Modified Electric System Cascade Analysis for optimal sizing of an autonomous Hybrid Energy System

Energy 116 (2016) 1374e1384

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Modified Electric System Cascade Analysis for optimal sizing of an autonomous Hybrid Energy System Hassan Zahboune a, *, Smail Zouggar a, Jun Yow Yong b, Petar Sabev Varbanov b, Mohammed Elhafyani a, Elmostafa Ziani a, Yassine Zarhloule a a

Laboratory of Electrical Engineering and Maintenance e LEEM, University Mohammed 1st, High School of Technology, Oujda, Morocco } Centre for Process Integration and Intensification e CPI2, Research Institute of Chemical and Process Engineering e MUKKI, Faculty of Information Technology, University of Pannonia, Egyetem u. 10, 8200, Veszpr em, Hungary

b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 15 December 2015 Received in revised form 14 July 2016 Accepted 19 July 2016

Ensuring sufficient generation for covering the power demand at minimum cost of the system are the goals of using renewable energy on isolated sites. Solar and wind capture are most widely used to generate clean electricity. Their availability is generally shifted in time. Therefore, it is advantageous to consider both sources simultaneously while designing an electrical power supply module of the studied system. A specific challenge in this context is to find the optimal sizes of the power generation and storage facilities, which would minimise the overall system cost and will still satisfy the demand. In this work, a new design algorithm is presented minimising the system cost, based on the Electric System Cascade Analysis and the Power Pinch Analysis. The algorithm takes as inputs the wind speed, solar irradiation, as well as cost data for the generation and storage facilities. It has also been applied to minimise the loss of power supply probability (LPSP) and to ensure the minimum of the used storage units without using outsourced electricity. The algorithm has been demonstrated on a case study with daily electrical energy demand of 18.7 kWh, resulting in a combination of PV Panels, wind turbine, and the batteries at minimal cost. For the conditions in Oujda city, the case study results indicate that it is possible to achieve 0.25 V/kWh Levelised Cost of Electricity for the generated power. © 2016 Elsevier Ltd. All rights reserved.

Keywords: ESCA Pinch analysis Hybrid system Power pinch analysis and hybrid cascade table

1. Introduction In a Hybrid Energy System (HES), it is important to improve the system reliability by adding storage facilities, at the same time minimising the number of batteries because of their high cost and shorter lifetime compared to the other renewable energy technology used in HES. Hybrid systems have the advantage of providing flexibility to the designer and users in choosing the rating of the wind and solar generators, based on particular site's resource availability and load conditions [1]. A set of methods was developed previously to improve the system, to maximise the power produced or decrease the cost of the system (installation and maintenance). Among these, Genetic Algorithm (GA) is used to optimise a hybrid system

* Corresponding author. Tel.: þ212 667 179 140. E-mail address: [email protected] (H. Zahboune). http://dx.doi.org/10.1016/j.energy.2016.07.101 0360-5442/© 2016 Elsevier Ltd. All rights reserved.

in the Palestinian Territories. The objective function minimises the Cost of Energy production while covering the load demand with a specified value for the loss of load probability (LLP) [2]. Particle Swarm Optimization (PSO) has been widely applied to the optimisation problems in a dispatch-coupled way and derives the optimal size of battery for systems with different penetration levels of renewables [3]. Akbar et al. [4] have presented a comparison between a set of three well-known heuristic algorithms: particle swarm optimisation (PSO), tabu search (TS) and simulated annealing (SA), as well as four recently invented metaheuristic algorithms: improved particle swarm optimization (IPSO), improved harmony search (IHS), improved harmony search-based simulated annealing (IHSBSA), and artificial bee swarm optimisation (ABSO), are applied to the system and the results are compared in terms of the TAC, for the maximum allowable loss of power supply probability LPSPmax is also considered to have a reliable system. Diaf et al. [5] have presented configurations, which can meet the desired system reliability, are obtained by changing the type and size of the

H. Zahboune et al. / Energy 116 (2016) 1374e1384

devices systems. The configuration with the lowest LCE represents the optimal choice. These design techniques can be used for small sites. But for a large site, some the obstacles can be noticed, including the calculation time, the great number of combinations. Power Pinch Analysis (PoPA) method, based on the Pinch Analysis ideas [6] has been applied to set the guidelines for proper Hybrid Power Systems sizing [7]. Conservation, optimisation of the raw materials such as heat, mass, water, carbon, gas, properties and solids during the design process of the networks has been successfully achieved using Pinch Analysis [8]. Ho et al. [9] present a numerical method called the Electric System Cascade Analysis (ESCA). ESCA is developed based on Pinch Analysis principles and useful for designing and optimising systems for non-intermittent power generation based on biomass, biogas, natural gas, diesel, etc., also including energy storage for Distributed Energy Generation (DEG). Despite the advantages of ESCA, there are still several limitations to this approach. The technique assumes that in order to design and size the non-intermittent backup generator, the worst case scenario without intermittent resource is considered. This is only applicable if the system consists of solar PV or solar thermal system. Ho et al. [10] applied the ESCA methodology for designing and optimizing an intermittent DEG system or specifically a stand-alone solar PV system for isolated communities, the new ESCA was applied to optimize a solar PV system for an isolated rural house with daily energy consumption of 5.575 kWh. Rozali et al. [11] developed two new digital tools PoPA (Power Pinch Analysis) known as Power Cascade Analysis (PoCA) and the Storage Cascade Table (SCT). The tools can be used to determine the minimum outsourced electricity supply and the available excess electricity, the maximum storage (e.g. Battery), the battery capacity of the stand-alone system, the amount of electricity demand necessary to be outsourced each time interval and the time interval in which the maximum power occurs. While graphical techniques provide an overview and useful visualisation, numerical tools provide faster and more accurate allocation of power and they enable to set goals for optimisation. Wan Alwi et al. [12] determine the minimum electricity targets via the introduced graphical representation of composite electricity variation with time, providing a useful visualisation tool for energy managers, electrical and power engineers called PoPA. Rozali et al. [13] showed how PoPA can reduce the storage capacity, also accounting for the losses during the electric conversion (DC/DC or AC/DC) and charging/discharging of the battery. Maximising the use of renewables with variable availability, which is frequently a key issue for using renewables, has been studied by Nemet et al. [14]. The main goal of this group of the methodologies is the reduction and possibly minimisation of Greenhouse Gas (GHG) [15] and Nitrogen footprints [16]. GHG footprint contributes to global warming and Nitrogen footprint to both global warming and creating of the haze [17]. In previous work [18], the ratio of the power generation between two sources (PV and wind turbine) were determined according to the climate conditions alone. The ESCA method was applied for the optimal design of hybrid systems taking into account the climatic conditions of the site, to minimise the total storage capacity and the analysis time is 24 h. However, the decision on this ratio should also account for the costs e most notably those for investment and maintenance. This paper presents the modelling and optimization for standalone hybrid solar-wind systems for electrification of a remote area located in the vicinity of Oujda, Morocco. The ratio of solar to wind capture is based on the minimum of the total annualised cost of the system and the climate conditions of the site. The maximum allowable loss of power supply probability and the Power pinch analysis are implemented together to optimise the sizing of the

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hybrid system. For the newly proposed method, a Modified ESCA (MESCA) algorithm is introduced for each system's component with their electrical parameters and discrete based Power Pinch Analysis as a guideline. For performance evaluation, the MESCA method begins with a search of the optimal sizes of the electricity generation and storage facilities, which would minimize the total annual cost (TAC) and will still satisfy the demand, and then to optimize the number of each component (Photovoltaic Panels PVPs, Wind turbines and batteries). The Final Excess of the energy (FEE) and the Total Annual Cost (TAC) are considered as the objective functions and the MESCA is employed to find the optimal number of the system components, but take in consideration the climate conditions for each remote area chosen. 2. Methodology When two or more forms of energy supply are used in combination, the energy system is referred to as a hybrid one. In the current article two forms of renewable energy are considered e solar and wind. The idea of combining them is to provide increased system efficiency as well as greater balance in energy supply. 2.1. Hybrid Energy System The system in this work uses a number of components e wind turbines, PV Panels, converters (DC/DC, AC/DC and DC/AC), DC bus and an electricity storage unit (Fig. 1). The combination of the two renewable types allows them to complement each other in terms of capture in time and facilitate the efficient operation of the system. Photovoltaic and wind generators can work together to meet the load demand with a voltage adaptation depending on the load. The MESCA method is applicable to whatever the chosen architecture is. For the specific cases, the appropriate conversion efficiencies should be specified. The connection of all energy sources to a DC bus simplifies power management, based on the fractions of the energy production from renewable sources (PV system 62% and wind system 38%). When the capture of renewable energy (solar and wind) is in excess, the remainder after meeting the load demand is used to charge the battery, until the latter it is fully charged. In contrast, when energy generation is insufficient, the battery releases power to help covering the load requirements, until storage is exhausted. 2.2. Modified Electric system cascade analysis Based on Power Pinch Analysis, the presented method is an extended adaptation of the ESCA [10] method for isolated systems relying on renewables. The first step of MESCA requires the extraction of relevant data for analysis. The list of data includes time period of analysis (design horizon), hourly energy demand, hourly wind speed and solar radiation, type of the PV panel, power generation capacity of a single solar PV module, solar PV module

DC bus PV Arrays

DC/DC

DC/DC

Batteries

Wind turbine

AC/DC

DC/AC

Load Demand

Fig. 1. Overall configuration of the system.

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efficiency, wind turbine power capacity, converters efficiency. The energy sources are connected to the DC bus via the generators. The energy losses during conversion, charging and discharging of the battery are accounted for. 2.2.1. Determination the share of RE The first step of the new algorithm concerns the decision on the share of each renewable source in the generated electricity, minimizing the system cost and accounting for seasonality. The shares of power generation from solar (PV) and wind are expressed as fractions of the overall power generation at any given time (Eq. (1)):

f PV þ f W ¼ 1

(1)

Where fpv ¼ 1 corresponds to power generation by PV panels only, while fw ¼ 1 corresponds to completely wind turbine based power generation. Fig. 2 illustrates the procedure for this step. The inputs to the procedure include the solar irradiation, wind speed, the PV panel characteristics: area and efficiency, the wind turbine characteristics: the rated power of the wind turbine, cut-in and cut-out speed values as well as rated speed of the wind turbine, the load demand, the cost of the components, the installation and maintenance costs, cost of the balance-of-system (BOS) components, system lifetime and an interest rate. Specifications for the battery types and performance are also provided. For every time step with duration of 1 h, the algorithm starts by calculating the generated power by a single wind turbine, EW(t) and a single PV panel, EPV(t), using their electrical performance characteristics and seasonal site conditions for each hour. The demand load at that hour, EL(t) is determined as well. Next, the total amounts for all time steps of the demand load EL,A are calculated by using Eq. (2), the generation by a single PV panel (EPV,A) Eq. (3) and wind turbine (EW,A) by Eq. (4) in one year.

EL;A ¼

T X

EL ðtÞ

(2)

t¼1

EPV;A ¼

T X

EPV ðtÞ

(3)

EW ðtÞ

(4)

t¼1

EW;A ¼

T X t¼1

Start

Analysis and step time, models and costs parameters, climat data and load profil. Calculation of NPV, NW and Csys for each fraction step Selection operation : Minimum CTACS Optimal configuration Npv, Nw, fw and fpv END Fig. 2. Procedure for determining the Ratios of the PVP and Wind turbine.

In Eq. (5), for each step, for fw between 0 and 1, with an increment of 0.01, the numbers of the PVPs and wind turbines are calculated depending on the load, the quantity of energy generated by the devices and their respective fraction. After the results are rounded up to the nearest integers. The fraction fpv is calculated from to Eq. (1).

 EL;A NK ¼ f k  ½; k2fPV; WTg EK;A

(5)

For each step of varying fw, using the PVP and wind turbine numbers, NK(fw), the Total Cost of the System CTCS(fw) is calculated, taking into account the cost of components, maintenance, BOS and the cost of installation (Eq. (6)):

X

CTCS ðf w Þ ¼

  N‘K ðf W Þ$ CC;K þ CBos;K þ CM;K þ CI;K

(6)

K2fPV;WTg

The objective function of the model is to minimise the Total Annualised Cost of the System (TACS) as defined in Eq. (7), thus selecting the corresponding values of the PVP and wind turbine numbers:

Min CTACS ¼ Min½CTCS ðf W Þ  CRFÞfw2½0;1

(7)

CRF is the Capital Recovery Factor (Eq. (8)):

CRF ¼

i 1  ð1 þ iÞL

(8)

Where L: System lifetime i: discount rate 2.2.2. Sizing using the MESCA method The second part of the proposed algorithm is intended to perform the sizing of the system components for the specified demands and availability of solar and wind energy, over the specified design horizon. The first step of MESCA requires specifying the relevant data for analysis. The data requirements include: design horizon (T); hourly energy demand; average hourly solar radiation; PVP data e type, power generation capacity and efficiency of a PV module; hourly wind speed values; wind turbine power capacity and power characteristics; inverters efficiency; type of the battery unit as well as charging and discharging efficiency, and its Depth of Discharge (DOD); life span of the wind turbines, PVP and battery components, number of the days of autonomous power system operation (expected days of lacking solar or wind power); the cost of components e for purchase, maintenance, BOS and installation and the setting for the shares of PV and wind power generation calculated by the first procedure described in Section 2.2.1. The design horizon T is a user-specified parameter. During the design horizon the user demands and the renewables availability vary and the variations are used to adjust the sizes of the system components e including the energy capture and storage ones. It is assumed that the user demands and the harvested renewable energy will repeat in a cycle for the specified system life. The Power Pinch Analysis is the guideline technique to design a system with minimum electricity storage. The numbers of PVPs and wind turbines are determined first, minimising the needs of the battery storage, using state of charge within the various time steps (time slices, periods), while meeting the load energy demand. The number of the batteries is determined at the end of the algorithm. The MESCA method is based on instantiating the hybrid Cascade Table (HCT)., where each row represents one-time step of the analysis and each column represents a system property. Thirteen

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columns (Table 4 and Table 5) are used. They are described next. Column 1: The time value (h) for the current step. Column 2: the wind speed v (m/s). Column 3: the generated power by a single wind turbine during the current time step [19]:

EW ðtÞ ¼

8 v  vin > > Pr > > < v  vout > > > > :

vin < vðtÞ < vr

Pr

vr < vðtÞ < vout

0

vðtÞ < vin or vðtÞ > vout

(9)

Column 4: the total generated power by Nw wind turbines during the current time step:

EW;T ðtÞ ¼ NW  EW ðtÞ

(10)

The initial value of NW is an output of the first procedure in Fig. 2. Column 5: the solar irradiation Rs(t). Column 6: power generated by a single PPV during the current time step:

EPV ðtÞ ¼ hPV  APV  RS ðtÞ

(11)

Column 7: the total generated power by NPV PVPs in during the current time step:

EPV;T ðtÞ ¼ NPV  EPV ðtÞ

(12)

The initial value of NPV is the result of the first process Fig. 2. Column 8: Power (load) demand EL(t). Column 9: Balance between the overall power generation and the demand during the current time step Er(t):

Er ðtÞ ¼ EPV;T ðtÞ  hDC=DC þ Ew;T ðtÞ  hAC=DC EL ðtÞ=hwr

(13)

Column 10: if Er(t) > 0 Wh, the generated power is used to charge the batteries ChBat.

ChBat ðtÞ ¼ Er ðtÞ  hch

(14)

Otherwise, the value in this cell is set to zero. Column 11: if Er(t) < 0 Wh, the energy discharge from the batteries DBat(t).

DBat ðtÞ ¼

Er ðtÞ

hDis

(15)

EN ðtÞ ¼ ChBat ðtÞ þ DBat ðtÞ

accumulation at the end of the design horizon represents the final surplus or deficit of energy.

Eacc ðt ¼ 0Þ ¼ minEacc ðtPinch Þ

FEE  100 EBat

(16)

Column 13: the accumulation of electrical energy in the storage units calculated from Eq. (17):

Eacc ðtÞ ¼ Eacc ðt  1Þ þ EN ðtÞ

(17)

The procedure starts with an initial state of the accumulation Eacc(t ¼ 0) ¼ 0 Wh by assuming no power usage from the battery, this procedure called Sk. During the variation of energy accumulation, it must not have any negative value. If a negative value of the battery charge level is encountered for any of the time steps, this indicates that power has to be drawn from the battery. The most negative value among all steps is taken as the initial state of the batteries (Eq. (18), and then the calculation of Eacc(t) is repeated, in order to obtain a feasible HCT and this procedure called Sk’. the difference between the two procedure is just the initial state of the batterie. After completing the calculation of Eacc(t), the energy

(18)

The procedure for MESCA takes initial values for the PVPs and wind turbines calculated by the first procedure previously described. The HCT is constructed and calculated, ensuring that there are no negative storage values resulting from Eq. (17). The calculation progress is illustrated in Fig. 3. It shows a typical variation of the accumulated electrical energy with time. For the specific case, at t ¼ 0 there is an initial value of the electrical storage, whose value is decreased during the first time steps. At t ¼ tPinch, the battery charge level becomes zero, thus defining a Pinch point, The latter represents the minimum energy stored and takes place at the condition of minimum energy availability in the system. Larger storage capacity and storage levels would be unused and would be potentially wasted. Therefore, the electrical energy storage at t ¼ tPinch is adjusted to be zero. Afterward, the accumulated electrical energy storage with time varies until the end of the procedure previously described, without any negative value and a generally increasing trend. At t ¼ T, the accumulated electrical energy Eacc(t ¼ T) minus the initial electrical energy Eacc(t ¼ 0) is called the Final Excess of Energy (FEE) Fig. 3. According to Ho [10], the power generator is oversized if FEE is larger than the initially stored electrical charge. Similarly, it is undersized if FEE is smaller than the initially stored electrical charge. This gives rise to defining a criterion for appropriate sizing of the power generators in the designed system. On the one hand, if the generator facilities are undersized, this leads to the potential need to import power from outside the system. This would conflict with the objective of obtaining a self-sufficient power system, this making the resulting design infeasible. On the other hand, if the generator facilities are oversized, then this leads to excessive investment and operating costs. Therefore, an interval for appropriate sizing is defined as follows, using the FEE value as the indicator. The lower bound on FEE is the battery charge at t ¼ 0. This ensures a feasible system design. The upper bound on the FEE is defined by a user-specified parameter, termed Maximum Final Energy Excess (MFEE). The MFEE was calculated using Eq. (19), in the current work, a value is used as MFEE ¼ 10% of the total battery capacity, leaving the freedom to other users to specify their own values based on economic analysis.

MFEE ¼

Otherwise, the value in this cell is set to zero. Column 12: the net electricity surplus/deficit EN(t).

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Fig. 3. The simple Eacc during the time.

(19)

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FEE for the first year of operation must be within this appropriate sizing interval. By implication, the cumulative electricity stored for any follow-up years cannot have negative value, and FEE values for follow-up years also should be within the appropriate sizing interval. If this condition is met, then the design procedure is finished. In the cases when the appropriate sizing criterion is not met, the algorithm will vary the numbers of the wind turbines and/or the PVPs, using the ratio between fW and fPV as a guideline. The ratio between fW and fPV and their optimal values are the result of the first algorithm (Fig. 2). According to the value of the Final Excess of Energy, there are several scenarios for varying the number of power generators. They are illustrated in Fig. 4, they differ by the best fit of the combinations of the components within the gap formed by the FEE. Whatever variation Eacc (t), four points are very important to know: ➢ Eacc(t ¼ 0): the initial amount of energy stored in the storage units for not having any negative value. ➢ Eacc(t ¼ tpinch): Energy stored in the storage units is completely released and discharged. ➢ Eacc(max): the maximum amount of energy in the storage units, this value used to calculate the number of batteries. ➢ Eacc(t ¼ T): the amount of energy stored in the storage units at the end of the analysis. This variation is going to take any of the scenarios, the first scenario with a high value of the FEE present the bad scenario, the best scenario and near to the optimal configuration is the scenario 4. Scenario 1. If FEE is larger than or equal to the generated power by a single wind turbine and a single PVP with the losses of the converters during the design horizon, then the numbers of PVP and wind turbines are changed (the numbers should be increased or decreased) according and round up to the nearest integer Eq. (20) and Eq. (21). Scenario 1 is shown in Fig. 4 by S1.

3

(20)

T

3

2

7ðEacc ðTÞ  Eacc ð0ÞÞ  f PV 6 NPVnew ¼ NPV  5 P 4 EPV  hch  hdc=dc

3

2

7 ðEacc ðTÞ  Eacc ð0ÞÞ 6 NWnew ¼ NW  5P 4 EPV  hch  hac=dc

(22)

T

Scenario 3. If FEE is larger than the generated power by a single PVP with the losses of the converter (DC/DC) during the design horizon, but too small to accommodate a wind turbine, then the PVP number is changed (the PVPs number should be increased or decreased) and round up to the nearest integer Eq. (23), Scenario 3 is shown in Fig. 4 by S3.

3 NPVnew

2

7 ðEacc ðTÞ  Eacc ð0ÞÞ 6 ¼ NPV  5P 4 EPV  hch  hdc=dc

(23)

T

Scenario 4. If FEE is smaller than the generated power by a single PV panel with the losses of the converter (DC/DC) during the design horizon, then the number of all power generators including PV panels and wind turbines is fixed and considered final. For more precision, the area of one the selected PV modules should be changed (the area should be increased or decreased) according to Eq. (24), Scenario 4 is shown in Fig. 4 by S4.

APV;new ¼ APV  P T

Eacc ðTÞ  Eacc ð0Þ Rs ðtÞ  hPV  hch  hdc=dc

(24)

The complete adjustment procedure is shown in Fig. 5. 2.3. Sizing of the battery

2

7ðEacc ðTÞ  Eacc ð0ÞÞ  f W 6 NWnew ¼ NW  5 P 4 EW  hch  hac=dc

design horizon, but too small to also fit a PVP, because the generated power by a single wind turbine is high compared to the generated power by a single wind PV panel, the remaining energy will be used to resize the PV Panel (Scenario 3), Then the wind turbine number is changed (the wind turbines number should be increased or decreased) and round up to the nearest integer Eq. (22). Scenario 2 is shown in Fig. 4 by S2.

(21)

T

Scenario 2. If FEE is larger than the generated power by a single wind turbine with the losses of the converter (AC/DC) during the

The battery bank is generally of the lead-acid type, as it offers a set of advantages [20]. Discharge and recharge cycles do not significantly affect energy storage capacity. It also offers a safety margin over a wet acid battery, since acid is contained in a gel and cannot be easily spilled [21]. The size of the battery can be obtained from Column 13 of HCT. First, the largest value in the column is selected, denoted as Eacc(max). It represents the largest electricity charge in the battery bank among all time steps, as required by the demand. At the same time, this is the minimum battery bank capacity in terms of demand. The selected capacity value has to be increased, to account for the Depth Of battery Discharge (DOD). The total energy in batteries including DOD is calculated by Eq. (25):

EBat ¼

Eacc ðmaxÞ DOD

(25)

Then, as a result, the number of the batteries is calculated by Eq. (26) and rounded up to the nearest integer.

 NBat ¼

 Eacc ðmaxÞ  Ld IBat  VBat  DOD

(26)

The initial battery state accounting for DOD is estimated as the sum of the initial battery charge from HCT and the battery remainder after maximum discharge: Fig. 4. Set scenarios for changing the number of power generators.

EBat;in ¼ Eacc ðt ¼ 0Þ þ EBat  ð1  DODÞ

(27)

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Fig. 5. Flowchart of the MESCA method with the 4 scenarios.

The Logical block diagram [22] for management the battery energy is shown in Fig. 6. When SOC is below SOCmax and EN(t)>0Wh, the energy excess is stored in battery up to SOC ¼ SOCmax. When the state of the battery is above SOCmin and EN(t)<0Wh, energy previously stored is used to support the lack of energy (battery discharging) as far as SOC¼ SOCmin. A switch is implanted between the power sources and the load, to cut the connection in the following cases:

always satisfied. Yang et al. [24] used LPSP to optimise the standalone PVewind hybrid system using genetic algorithm minimising the annualised cost. For a given period LPSP is defined by Eq. (28):

PT LPSP ¼

t¼0

PT

EDeficit ðtÞ

t¼0

➢ The surplus will be conducting to the auxiliary loads (for example: pump water) when the state of charge is equal than the SOCmax and EN(t) > 0 Wh. ➢ All load will be off for the state of charge is equal than the SOCmin and EN(t) <0Wh, but If all MESCA conditions are respected, we cannot run across this two situations.

EL ðtÞ

(28)

Where Edeficit (t): the deficit of energy supply during the time step, when the generated energy not satisfied to meet the power demands. One of the objectives of the optimisation procedure is to discover combinations of elements that give an LPSP lower than the maximum allowed by the user. The following formula to calculate the Levelised Cost of Energy (LCE).

2.4. Power reliability model based on LPSP concept LPSP is defined as the probability that an insufficient power supply when the hybrid system (solar, wind and battery storage) is unable to meet the load demand [23]. LPSP ¼ 1 means that the load will never be satisfied and LPSP ¼ 0 means that the load will be

C LCE ¼ PT TACS t¼0 EL ðtÞ

(29)

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6

Battery charging

NO

Wind speed (m/s)

Start

SOC >=SOC min

All load off

SOC =SOC max

YES

NO NO

SOC=SOCmin NO

Nt >0

4

3 2 1

0

SOCmin >SOC >SOC max

1

YES

NO

YES Battery discharging

Nt<0 NO

4

7

Jan May Sep

Nt<0 YES

YES Battery charging

5

10

13

16

Time ( Hour) Feb Jun Oct

19

Mar Jul Nov

22 Apr Aug Dec

Fig. 8. Hourly solar radiation for an average day in month for all year.

SOC=SOCmin

SOC=SOCmax

1200 Load auxiliare

Fig. 6. Logical block diagram for management the battery energy.

EL(Wh)

1000 Load off

800

600 400 200

3. Case study

0

The developed methodology has been applied to design a standalone hybrid PV/wind system, in order to power supply residential, with daily electrical energy demand of 18.7 kWh, located in the city Oujda Morocco (latitude: 34 410, longitude 1 540 ). The wind and solar power are assumed to be constant during the time step (1 h in this study). Various solar radiations, wind speeds values and the load demand values are shown in Fig. 7, Fig. 8 and Fig. 9. This data set represents the inputs to the MESCA algorithm (Fig. 5). MATLAB environment is used to implement and programming the proposed methodology. The exploited site parameters, in this case, are shown in Table 1: For constructing the hybrid cascade table, the data for the column 2, the column 5 and the column 8 are presented in Figs. 7e9, respectively. LPSP must be equal to 0 for MESCA result based the average hourly for each month (1 month / 24 h) throughout the year

1,00

Rs (kW/m2 )

0,80 0,60 0,40

0,20 0,00

1 2 3 4 5 6 7 8 9 101112131415161718192021222324

Jan May Sep

Feb Jun Oct

Time ( Hour)

Mar Jul Nov

Apr Aug Dec

Fig. 7. Hourly wind speed for an average day in month for all year.

1

4

7

10

13

16

19

22

Time ( Hour) Jan May Sep

Feb Jun Oct

Mar Jul Nov

Apr Aug Dec

Fig. 9. Hourly load demand for an average day in month for all year.

(T ¼ 24*12 ¼ 288 h) for solar radiation, wind speed, and load demand. In the first step, the ratio of the two energy sources has been calculated according to site geometric climates and the system cost, with the objective of meeting electricity demand. The obtained result of the total annualised cost of the system for every fraction step is shown in Fig. 10. The numbers of the PVPs and wind turbines are calculated depending on the load and the quantity of energy generated by the devices and the ratio results are present in Table 2. The result of the first procedure is: Nw ¼ 16, NPV ¼ 65 and FEE ¼ 444 kWh. In this case, Fig. 11 shows the accumulation of electrical energy in the storage unit. Table 3presented the MESCA results from all the scenarios of the case study. The MESCA process is repeated, until finding an optimal result. The minimisation process of the first case in the tables had been computed as follows: ➢ (Nw ¼ 16, Npv ¼ 65) is oversized because FEE >SEpvþ SEw, for this are used Eq. (20) and Eq. (21), to calculate the new PVP and wind turbine numbers. ➢ (Nw ¼ 4, Npv ¼ 24 with initial value) is undersized sizing because Eacc(t ¼ T) << Eacc(t ¼ 0), for this Eq. (20) and Eq. (21) are used to add PV panels and wind turbines.

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Table 1 Required data of the system. Period of analysis Time step Characteristics of PVP Type of solar PV A

1y 1h Mono-crystalline silicon 1.07 m2 12% 120 W 110 V 10 V 15 V

hPV Peak power of a single solar PV module CC.PV Cm,PV CI,PV Characteristics of Wind turbine Pr vin vout vr Cc.w Cm,w CBos

1 kW 2.5 m/s 13 m/s 11 m/s 1300 V 80 V 150 V 98% 95% 95% 95% 5% 25 y 25 y

hWr hDC/DC hAC/DC hDC/AC

i LPV LW Characteristics of the Battery IBat VBat DOD

Fig. 11. The accumulation of electrical energy in the storage unit for Nw ¼ 16 and Npv ¼ 65.

210 Ah 24 V 70% 90% 90% 620 V 430 V 5y

hch hdch Cc,bat Cr,bat LBat

Fig. 10. The total annualized cost of the system for different fw step (0 < fw < 1).

Table 2 Required data to star MESCA method. NW

NPV

Fpv(%)

Fw(%)

LPSP(%)

FEE(kWh)

CTACS(V/y)

16

65

62

38

0

444

2360

➢ (Nw ¼ 5, Npv ¼ 26 with value initial) is near to optimal sizing because SEw > FEE >SEpv, for this Eq. (23) is used to calculate the new number of PVPs. ➢ (Nw ¼ 5, Npv ¼ 25 with initial value) is the optimal solution with Eacc(T)zEacc(t ¼ 0) ¼ 3,733Wh. The difference between S3 and S30 is the initial energy in the storage units. Scenario S3 contains without initial energy in the

storage units Eacc(t ¼ 0) ¼ 0 kWh. But the scenario S30 , it is the opposite during this configuration, the initial state of the storage units is Eacc(t ¼ 0) ¼ 3,351 kWh. The same for S4 with Eacc (t ¼ 0) ¼ 0 kWh but S40 with Eacc (t ¼ 0) ¼ 3,733 kWh. As a result, the battery Eacc(max) ¼ 25.5 kWh, the optimal configuration includes 25 PVPs, 5 wind turbines, and 8 batteries. The total generated power flows by PVPs and the wind turbines during the design time are presented in Fig. 12. Fig. 13 shows the accumulation of electrical energy in the storage unit (NW ¼ 5 and NPV ¼ 25 with and without the initial value of the battery). The MESCA method has for each month a table showing the energy generated by sources, energy charged and discharged by the battery and the variation of energy storage units. The two tables in the Annex show that the pinch point is located at 8 Am/February, and the maximum of energy stored in the batteries is located at 6 p.m./August. In Fig. 14, the excess energy at the end point represents a small increase of 1.5 kWh. This FEE (1.5 kWh) is equivalent to 4.11% of the total battery capacity with the DOD (36.43 kWh) according to Eq. (19), less the MFEE fixed (10%) in the beginning of the algorithm. Any negative values in the accumulation of the energy would result in LPSP ¼ 0%. Consequently, the captured energy from PV and wind meets the load demand completely. The optimal size of the systems is as follows: NW ¼ 5, NPV ¼ 25 and NBat ¼ 8. Table 4 shows the optimal number of each component and the system costs in detail for the hybrid systems. The annual energy demand for the case study is 7715 kWh/y. LCE, as calculated from Eq. (28), is 0.25 V/kWh and future work should be carried out in order to compare the result of the MESCA method with the result obtained by Homer pro software. Depending on the algorithm results, one can observe that:  The climate condition and economic data influence on the sizing of the system hybrid, each influence in the design of the hybrid system influence in turn on LPSP and TCA. The battery storage capacity has an important effect on LPSP.  The sizing of the system depends on the system reliability. Thus, to meet high reliability (low LPSP), there is a considerable increase in the system size. For small fluctuation of LPSP near to 0%, the TAC increases greatly for small reductions in LPSP.  An increasing number of the PV panels and the wind turbine in the LPSP interval less of 2%, it has a very little influence on the reduction of the LPSP. Decreasing the objective function value during the iterations confirms the performance of MESCA method. It is observed that the MESCA quickly finds the optimum sizing of the hybrid systems.

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Table 3 Various iterations for MESCA method. Sp

NW

NPV

Eacc(t ¼ 0)(Wh)

LPSP(%)

Eacc(t ¼ T)(Wh)

FEE(kWh)

Nbat

CTACS(V/y)

S1 S2 S3 S30 S4 S40

16 4 5 5 5 5

65 24 26 26 25 25

0 0 0 3351 0 3733

0.01 9.3 1.7 0 1.6 0

444 21.87 8.59 11.94 1.6 5.3

444 21.87 8.59 8.58 1.6 1.5

2 4 5 9 8 8

2658 1237 1507 2080 1927 1927

Table 4 Economic analysis results for the hybrid system with NW ¼ 5, NPV ¼ 25 and NBat ¼ 8. Components

Number

Lifetime (y)

Annual cost (V/y)

PV Wind turbine Batteries All system

25 5 8 1

25 25 5 25

257 543 1127 1927

Energy (kWh)

Fig. 12. Generated power by solar PV, wind turbine, demand load in hourly data for 12 months.

Fig. 14. The accumulation of electrical energy in the storage unit.

Eacc without initial value 281 267 253 239 225 211 197 183 169 155 141 127 113 99 85 71 57 43 29 15 1

30 25 20 15 10 5 0 -5 -10

Time (h) Fig. 13. The accumulation of electrical energy in the storage unit.

4. Conclusion In this work, the optimal sizing method has been proposed for autonomous hybrid PV/wind system with battery storage, which uses the Power Pinch Analysis as a guideline. The techno-economic optimisation using MESCA is developed to select the components sizes of the hybrid renewable energy system with battery storage. The optimal configuration and reliability evaluation of the MESCA result are obtained in such a way that to minimise the Total Annualised Cost of the System (TACS), the FEE and the loss of power supply probability. The optimal sizing method of the autonomous hybrid PV/wind system is very sensitive to the change in input data such as climate condition and the constraints fixed by the user. A case study has been performed for the electricity supply of a residential compound located in Oujda, Morocco (latitude: 34 41 0, longitude 1 540 ). To optimally size the hybrid system, different iterations are applied to find the optimum number of each component. The optimal configuration found by MESCA includes NW ¼ 5 and NPV ¼ 25 and NBat ¼ 8 with CTACS ¼ 1927 V/y. The

storage level of the battery bank for optimal configuration is shown in Fig. 14. It can be obtained that FEE ¼ 1.5 kWh, and EBat ¼ 36.4 kWh, calculated from Eq. (25). The performance of the proposed method has been confirmed by the quick convergence of the procedure e as illustrated in the case study. The procedure is simple enough to implement also in spreadsheet software such as MS Excel. The combination of these advantages makes the MESCA tools potentially powerful means for improving the sustainability of cities and remote locations. The proposed methodology can benefit from the visualization advantages of the numerical method. The MESCA method can provide to reduce the use of the renewable energy size and contribute to minimising the system cost. MESCA method is capable of optimising hybrid system consisting two power generators (PV/Wind turbine) with battery storage. For more than two power generators, the user can be fixed the fraction for each power generators, according to electrical parameters of the power generators, climatic conditions, and TAC. An important direction for future work is the method validation with Homer Pro, to optimize renewable energy with pumped storage systems to supply remote areas and the load shedding operations can be included. Acknowledgment The authors would like to acknowledge the EC supported project “Distributed Knowledge-Based Energy Saving Networks” DISKNET, Grant Agreement No: PIRSES-GA-2011-294933.

H. Zahboune et al. / Energy 116 (2016) 1374e1384

1383

Annex

Table 5 HCT for Nw ¼ 5, Npv ¼ 25, NBat ¼ 8 and Eacc (t ¼ 0) ¼ 3733Wh month: February. Col 1

Col 2

Col 3

Col 4

Col 5

Col 6

Col 7

Col 8

Col 9

Col 10

Col 11

Col 12

Col 13

t (h)

v (m/s)

Ew (Wh)

Ew.T (Wh)

Rs (W/m2)

EPV (Wh)

EPV,T (Wh)

EL (Wh)

Er (Wh)

Chbat (Wh)

Dbat (Wh)

EN (Wh)

Eacc (Wh)

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

3.86 3.82 3.74 3.63 3.51 3.40 3.30 3.24 3.31 3.57 3.82 4.08 4.35 4.58 4.70 4.67 4.46 4.33 4.16 4.01 3.88 3.81 3.81 3.82

75.4 72.7 67.4 60.4 52.9 46.3 40.4 37.0 41.0 56.6 72.7 90.6 110.4 128.3 138.0 135.6 118.9 108.9 96.3 85.7 76.7 72.0 72.0 72.7

377 364 337 302 264 231 202 185 205 283 364 453 552 642 690 678 594 545 482 428 384 360 360 364

0 0 0 0 0 0 7 108 289 457 571 602 604 567 434 273 100 7 0 0 0 0 0 0

0 0 0 0 0 0 1 13.9 37.1 58.7 73.3 77.3 77.6 72.8 55.7 35.1 12.8 0.9 0 0 0 0 0 0

0 0 0 0 0 0 22 347 928 1467 1833 1932 1939 1820 1393 876 321 22 0 0 0 0 0 0

240 240 240 240 358 1038 985 1069 1015 1038 626 724 806 1038 985 1038 985 724 895 1069 1015 1069 1015 368

144 131 105 70 72 724 686 475 142 703 1505 1592 1612 1363 1050 493 68 153 402 624 618 697 649 16

130 118 94 63 0 0 0 0 128 633 1355 1433 1451 1227 945 444 0 0 0 0 0 0 0 0

0 0 0 0 91 905 857 593 0 0 0 0 0 0 0 0 85 191 502 780 773 872 811 20

130 118 94 63 91 905 857 593 128 633 1355 1433 1451 1227 945 444 85 191 502 780 773 872 811 20

2171 2288 2382 2446 2355 1451 593 0 128 761 2116 3548 4999 6226 7171 7614 7530 7339 6837 6057 5284 4412 3601 3581

Col 8

Col 9

Col 10

Col 11

Col 12

Col 13

Table 6 HCT for Nw ¼ 5, Npv ¼ 25, NBat ¼ 8 and Eacc (max) ¼ 25.5 kWh month: August. Col 1

Col 2

Col 3

Col 4

Col 5

Col 6

Col 7

t (h)

v (m/s)

Ew (Wh)

Ew.T (Wh)

Rs (W/m2)

EPV (Wh)

EPV,T (Wh)

EL (Wh)

Er (Wh)

Chbat (Wh)

Dbat (Wh)

EN (Wh)

Eacc (Wh)

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

2.13 2.20 2.24 2.23 2.26 2.23 1.97 1.81 1.85 2.02 2.26 2.51 2.75 3.00 3.27 3.56 3.78 3.89 3.61 3.06 2.63 2.36 2.15 2.06

0 0 0 0 0 0 0 0 0 0 0 0 11.4 24.0 38.7 56.0 70.1 77.4 59.1 27.1 6 0 0 0

0 0 0 0 0 0 0 0 0 0 0 2 57 120 194 280 350 387 296 136 29 0 0 0

0 0 0 0 0 14 134 340 560 739 849 902 885 816 656 481 288 114 13 0 0 0 0 0

0 0 0 0 0 1.80 17.20 43.70 71.90 94.90 109.00 115.80 113.60 104.80 84.20 61.80 37.00 14.60 1.70 0 0 0 0 0

0 0 0 0 0 45 430 1091 1798 2372 2725 2895 2841 2619 2106 1544 924 366 42 0 0 0 0 0

296 302 296 302 296 673 660 704 690 686 457 504 605 740 724 740 755 538 664 761 743 761 743 314

330 336 329 335 329 703 322 258 945 1496 2085 2197 2087 1787 1389 919 382 125 407 705 786 832 812 343

0 0 0 0 0 0 0 232 851 1346 1876 1977 1878 1609 1250 827 344 113 0 0 0 0 0 0

412 420 411 419 411 879 402 0 0 0 0 0 0 0 0 0 0 0 509 881 982 1040 1015 429

412 420 411 419 411 879 402 232 851 1346 1876 1977 1878 1609 1250 827 344 113 509 881 982 1040 1015 429

16,104 15,684 15,273 14,854 14,443 13,565 13,162 13,395 14,245 15,592 17,468 19,445 21,323 22,932 24,182 25,009 25,353 25,466 24,957 24,076 23,094 22,054 21,039 20,609

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Nomenclature

Symbols T: End of analysis to prevent Eacc (h) t: Time step (h) i: Interest rate L: System lifetime(y) Lbat: battery lifetime(y) LW: Wind turbine lifetime(y) LPV: PVP lifetime(y) Ck: Total cost of the system(V) CC,W: Initial capital cost of each wind turbine(V) CM,W: Maintenance cost of each wind turbine (V)

CI,W: Installation cost of each wind turbine (V) CC,PV: Initial capital cost of each PVP (V) CM,PV: Maintenance cost of each PVP (V) CI,PV: Installation cost of each PVP (V) CC,bat: Initial capital cost of each battery (V) CI,bat: Installation cost of each battery (V) CBOS: Balance-of-system cost(V) CTCS: Total Cost of the System CTACS: Total Annualized Cost of the System fw: Fraction of the wind turbines power (%) fPV: Fraction of the PVPs power (%) EPV: Power generated by a single PVP during the time step (Wh) EW: power generated by a single wind turbine during the time step (Wh) EL: Power (load) demand during the time step (Wh) EPV,A: Total amount generation by single PVP (Wh) EW,A: Total amount generation by single wind turbine (Wh) EL,A: Total amount of the demand load(Wh) EPV,T(t): Power generated by all NPV PVPs during the time step (Wh) EW,T(t): Power generated by all Nw wind turbines during the time step (Wh) NK: Number of the hybrid components used K: the hybrid components used (PVP, wind turbine and batter) Npv: Number of PVPs (dimensionless) Nw: Number of wind turbines (dimensionless) Nbat: Number of batteries (dimensionless) v: Wind speed (m/s) Pr: Rated power of the wind turbine (W) vin: Cut-in of the wind turbine (m/s) vout: Cut-out of the wind turbine (m/s) vr: Rated speed of the wind turbine (m/s) hPV: Efficiency of the installed PV module (%) APV: Area of the installed PV module(m2) Rs: Average solar radiation (W/m2) Er(t): Energy absorbed from or injected into the storage unit (Wh) Chbat(t): Energy charge in the batteries (Wh) Dbat(t): Energy discharge from the batteries(Wh) EN(t): Net Electricity surplus/deficit(Wh) Eacc(t): Accumulation of electrical energy in the storage unit (Wh) Eacc (t ¼ 0): Initial accumulation of electrical energy not according DOD EBat,in: Initial battery according DOD (Wh) Ld: Number of days of autonomy(day) Vbat: Battery bank voltage (V) Ibat: Battery Nominal capacity (Ah) hwr: Wires losses' factor (%) Sp: Iteration of the ESCA algorithm with Eacc(t ¼ 0) ¼ 0 Wh Sp0 : Iteration of the MESCA algorithm with Eacc(t ¼ 0) > 0 Wh p: Iteration number ] [: Operator rounding up the value of “expression” to the nearest integer Subscripts AC: Alternative Current DC: Digital Current ESCA: Electric System Cascade Analysis MESCA: Modified Electric System Cascade Analysis LPSP: Loss of Power Supply Probability HES: Hybrid Energy System PA: Pinch Analysis PoPA: Power Pinch Analysis PoCA: Power Cascade Analysis SCT: Storage Cascade Table HCT: Hybrid Cascade Table DEG: Distributed Energy Generation PV: Photovoltaic PVP: Photovoltaic Panel BOS: Balance-Of-System FEE: Final excess of the energy(Wh) MFEE: Maximum Final Energy Excess TACS: Total Annualized Cost of the System(V/y) COE: Cost Of Energy (V/kW h) SOC: State Of Charge (%) DOD: Depth Of Discharge (%) Col: Column