Chapter 8: Optimum Design of Small Scale Stand-Alone Hybrid Renewable Energy Systems (by Dr. Juan M. Lujano-Rojas from C-MAST, University of Beira Interior – Covilhã, Portugal and INESC-ID, Instituto Superior Técnico, University of Lisbon – Lisbon, Portugal, Prof. Rodolfo Dufo-López and Prof. José L. Bernal-Agustín from Department of Electrical Engineering, University of Zaragoza – Zaragoza, Spain, Dr. Gerardo J. Osório from C-MAST, University of Beira Interior – Covilhã, Portugal, and Prof. João P. S. Catalão from C-MAST, University of Beira Interior – Covilhã, Portugal and INESC-ID, Instituto Superior Técnico, University of Lisbon – Lisbon, Portugal, and INESC TEC and Faculty of Engineering of the University of Porto – Porto, Portugal) Abstract A crucial factor for the sustainable development of human society is access to electricity. This fact has motivated the development of renewable energy systems isolated or connected to the electric distribution network. Evaluation of autonomous hybrid energy systems from a technical and economic perspective is a difficult problem that requires using complex mathematical models of renewable sources and generators, such as photovoltaic (PV) panels and wind turbines, and the implementation of optimization techniques in order to obtain an economically successful design. This chapter describes and analyzes traditional isolated energy systems powered by solar PV and wind energies provided with a battery energy storage system (BESS). Simulation and optimization are illustrated through the analysis of a rural electrification project in Tangiers (Morocco) in order to provide electricity to rural clinic. Optimization analysis suggests the installation of a PV/BESS system due to the magnitude of the load to be supplied, operating costs, and environmental conditions.
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Chapter 8: Optimum Design of Small Scale Stand-Alone Hybrid Renewable Energy
Systems (by Dr. Juan M. Lujano-Rojas from C-MAST, University of Beira Interior –
Covilhã, Portugal and INESC-ID, Instituto Superior Técnico, University of Lisbon –
Lisbon, Portugal, Prof. Rodolfo Dufo-López and Prof. José L. Bernal-Agustín from
Department of Electrical Engineering, University of Zaragoza – Zaragoza, Spain, Dr.
Gerardo J. Osório from C-MAST, University of Beira Interior – Covilhã, Portugal, and
Prof. João P. S. Catalão from C-MAST, University of Beira Interior – Covilhã,
Portugal and INESC-ID, Instituto Superior Técnico, University of Lisbon – Lisbon,
Portugal, and INESC TEC and Faculty of Engineering of the University of Porto –
Porto, Portugal)
Abstract
A crucial factor for the sustainable development of human society is access to
electricity. This fact has motivated the development of renewable energy systems
isolated or connected to the electric distribution network. Evaluation of autonomous
hybrid energy systems from a technical and economic perspective is a difficult problem
that requires using complex mathematical models of renewable sources and generators,
such as photovoltaic (PV) panels and wind turbines, and the implementation of
optimization techniques in order to obtain an economically successful design. This
chapter describes and analyzes traditional isolated energy systems powered by solar PV
and wind energies provided with a battery energy storage system (BESS). Simulation
and optimization are illustrated through the analysis of a rural electrification project in
Tangiers (Morocco) in order to provide electricity to rural clinic. Optimization analysis
suggests the installation of a PV/BESS system due to the magnitude of the load to be
supplied, operating costs, and environmental conditions.
Keywords: Autonomous energy systems, Genetic algorithm, Hybrid power systems,
Wind speed time series was synthetically generated by using the model developed by
Nfaoui et al. [40], which is based on the Autoregressive Model (AR) model of order p
(AR(p)) shown in (8.36).
푤( ) = ø 푤( ) + ø 푤( ) +··· +ø 푤( ) + 휀( ) (8.36)
Let 푤( ) be the wind speed time series measured in situ, a transformation and
standardization processes are required to obtain the parameters of the corresponding
AR(p) model. These processes could be briefly described in (8.37), where the
transformation is carried by elevating 푤( ) at the power 푚, so that a Gaussian
Probability Density Function (PDF) is obtained.
Then, the transformed time series is normalized by using the hourly mean (휇 ) and the
hourly standard deviation (휎 ) as shown in (8.37); it is important to note that these
signals are considered to be periodical, hence: 휇( ) = 휇( ), 휇( ) = 휇( ), and 휎( ) =
휎( ), 휎( ) = 휎( ), and so on.
푤( ) =푤( ) − 휇( )
휎( ); 푡 = 1, … ,푇;ℎ = 1,2, … ,퐻 (8.37)
However, the goal of this work is not to fit the AR(p) model from measured data; on the
contrary, it needs to undo this process in order to obtain a simulation of Typical
Meteorological Year (TMY) for Tangiers from data already reported in the literature.
Wind speed is statistically described by Weibull PDF, shown in (8.38).
퐹 ( ) = 1 − 푒푥푝 −푤휃 . (8.38)
Table 8.1 presents the information related to Weibull PDF and autocorrelation function
for each month: specifically, the factors for the first two lags. According to the original
work [40], the order of AR(p) model is two (p=2); then using 푟 and 푟 from Table 8.1,
the parameters ø and ø , and the standard deviation for the white noise (휀( )) can be
estimated.
Once all parameters of (8.36) are known, a transformed and standardized time series
could be synthetically generated. After that, the obtained series is multiplied by 휎( ) and
summed to 휇( ) (equation (8.37)). Hence, a transformed time series is obtained, or, in
other words, a time series with Gaussian PDF. In order to obtain a Weibull PDF with
the parameters presented in Table 8.1, each value of the transformed time series is
evaluated on (8.39) [41]; this probabilistic transformation allows modifying the
transformed time series from a Gaussian PDF to a Weibull PDF of (8.38). This
procedure is repeated for each month of the year using the data of Table 8.1, and the
hourly values of 휇( ) and 휎( ) reported in Tables 8.2 and 8.3.
푤( ) = 퐹 퐹 휇( ) + 휎( )푤( ) . (8.39)
“Insert Table 8.1”
“Insert Table 8.2”
“Insert Table 8.3”
The most important results obtained from the aforementioned procedure for the
simulation of wind speed time series are shown in Figs 8.9-8.11. Fig. 8.9 presents PDF
of simulated wind speed time series with scale factor of 7.101 m/s and shape factor of
1.65. Fig. 8.10 shows the simple and partial autocorrelation functions, which effectively
correspond to a AR(2) model, and Fig. 8.11 presents the hourly average profile for each
season of the year.
“Insert Fig. 8.9 here”
“Insert Fig. 8.10 here”
“Insert Fig. 8.11 here”
Simulation and optimization processes were carried out by considering the values
presented in Table 8.4. In a general sense, a single battery string of 50 Ah and a single
PV string of 50 Wp were defined so that, through the optimization process, the optimal
capacity of the wind turbine (between 0 W and 1,000 W), the optimal number of battery
strings (between 1 and 10), and the optimal number of PV strings (between 0 and 20)
were determined.
The wind turbine was modeled by means of the normalized power curve of Fig. 8.3;
hence, 푃 ϵ[0 W; 1,000 W]. Similarly, the PV generator was modeled by using (8.1)-
(8.4) and scaled according to the number of PV strings (푁 ϵ [0; 20]), while the battery
bank was modeled by using the parameters of OGi batteries presented in [23], whereas
battery bank size is obtained by scaling the results for a single string according to the
number of battery strings (푁 ϵ [1; 20]).
Regarding the simulation process, taking into account the available resources and load
demand at a determined time instant, the current to be absorbed or delivered by the
battery bank is determined by using system voltage (푉 ); then the current to be
absorbed or delivered by a single cell (퐼 ( )) is estimated by using the number of
battery strings. After that, the current 퐼 ( ) is obtained from the evaluation of the control
actions of the charge controller (bulk, absorption, equalization, and float charges).
Finally, this current value is used to evaluate the impact of the different aging
mechanisms on battery lifetime.
“Insert Table 8.4 here”
Technical and economic analysis were carried out by considering wind turbine capital
cost as $4,200/kW and a lifetime of 10 years, replacement cost US$3,300/kW, and
Operation and Maintenance (O&M) cost as US$120/kW. Capital and replacement costs
of the power converter were estimated by assuming it as US$875/kW and a lifetime of
10 years, while O&M cost was assumed to be 1% of the initial investment.
Regarding BESS, capital and replacement costs were estimated as US$100/kWh and
O&M was assumed to be 1% of the initial investment. Capital and replacement costs of
PV panels were assumed as US$1.5/W, and O&M cost was assumed to be 1% of the
initial investment with a lifetime of 20 years. Nominal interest rate considered was 7%
with an inflation rate of 3%.
Convergence of GA during the optimization process is shown in Fig. 8.12, where the
optimal design corresponds to a PV/BESS system with a PV generator with 7 strings of
50 Wp (total 350 Wp) and a battery bank with 9 strings of 50Ah (total 5.4 kWh) with an
estimated NPC of US$3,924 (levelized cost of energy US$0.53/kWh).
The expected battery lifetime of the optimal solution is 3.42 years. Simulation and
optimization models were implemented in MATLAB® in a standard personal computer
provided with an i7-3630QM CPU at 2.40 GHz, 8 GB of RAM and 64-bit operating
system, obtaining similar results to those provided by iHOGA software [11] in less than
one minute.
“Insert Fig. 8.12 here”
The hourly PV output power is shown in Fig. 8.13 (all the years are considered similar).
SOC time series during the first four years of the optimized solution is presented in
Fig. 8.14, and Fig. 8.15 shows the SOC of 10 days of January of the 3rd year. As can be
observed, the battery bank remains with a very high SOC during its operative lifetime
with a cycle operation during short-time intervals without deep discharges; as a
consequence, discharging capacity is mainly influenced by the corrosion process (Fig.
8.16), while the number of bad charges (Fig. 8.17) impacts battery bank lifetime just at
its end, which could be identified by analyzing the number of weighted cycles (Fig.
8.18).
In order to get a cost-effective solution, on one hand GA looks for those configurations
that are able to extend the battery bank lifetime as long as possible, so that deep
discharges and the operation during long-time under low SOC are avoided. On the other
hand, as the battery lifetime is simulated all over its float lifetime on an hourly basis, it
represents an important increment on the computational burden of the optimization
problem.
“Insert Fig. 8.13 here”
“Insert Fig. 8.14 here”
“Insert Fig. 8.15 here”
“Insert Fig. 8.16 here”
“Insert Fig. 8.17 here”
“Insert Fig. 8.18 here”
8.5. Conclusions
Renewable energy systems are a good option to provide electric service in a sustainable
way by taking advantage of the natural resources locally available. A direct application
of this philosophy is rural electrification, in which electricity in remote areas is provided
by means of autonomous systems, EDN extensions, or mini-grids installation. To carry
out this task in a cost-effective manner, simulation and optimization techniques are
applied by considering an estimation of the renewable resources, ambient temperature,
and load demand, as well as the behavior of the different components of the system
such as wind turbine, PV generator, and BESS, so that a reliable and affordable energy
system is finally installed.
All of these topics have been studied in this chapter through the analysis of an
autonomous HPS composed of a wind turbine, a PV generator, a storage system based
on lead-acid batteries, a power converter, and a dump load. Wind speed and solar
radiation time series were synthetically generated by using information previously
reported in the literature and public databases for the location under analysis (Tangiers,
Morocco); variations on the efficiency of the power converter with the AC load, as well
as charge controller operation including bulk, absorption, equalization, and float
charges, battery bank performance and aging mechanisms, were integrated in a
optimization model based on GA. From the obtained results, it was possible to observe
how the optimization algorithm looks for those HPS configurations able to prolong
battery bank lifetime by avoiding the operation of it at low SOC during long time
periods.
List of symbols
훥푡 Time step (1h) 푡 Index for time of the year 푡∊[1,푇] 푇 Total simulation time (8760h) ℎ Index for time of the day ℎ∊[1,퐻] 퐻 Total daily time (24h) 푞 Index for each individual in the population 푄 Total number of individuals in the population (Population size) 푌 Total number of generations of GA 푦 Index for each generation of GA 푃 ( ) Power consumed by dump load at time 푡 (W) 푃 ( ) Load demand at time 푡 (W) 퐸푁푆( ) Energy not supplied at time 푡 (Wh) 푁 Number of PV strings 푃 ( ) PV generation of a single panel at time 푡 (W) 퐴 Area of PV panel (m2) 푃 Power generation of PV panel under standard test conditions (W) 퐺( ) Incident solar radiation at time 푡 (kW/m2) 훼 Temperature coefficient of power (%/°C) 푇 ( ) PV cell temperature (°C)
푇 ( ) Ambient temperature (°C) 푇 Daily mean ambient temperature (°C) 푇 Daily maximum ambient temperature (°C) 푇 Daily minimum ambient temperature (°C) 푇 Nominal operating cell temperature (°C) 푊푇( ) Wind turbine power curve (W) 푃 Rated power of wind turbine (W) 푃 ( ) Wind power production at time 푡 (W) 푤( ) Wind speed at time 푡 (m/s) 푤( ) Transformed and standardized wind speed at time 푡 (m/s) 푤( ) Simulated wind speed at time 푡 (m/s) 푚 Transformation power of wind speed time series ø , … , ø Autoregressive coefficients of AR(p) model 휀( ) White noise autoregressive model at time 푡 휇 Hourly average of transformed wind speed at time ℎ (m/s) 휎 Hourly standard deviation of wind speed at time ℎ (m/s) 퐹 Cumulative Weibull distribution function 퐹 Inverse Weibull distribution function 퐹 Cumulative normal distribution function 휆 Shape factor of Weilbull distribution 휃 Scale factor of Weilbull distribution (m/s) 푟 Value of autocorrelation function in one lag 푟 Value of autocorrelation function in two lags 휂 Efficiency of power inverter 푃 Rated power of inverter (W) 푚 , 푚 Parameters of converter model 푃 ( ) Power from/to battery bank at time 푡 (W) 푉 ( ) Battery voltage at time 푡 (V) 푉 Open-circuit voltage (V) 푉 Corrosion open-circuit voltage (V) 푉 Nominal gassing voltage (V) 푉 Reference voltage for reduction of acid stratification (V) 푉 Nominal voltage of the system (V) 훥푊( ) Effective layer thickness 훥푊 Effective layer thickness at the end of battery float life 푘 Corrosion speed parameter 푘(·) Lander corrosion speed vs. voltage curve 푘 Corrosion speed parameter at float voltage 푔 Electrolyte proportionality constant (V) 퐷푂퐷( ) Depth of discharge of the battery at time 푡 푆푂퐶( ) State of charge of the battery at time 푡 푆푂퐶 Minimum SOC of battery bank 푆푂퐶 Maximum SOC reached during fully-charged period 퐼 ( ) Current from/to battery bank at time 푡 (A) 퐼 ( ) Gassing current at time 푡 (A) 퐼 ̅ ( ) Normalized gassing current respect to a 100 Ah battery (A) 퐼 ( ) Discharging current at time 푡 (A)
퐼 Reference current of the battery (A) 퐼 ( ) Current supplied or demanded for a single battery at time 푡 휌 ( ), 휌 ( ) Aggregated internal resistance for charging and discharging (Ω Ah) 휌 Internal resistance at the end of battery float life (Ω Ah) 훥휌( ) Increment in the internal resistance due to corrosion (Ω Ah) 푀 , 푀 Charge-transfer overvoltage coefficient for charging and discharging 퐶 , 퐶 ( ) Normalized capacity for charging and discharging, respectively 퐶 Nominal capacity of the battery (Ah) (Capacity in 10h) 푇 Nominal gassing temperature (K) 푇 Nominal corrosion temperature (K) 푐 Parameter for the increment of acid stratification 푘 , Temperature factor (1/K) 푐 Voltage coefficient (1/V) 푐 Temperature coefficient (1/K) 푐 Parameter used in the estimation of capacity loss due to degradation 푐 Parameter for the reduction of acid stratification by gassing
푐 Coefficient to represent influence of the minimum state of charge in state of charge weighting factor (1/h)
푐 Increase in 푓( ) factor at state of charge equal to zero (1/h) 퐶 Lost capacity at the end of battery float life due to corrosion 퐶 Loss of capacity at the end of battery float life due to degradation 훥퐶( ) Increment in the loss of capacity at time 푡 due to corrosion 훥퐶( ) Increment in the loss of capacity at time 푡 due to degradation 푡 During a charging cycle, this is the time of the last full charge (h) 푧 Number of lifetime cycles under standard conditions 푍 ( ) Weighted number of cycles at time 푡 푓( ) State of charge weighting factor 푓( ) Factor for total impact of acid stratification 푓( ) Weighting factor for degree of acid stratification factor 푓( ) Weighting factor for the increment of acid stratification 푓( ) Weighting factor for the total decrement of acid stratification 푓( )
, Factor for the decrement of acid stratification at time 푡 by gassing 푓( )
, Factor for the decrement of acid stratification at time 푡 by diffusion 퐿 Battery float life (yr) 푛 Cumulative number of bad recharge cycles 퐷 Effective diffusion constant (m2/s) 푧 Height of the battery (cm) 푎,푠,푥 Intermediate variables 푁 Number of battery strings 퐸퐼푈 Energy index of unreliability 퐸퐼푈 Required 퐸퐼푈 of the hybrid system 푉 Voltage during absorption stage of charge controller (V) 푉 Voltage during equalization stage of charge controller (V) 푉 Voltage during float stage of charge controller (V) 푡 Duration time of absorption stage (h) 푡 Duration time of equalization stage (h)
푖 Real interest rate 푗 Project lifetime (yr) 퐶푅퐹( , ) Capital recovery factor for real interest rate 푖 and project lifetime 푗 푁푃퐶 Net present cost (US$) 퐴퐶퐶 Annualized capital cost (US$/yr) 퐴푅퐶 Annualized replacement cost (US$/yr) 퐴푀퐶 Annualized maintenance cost (US$/yr) 훥퐾 Crossing rate of genetic algorithm 훥푀 Mutation rate of genetic algorithm 퐹 ( ) Fitness of individual 푞 퐺 Chromosome to represent the type of wind turbine 퐺 Chromosome to represent number of wind turbine 퐺 Chromosome to represent the type of photovoltaic panel 퐺 Chromosome to represent the number of photovoltaic panel strings 퐺 Chromosome to represent the type of batteries 퐺 Chromosome to represent the number of battery strings 퐺 Maximum amount of wind turbine types 퐺 Maximum amount of wind turbines 퐺 Maximum amount of photovoltaic panel types 퐺 Maximum amount of photovoltaic panel strings 퐺 Maximum amount of battery types 퐺 Maximum amount of battery strings
Acknowledgment
This work was supported by FEDER funds through COMPETE and by Portuguese
funds through FCT, under FCOMP-01-0124-FEDER-020282 (PTDC/EEA-
EEL/118519/2010), PEst-OE/EEI/LA0021/2013 and SFRH/BPD/103079/2014.
Moreover, the research leading to these results has received funding from the EU
Seventh Framework Programme FP7/2007-2013 under grant agreement no. 309048.
This work was also supported by the Ministerio de Economía y Competitividad of the
Spanish Government under Project ENE2013-48517-C2-1-R.
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