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Renewable Energy 72 (2014) 377e385

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Renewable Energy

journal homepage: www.elsevier .com/locate/renene

An energy management approach for renewable energy integrationwith power generation and water desalination

Malak Al-Nory a, b, *, Mohamed El-Beltagy a, c

a College of Engineering, Effat University, Jeddah, Saudi Arabiab Engineering Systems Division, Massachusetts Institute of Technology, Cambridge, MA, USAc Engineering Math. & Physics Dept., Faculty of Engineering, Cairo University, Giza, Egypt

a r t i c l e i n f o

Article history:Received 21 April 2014Accepted 17 July 2014Available online

Keywords:Renewable energyStorageEnergy managementOptimizationRandom variationsDesalination

* Corresponding author. College of Engineering, EffJeddah 21478, Saudi Arabia. Tel.: þ1 966 50 5527266

E-mail addresses: malnory@effatuniversity.edu.saeffatuniversity.edu.sa (M. El-Beltagy).

http://dx.doi.org/10.1016/j.renene.2014.07.0320960-1481/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

The share of the renewable energy sources (RES) in the global electricity market is substantiallyincreasing as a result of the commitment of many countries to increase the contribution of the RES totheir energy mix. However, the integration of RES in the electricity grid increases the complexity of thegrid management due to the variability and the intermittent nature of these energy sources. Energystorage solutions such as batteries offer either short-term storage that is not sufficient or longer periodstorage that is significantly expensive. This paper introduces an energy management approach which canbe applied in the case of power and desalinated water generation. The approach is based on mathe-matical optimization model which accounts for random variations in demands and energy supply. Theapproach allows using desalination plants as a deferrable load to mitigate for the variability of therenewable energy supply and water and/or electricity demands. A mathematical linear programmingmodel is developed to show the applicability of this idea and its effectiveness in reducing the impact ofthe uncertainty in the environment. The model is solved for the real world case of Saudi Arabia. Theoptimal solution accounts for random variations in the renewable energy supply and water and/orelectricity demands while minimizing the total costs for generating water and power.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The development and use of renewable energy has experiencedrapid growth over the past few years. In the next few decades allsustainable energy systems will have to be based on the rationaluse of traditional resources and greater use of renewable energy[1]. As a result, the share of the renewable energy sources (RES) inthe global electricity market will substantially increase. The inte-gration of the RES in the electricity grid will increase thecomplexity of the grid management due to the variability and theintermittent nature of these energy sources. The success in inte-grating the RES into the grid depends on many technological de-velopments of the electricity grid in network communications,decentralized generation, and demand response. In addition, thegrid will be characterized by the level of adoption and integrationof the renewable energy sources such as wind and solar. However,

at University, P.O. Box 34689,.(M. Al-Nory), melbeltagy@

the dominant types of renewable energy sources are non-dispatchable, i.e., cannot be turned on and off at will or its outputadjusted as in regular fossil fuel power plants. The gridmust be ableto manage this type of variations to supply power to its clientsefficiently.

Distribution Management Systems operated by distributionutilities and Energy Management Systems operated by end con-sumers are typically used to manage the supply. Demand SideManagement including demand response, intelligent energy sys-tems, and smart loads improves the stability by focusing on theconsumption side [2]. With a large portfolio of 40% or morerenewable energy sources integrated into the grid, a critical situa-tion is created because of the sudden interruption or variation of alarge portion of the supply. Other types of storage technologies arebeing developed and implemented to meet the variable supply anddemand. This has led to the emergence of storage as a crucialelement in the management of energy from renewable sources,allowing energy to be released into the grid during peak hourswhen it is more valuable [1]. Several studies have also examinedthe operational challenges in the development of renewable power,such as the mismatch between capacity and generation, the

M. Al-Nory, M. El-Beltagy / Renewable Energy 72 (2014) 377e385378

contradictions of high generation cost and the fixed feed-in tariff,the lag in grid construction, and regulatory uncertainty and policyinconsistency. Despite the promising recent growth rates in thecapacity of RES, it is established that the two most pressing issuesfor successful integration into the grid are the capability of theelectricity grid infrastructure and the availability of backup systems[3].

In addition, increased environmental concerns have led to theformation of energy and climate policies which suggest a signifi-cant reduction of CO2 emissions. As a result, the integration of RESin the energy mix is expected to rise rapidly as shown in Fig. 1 [4].Yet, electricity generated from renewable sources can rarely pro-vide immediate response to demand as these sources do not delivera regular and easily adjustable supply to consumption needs. Theconstant mismatch between supply and demand can have a seriousimpact on grid reliability and security of supply. This constitutes achallenge, which requires the introduction of advanced energystorage solutions. But it is widely known that electricity is difficultto store as this requires bulky and costly equipment [1].

This study proposes an energy management approach tomanage renewable energy connected to the grid based on mathe-matical model which considers the randomvariations of the supplyand the demand (of both water and electricity) through anexpansion method discussed in Section 5. The approach can beimplemented in the case of power and water generation. The waterstorage capacity can be used allowing for the release of power backto the gird to absorb variability of supply from renewable energy.The case of Saudi Arabia is solved using the proposed approach andmodel to provide the decision makers with a strategy to comple-ment their announced ambitious plan of integrating renewableenergy to the national energy mix to produce 52 GW by 2032 [5].

The remaining sections of this paper is organized as follows.Section 2 reviews the energy storage techniques. Section 3 dis-cusses the random variations of the renewable sources and thevarious demands. Section 4 describes the modes of integration ofdesalination capacity with the electricity grid. Section 5 describesthe proposed mathematical model and the expansion method.Section 6 uses a case study to illustrate the mathematical modeland discusses the analysis results. Finally, Section 7 concludes thepaper and provides interesting directions for future work.

Fig. 1. Expected scenario for a world

2. Storage techniques

There is a plethora of work on the integration of power storageinto the grid to compensate for sudden supply reduction. Yet, theoptimal active integration of storage devices and energy storagesystems into the grid is still not fully developed and faces manyoperational, technical and market challenges [6,7]. The integrationof energy storage techniques into the grid could obviously providean important and even crucial approach to deal with the inter-mittency of renewable energy and the associated unpredictabilityof its output, allowing the surplus to be stored during the periodswhen generation exceeds the demand and later the stored energycan be used to cover periods when the load is greater than thegeneration [8]. There are various types of storage techniques pro-posed, some of which are well developed, while others are still inthe development phase. These storage techniques differ in porta-bility (permanent or portable), durability (long or short term),maximum power requirement, and other factors which determinetheir characteristics and their proposed field of application [1].

Electrical energy storage refers to a process of converting elec-tricity from a power network into a form that can be stored forconverting back to electricity when desired. This technique whichcan provide many benefits by reducing on-peak energy and loadleveling has numerous applications in commercial buildings,portable devices, transport vehicles and stationary energy re-sources [9]. It is expected that electricity storage will have a dualpurpose in the next few years [4]. On one hand, it will enablerenewable energy to be captured and stored for later use, withoutwasting additional resources for electricity generation; therefore,increasing its efficiency. On the other hand, it can also serve as avaluable tool that will provide the needed flexibility in energysupply, by smoothing out the mismatch between supply and de-mand. Given the current attempts being made toward the reduc-tion of CO2 emissions, electrical energy storage technologies alongwith renewable energy technologies are expected to be a necessaryelement of the built environment in the future [4].

The Pumped Hydro Storage (PHS) technology has the advantagethat it is readily available. It uses the power of water as a highlyconcentrated renewable energy source. This technology is currentlythe most used for high-power applications (a few tens of GWh or

wide energy mix until 2050 [4].

Fig. 2. Pumped Hydro Storage with the pumping energy supplied by wind turbines [1].

M. Al-Nory, M. El-Beltagy / Renewable Energy 72 (2014) 377e385 379

100 of MW). Pumped storage subtransmission stations will beessential for the storage of electrical energy. The principle isgenerally well known: during periods when demand is low, thesestations use electricity to pump the water from the lower reservoirto the upper reservoir as shown in Fig. 2. When demand is veryhigh, the water flows out of the upper reservoir and activates theturbines to generate high-value electricity during the peak hours[1].

It is becoming increasingly important for any market with asignificant fraction of energy portfolio from renewable sources tocreate mechanisms through which it can respond to the unpre-dictable and the correlated changes in electricity supply. Theelectrical energy from RES can be stored in storage batteries andcan be used when needed. However, this solution (i.e., the batte-ries) has proven to be very expensive and difficult to implement ona large scale [2]. Desalination facilities connected to the electricitygrid represent an opportunity to overcome such a challenge. Thework in Ref. [10] proposed an alternative approach to energystorage based on integration with large desalination plants. Theidea is to use desalination plants as a storage for excess renewableenergy supply and to work as deferrable load to mitigate for therenewable energy supply interruption. In essence, we are replacingpower storage with water storage. The implementation of this idearequires solving a decision optimization question (described inSection 5) which accounts for the random variations of the de-mands and the renewable energy supply which is exactly thecontribution of the present work. The optimal solution provided bythis work involves determining how to optimally schedule

Fig. 3. Probabilistic renewable powe

desalination production so as to integrate it with the electricity gridto provide the required buffer given the random variations in de-mands and energy supply.

3. Random behavior of renewable energy and demands

The behavior of the renewable energy sources is a stochasticphenomenon. In particular, the wind speed is highly dependent onthe weather conditions, the geographical region, and the seasons ofthe year. The analytical method proposed in Ref. [11] estimates themean and the variance of power output variation due to the sto-chastic wind speed. The proposed analytical method was validatedby comparing the data from simulations. The energy productionfrom wind farms can be treated as a random variable due to thestochastic nature of the wind behavior.

Many probabilistic models have been proposed to evaluate andpredict the reliability performance of wind power generation withthe presence of stochastic wind speeds, uncertain power demands,and challenging maintenance activities (e.g. off-shore farms). Themain objective of these studies is to quantify (and hence mitigate)the uncertainties in the wind energy production by considering allpossible risk scenarios that could occur during the energy pro-duction process. Fig. 3 (left-side) shows the probabilistic behaviorof the renewable power generated as a function of the wind speed.The renewable power generated can be approximated as a randomvariable with Weibull or normal (Gaussian) distribution. Fig. 3(right-side) shows a typical simulation of the Probability Distribu-tion Function (PDF) of generated renewable energy after assuming

r generated from the wind [11].

Fig. 4. Fluctuation of instantaneous power on March 2004 at the Cap-Chat (Canada)wind farm [1].

M. Al-Nory, M. El-Beltagy / Renewable Energy 72 (2014) 377e385380

Gaussian distribution of thewind speed. As shown in the figure, thedeviation in the generated power is around 30% of the mean value.

Renewable resources fluctuate independently from demand asshown in Fig. 4 [1]. Power consumption (electricity demands) byusers during the day is characterized by disparity and fluctuation,meaning that minimum consumption is nearly half of themaximum peak. Fig. 5 shows a typical daily consumption pattern inSaudi Arabia during a holiday in January 2012 and a work day inAugust 2012. The ratio between peak and average power levels ofend-user demand often reaches a value of 10.

4. Integration of desalination with the electricity grid

Desalination has been realized as a viable solution to waterscarcity issues around the world. Thermal desalination in whichfossil fuel (i.e., oil, gas, or coal) is the main drive to operate theprocess such as in Multi-Stage Flash (MSF), Multi-Effect Distillation(MED) and Vapor Compression (VC) is an energy intensive processespecially in areas with higher water salinity levels such as in theMiddle East and the Gulf countries (35,000e45,000 ppm salinitylevels). Therefore, these technologies are typically feasible only inthe case of power and water cogeneration. The power plant istypically connected to the grid to export produced electricity.Membrane-based desalination such as Reverse Osmosis (RO) andElectrodialysis (ED) can be built as stand-alone plants and areconnected to the grid to import electricity required for the opera-tion (i.e., pumping and mechanical processes). For detaileddescription of commercially available desalination technologies thereader is referred to Ref. [12].

Desalination can also be powered by renewable energy sourcessuch as Photovoltaic (PV)-RO, Wind-RO and Wind-Mechanical VC.

Fig. 5. Typical average daily power consumption in Saudi Arabia [5].

In this case, the plant can be designed to be coupled to the grid andthe renewable energy sources are used as a fuel substitute in case ofgrid supply interruption [13]. The electricity consumption levels fornormal desalination operation for different technologies are shownin Table 1 [14,15].

Desalination plants have storage tanks with capacities from afew hours to a few days for large-scale plants to cover shortagesduring shutdowns for maintenance or emergency conditions.Aquifer storage and recovery (ASR) can store billions of cubic me-ters of desalinated water and are used for strategic long-termstorage. ASR systems need to be in strategic locations such asnear plants and close tomajor pipelines to deliver water to demandconcentrations, or near pumping stations associated with munic-ipal high water use centers. In addition to strategic storage, distri-bution systems need to provide certain storage capacity to meetshorter demand fluctuations and system emergencies of a shortduration. The normal operating storage is the storage required tocompensate for the impact of the variation onwater demand on thewater production facilities. Two hours of an average day flow maybe used as normal operating storage (i.e., operatingstorage ¼ average day demand/24 h) � 2 h [16].

Typically, the connectivity of the conventional stand-alonedesalination plants, such as the dominant technology in the mar-ket today i.e., Reverse Osmosis (RO), to the grid is a one-way link inwhich the desalination plant imports the electricity required fromthe grid. However, desalination plants with appropriate technolo-gies can implement a two-way link in which the plant wouldimport the electricity needed for the operation (pumping andmechanical processes) but also would act as a storage device andexport electricity to the grid during interruption of the powersupply, which is the focus of this paper.

Desalination units (of appropriate technologies) can use smartcontrols to be able to dynamically adapt the power consumption toconsume electricity when there is enough power in the grid andnot to consumewhen the power is scarce. Based on the desalinatedwater demand, the capacity of the plant, and the typical energyconsumption, each desalination plant realizes specific electricityneeds for each time period. The desalination plant typically realizesminimum energy consumption and the energy consumptionrequired for operating optimally. The difference between these twolevels of consumption is the range of the amount of energy that theplant is willing to deliver to the grid should the need arise. From thegrid point of view the desalination plant acts like a virtual batterywhich is capable of delivering this amount of power for each timeperiod. Fig. 6 shows a schematic representation of the integration ofdesalination plants into the grid.

In this case of integration, between power generation anddesalination plants there will be a market interface. In the case of acentralized authority to control desalination and power productionmodeling this interface is straightforward. The model can expressthe overall costs or benefits of generation of power and productionof desalinated water. However, the incentive of desalination plantsto collaborate with the grid and act as storage devices must be

Table 1Electricity consumption of desalination technologies [14,15].

Technology Electricity (kWh/m3) Feed watersalinity (ppm)

RO without energy recovery 5.9 25,000RO with energy recovery 3e4 25,000ED 1.22 (þ50% after 3 years) 3000VC 8.5e16 45,000MSF 4e5 AnyMED 1e1.5 Any

Table 2Different values of k and the corresponding probabilities.

k P½4� ks4 � 4ðqÞ � 4þ ks4�1 68.3%2 95.4%3 99.7%

Fig. 6. Schematic representation of desalination plants integrated with the grid [10].

M. Al-Nory, M. El-Beltagy / Renewable Energy 72 (2014) 377e385 381

defined for the case of separate authorities running the operationsof desalination and power. The desalination plants might bemotivated by reduced rate of energy consumption or a more flex-ible pricing scheme which creates a market interface between po-wer production and desalination plant. The interface can be suchthat there is no fixed demand or commitment that desalinationplant has to provide of power, but rather the amount is variable i.e.,a contract if the desalination plant commits a certain amount theywill be paid certain dollar amount per year. This might be expressedas a price curve that they are getting paid for every level ofcommitment they make. The commitment then is variable and theprice that they will be paid for the commitment is a function of thecommitment so they can select whatever commitment they want.

The desalination units make the independent decision and theinteraction with power units is this contractual interface based onthe agreement. Section 5 presents the mathematical model for theoptimal scheduling of desalination production and storageassuming the case of a centralized authority to control both desa-lination and power generation.

5. Optimal scheduling of desalination production and storage

In a previous work we developed a deterministic Mixed IntegerLinear Programming (LP) model to support strategic decisions ondesalination production and strategic storage to optimally allocatedesalinated water to demand points [14,15]. We also extended theLP model to support strategic decisions on investment alternativescomprising combinations of the different desalination locations,capacities, technologies, and energy sources [17]. Themathematicalmodel we propose in the present work identifies the optimalscheduling of the production and the storage of desalinated watersuch that the water stored is harnessed as a buffer for the grid. Thetrade-off between the production of power versus particularscheduling of desalination plants production and storage isexpressed in themodel directly by the cost of power generation andwater desalination.

In case of uncertainty in one of the input parameters to thesystem (e.g. renewable supply, water and electricity demands), theuncertainty will propagate to the different decision variables of thesystem. The uncertainty may be due to random (probabilistic)variations of the input parameters or due to noise imposed overthese parameters. In the current work we consider uncertainty dueto random variations and we look into uncertainty due to noise infuture work.

Parameters with random variation can be expanded using thePolynomial Chaos Expansion (PCE), inwhich the randomparameteris evaluated as a summation of nonlinear functionals of a set of

standard Gaussian random variables fxiðqÞg∞i¼1 multiplied bydeterministic kernels [18]. The parameter q is the output of arandom experiment. PCE has advantages in evaluating both sta-tistical moments of any order and the PDF of a system's responsewhich represents a complete solution of the random systems. Aftertruncation at order P andM random variables fxiðqÞgMi¼1, the systemvariable 4 in terms of PCE is written in the form [18]:

4ðqÞ ¼XPCi¼0

4iJi½fxnðqÞg� (1)

where fJigPCi¼0 is a set of orthogonal polynomials of random vari-ables, 4i are the deterministic kernels and PC þ 1 is the number ofterms after truncation. Random variation of any variable will causeall other variables in the system to have components in the sto-chastic dimensions and hence expanded as in equation (1) usingPCE.

In the LP models we can follow the same procedure given in Ref.[18] for a system of equations to find the equivalent deterministicLP model. This is done by (a) expanding all variables using PCE (asin equation (1)), (b) substituting in the objective function and in theconstraints, and then (c) taking the ensemble average after multi-plying byJk; 0 � k � PC. The equivalent system contains the meanvalues of the system variables in addition to the new kernels.

A simplifiedmodel can be derived if we assume that the randomvariations occur only due to one Gaussian random variable x1(q) inthe system. This is the case of applying the first order firstdimension PCE (i.e. P ¼M ¼ 1). In this case, the system variable 4 issimplified as

4ðqÞ ¼ 4þ s4x1ðqÞ (2)

where 4 is the mean value and s4 is the standard deviation. Forsimplicity we write the mean value as 4 instead of 4. The range ofeach decision variable 4 is

4� ks4 � 4ðqÞ � 4þ ks4 (3)

where k is chosen according to the required probability (i.e., con-fidence factor). Table 2 shows typical values for k and the corre-sponding probabilities.

The LP deterministic model representing scheduling of desali-nated water production and storage and considering random var-iations of the renewable energy supply and water and/or electricitydemands as explained above can be expressed as follows:

Renewable energy supply: REtðqÞ ¼ REt þ sREtx1ðqÞ

Water demand: DWt ðqÞ ¼ DW

t þ sDWtx1ðqÞ

Electricity demand: DEt ðqÞ ¼ DE

t þ sDEtx1ðqÞ

For simplicity, we assume that the uncertainty in both renew-able energy supply and water and electricity demands depends onthe same random variable x1ðqÞ. Adding more random variables tothe model is then straightforward.

The decision variables are extended in a similar fashion and weget:

M. Al-Nory, M. El-Beltagy / Renewable Energy 72 (2014) 377e385382

The amount of desalinated water produced by desalinationplant i at day t:

QitðqÞ ¼ Qit þ sQitx1ðqÞ

The amount of desalinated water pushed out to various distri-bution points from desalination plant i at day t:

DWitðqÞ ¼ DWit þ sDWitx1ðqÞ

The amount of desalinated water pumped to the storage tank ofdesalination plant i at day t:

PWitðqÞ ¼ PWit þ sPWitx1ðqÞ

The amount of desalinated water stored at the storage tank ofdesalination plant i at day t:

VitðqÞ ¼ Vit þ sVitx1ðqÞ

The amount of desalinated water pushed out to various demandpoints from storage tank of desalination plant i at day t:

WitðqÞ ¼ Wit þ sWitx1ðqÞ

The amount of electricity produced by all power plants at day t:

PtðqÞ ¼ Pt þ sPt x1ðqÞThen the objective function can be expressed as

FðqÞ ¼ F þ sFx1ðqÞ

where DWt , DE

t , Qit, DWit, Vit,Wit, Pt, REt and F are the mean (average)values and sDW

t, sDE

t, sQit

, sDWit, sVit

, sWit, sPt , sREt

and sF are thestandard deviations.

Comparing to the deterministic LP model, we now have threeextra inputs sRE, sDE

t, sDW

tand five extra decision variables sQit

,sDWit

, sVit, sWit

, sPt in addition to the standard deviation of theobjective function sF .

The random LP model can be formulated as follows:

MinXt

Xi

COMit

�Qit þ ksQit

�þXt

Xi

CVit

�Vit þ ksVit

�þXt

CEt�Pt þ ksPt

�(4)

where COMit is the operational and management cost of producing

one m3 of desalinated water from desalination plant i at day t, CVit is

the cost of storing one m3 of desalinated water in the storage tankof desalination plant i at day t and CE

t is the electricity generationcost at day t and the objective function minimizes the maximumpossible cost (i.e., F þ ksF ).

Such that the following constraints apply:The minimum possible value of all decision variables and all

standard deviations should be non-negative, i.e.:

Qit � ksQit� 0

DWit � ksDWit� 0

PWit � ksPWit� 0

Vit � ksVit� 0

Wit � ksWit� 0

Pt � ksPt � 0

(5)

and sQit, sDWit

, sVit, sWit

andsPt are also non-negative quantities.The amount of desalinatedwater pumped to the storage tanks at

desalination plant i at dayt is defined as

PWit ¼ Qit � DWit (6)

Applying the PCE procedure and due to linearity of the problem,the deviations will be computed similarly as

sPWit¼ sQit

� sDWit(7)

The amount of desalinated water stored at the storage tanks atdesalination plant i at day t is defined as

Vit ¼ Viðt�1Þ þ PWit �Wit ; where Viðt�1Þ ¼ V0i at t ¼ 0 (8)

Applying the PCE procedure and due to linearity of the problem,the deviations will be computed similarly as

sVit¼ sViðt�1Þ þ sPWit

� sWit; where sViðt�1Þ ¼ sV0

iat t ¼ 0 (9)

The maximum possible quantity produced by a desalinationplant i at any day t is limited to its maximum capacity Si.

Qit þ ksQit� Si (10)

The upper and lower bounds of the volume of water stored ateach water storage tank of desalination plant i are limited to itsmaximum ðVmax

i Þ and minimum ðVmini Þ capacities:

Vit þ ksQit� Vmax

i

Vit � ksQit� Vmin

i(11)

The electricity produced is bounded by the maximum genera-tion capacity Pmax:

Pt þ ksPt � Pmax (12)

The total minimum quantities pushed directly from desalinationplants and the total minimum quantities pushed out of the storagetanks should satisfy the maximum possible demand on the desa-linated water:Xi

�DWit � ksDWit

�þXi

�Wit � ksWit

� � DWt þ ksDW

t(13)

The maximum possible amount of water distributed from stor-age tank of desalination plant i at any dayt is bounded by theminimum of what we have stored in the previous day:

Wit þ ksWit� Viðt�1Þ � ksViðt�1Þ ; with Viðt�1Þ ¼ V0

i at t ¼ 0

(14)

The maximum possible amount of water distributed directlyfrom desalination plant i at any dayt is bounded by the minimumquantity produced in this day:

DWit þ ksDWit� Qit � ksQit

(15)

The minimum demand on power by desalination plant i at day tis always greater than the minimum ðDESmin

i Þ to run basic opera-tions and maintain steady operation to avoid shutdowns:

�Qit � ksQit

�EQi þ �

PWit � ksPWit

�; EVi � DESmin

i (16)

where EQi and EVi are the power required to produce and store onem3 of desalinated water respectively.

The maximum expected generated power should be limited bythe maximum capacity of the power plant:

Pt þ ksPt � Pmax (17)

Table 3Case study desalination plants data.

Technology Dailycapacity(thousand m3)

Min. storage(thousandm3)

Max. storage(thousandm3)

Electricityrequired(kWh/m3)

Initialstorage(thousandm3)

RO 737.23 61.44 2211.69 4.5 200MED-VC 113.42 9.45 340.26 1.0 35MSF 4820.35 401.7 14,461.05 4.0 1400

Table 4The average daily RE and electricity demands.

Day Average dailyRE supply (MWh)

Average dailyelectricity demandðDE

t Þ (MWh)

1 20,400 597,8472 2160 747,3103 20,400 672,5794 20,400 896,7725 2160 747,3106 20,400 747,3107 20,400 672,579

M. Al-Nory, M. El-Beltagy / Renewable Energy 72 (2014) 377e385 383

The maximum expected supply by renewable sources and theminimum power of generation plants should meet the maximumpossible demand on electricity including the maximum possibledesalination electricity demand:

ðREt þ ksREÞ þ�Pt � ksPt

� � �DEt þ ksDE

t

�þXi

�Qit þ ksQit

�EQi

þXi

�PWit þ ksPWit

�EVi

(18)

For situations of interruption or reduction to minimum of sup-ply by renewable sources, the power deviations should compensatethis reduction.

ðREt � ksREÞ þ�Pt þ ksPt

� � �DEt þ ksDE

t

�þXi

�Qit þ ksQit

�EQi

þXi

�PWit þ ksPWit

�EVi

(19)

The deviation in the generated power will be due to deviation inthe water demand and deviation in the electricity demand. Thismeans that the deviation in the generated power should be greaterthan the deviation in the electricity demand:

sPt � sDEt

(20)

The excess power of the renewable energy sources should beexploited in producing and pumping extra desalinated water ðXitÞThis can be modeled by computing the difference between therenewable energy sources and the power required for the pro-duction and the pumping of desalinated water to the demandpoints and to the storage tanks:

Xi

Xit

�EQi þ EVi

�� ðREt þ ksREÞ �

Xi

QitEQi �

Xi

PWitEVi

(21)

To simplify the computation of Xit, we can assume that it isproportional to the capacities of the storage tanks, i.e.:

Xit

�EQi þ EVi

�� Vmax

iPiVmaxi

"REt �

Xi

QitEQi �

Xi

PWitEVi

#(22)

Then the amount of water stored in the tanks can be expressedas

Vit ¼ Viðt�1Þ þ PWit �Wit þ Xit ; where Viðt�1Þ ¼ V0i at t ¼ 0

(23)

6. Case study results and analysis

The above described LP model can be implemented in a math-ematical modeling language (e.g. AMPL or GAMS) and solved usinga mathematical programming solver (e.g. CPLEX) to produceoptimal scheduling for production (of water and power) and stor-age using a specific case study. We use the case of Saudi Arabia theworld largest producer of desalinated water. Saudi Arabia hasrecently directed its policies toward building an optimum energymix that diversifies the energy source from its current focus onfossil fuels. This is due to the growth of the energy drivers accordingto 2011 statistics; a 3.2% increase in population, a 4.5% growth ineconomics, and a 6% in industrial production. Saudi Arabia alsowitnessed a 27% growth in fossil fuel consumption in the last 4

years. The domestic consumption of fossil fuels is expected tonearly triple by 2030. The annual energy consumption in SaudiArabia is 1766 TWh (comprising of 54% oil and 46% gas) [5].

We used Saudi Water Conversion Corporation (SWCC) plants forthe desalination capacity [19]. We aggregate the plants by thetechnology as shown in Table 3. The total planned desalinationcapacity by 2014 by all plants is 2070 million m3/annual [20] with13% RO, 2% MED, 85% MSF. We assumed the minimum storage re-quirements of 2 h of operation for each desalination technologycapacity, maximum of 3 days, and initial storage of 10% of themaximum capacity.We also assumed that the storage tanks containinitially around 10% of their maximum capacities. The daily demandon desalinated water is 2.871 million m3 [20]. The electric powergeneration capacity of Saudi Electricity Company (SEC) is50,043 MW and from SWCC and major subscribers such as ARA-MCO and SABIC is 15,781MW [20]. The total energy consumption is272,768 million kWh [20].

We used the National Energy Plan released by King AbdullaCenter for Atomic and Renewable Energy (KACARE) [5] to guide ourassumptions on the capacity of the Renewable Energy sources. Theproposed energy mix advertises a total of 52 GW by 2030 (41 GWofSolar, 7 GW of Wind, 1 GW of Geothermal, and 3 GW of Waste toenergy). For cost data we assumed 7.84 $/MWh for operationalcosts to generate power, we assumed fixed water storage costs of$100 for 1 thousand m3 and 0.47, 0.54, 0.65 $/m3 as the O&M costsof the three desalination technologies respectively [19].

We assumed a planning horizon of one week. The model isassumed to be run every period to adjust the scheduling of pro-duction and storage for the next periods. Other parameters valuesare as follows.

� k ¼ 1 (68% probability)� Time horizon : 7 days� The mean daily renewable energy supplies are shown in Table 4.Deviation of 40% is considered.

� The mean water demand DWt ¼ 2871 (thousand m3) for each

days.� The daily mean electricity demands are shown in Table 4.� Maximum generated power by all plants Pmax ¼ 1,579,776 MW/day

Table 5Model output for mean values.

Day Qit (Thousandm3)

DWit (Thousandm3)

Vit (Thousandm3)

Wit (Thousandm3)

1 1709 1709 473 11622 2871 2871 473 03 2871 2871 473 04 2871 2871 473 05 2871 2871 473 06 2871 2871 473 07 2871 2871 473 0

Total Cost ¼ 52 million $/week.

Table 6Model power outputs for mean values.

Day Pt (MWh) REt (MWh) sPt (MWh) Water power Excess power

1 594,510 20,400 10,200 6863 �13,5372 757,742 2160 1080 11,512 93523 673,891 20,400 10,200 11,512 �88884 898,084 20,400 10,200 11,512 �88885 757,742 2160 1080 11,512 93526 748,622 20,400 10,200 11,512 �88887 673,891 20,400 10,200 11,512 �8888

Table 8Model output for 5% deviation in water demand.

Day Qit

(Thousand m3)DWit

(Thousand m3)Vit

(Thousand m3)Wit

(Thousandm3)

Xit

(Thousandm3)

1 1380 1380 3769 1635 37692 1380 1380 2278 1635 1443 737 737 4335 2278 43354 0 0 6641 2871 51775 0 0 4318 2871 5486 0 0 6623 2871 51777 0 0 8829 2871 5177

Total Cost ¼ 45.5 million $/week.

M. Al-Nory, M. El-Beltagy / Renewable Energy 72 (2014) 377e385384

We start by running the model with zero deviations in the de-mands (i.e. sDE

t¼ sDE

t¼ 0) and without exploiting the excess power

from the renewable energy sources (i.e. Xit ¼ 0; ci; t).Table 5 shows the results obtained from this runwith a total cost

of 52 million dollars per week for the cogeneration of electricityand desalinated water shown in the table are the summation of alldesalination plants. All deviations in the water variables are zero inthis case and hence not displayed in the table. The initial storedwater in the tanks are used with the produced desalinated water tomeet the demand in the first day, then the total stored water rea-ches a steady state of 473 thousands m3 (3% of the maximumavailable storage). This means that the optimal cost-effective so-lution does not require initial huge amounts of stored water. Also, itmeans we have enough storage capacity in Saudi Arabia for futureexpected increase in the demands. We can notice also from Table 5that the generated power is directly proportional to the electricitydemand.

Due to variations in the renewable energy sources, the powergenerated will deviate from the mean value. Table 6 shows thegenerated power, available renewable power, power required toproduce and store desalinated water, and the excess power due torenewable sources. Negative excess power means that we haveexcess power to be exploited.

The model is solved again after activating the production ofexcess water, as in equation (21). The results are shown in Table 7.The cost is reduced by 12% which is a considerable reduction.

According to the optimal scheduling, the desalination plantsmay not producewater at all in some days as we have enoughwaterstored in the tanks. As the system reaches steady state (day 4 in this

Table 7Model output for mean values and excess water produced.

Day Qit (Thousand m3) DWit (Thousand m3) V

1 1236 1236 32 1236 1236 23 677 677 44 366 0 65 0 0 46 366 0 67 366 0 8

Total Cost ¼ 45.8 million $/week.

model), the desalinated water will leave the system directly fromthe storage tanks and not from the desalination plants. This will becost-effective and has an additional advantage to renew the waterstored in the storage tanks.

We can also see as shown in Table 7 that the water level in-creases with time as we have excess power from the renewablesources. This was one of the main objectives of the current model.It is expected with the time to reach the maximum capacity of thestorage tanks. In this case, the excess renewable power can beswitched to the grid to reduce the cost of the power productionand switch back again when the level of the stored water de-creases. Switching the renewable power is not implemented in thecurrent mathematical model but we plan consider it in futurework.

Table 8 shows the results in case of 5% deviation in the waterdemand at all days (i.e. 144 thousandm3). The cost is approximatelythe same as in the previous case. The deviations in the water de-mand will be compensated by the extra produced water ðXitÞ asshown in the table. It will be decreased or increased to cover thedecrease or increase in thewater demand. As the system reaches itssteady state (from day 4), the 5% deviation in thewater demandwillcause equivalent 5% deviation in the desalinated water comes outfrom the storage tanks ðWitÞ. This is reasonable as the demand willbe satisfied only fromwater that comes out from the storage tanks.Other deviations in the water quantities (Qit , DWit and Vit) will bezero.

Table 9 shows the power generated in the case of 5% deviation inelectricity demand. As it is expected the cost is increased to reach50.9 million $/week (12% increase) due to deviations in thegenerated power. The water quantities are the same as the quan-tities shown in Table 5 but they resulted in a different cost. Asshown in the table, 5% deviations in electricity demand will resultin approximately 4.6% in the generated powerwith no deviations inthe water quantities.

The effect of deviations in the renewable sources will havesimilar effect as deviations in the water demand. This is clear fromequation (21) which exploit the excess renewable energy to pro-duce and pump extra water (Xit) to the storage tanks. This willresult in a total deviations in Xit that can be estimated as

it (Thousand m3) Wit (Thousand m3) Xit (Thousand m3)

829 1635 3829194 1635 0403 2194 4403648 2871 4749325 2871 548569 2871 4749813 2871 4749

Table 9Model output for 5% deviation in electricity demand.

Day Pt (MWh) sPt (MWh)

1 642,545 29,892 (4.7%)2 824,853 37,366 (4.5%)3 722,485 33,629 (4.7%)4 967,734 44,839 (4.6%)5 819,881 37,366 (4.6%)6 803,326 37,366 (4.7%)7 721,122 33,629 (4.7%)

M. Al-Nory, M. El-Beltagy / Renewable Energy 72 (2014) 377e385 385

sXity

sRE

EQi þ EVi

0B@ Vmax

iPiVmaxi

1CA

And the change in the cost can be estimated as

sF ¼Xt

Xi

CVitsXit

For 25% deviations in the renewable energy in day 1(REt ¼20,400 MWh), we will have total deviations in Xit around1294 thousands m3 (33.8%) and the equivalent deviation in the costwill be around 0.13 million dollars for the same day (2%).

7. Conclusion

We proposed an energy management approach based on amathematical model which takes into consideration the deviationsin the demands and the renewable energy. This allows for man-aging the interruption of the supply from renewable energy in caseof the generation of water and power. Exploiting excess power fromrenewable sources to store additional desalinated water was esti-mated and implemented in the mathematical model. Our resultsshowed 12% cost reduction caused by the system ability to produceexcess water. The level of the excess water produced increased withtime as a result of the availability of the excess power fromrenewable sources. When the maximum capacity of the storagetanks is reached, the excess renewable power can be switched tothe grid to reduce the cost of the power production and switch backagain when the level of the stored water decreases. This was notimplemented in the current mathematical model but we planconsider it in future work.

The model was used in estimating the variations in the differentsystem parameters; water quantities and the power generated. Theeffect of deviations in the water demand, electricity demand andrenewable energy supply was carefully studied. Our results showedan increase of 12% of the expected cost and 4.6% increase in thepower generation due to 5% deviation in electricity demand. Wealso provided an analysis of the relationship between the renew-able energy deviations and the produced water and the equivalentcost deviations. Our results showed large deviations in therenewable energy (e.g., 12%) would result in 33.8% deviations in theexcess water produced but only 2% increase in the total cost. Ourproposed model has proved to provide an optimal energy

management solution for the renewable energy sources whencoupled with desalination capacity.

Acknowledgment

The first author would like to thank King Fahd University ofPetroleum and Minerals (KFUPM) in Dhahran, Saudi Arabia, forpartially funding the research in this paper through the Center forClean Water and Clean Energy (CCWCE) at MIT and KFUPM underthe Ibn Khaldun Fellowship granted to the first author.

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