Daily operation optimisation of hybrid stand-alone system by model predictive control considering ageing model

Energy Conversion and Management 134 (2017) 167–177

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Daily operation optimisation of hybrid stand-alone system by model predictive control considering ageing model Rodolfo Dufo-López a,⇑, L. Alfredo Fernández-Jiménez b, Ignacio J. Ramírez-Rosado a, J. Sergio Artal-Sevil a, José A. Domínguez-Navarro a, José L. Bernal-Agustín a a b

Department of Electrical Engineering, University of Zaragoza, Calle María de Luna, 3, 50018 Zaragoza, Spain Department of Electrical Engineering, University of La Rioja, Logroño, Spain

a r t i c l e

i n f o

Article history: Received 18 September 2016 Received in revised form 13 December 2016 Accepted 14 December 2016

Keywords: Hybrid renewable standalone systems Battery Diesel generator Predictive control Optimisation Ageing models

a b s t r a c t This article presents a method for optimising the daily operation (minimising the total operating cost) of a hybrid photovoltaic-wind-diesel-battery system using model predictive control. The model uses actual weather forecasts of hourly values of wind speed, irradiation, temperature and load. Five control variables are optimised, and thus their optimal set points values determine the optimal control strategy for each day. This involves the use of an accurate model for estimating the degradation of the batteries by considering the capacity loss due to corrosion and degradation. The model considers the extra costs of maintaining and replacing the diesel generator due to running out of its optimal conditions. The optimisation is carried out by means of genetic algorithms. An example of application compares the total operating cost obtained using the optimal control strategy for each day with the cost of using the optimal control strategy found for the whole year, obtaining savings of up to 7.8%. Also the comparison with the cost of using the ‘‘load following” control strategy is analysed, obtaining savings of up to 37.7%. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction In many cases, standalone systems (off-grid systems) for energy supply are more cost-effective than building new power lines to supply those consumers energy from a power distribution grid [1]. Hybrid standalone systems, which use more than one energy source, are usually better from an economic point of view than standalone systems that only use one energy source [2]. Photovoltaic (PV) generators with lead-acid battery storage are the technologies most widely used in small standalone systems [3]. Hybrid PV-diesel-battery systems are also widely used, as they are usually cost-effective (for any size or power) compared to diesel-only systems [4]. Also, they can be cost-effective compared to PV-only systems in areas where solar irradiation is much lower in winter than in summer [5]. Moreover, in these areas, the PV-diesel-battery system usually has lower life cycle emissions than non-hybrid systems [6]. In areas with high wind speeds, wind-diesel-battery, PV-wind-battery or PV-wind-diesel-battery systems can be cost-effective [7]. The control of a hybrid standalone system is usually carried out using a bidirectional inverter [8] (also called bidirectional converter or inverter/charger). ⇑ Corresponding author. E-mail address: [email protected] (R. Dufo-López). http://dx.doi.org/10.1016/j.enconman.2016.12.036 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.

Controlling the system includes managing the battery by preventing over-charge or over-discharge to maximise the battery’s lifetime and managing the start/stop of the DG. Many inverter/ chargers include state of charge (SOC) control, which calculates the SOC of the battery bank. They disconnect the battery from the load when a minimum SOC setpoint is reached and reconnect it after it achieves a specified higher value of SOC. Controllers can implement different strategies, most typically [9] the load following (LF) strategy, which determines that the DG operates just enough to meet the net load (that is, the DG only supplies the net load when the battery bank cannot), and the cycle charging (CC) strategy, which establishes that the DG runs at rated power when the batteries cannot meet the net load not only to meet the demand but also to charge the batteries until a specified SOC is reached. This article contains a method for optimising the daily operation of a hybrid PV-wind-diesel-battery standalone system (Fig. 1). The objective is to minimise the total operating cost of the standalone system for each day using a model predictive control (MPC) scheme. MPC utilises predictions of the hourly load and actual hourly weather forecasts for wind speed, irradiation and temperature based on numerical weather prediction (NWP) models. A computer tool has been developed for simulating the expected performance of the hybrid system (using past data and

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PV (with inverter) Small wind turbine (with inverter)

GFS model

LOAD

AC

PC with optimisation tool with MPC

Bidirectional inverter AC Diesel

DC

WRF model

Data

Battery bank

Data

Fig. 1. PV-wind-diesel-battery system (AC coupled).

current-day forecast data) and optimising the operation of the standalone system (by minimising its total operating cost during the day). The NWP model used in this paper is the Weather Research and Forecasting (WRF) model [10], which gets data from a global forecasting system (GFS) model [11]. Each day, before 12:00 a.m., the computer tool is fed with actual local hourly weather forecasts as well as forecasts of hourly load. Then it optimises the control strategy for that day (24 h), sending the control set points to the bidirectional inverter. This article is structured as follows. Section 2 presents the literature review and research gaps. Section 3 shows the method for optimising the system daily operation, including the description of the control variables which set points must be optimised, the mathematical models of the components of the hybrid PV-winddiesel-battery standalone system to perform the simulations, the economic calculation of the total cost of operating this hybrid system for one day and the genetic algorithm (GA) used in the optimisation. Section 4 includes the results and discussion of the optimisation, using the MPC for several days as a case example. Conclusions are shown in Section 5.

2. Literature review Several reviews of works related to hybrid standalone systems have been published. Bajpai and Dash [12] presented a review of the most relevant works related to this kind of system. Mohammed et al. [13] published a complete review in the same way. Nema et al. [14] highlighted the current and future state-of-the-art hybrid PV-wind systems. Mohammed et al. [15] reviewed the state-of-the-art hybrid PV-diesel-battery system control strategies. Typical LF and CC strategies were used in many prior works. DufoLópez et al. [16] demonstrated the optimisation of design and control strategies (for a whole year) for PV-diesel-battery systems using the LF strategy, the CC strategy and a combined strategy. Ameen et al. [9] presented MATLAB simplified performance models of PV-diesel-battery systems using LF and CC strategies. Maatallah et al. [1] optimised a PV-wind-diesel-battery system using HOMER commercial software and compared the LF and CC strategies, showing that the LF strategy implies a lower net present cost. Bortolini et al. [5] used the LF strategy to integrate PV and batteries in a diesel-based system. On the other hand, Upadhyay and Sharma [17] used the CC strategy to optimise a PV-hydro-biomass-bio

gas-diesel-battery system. In an earlier work, Dufo-López et al. [18] presented a novel strategy using GA to optimise up to 12 control variables to be applied in a general PV-wind-hydrodiesel-hydrogen system. They optimised the control variables to minimise the net present cost—that is, to minimise the operational cost of a whole year—thus obtaining set points for the control variables to be used for the whole year. In all these studies, the control strategies were evaluated over long periods typically lasting one year. In other studies, researchers have demonstrated daily optimisation (minimising the total operating cost for 24 h). Kusakana [19] evaluated two control strategies for minimising the daily operational cost of a PV-diesel-battery system: ‘‘continuous” (similar to the LF strategy) or ‘‘On/Off” (similar to the CC strategy) operation of the DG. Ashari and Nayar [20] optimised dispatch strategies for operating a PV-diesel-battery system by obtaining the optimal set points for starting and stopping the DG, the battery charger and the maximum power of the DG and the charger with the objective of minimising the overall system costs. Tazvinga et al. [21] used the LF strategy in a PV-diesel-battery system and gave an accurate estimation of the daily diesel fuel cost and how much they saved in relation to the cost of a diesel-battery system. Balamurugan and Kumaravel [22] generalised an algorithm to optimise the operation of hybrid power systems by shedding non-priority loads when the available energy sources and energy storage cannot meet the whole load. Muselli et al. [23] put forth a method of optimally sizing PV-diesel-battery systems with two battery charge threshold parameters to start and stop the DG. Baghadi et al. [24] optimised a PV-wind-diesel-battery standalone system in Algeria that included a mathematical model to ensure efficient energy management on the basis of LF strategy. Bortolini et al. [5] optimised a PVdiesel-battery system designed to minimise both the levelised cost of the electricity and the carbon footprint of energy using the LF strategy. Moghavvemi et al. [25] showed a hybrid PV-diesel system for supplying remote-controlled FM transmitters in remote locations, including applications for sensing, managing, controlling and using the CC strategy. Merei et al. [26] presented a method for modelling and optimising a PV-wind-diesel-battery system using batteries of lithium-ion, lead-acid, vanadium redox-flow or a combination. The battery control included different battery operating points and ageing mechanisms. Few works use an MPC to optimise the operation of hybrid standalone systems. Al-Alawi et al. [27] presented an MPC applied to a PV-diesel-battery system to supply water and power using an

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artificial neural network (ANN) to control the DG on/off status. The ANN is fed with data about the power from the PV, the power from the battery, the power from the inverter and the time to obtain the DG’s on/off status and the amount of power it produced. This strategy maintains a minimum level of loading on the generator under low load and high irradiance conditions, and it also reduces the fuel consumption by switching the diesel off when it is expected that it will not be needed to supply load. Dagdougui et al. [28] used a dynamic MPC model to integrate wind and solar energy and storage to supply the thermal and electrical load of a building connected to the electrical grid. The MPC controller integrates PV panels, wind turbines, a flat plate collector, storage systems and energy demand (electricity, heat and water pumping) under the assumption that the forecasted data from which the optimisation problem must be solved are exactly equal to the historical data recorded at the site. The data consisted of the hourly wind speed, recorded at a height of 10 m, and the hourly solar irradiance. Bruni et al. [29] used an MPC model based on weather data taken from the EnergyPlus database [30] and related to Rome, Italy. They applied it to the analysis of power management in a domestic PV-battery-fuel cell system where the control strategy was optimised to minimise energy costs. Also few works are related to optimisation of the operation and maintenance (O&M) of isolated DG. Karnavas and Papadopoulos [31] used a maintenance-oriented algorithm for the economic operation of an off-grid diesel electric station. However, the O&M and ageing of the DG, which depend on partial load operation, were not considered. Matt et al. [32] optimised the off-grid DG costs by selecting the best number, size and dispatch schedule of the generators, considering, among other factors, the size and O&M costs that depend on the dispatch. All the models shown in the literature review that were related to hybrid systems (except for the work of Merei et al. [26], which considered an ageing model that was dependent on temperature and SOC) used simple models for the batteries. The battery’s lifetime is estimated by means of the number of equivalent full cycles [20] assuming that the operating conditions are the same as the conditions of the standard tests that battery manufacturers use to obtain the lifetime number of IEC cycles. These assumptions lead, in many cases, to a too-optimistic estimate for the battery’s lifetime. Dufo-López et al. [33] showed that the Schiffer et al. weighted Ah-throughput model [34] obtained more accurate results in terms of battery ageing than did simpler models. In the optimisation the daily operations (i.e., the minimisation of the total cost of operating over 24 h), erroneous estimations of battery ageing can lead to erroneous estimations of the total operating cost, as it must include the proportional replacement cost of the battery bank. Moreover, none of the previous studies related to hybrid systems found during the literature review consider the extra O&M costs and ageing of the DG when it runs out from the optimal load conditions [32]. In the present article, it is proposed a new method for optimising daily (24 h) operations by using forecasts of the hourly load (from the forecast model of Hong et al. [35]) and weather forecasts to determine the hourly values of the wind speed, irradiation and temperature for the physical location of the hybrid standalone system (using the NWP models indicated in Ramírez-Rosado et al. [36–38]). An accurate model for estimating the performance and ageing of the battery bank (Schiffer et al. weighted Ahthroughput model [34]) is used. The control variables to be optimised are based on the ones Dufo-López et al. [18] used. They are applied to daily (24 h) operations to minimise the total system operating cost during the day, including diesel fuel cost, DG O&M costs, battery ageing cost and DG ageing cost. The optimisation is efficiently performed by using a GA.

The most important novelties of the paper includes:
MPC is used to optimise the daily operation of the system.
Previous works just consider the cost of the diesel fuel. In this work the total system operating cost during the day includes diesel fuel cost, DG O&M costs, battery ageing cost and DG ageing cost.
For the first time, an accurate model for estimating the performance and ageing of the battery bank is used in the MPC.
Previous works just use LF or CC control strategies; some of them optimise the minimum SOC of the battery bank. In this work five control variables are optimised by using GA.
For the first time, the extra O&M costs and ageing of the DG when it runs out from the optimal load conditions are considered. 3. Method of optimising the daily operation of PV-wind-dieselbattery standalone systems This section presents the control variables, the mathematical models of the components, the calculation of the daily operation cost and the GA used. The models and optimisation tool were programmed in the C++ programming language. 3.1. Variables involved in optimisation Defined below are the five control variables involved in optimising the hybrid system’s operation during the day: Pmin_gen, Plimit_discharge, Pcritical_gen, SOCstp_gen, and SOCmin. Dufo-López et al. [18] introduced these variables to optimise the overall annual operational cost; however, in the present work, the optimisation is performed daily, minimising the operational cost of each day. Pmin_gen is the minimum output power of the DG. Plimit_discharge is the power set point limit: lower net load is supplied by the battery bank; higher net load is supplied by the DG. Pcritical_gen is the DG critical power: when the net load is lower than this value, DG runs at its maximum power to supply the load and also to charge the battery bank up to the SOCstp_gen limit. SOCmin is the minimum SOC allowed for the battery bank. The optimal values of the set points for the control variables of each day depend on the current and past values of many variables, so they cannot be calculated using analytical methods. These set points must be optimised by considering different combinations of their values, simulating the performance of the hybrid standalone system for each combination and evaluating the total operating cost of the hybrid system during the day. The optimal values of the set points will be the combination of values that minimises the total cost. 3.2. Mathematical model for the hourly simulation of the hybrid system Next the mathematical models of the components of the hybrid system used in the simulation of its hourly operation are described. 3.2.1. PV generator model The power the PV generator inputs into the bidirectional converter, P PV ðtÞ, can be calculated by (1) assuming that a maximum power point tracking (MPPT) is included in the PV inverter or bidirectional inverter:

PPV ðtÞ ¼ PSTC 

Gh ðtÞ f f l 1kW h=m2 mm dirt wire

PV

 f temp ðtÞ

ð1Þ

where PSTC (Wp) is the output power in standard test conditions, Gh(t) (kW h/m2) is the average irradiation over the surface of the

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PV panels during hour t, fmm is the module mismatch or power tolerance, fdirt is the dirt derating factor, lwire_PV is the wire efficiency (from the PV generator to the bidirectional inverter) and ftemp(t) is the temperature derating factor. The temperature derating factor is calculated by (2):

a

P (W)

1400 1200 1000

where a (%/°C) is the power temperature coefficient and Tc(t) (°C) is the average PV cell temperature during hour t, which can be calculated by (3) [39],

600

100

ðT c ðtÞ  25Þ


 NOCT  20 Gh ðtÞ  T c ðtÞ ¼ T a ðtÞ þ 0:8 1kW h=m2

gM RL

T0  T a ðtÞ

ð4Þ

where q(t) (kg/m3) is the air density at the altitude H above sea level and temperature Ta(t), q0 (1.225 kg/m3) is the air density at sea level and 1 atm of pressure, T0 is 288.15 K, L is the variation rate of temperature vs. height (0.0065°K/m), g = 9.80665 m/s2, M is the molecular weight of dry air (28.9644  103°kg/mol) and R is the ideal gas constant (8.31432 J/mol°K). The output power of a wind turbine at height H and temperature T(t) can be calculated as the output power at standard conditions multiplied by the ratio q/q0 (see example in Fig. 3). If the hub height of the wind turbine zhub (m) is different from the anemometer height zanem (m) where the wind speed is measured, the wind speed wHUB h ðtÞ at the hub height can be obtained from the wind speed wh ðtÞ using (5),

wHUB h ðtÞ ¼ wh ðtÞ 

ln zzhub 0

ð5Þ

ln zanem z0

where z0 is the surface roughness length (m).

Efficiency (%) 100 98 96 94 92 90 88 86 84 82 80

0

20

40

60

Output Power (%) Fig. 2. Inverter efficiency.

400 200 0

2

4

6

8

10 12 14 16 18 20 22 24 26

Wind speed (m/s)

3.2.2. Wind turbine model The power curve supplied by the manufacturer of the wind turbine corresponds to standard conditions (sea level, 1 atm, 288.15°K). It must be converted to the power curve at the height H (m) of the location over the sea level and an average temperature Ta(t) (K) (of the air) associated to each hour. With the ideal gas law in mind, Eq. (4) from [40] can be used:




800

0

ð3Þ

where T a ðtÞ (°C) is the average ambient temperature during hour t and NOCT (°C) is the nominal operation cell temperature. If the bidirectional inverter is AC coupled (Fig. 1), the inverter between the PV generator output and the bidirectional inverter is needed. The efficiency of the inverter is modelled as dependent on the output power, as in the example shown in Fig. 2.

qðtÞ LH ¼ 1 To q0

400 m, 298 K

1600

ð2Þ

f temp ðtÞ ¼ 1 þ

Standard condions

1800

80

100

Fig. 3. Example of power curve of a commercial wind turbine in standard conditions and other conditions (400 m height, 298 K).

For each hour t, the value of wHUB h ðtÞ is used as an input in the power curve corresponding to H and T(t) to obtain the power generated by the wind turbine PWT (t) during hour t. The power input into the bidirectional inverter is also affected by the wire efficiency, lwire_WT, from the wind turbine to the inverter/charger. If the bidirectional inverter is AC coupled and the wind turbine output is in DC (Fig. 1), an inverter is needed between the wind turbine and the bidirectional inverter (see typical efficiency shown in Fig. 2). 3.2.3. Diesel generator model The output power PGEN(t) (kW) of the DG during hour t will be higher than zero if the renewable sources cannot meet the load and the control strategy in that hour determines that DG must run (instead of the load being supplied by the battery bank). The DG can run just to meet the load or it can also charge the battery bank, depending on the control strategy. The diesel fuel consumption, Consfuel ðtÞ in L/kW h, during hour t is calculated using (6) or (7):
If the DG was running during the previous hour, then:

Consfuel ðtÞ ¼ B  PGEN; rated þ A  P GEN ðtÞ

ð6Þ


Otherwise, the DG must be started with extra consumption, and then

Consfuel ðtÞ ¼ ð1 þ F START Þ  ðB  PGEN; rated þ A  PGEN; rated Þ

ð7Þ

where A = 0.246 L/kW h and B = 0.08415 L/kW h are the fuel curve coefficients [41], PGEN,rated (kW) is the rated power and FSTART is a factor that accounts for the extra fuel due to the start of the generator (usually lower than 0.0083, equivalent to 5 min at rated power [42]). DG manufacturers usually recommend a minimum output power (usually 30% of the DG rated power) [43] to prevent the DG from ageing prematurely due to a poor combustion process. In some cases, to supply the load when it is lower than the recommended minimum, a dummy load can be used [44]. The O&M and ageing costs of the DG are higher when the generator falls out of the range of 50–80% of the rated power (optimal conditions) [32]. Higher O&M costs and shorter lifetime (higher ageing costs) are considered when the output power of the DG is between its minimum output power and 50% of its rated power. Also, when the DG output power is between 80% and 100% of the DG rated power, higher O&M costs and ageing have taken into account [32]. Every hour the DG runs, the factor fextra_GEN(t) is applied to obtain the equivalent number of hours of operation (HGEN) given

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by (8); this value is used to obtain the real O&M costs during the day as well as the cost due to the ageing of the DG (proportional to the cost of replacement, according to Section 3.3).

HGEN ¼

24 X don ðtÞ  f extra

GEN ðtÞ

ð8Þ

t¼0

f extra

GEN ðtÞ

¼ a  PGEN ðtÞ=PGEN; rated þ b

ð9Þ

where don(t) is a binary variable that indicates whether the DG is running during hour t (it is 0 if DG is off during that hour and 1 if it is on) and a and b are the parameters corresponding to portions of the linear functions (Fig. 5) that determine the extra ageing of the DG if it works at less than 50% or more than 80% of its rated power. There are different a and b parameters depending on the specific power that the DG is supplying (Fig. 4); they are given by (10):

If 0:5 P PGEN ðtÞ=PGEN;rated > 0:3 then a ¼ a1 ; b ¼ b1 If 0:8 P PGEN ðtÞ=PGEN;rated > 0:5 then a ¼ 0; b ¼ 1

ð10Þ

If PGEN ðtÞ=PGEN;rated > 0:8 then a ¼ a2 ; b ¼ b2

commercial units are AC coupled (Fig. 1), so the PV generator must include its own inverter (usually with MPPT). The wind turbine must also have its own inverter if its output power is in DC. The input power to charge the battery bank is affected by the charge efficiency, whereas the output inverter efficiency depends on the output power (see the example shown in Fig. 2). The control of the system proposed in this work is done by the bidirectional inverter. No extra cost would be needed, as commercial bidirectional inverters already measure SOC, load and power from renewable sources, and they manage the battery bank and the DG. They just should be programmed each day with the specific setpoints to optimally manage the battery bank and the DG. 3.3. Objective of optimisation: Minimisation of the total operating cost of the hybrid system during the day The objective of this work is to minimise the total daily (24 h) hybrid system operating cost, which will be denoted by Ctotal (€). This cost includes:
Cost of the fuel, C fuel , used during the day, given by (12),

3.2.4. Battery bank model In this work, the weighted Ah-throughput lead-acid battery model presented by Schiffer et al. [34] has been used. This model is based on the assumption that operating conditions are generally more severe than those used in standard tests of cycling and float lifetime that manufacturers provide in their data sheets. The actual Ah-throughput is continuously multiplied by a weighting factor that represents the actual operating conditions, thereby affecting battery capacity loss due to degradation. The weighting factor depends on the depth of discharge, the current rate, the existing acid stratification and the time elapsed since the last full battery bank charge. Further, the model includes capacity loss due to corrosion. The model is used to calculate the battery bank capacity loss by corrosion, Ccorr(t), and the capacity loss by degradation, Cdeg(t), in the hour t. During each hour, the remaining normalised capacity of the battery bank during its discharge, C D ðtÞ, can be calculated as the normalised initial battery bank capacity during its discharge (CD_beginning_of_life, at the beginning of the life of the battery bank) minus the capacity loss, Ccorr(t), by corrosion and the capacity loss, Cdeg(t), by degradation according to (11).

C D ðtÞ ¼ C D

beginning of life

 C corr ðtÞ  C deg ðtÞ

ð11Þ

3.2.5. Bidirectional inverter model The bidirectional inverter includes the output inverter (DC/AC) that supplies the AC load from the DC bus, the rectifier (AC/DC, also called battery charger) that allows the AC sources to charge the battery bank and the control unit that comprises the battery charge controller and the switches to connect/disconnect the DG. Many

fextra_GEN 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0.3

C fuel ¼

24 X

Consfuel ðtÞ  Prfuel

where t is the hour of the day (from 0 to 24) and Prfuel (€/L) is the diesel fuel price.
Costs of the O&M of the DG, CO&M, according to (13),

CO&M ¼ HGEN  PrO&M

0.7

0.9

PGEN (t) /PGEN,rated Fig. 4. Factor fextra_GEN, calculated from data of Ref. [32].

ð13Þ

where PrO&M (€/h) is the O&M cost per hour.
Cost of ageing of the DG, CGEN_ageing, during the day. The DG expected lifetime LifeGEN is usually considered to be a number of hours of operation. Then, the ageing of the diesel during the day is proportional to the number of hours it operates that same day. This cost is the proportional cost of replacing DG when its lifespan ends—that is, the proportional cost of replacing it due to the hours the generator spends running that day. This cost CGEN_ageing is calculated using (14),

C GENageing ¼ PrGEN  HGEN =LifeGEN

ð14Þ

where PrGEN (€) is the acquisition cost of the DG.
Cost of ageing of the battery bank, CBAT_ageing, during the day. The battery bank’s expected lifetime is not a fixed value measured in years or hours of operation. Rather, it depends on the operating conditions. Therefore, the cost of ageing of the battery bank, CBAT_ageing, due to the day’s operation is calculated using (15),

C BAT

ageing

¼ PrBAT  Deg BAT

ð15Þ

where PrBAT (€) is the acquisition cost of the battery bank, Degbat (per unit) is the degradation of the battery bank during the day. The latter can be calculated using (16), taking into account that the battery bank’s lifetime begins with a normalised initial battery bank capacity during discharge (CD_beginning_of_life) and ends when CD is 0.8:

Deg BAT ¼ ðC D ð24Þ  C D ð0ÞÞ=ðC D

0.5

ð12Þ

t¼0

beginning of life

 0:8Þ

ð16Þ


The cost, C SOCð0Þ- SOCð24Þ , of using the DG to supply the difference between the SOC at the beginning of the day (hour t = 0) and the SOC at the end of the day (hour t = 24). If the difference is greater than 0, that means that the amount of energy calculated will not be available at the beginning of the next day, so it will have to be supplied by the DG. This is supposing that the next day, the renewable sources will not be available to supply the

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whole load plus that difference. Therefore, after some days without a full charge of the battery bank, the DG will fully charge it, as it is programmed to do periodically. The cost, C SOCð0Þ- SOCð24Þ , is calculated according to (17),

C SOCð0Þ- SOCð24Þ ¼ X  ðA  DE  Prfuel Þ

ð17Þ

where DE (kW h), calculated using (18), is the difference between the energy stored in the battery bank at the beginning of the day and the energy stored at the end of the day and X is a binary variable used to determine whether this cost can be considered or not.

DE ¼ maxð0; ðSOCð0Þ  U bat ð0Þ  SOCð24Þ  U bat ð24ÞÞ  C N  =1000Þ ð18Þ where Ubat(t) (V) is the battery bank voltage and CN is the nominal capacity of the battery bank (Ah). If it is expected that the next day, the renewable sources will be able to restore the SOC level of the battery bank to the value of SOC (0) or higher, then this cost should not be considered (X = 0). Otherwise, this cost should be considered (X = 1). The term BPGEN,rated (the fixed term of diesel fuel consumption) is not added to ADE to calculate the fuel consumption, as it is expected that the DG will fully charge the battery bank during the hours it must also supply the load, meaning that such a term would already be considered during those hours. The total cost of the hybrid system operation, C total , during the day is given by (19).

C total ¼ C fuel þ C O&M þ C GEN

ageing

þ C BAT

ageing

þ C SOCð0Þ- SOCð24Þ

ð19Þ

The cost of replacing the PV generator, the inverters and the bidirectional inverter are not considered here, as they are usually modelled as independent of the system operation (typically, these components are considered to have a fixed lifetime). 3.4. Genetic algorithm for optimisation

inhibiting premature convergence). The individuals obtained through reproduction and mutation are evaluated, and the best individuals replace the worst ones in the previous generation, thereby obtaining the next generation. The process continues until a determined number of generations, Ngen_max, has been evaluated. The best solution (best individual) obtained is that which has the lowest total operational cost for the hybrid system during the day. 4. Results An off-grid, isolated, small agricultural installation located in the municipality of Aguilar in La Rioja (Spain) is an example of the method for optimising the system operation described in previous sections. The electrical load is supplied by a PV-winddiesel-battery system. The average daily load is 61.5 kW h/day (maximum hourly load 7.1 kW). The system data are shown in Table 1. First, the global control strategy for the whole year will be optimised. Afterwards, the control strategy for several days will be optimised to show the application of this work.

Table 1 System data. Parameter PV generator: PSTC Orientation Slope NOCT

a

fmmfdirtlwire_PV Inverter efficiency Wind turbine: Output curve (standard conditions)

lwire_WT

Five control variables (presented in Section 3.1) are considered in the optimisation. Given that many combinations of the set point values of the control variables can be considered, if the number of possible combinations is too high, then it would imply an inadmissible computation time. Therefore, a GA is used to perform the optimisation (i.e., to minimise the total operating cost of the hybrid system, C total , during the day) in a reasonable computation time. The first generation of the GA is composed of a population of randomly obtained N vectors, or individuals, each composed of random values of the five control variables. With the weather forecasts of hourly values of wind speed, irradiation and temperature and forecasts of hourly load, each individual is evaluated by simulating the hourly operation of the system during the 24 h. The set of individuals is sorted by objective function values (total operating cost of the hybrid system during the day). The first vector (rank 1) is the best individual (minimum cost), whereas the last vector (rank N) is the worst individual (maximum cost). The fitness function value, fitnessi , of the individual with rank i is given by (20).

ðN þ 1Þ  i fitnessi ¼ X ½ðN þ 1Þ  j

j ¼ 1...N

ð20Þ

j

The best individuals (higher fitness) have a higher probability of reproducing and crossing with other vectors, thus obtaining two new vectors in each cross. Some individuals randomly change some of their set point values; in other words, a control variable of the vector is randomly selected and its value is randomly changed by another one (mutation) to avoid a local minimum (maintaining diversity within the population of individuals and

Inverter efficiency Diesel generator: PGEN,rated Minimum output power recommended A B a1 b1 a2 b2 Prfuel PrO&Ma LifeGEN PrGEN Battery bank: CN Nominal capacity (kW h) Lifetime number of IEC cycles [45] Float life Minimum SOC recommended PrBAT Other parameters Bidirectional inverter: Rated power Type Charger efficiency Inverter efficiency Other data: Nominal DC bus voltage X

Value 4.4 kWp South 60° 49 °C 0.2%/°C 0.85 Fig. 2 Fig. 4 (standard conditions) 0.98 Fig. 2 7 kW 2.1 kW (30% of rated) 0.246 L/kW h 0.08415 L/kW h 1.25 1.625 2.5 1 0.7 €/L 0.66 €/h 35,000 h 4050 € 1800 Ah 86.4 kW h (24  2 V  1800 Ah) 1200 cycles 18 years 20% 28,800 € (333.33 €/kW h) Schiffer et al. [34] 8 kW AC coupled 0.9 Fig. 2 48 V 1

a Diesel O&M costs include minor maintenance services (e.g., oil changes; topping off of oil; and air, fuel and oil filter changes) at a cost of 60 € every 250 h; major maintenance services (e.g., decarbonisation, adjustments, oil changes and filter replacements) at a cost of 300 € every 1000 h; and minor and major overhaul services (e.g., replacement of crankshafts and drilling of cylinders) every 10,000 h at a cost of 30% of the DG acquisition cost [48].

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4.1. Annual optimal global strategy Following the method shown by Dufo-López et al. [18] and using the battery model shown by Schiffer et al. [34], the annual global strategy was optimised. The renewable sources cannot meet the load during most hours of the year, so the battery bank and the DG must supply the load for a large number of hours. The battery bank will thus be at low SOC for long periods, which would imply a very short lifetime [34]. To lengthen the battery bank’s lifetime, the DG is programmed to deliver a periodic full charge of the battery bank by default through some bidirectional inverters; this is scheduled every 14 days or every eight nominal charge throughputs [46]. However, these values are too high; therefore, to lengthen the battery’s lifetime, several tests were performed. They showed that, in this case, a full charge of the battery bank must be done every six days or every four nominal charge throughputs. The measured hourly values for a whole year (2014) of irradiation, wind speed, temperature and load were considered. The hourly irradiation values over the horizontal surface were converted to hourly irradiation values on the tilted surface of the PV panels using the methodology of Hay and Davies [47]. Table 2 shows the ranges of control variables used in the optimisation. The following results for the annual optimal control variables were obtained: Pmin_gen = 6000 W; Plimit_discharge = 6500 W; Pcritical_gen = 7100 W (maximum load); and SOCstp_gen = SOCmin = 50%. With these optimal values, the total operating cost was minimal (238,410 €) based on the fuel cost, the O&M and the replacement of the DG and the battery bank during the system’s lifetime (25 years). The battery bank’s expected lifetime was 6.7 years. The annual energy values were as follows: load = 22,447 kW h/yr; energy generated by PV = 5560 kW h/yr; energy generated by wind turbine = 1853 kW h/yr; battery-cycled energy = 9382 kW h/yr; and energy generated by DG = 20,214 kW h/yr (including the energy consumed by the dump load when the load was lower than the minimum DG output power). A minimum SOC of 50% was needed to lengthen the battery’s lifetime, so this value was set as the minimum allowed in daily operation. 4.2. Optimal daily strategy The optimal strategy to minimise the total operating cost of the hybrid system during each day (24 h) is in general different from to the optimal annual global strategy. Each day at 0 h (12:00 a.m.), the MPC utilises the present SOC of the battery bank; hourly weather forecasts for the next 24 h for wind speed, temperature and irradiation on a horizontal surface; and hourly load forecasts (Fig. 1). The MPC has previously stored all the values for the previous days’ variables related to the Schiffer battery model. Then, at 0 h (12:00 a.m.), the MPC obtains the optimal strategy by simulating and evaluating all the possible combinations of values considered for the control variables’ set points; it then chooses the combination with the lowest Ctotal. The same ranges that were

Table 2 Ranges of control variables for the optimisation of the annual global strategy. Variable

Possible values

#

Pmin_gen (W)

2100 (30% of rated power), 2500, 3000, 3500, 4000, 4500, 5000, 5500, 6000, 6500 7000 (rated power) 0, 500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500, 5000, 5500, 6000, 6500 7100 W 20, 30, 40, 50, 60, 70, 80, 90, 100

11

Plimit_discharge and Pcritical_gen (W) SOCstp_gen and SOCmin (%)

15

9

173

considered for the possible values of the control variables’ set points (presented in Section 4.1) are used in the optimisation of daily operations, except for the SOCstp_gen and SOCmin, which can vary from 50 to 100% of SOC with 11 possible values at 5% intervals (i.e., 50, 55, 60, 65, 70, 75, 80, 85, 90, 95 and 100%). The number of possible combinations of control variables is 11  15  15  11  11 = 299,475. These combinations must be evaluated each day at 0 h (12:00 a.m.). At a rate of around 15 combinations per second (based on a 2.4 GHz computer with 4 GB of RAM), it would take 5.5 h to evaluate all of them. This computation time is unacceptable, as the optimal control strategy must be applied each day near 0 h (12:00 a.m.). Therefore, GA are applied using the following parameters [49]: Npop = 1000, Ngen_max = 15, crossing rate = 90% and mutation rate = 1%. Around 9000 combinations are evaluated using GA, with a total computation time of around 10 min. Then, at 0:10 h (12:10 a.m.) every day, the optimal predictive control strategy is determined, and the optimal values of the control variables are sent to the bidirectional inverter (Fig. 1) to optimally manage the system during that day (from t = 0 to t = 24 h). As an example, the control strategy for six days (9–11 July and 16–18 October 2014) was optimised using the forecast values shown in Fig. 5. Each day will have its own optimal control strategy. In Fig. 5, each forecast hourly load value is quite similar to the actual measured value; this is because most of the farm’s power demands (e.g., lighting and ventilation) are automatically programmed, so they were easily predicted. Table 3 gives the optimal set points for the control strategy for each day as well as the following: a) the total cost (Ctotal) expected for the optimal strategy using forecast values; b) the total cost for the optimal daily strategy using actual measured values; c) the total cost that would have been obtained using the optimal annual strategy (that is, applying the strategy found in Section 4.1 to all the days); and d) the total cost that would have been obtained using the LF strategy (which is the usual strategy for this kind of system, with Pcritical_gen = 0 and Plimit_discharge P maximum load), with the DG minimum output power recommended by the manufacturer. Table 3 shows that the optimal values for all days were Pcritical_gen = 7100 W (maximum load) and SOCstp_gen = SOCmin = 50%. Pcritical_gen = maximum load means that the CC strategy was selected; however, as SOCstp_gen = SOCmin, the DG did not have to run at rated power because the SOCstp_gen was always reached. The optimal strategy for all the days is thus summarised as: – The battery bank will supply the net load (the total load minus the load covered by the renewable sources) if the net load is lower than Plimit_discharge and the battery bank’s SOC is higher than SOCmin; otherwise, the DG will cover the net load. – The minimum output power of the DG is Pmin_gen. If Pmin_gen is higher than the net load, the excess power will be used to charge the battery bank. As shown in Table 3, in all cases, the optimal strategy for SOCmin was 50% (the minimum value allowed, considering the results of Section 4.1). This is because higher values for SOCmin would cause less energy to be available from the battery bank during the day. In addition, Pmin_gen was 4000 W (57% of rated power) or higher in all cases; that is, the values were much higher than the minimum output power recommended by the manufacturer. This fact was due to the fact that, at low loads, the specific fuel consumption is higher and both the O&M costs and ageing of the DG are higher, affecting the total operating cost of the hybrid system during the day. For all the days studied except 11 July, the total cost expected for the optimal strategy using the forecast values (Table 2, Column

174

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Hourly irradiaon (kWh/m2)

Hourly irradiaon (kWh/m2) Forecast

1.2

Measured

Forecast

0.8

Measured

0.7

1

0.6 0.8

0.5 0.4

0.6

0.3

0.4

0.2 0.2

0.1 0

0 0:00

12:00

0:00

9 JULY

12:00

0:00

10 JULY

12:00

0:00

16 OCT.

11 JULY

Hourlywind speed (m/s)

12:00

0:00

17 OCT.

12:00

18 OCT.

Hourlywind speed (m/s) Forecast

8.0

0:00

12:00

Measured

Forecast

9.0

7.0

8.0

6.0

7.0

Measured

6.0

5.0

5.0

4.0

4.0

3.0

3.0

2.0

2.0

1.0

1.0

0.0

0.0 0:00

12:00

0:00

9 JULY

12:00

0:00

10 JULY

12:00

11 JULY

Hourlytemperature(ºC) Measured

30.0 25.0 20.0 15.0 10.0 5.0 0.0 12:00

0:00

9 JULY

0:00

16 OCT.

12:00

0:00

17 OCT.

12:00

0:00

10 JULY

Forecast

20.0 18.0 16.0 14.0 12.0 10.0 8.0 6.0 4.0 2.0 0.0

35.0

0:00

12:00

12:00

18 OCT.

Hourlytemperature(ºC) Forecast

40.0

0:00

12:00

0:00

11 JULY

Hourly load (W)

12:00

0:00

16 OCT.

12:00

Measured

0:00

17 OCT.

12:00

18 OCT.

Hourly load (W) Forecast

7000

Measured

Forecast

8000

Measured

7000

6000

6000

5000

5000

4000

4000 3000

3000

2000

2000

1000

1000 0

0 0:00

12:00

9 JULY

0:00

12:00

10 JULY

0:00

12:00

11 JULY

0:00

12:00

16 OCT.

Fig. 5. Forecasts and measured values.

0:00

12:00

17 OCT.

0:00

12:00

18 OCT.

175

R. Dufo-López et al. / Energy Conversion and Management 134 (2017) 167–177 Table 3 Cost comparison of the optimal daily control strategy, the optimal annual strategy and the LF strategy for several days. Day

Optimal daily strategy a

(a) Ctotal for forecast values and optimal daily strategy (€)

(b) Ctotal for measured values and optimal daily strategy (€)

% Error: (a-b)/b100

(c) Ctotal for measured values and optimal annual strategy (€)

(d) Ctotal for measured values and LF strategy (€)

9 July

Pmin_gen = 5000 W Plimit_discharge = 3500 W Pmin_gen = 5000 W Plimit_discharge = 3500 W Pmin_gen = 4000 W Plimit_discharge = 3500 W Pmin_gen = 6000 W Plimit_discharge = 3500 W Pmin_gen = 4000 W Plimit_discharge = 3500 W Pmin_gen = 4000 W Plimit_discharge = 3500 W

24.24

25.13

3.5

27.19

32.29

23.32

24.61

5.2

26.56

32.82

26.22

24.63

6.5

25.24

27.83

18.55

21.35

13.1

23.15

34.28

20.73

24.28

14.6

25.47

35.72

23.3

24.61

5.3

25.7

35.72

10 July 11 July 16 Oct. 17 Oct. 18 Oct. a

In all cases, the optimal values for the rest of the control variables are Pcritical_gen = 7100 W (maximum load) and SOCstp_gen = SOCmin = 50%.

Table 4 Cost savings using the optimal daily control strategy compared to other strategies.

9 July 10 July 11 July 16 Oct. 17 Oct. 18 Oct.

Cost savings using optimal daily control compared to optimal annual control strategy (%) [0-(b-c)/c100]

Cost savings using optimal daily control compared to the LF strategy (%) [0-(b-d)/d100]

7.6 7.3 2.4 7.8 4.7 4.2

22.2 25.0 11.5 37.7 32.0 31.1

Table 5 Limit value (to obtain LF as the optimal strategy: Pcritical_gen = 0 and Plimit_discharge P maximum load) for the most important parameters that affect the optimisation of the daily control strategy for 10 July. Parameter

Limit value

Min. or Max.

PrBAT ZIEC Prfuel PrO&M LifeGEN PrGEN

21,600 € (250 €/kW h) 1500 cycles 0.97 €/L 1.8 €/h 4000 h 46,000 €

Max. Min. Min. Min. Max. Min.

4.3. Sensitivity analysis a) was lower than the same cost using actual measured values (Table 2, Column b). This was largely because, for these days, the forecast values for the hourly wind speeds were higher than the measured values. Cost savings from 4.2 to 7.8% (Table 4) were obtained by comparing the total cost of the optimal daily strategy using actual measured values (Table 2, column b) to the total cost of the optimal annual strategy (Table 2, column c). Cost savings from 11.5% to 37.7% (Table 4) were obtained by comparing the total cost of the optimal daily strategy using measured values (Table 2, column b) to the total cost of the LF control strategy (Table 2, column d). The simulation of the optimal control strategy for each day (9–11 July) using forecast values is shown in Fig. 6.

The optimal values for the set points of each day’s control variables depend on many parameters (cost of the battery bank, cost of the diesel generator, cost of the fuel, O&M cost of the diesel, number of IEC cycles of the battery bank, expected diesel lifetime, internal parameters of the battery as resistance, remaining capacity, etc.). The most important parameters were modified to analyse their influence in the optimisation of the control strategy. Each parameter was modified until the optimal control strategy for each day was the LF strategy (Pcritical_gen = 0 and Plimit_discharge P maximum load), fixing the rest of the parameters to the values used in Section 4.2. Table 3 gives the limit value (i.e., the minimum or maximum value needed to obtain LF as the optimal strategy) for the most important parameters in the optimisation of the daily control strategy, using the case of 10 July.

SOC

Power (W)

1

8000

SOC real 10 July, 0 h

6000

SOC real 11 July, 0 h

0.9 0.8

4000

0.7 0.6

2000

0.5

0

0.4

2000-

0.3 0.2

400060000:00

0.1 0

6:00

12:00

18:00

0:00

6:00

9 JULY Load

12:00

18:00

0:00

6:00

10 JULY PV

Wind T.

Diesel

12:00

18:00

11 JULY Bat. Charge

SOC

Fig. 6. Optimal control strategy for each day (9–11 July) using forecast values.

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Table 5 shows that a low reduction in PrBAT or a low increment in either ZIEC or Prfuel (compared to values used in Section 4.2) led to the LF strategy being optimal. However, the DG parameters PrO&M, LifeGEN and PrGEN needed very high variation (much worse than for the values used in Section 4.2) to obtain the LF strategy. Similar results were obtained for the other the days. 5. Conclusions This work presents a method for the optimisation of the daily operation of a hybrid PV-wind-diesel-battery system with a MPC. The MPC utilises forecasts for the hourly load and weather forecasts for hourly wind speed, irradiation and temperature in the physical location of this hybrid system. The objective is to minimise the hybrid system’s total operating cost, which includes the diesel fuel cost, the DG’s O&M costs, the proportional battery ageing cost and the proportional DG ageing cost. As an example, the method is applied to a hybrid system in Spain for six days; the control strategy was optimised for each day. The results of the studied example showed that the optimal daily control strategy achieved a cost savings of up to 7.8% relative to the annual optimal strategy (only one of the six days had no cost savings). A comparison with the cost of the LF strategy showed that the optimal daily control strategy saved up to 37.7%. Sensitivity analysis showed that, when the rest of the parameters are fixed, if the battery acquisition cost is 250 €/kW h or lower, the battery number of IEC cycles is 1500 or higher, or the price of fuel is 0.97 €/L or higher, then the optimal control strategy is the LF strategy. DG parameters such as O&M, acquisition cost and lifetime have a very low impact on the optimal control strategy, as the values must be much worse than the typical ones to indicate that the LF strategy is the optimal one. Acknowledgments The authors would like to thank the Ministerio de Economia y Competitividad of the Spanish government for supporting this research under Project ENE2013-48517-C2-1-R, Project ENE201348517-C2-2-R and the European Union’s ERDF funds. References [1] Maatallah T, Ghodhbane N, Ben Nasrallah S. Assessment viability for hybrid energy system (PV/wind/diesel) with storage in the northernmost city in Africa, Bizerte, Tunisia. Renew Sustain Energy Rev 2016;59:1639–52. http://dx. doi.org/10.1016/j.rser.2016.01.076. [2] Muselli M, Notton G, Louche A. Design of hybrid-photovoltaic power generator, with optimization of energy management. Sol Energy 1999;65:143–57. http:// dx.doi.org/10.1016/S0038-092X(98)00139-X. [3] Akikur RK, Saidur R, Ping HW, Ullah KR. Comparative study of stand-alone and hybrid solar energy systems suitable for off-grid rural electrification: a review. Renew Sustain Energy Rev 2013;27:738–52. http://dx.doi.org/10.1016/j. rser.2013.06.043. [4] Dufo-López R, Pérez-Cebollada E, Bernal-Agustín JL, Martínez-Ruiz I. Optimisation of energy supply at off-grid healthcare facilities using Monte Carlo simulation. Energy Convers Manage 2016;113:321–30. http://dx.doi.org/ 10.1016/j.enconman.2016.01.057. [5] Bortolini M, Gamberi M, Graziani A, Pilati F. Economic and environmental biobjective design of an off-grid photovoltaic-battery-diesel generator hybrid energy system. Energy Convers Manage 2015;106:1024–38. http://dx.doi.org/ 10.1016/j.enconman.2015.10.051. [6] Dufo-López R, Bernal-Agustín JL, Yusta-Loyo JM, Domínguez-Navarro JA, Ramírez-Rosado IJ, Lujano J, et al. Multi-objective optimization minimizing cost and life cycle emissions of stand-alone PV-wind-diesel systems with batteries storage. Appl Energy 2011;88:4033–41. http://dx.doi.org/10.1016/j. apenergy.2011.04.019. [7] Shezan SA, Julai S, Kibria MA, Ullah KR, Saidur R, Chong WT, et al. Performance analysis of an off-grid wind-PV (photovoltaic)-diesel-battery hybrid energy system feasible for remote areas. J Clean Prod 2016;125:121–32. http://dx.doi. org/10.1016/j.jclepro.2016.03.014. [8] Salas V, Suponthana W, Salas RA. Overview of the off-grid photovoltaic diesel batteries systems with AC loads. Appl Energy 2015;157:195–216. http://dx. doi.org/10.1016/j.apenergy.2015.07.073.

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