energy supply solutions entirely based on renewable energies are required[2], [3], [4]. Here especially photovoltaics (PV) plays an important role due to its modularity, good scalability, wide availability and significant cost reduction potential with estimated costs below 0.05€/kWh in the near future [5].Fluctuations of PV-power and energy demand require adequate balancing and flexibility technologies. Combinations of a short-term battery and a long-term hydrogen storage path can be a beneficial solution [6], [7], [8]. Algorithm for the optimal sizing of all components of a renewable autonomous energy supply system are essential. This paper presents new results from employing a particle swarm optimization algorithm for this purpose. 2. PV-battery-H2-hybrid system 2.1. Structure and parameters Nowadays, renewable autonomous energy supply systems often consist of a PV-plant,a battery and a diesel generator[9], [10]. To overcome the limitations of fossil energy sources, the diesel generatorcan replaced by the sustainable zero emission H2-storage path. The paper presents a PV-battery-H2-hybrid system containing of a PVplant to provide the energy, a domestic electric load, a hydrogen storage path to cover long-term variations and a battery storage to cover short-term variations. The H2-storage path consists of an electrolyser, which produce hydrogen from water in time with excess of PV-energy, a pressure storage tank and a fuel cell, which reconvert the hydrogen to electricity and heat in times of energy deficit. The hybrid system topology is shown in Fig. 1. A grid connected version of this PV-battery-H2-hybrid system and the experimental test system at H2-container at TU Chemnitz is described in [6].The following parameters can be varied to size the hybrid system:nominal power of the PV-plant Ppv,nom,battery capacity Ebatt,nom,nominal electrolyser power Pel,nom,nominal fuel cell power Pfc,nom. PV plant

SOCmax,on, SOCmax,off , SOCmin,on, SOCmin,off

Ppv,nom

input values

electr. load

Ppv,max Pdiff

energy management

control vector

AC-Bus

short-term storage

Pfc,nom

PH2

fuel cell

H2 storage electrolyser

Ebatt,nom

battery

SOCbatt

Pel,nom

long-term storage

Fig. 1. The structure of the PV-battery-H2-hybrid system. Sizing parameters are highlighted in orange, control values are shown in red and measured values are labelled in green.

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2.2. Energy management An energy management is required to control the power flow distribution between the battery and H2-storage path. In this paper a simple two point hysteresis control strategy was chosen. This approach regulates the state of charge SOC of the battery by switching the hydrogen converters. When a maximum battery state of chargeSOCmax,onis exceeded the electrolyser will be switched on with nominal powerPel,nom. Thereby, surplus PVenergy will be stored in form of hydrogen. In the state of complete charge of the battery and a still existing excess of PV-energy, the PV-plant will reduce the energy production (curtailment). If the battery state of charge falls below the threshold SOCmax,offthe electrolyser shuts down. Conversely, if the state of charge drops below the minimum value SOCmin,on, the fuel cell is switched on at nominal powerPfc,nom. The supply task cannot be guaranteed in case of an empty battery combined by a demand load exceeding the combined power produced by fuel cell and the PVplant. If the battery SOC exceeded SOCmin,offthe fuel cell is switched off. 2.3. Quality values The performance of the PV-battery-H2-hybrid system is determined by the life cycle costs of the components (Cpv, Cbatt,Cfc, Cel) calculated from the specific costs (ppv, pbatt, pfc, pel), component size (Ppv,nom, Ebatt,nom, Pfc,nom, Pel,nom) and the component lifetime (Lpv, Lbatt, Lfc, Lel). The lifetime of the PV-plant is a fixed parameter (e.g. assumed to 20 years). The lifetime of the battery is calculated from the ratio of full cycles in one year in reference to the maximum number of cycles. This approach calculating the lifetime of the battery applies as long as the calendrical lifetime (e.g. 10 years) is not exceeded. The lifetime of the electrolyser and the fuel cell are calculated based on the total possible number of operations divided by the number of operations in one year. Thus a rating of the dynamic stress of the components is implemented. ‫ ݒ݌ܥ‬ൌ ‫ ݂ܿܥ‬ൌ

‫ ݒ݌ ݌‬ήܲ‫ ݒ݌‬ǡ݊‫݉݋‬ ‫ݒ݌ܮ‬ ‫ ݂ܿ ݌‬ήܲ ݂ܿ ǡ݊‫݉݋‬ ‫݂ܿܮ‬

(1)

‫ ݐݐܾܽܥ‬ൌ

(3)

‫ ݈݁ܥ‬ൌ

‫ ݐݐܾܽ ݌‬ή‫ ݐݐܾܽܧ‬ǡ݊‫݉݋‬ ‫ݐݐܾܽܮ‬

‫ ݈݁ ݌‬ήܲ ݈݁ ǡ݊‫݉݋‬ ‫݈݁ܮ‬

(2) (4)

Furthermore, two penalty functions are introduced to increase the supply security. The first function (6) penalize the minimal battery SOC of the whole year, when the SOC falls under 10%, as follows: ‫ ݐݐܾܽܥ‬ǡ‫  ݁ݎݑܿ݁ݏ‬ൌ  ݂ܾܽ‫ ݐݐ‬ǡ‫ ݁ݎݑܿ݁ݏ‬ή ቀͳ െ

݉݅݊ ሺܱܵ‫ ݐݐܾܽ ܥ‬ሻ ͳͲΨ

ቁ

(5)

The second function (6) penalizes the amount of hydrogen remaining in the storage at the end of year. It was implemented to ensure the energy supply of the system in case of possible occurring marginally changes in the load and solar radiation in the next year. ‫ ʹܪܥ‬ǡ‫ ݁ݎݑܿ݁ݏ‬ൌ  ݂‫ ʹܪ‬ǡ‫ ݁ݎݑܿ݁ݏ‬ή ቀͳ െ

‫ ʹ ܪܧ‬ሺ‫ ݀݊݁ ݐ‬ሻെ‫ ʹ ܪܧ‬ሺ‫ ݐݎܽݐݏ ݐ‬ሻ ͷΨή‫݀ܽ݋݈ܧ‬

ቁ

(6)

The sum of all individual cost factors Cdescribes the energy supply system economically and technically (7). The factors fbatt,secureand fH2,securedescribes the weighting between economical costs end the supply security. ‫ ܥ‬ൌ ‫ ݒ݌ܥ‬൅ ‫ ݐݐܾܽܥ‬൅ ‫ ݂ܿܥ‬൅ ‫ ݈݁ܥ‬൅ ‫ ݐݐܾܽܥ‬ǡ‫ ݁ݎݑܿ݁ݏ‬൅ ‫ ʹܪܥ‬ǡ‫݁ݎݑܿ݁ݏ‬

(7)

Furthermore, the PV-battery-H2-hybrid system should contain equal or increased amount of stored hydrogen over an annual cycle. An external recharge of the H2-storage is typically not possible. A system configuration, which

Martin Paulitschke et al. / Energy Procedia 73 (2015) 154 – 162

does not fulfill this condition, is considered invalid. Likewise the system configuration is invalid, if the battery is completely discharged at any time and the system can’t provide the energy supply task anymore. 2.4. Simulation tool A simulation model that described the PV-battery-H2-hybrid system wasimplemented in Matlab. The program is organized in two parts. The first part is a computing function to compute the power distribution between battery and H2-storage path. The computing function is based on the energy management, which returns the time series of power and state of charge of the components. The time series correspond to a time period of one year with a sample time of one minute. This is implemented in C++ (mex-function) to speed up the computation. The second part of the simulation tool is a Matlab function that calculates the quality value from this time series. It is often necessary to compute different sets of parameters simultaneously for analyzing and optimizing the PVbattery-H2-hybrid system. To reduce computation time, the twofunctions were implemented in a parallelized loop with the Parallel Computing Toolbox of Matlab. The structure of the simulation tool is shown in Fig. 2.

vectorized set of scaling parameters ܲ௣௩ǡ௡௢௠ ǡ ‫ܧ‬௕௔௧௧ǡ௡௢௠ ǡ ܲ௙௖ǡ௡௢௠ǡ ܲ௘௟ǡ௡௢௠ǡ ܱܵ‫ܥ‬௠௔௫ǡ௢௡ǡ ܱܵ‫ܥ‬௠௔௫ǡ௢௙௙ ǡ ܱܵ‫ܥ‬௠௔௫ǡ௢௙௙ǡ ܱܵ‫ܥ‬௠௜௡ǡ௢௡, ܱܵ‫ܥ‬௠௜௡ǡ௢௙௙ parallelized computing loop

scaling parameters of the components:ܲ௣௩ǡ௡௢௠, ‫ܧ‬௕௔௧௧ǡ௡௢௠, ܲ௙௖ǡ௡௢௠, ܲ௘௟ǡ௡௢௠, ܱܵ‫ܥ‬௠௔௫ǡ௢௡, … model parameters: ߟ௔௖Ȁௗ௖, ܴ݅, … PV-power and load profiles: ܲ‫ݒ݌‬ሺ‫ݐ‬ሻǡ ݈ܲ‫ ݀ܽ݋‬ሺ‫ݐ‬ሻ

model of PVbattery-H2-system

relevant time series: ܱܵ‫ܥ‬௕௔௧௧ ሺ‫ݐ‬ሻ, ܱܵ‫ܥ‬ுଶ ሺ‫ݐ‬ሻ, ܲ௕௔௧௧ ሺ‫ݐ‬ሻ, …

time series evaluation

quality value: (costs in €/a)

specific costs, cycles and lifetimes: ‫݌‬௕௔௧௧ ǡ ‫݌‬௙௖ ǡ ‫ ܮ‬௕௔௧௧ ǡ ܼ௙௖ ǡ ǥ

quality vector ‫ܥ‬Ԧ Fig.2.Structure of the simulation tool: showing the two main functions to receive the quality value (green).

3. Sizing problem and particle swarm optimization 3.1. Structure of the search-space To get a stable and cost efficient design the component sizes and energy management parameters has to be optimized. In order to receive a minimized quality value C combining the previously described parameters the objective function forms a multi-dimensional optimization problem. Due to restrictions of the battery SOC and the state of charge of the hydrogen tank after one year of operation the objective function generates invalid solutions in certain areas of the search-space. The switching behaviour of the energy management implies a non-linear and

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discontinuous search-space. Fig. 3 shows the objective function for an hybrid system example in two dimensions (Pel,nom, Pfc,nom). The fixed parameter are shown in Tab. 1. Multiple local optima, discontinuous behaviour of the costs (here at about 1.05kW nominal fuel cell power) and invalid areas can be observed.

1700 1650

1.4

1600

local optimum

1550

1.2

1

discontinuous

local optimum

1500

annual costs in €/a

Pfc,nom in kW

1.6

invalid area

1.8

1450 1400

0.8 1.2

1.4

1.6

1.8

2

Pel,nom in kW Fig. 3.Example of the complex search-space with local optimum, invalid areas and discontinuous behaviour. Table 1. Fixed parameters for example from Fig. 3. Parameter

value

Ppv,nom

8.5kW

Ebatt,nom

19.6kWh

SOCmax,on

92.5%

SOCmax,off

91.5%

SOCmin,off

48.9%

SOCmin,on

39.2%

3.2. Overview of particle swarm optimization The particle swarm algorithm was first presented by Kennedy and Eberhart in 1995 as an optimization method to solve non-linear optimization problems. The authors had been inspirited by the behaviour of a flock of birds or fish swarms [11]. ‫ݔ‬Ԧ ൌ ൫ܲ‫ ݒ݌‬ǡ݊‫ ݉݋‬ǡ‫ ݐݐܾܽܧ‬ǡ݊‫ ݉݋‬ǡ݂ܲܿ ǡ݊‫ ݉݋‬ǡ݈ܲ݁ ǡ݊‫ ݉݋‬ǡܱܵ‫ ݔܽ݉ܥ‬ǡ‫ ݊݋‬ǡܱܵ‫ ݔܽ݉ܥ‬ǡ‫ ݂݂݋‬ǡܱܵ‫ ݊݅݉ܥ‬ǡ‫ ݊݋‬ǡܱܵ‫ ݊݅݉ܥ‬ǡ‫ ݂݂݋‬൯

(8)

In the implemented particle swarm algorithm, a set of random points‫ݔ‬Ԧ (8)considering of the parameters to optimize will be placed in the search-space, and the associated quality values C will be calculated with the simulation tool. These points, called particles, are moving iteratively around the search-space with a velocity‫ݒ‬Ԧ, which is initialized randomly. With each step of a particle the quality value of the actual point ‫ݔ‬Ԧ is calculated. The particles save their actual position in ‫ݔ‬Ԧ best, if the actual quality is better compared to the best past step ‫ ܥ‬best. Furthermore, the best position of all particles ‫ݔ‬Ԧ global best will be kept as the representation of the optimal solution of the iteration step.The optimization is performed by the evaluation of the particle velocity following each movement step.

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The velocity vector consists of three components (s. Fig. 4). First is the inertia, which is composed of the last velocity and a factor݇݅݊݁‫ ݐݎ‬. The second one is the cognitive component, which comprises of the direction to the own best position, a factor ݇cog and a uniformly distributed random number. The last is a social component,which is guided towards the best position of a group of particles ݃Ԧܾ݁‫ ݐݏ‬with a factor ݇‫ ݈ܽ݅ܿ݋ݏ‬and also a random number (9). The neighbourhood group is formed by two direct neighbours of a particle in the whole particle list (LBEST method) [12]. This method was selected to avoid convergence to local optima. The parameter setting was chosen according to the recommendations of Carlisle [13], which is a good compromise between fast convergence behaviour and search scope: ‫ݒ‬Ԧ݅ ൌ kinert ή ‫ݒ‬Ԧ݅െͳ ൅ kcog ή ‫ ݀݊ܽݎ‬ή ሺ‫ݔ‬Ԧܾ݁‫ ݐݏ‬െ ‫ݔ‬Ԧሻ ൅ ksocial ή ‫ ݀݊ܽݎ‬ή ሺ‫ݔ‬Ԧ݈݃‫ ݐݏܾ݁ ݈ܾܽ݋‬െ ‫ݔ‬Ԧሻ

(9)

parameter 2

with: kinert =0.7298,kcog =2.0436,ksocial =0.9488

parameter 1 Fig.4. Components of particle velocity.

start

create random particle (‫ݔ‬Ԧ)

yes

iterations without improvement > nmax compute quality values (‫)ܥ‬

no compute velocities ‫ݒ‬Ԧ of the particle

save ‫ݔ‬Ԧwhen ‫ ܥ‬൐  ‫ܥ‬௕௘௦௧ in ‫ݔ‬Ԧ௕௘௦௧ save best ‫ݔ‬Ԧ ௕௘௦௧ in ‫ݔ‬Ԧ௚௟௢௕௔௟௕௘௦௧

‫ݒ‬Ԧ ൏ ‫ݒ‬௠௜௡

yes

no update particle position ‫ݔ‬Ԧ ൌ ‫ݔ‬Ԧ ൅ ‫ݒ‬Ԧ

Fig. 5. Flowchart of the particle swarm algorithm.

end

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The number of the particles was set to 30. To break the iteration loop two conditions were tested, a maximal number of iterations without improvements and a minimal average velocity. The algorithm with the used abort criteria is shown in Fig. 5. 3.3. Particle movement In Fig. 6 an example of the particle movement across parameters of the nominal fuel cell and electrolyser power is shown. The first picture (top, left) shows the randomized spreading of the particle in the whole search-space. The positions of the particles are labelled as points. The best positions of the particles are marked as stars. The global best value is displayed with a yellow cross. During the first 5 iterations the particles were moving around the entire search-space. After iteration 5 most particles found a good position, which is already close to the optimal regions (top, right). After several further iterations the particles were concentrating in the two local optima (bottom, left). Because of the “social behaviour” the particles have left the local optima and have concentrated in the global optimum (bottom, right). start spread of particles

5. iteration

1.8 1700

annual costs in €/a Pfc,nom in kW

Pfc,nom in kW

1.6

1650 1600

1.4

1550

1.2

1500

1 0.8 1.2

1450 1400 1.4

1.6

1.8

2

1700 1.6

1600

1.4

1550

1.2

1500

1 0.8 1.2

Pel,nom in kW

1450 1400 1.4

1.6

1.8

2

Pel,nom in kW

50. iteration

1.8

1650

180. iteration

1.8 1700 1650 1600

1.4

1550

1.2

1500

1

1450 1400 1.4

1.6

1.8

Pel,nom in kW

2

1700 1.6

annual costs in €/a

annual costs in €/a Pfc,nom in kW

Pfc,nom in kW

1.6

0.8 1.2

annual costs in €/a

1.8

1650 1600

1.4

1550

1.2

1500

1 0.8 1.2

1450 1400 1.4

1.6

1.8

2

Pel,nom in kW Fig. 6. Particle spread at iterations 1, 5, 50 and 180.

3.4. Convergence at higher dimensions To present the process of particle search in more than two dimensions each parameter is shown in a separate plot over the iterations (s. Fig. 7). The particles are indicated by actual (red dot), best (blue dots) and the global best positions (green line). After the first iteration the particles are wide spread over the complete search-space. After a few iterations the particles concentrate in a smaller area. Especially for the nominal PV-power parameterPpv,nom the particles move fast to a range of 7kW to 8kW, indicating a fast determination of the global optimum. This fact points towards a high gradient to optimal solution, and no or few local optima appear at other power settings. On the

Martin Paulitschke et al. / Energy Procedia 73 (2015) 154 – 162

other hand, e.g. at the nominal fuel cell power Pfc,nom emerging several concentrations on different power levels, which indicates the existence of local optima particularly at about 0.7kW and 1kW. The phenomenon of an optimum drift to higher levels is witnessed over the iterations in the dimension of the nominal electrolyser power Pel,nom. One reason for this observation is a small and long area with similar good solutions, on which the particles move slowly to the global optimum point. The algorithm was stopped after 600 iterations, which corresponds to 18,000 calculations of the objective function in a time of about 24 minutes. With a higher number of iterations the precision increases, but a similar good solution could be found with less iterations. The found optimal configuration is shown in Tab. 2.

Fig. 7. Movement of the particles in eight dimensions. Particle positions (red), best particle positions (blue), overall best solution (green).

Table 2. Found optimal configuration. parameter

value

Ppv,nom

7.9kW

Ebatt,nom

19.66kWh

Pfc,nom

1028W

Pel,nom

1752W

SOCmax,on

94.5%

SOCmax,off

92.4%

SOCmin,off

50.6%

SOCmin,on

40.7%

4. Summary and conclusion The sizing of an autonomous energy supply system to get an economically and technical optimal solution is a complex task. This paper has presented a model of a PV-battery-H2-hybrid system and the simulation tool that compute the quality of the system. It has shown that the formulated objective function for the PV-battery-H2-hybrid

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system produces a high dimensional, non-linear and discontinuous search-space with large parts being invalid. A particle swarm algorithm and its implementation to find the optimal parameter set was described. It has shown that the implemented sizing algorithm can handle these problems well and can provide accurate results at fast computational speed. The investigations have shown that local optima can be overcome during the optimization process. Analysis of the detected best solution and their neighbourhood with grid computations indicate that the solution can be in the immediate proximity of the global optimum. Further investigations on the particles caught in these local optima could provide additional hints on alternative solutions. Furthermore, a dependency of the solution on variations of the input demand and PV-power profiles should be investigated, as well as the cost and technical parameters of the used model. Benchmark tests with other methods like genetic algorithm on the same problem should be done to find out whether the particle swarm algorithm is the most sensible. The tool provides a basis for further investigations of autonomous energy supply systems. References [1] [2] [3] [4] [5]

[6] [7]

[8]

[9] [10] [11] [12] [13]

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