Optimization of a stand-alone photovoltaic–wind–diesel–battery system with multi-layered demand scheduling

Accepted Manuscript Optimization of a stand-alone photovoltaic–wind–diesel–battery system with multilayered demand scheduling Tu Tu, Gobinath P. Rajarathnam, Anthony M. Vassallo PII:

S0960-1481(18)30826-7

DOI:

10.1016/j.renene.2018.07.029

Reference:

RENE 10303

To appear in:

Renewable Energy

Received Date: 11 December 2017 Revised Date:

6 June 2018

Accepted Date: 7 July 2018

Please cite this article as: Tu T, Rajarathnam GP, Vassallo AM, Optimization of a stand-alone photovoltaic–wind–diesel–battery system with multi-layered demand scheduling, Renewable Energy (2018), doi: 10.1016/j.renene.2018.07.029. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Optimization of a Stand-Alone

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Photovoltaic–Wind–Diesel–Battery

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System with Multi-Layered Demand

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Scheduling

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Tu Tu, Gobinath P. Rajarathnam, and Anthony M. Vassallo*

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The University of Sydney, School of Chemical and Biomolecular Engineering, Sydney, NSW

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2006, Australia.

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*Corresponding author contact information

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Corresponding author: Anthony M. Vassallo Telephone: +61 2 9351 6740

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Fax: +61 2 9351 2854

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Email: [email protected]

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Postal address: School of Chemical and Biomolecular Engineering, J01, University of Sydney,

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NSW 2006, Australia

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E-mail addresses of other authors

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Tu Tu: [email protected]

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Gobinath P. Rajarathnam: [email protected]

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Version: 0.10b

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1. Abstract

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Operational and financial optimization of a renewable energy-based stand-alone electricity

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micro-grid is described. Due to the large problem size in time-series models, we construct

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the model using mixed integer linear programming (MILP). As the constraints required in this

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model generally have modest complexity, we were able to perform piece-wise linearization

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on any non-linear variable relationship. Additionally, controls have also be applied on the

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demand side. Here, a two stage MILP model has been developed to minimize the overall

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levelized electricity cost for a micro-grid containing a photovoltaic power source, wind

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turbine, diesel generator, and an energy storage system. The model aimed to converge on a

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balance of decision accuracy and computational efficiency. Model outputs were capable of

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defining both the optimal system sizing and scheduling for each system component, with

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additional demand management control levers on the loss of power supply probability and

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load deferring allowance. We believe that this model is one of the first to explore the

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possibilities of the influences of potential demand management strategies in overall system

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cost reduction, while presenting a relatively efficient first-pass component sizing for stand-

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alone micro-grids.

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Keywords

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MILP; demand scheduling; load shifting; off-grid; optimization; energy storage

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2. Introduction

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In recent years, both renewable and alternative energy sources which generate power

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discretely from naturally replenishing resources are getting more attention, especially in

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rural locations. Renewable energy systems operate with high reliability and low

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maintenance requirements, and emits less greenhouse gas (GHG) compared to fossil fuel-

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based combustion energy sources. Therefore renewable energy sources are often suitable

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for remote and inaccessible areas. In the context of islands without local fossil fuel

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production, fossil fuel based generators are operationally expensive due to the high

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transportation costs of the fuel to site as well as the fuel cost. Therefore it is reasonable to

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consider a renewable energy source driven stand-alone micro-grid for islands and other

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isolated regions. This would provide competitive energy costs while reducing the energy

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dependence of the island to the mainland, thereby increasing the island’s self-sustainability.

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Apart from generating low carbon electricity, demand side management could also be used

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in micro-grids to improve the balance between supply and demand. By enabling some

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demand management strategies, the burden placed on battery storage units were

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significantly reduced, which resulted in a reduced overall system cost, hence a more

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affordable levelized energy cost.

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De Groot et al. [1] analysed the impact of demand response in isolated power systems,

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concluding that recent technical studies have followed a trend of focusing on the supply side

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(namely renewable energy systems), with little consideration of demand management

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possibilities. The authors noted that consideration of the latter could be a promising way to

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mitigate demand–supply balancing problems caused by intermittent energy supply, hence

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directly influencing component sizing optimization and operational improvements, and

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finally translating into an overall system cost reduction. Fezai et al. [2] proposed a study on

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load amplitude clipping and load shifting for a stand-alone photovoltaic system, concluding

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that acting on the load profile to match generation is a positive option toward higher

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performances. Bilal et al. [3] modeled the levelized cost of energy on three independent load

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profiles, whereas the demand profile correlated the best with PV generation profile and

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yielded the lowest levelized cost of energy.

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Following from that point, stand-alone micro-grid applications are suitable candidates for

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renewable energy-centric system designs. Wang et al. [4] investigated and simulated the

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operational performance of a solar-wind-fuel cell based energy system for stand-alone

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applications. Yang et al. [5] proposed a sizing method for stand-alone hybrid solar-wind

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ACCEPTED MANUSCRIPT systems, utilizing five objective variables: number of PV/WT/Bat modules, PV tilt angle and

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turbine installation height. The authors discussed impacts of loss of power supply probability

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(LPSP) on the levelized electricity cost (LEC), i.e. the fitness variable of the model. It was clear

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that as maximum LPSP increased, LEC decreased with it. The impact was most significant

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during low LPSP allowances, which was potentially more relevant to practical applications as

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high LPSP could result in severe interruptions to services and operations. Going from 1% to 2%

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LPSP, the PV module and wind turbine power were more moderate, yielding an levelized

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system cost to be 8.5% lower, thereby indicating the sensitivity of the output to the LPSP

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parameter.

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Merei et al. [6] modeled an off-grid hybrid photovoltaic-wind-diesel system with different

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battery technologies to power a constant AC load. The study incorporated three battery

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technologies in order to explore the opportunities in constructing an effective battery power

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bank that consists of multiple battery types, to maximize each battery technology’s

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strengths and minimize its weaknesses. The authors emphasized system reliability and

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availability, including a diesel generator which was sufficient to supply the load by itself was

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enforced into the designed system, hence ensuring no loss of power supply. Another

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emphasis was the possibility of different battery technologies working together in the same

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system. The authors discussed and modeled in detail three types of batteries (lead-acid,

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lithium-ion and vanadium redox-flow), with the important characteristics of each battery

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type formulated and quantified, such as the battery state-of-health, cycling, and ageing

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effects. Thresholds were placed on each battery, such as component capacity degradation

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and replacement. The model used net present value as the objective and optimized to

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minimize the overall system cost, under the condition of no loss of supply, and with the

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freedom of utilizing one or more batteries of arbitrary size. The optimization result

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suggested that the renewable energy system set up was cost effective compared to the

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diesel only set-up, by having energy cost about 50% cheaper. However, multiple battery

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configurations were not favoured against single battery technology configurations utilizing

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only the redox-flow battery, due to two potential reasons: the strengths of lithium-ion

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batteries in high energy density and high cell voltage were not required for the project, and

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the relatively short lifespan in lead acid battery translated to high maintenance costs and

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was not favoured. Vanadium redox-flow battery, despite low energy density and

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charge/discharge efficiency, the long lifespan and low cost made it to be the most suitable

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battery technology for the project. This finding suggests that Li-ion is not a unique solution

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to the issue of widespread energy storage.

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ACCEPTED MANUSCRIPT Shang et al. [7] discussed an unconventional amenity metric to describe the quality of power

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supply: instead of LPSP (discussed in most of the open literature), the authors quantified and

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correlated each end-use demand to comfort level, including air quality or carbon dioxide

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level from ventilation systems, internal temperature from air-conditioning systems and

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illumination from lighting. This relatively unique approach differs from allowing a maximum

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LPSP over the modeling period, as the mathematical model set a discomfort level

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representing the combined occupant discomforts caused by the unfulfilled end-use demands.

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This approach is an improvement over the LPSP approach in two ways: firstly, it was applied

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to each time-series point in the modeling, compared to the LPSP approach that was placed

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on the whole model. The comfort level approach allowed better visualization on the

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modeled result on unfulfilled time points, because it is highly likely that the LPSP approach

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would completely sacrifice the amenity of the scheduled loss of power points, in order to

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maintain resources for better optimization of the objective. Secondly, the discomfort

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approach allowed discrete settings of discomfort for each time-series point. An array of

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discomfort constraints could be imported into the model to better reflect the occupants

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comfort level desires. Although similar implementations could be made for the LPSP

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approach, it lacked flexibility as each time-series points could only be set with a Boolean

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variable to either allow or disallow loss of electricity. However, the addition of comfort level

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quantification introduced new variables and constraints in the optimization model, making it

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more complicated and harder to solve. At the same time, the weighting of each end-use to

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comfort level could be highly subjective, hence the weighting variables had to be selected

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carefully to reflect the reality.

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Genetic algorithms (GA) have been increasingly used for such computations, such as in the

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work by Koutroulis et al. [8], where the authors proposed a detailed model of a hybrid

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photovoltaic–wind–battery (PV-WT-BA) system. Their proposed model included modular

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system specifications and was aimed at optimizing over the system’s lifetime, accounting for

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capital and maintenance costs. The objective function used covered aspects such as the

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number of components required in each of the modules, photovoltaics tilt angle, and the

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wind turbine installation height. A two staged GA approach was utilized, where the first

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optimization stage focused on system configuration on a general scale, while the second

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stage took the output of the first system and generated another computational efficient

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model using the known information, seeking global maximum values for a finer resolution of

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output result.

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ACCEPTED MANUSCRIPT Nafeh [9] proposed a simplified alternative to the PV-WT-BA system by Koutroulis et al., with

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non-integer variables. While the fitness function of the former and latter was the same (to

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minimize the total system cost), the latter was constructed as a theoretical model with the

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pricing section utilizing units such as unit cost of PV panels, normalized WT swept area, and

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battery capacity. Additionally, PV generation was set to be a linearly proportional to solar

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irradiance, while WT generation was set to be cubically proportional to the wind speed

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(typically a value between the cut-in speed and rated wind speed). However, while these

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simplifications in model construction would reduce computational runtime, it is noted that

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there could be increased inaccuracies in cost estimation. While PV panels and battery

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systems are available in relatively smaller modules, WT towers are larger in terms of both

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capacity and physical dimensions (and hence better on a cost-basis to be modeled

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modularly). Modular pricing provides a more realistic indication of system sizing and costs,

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as well as limits the stepwise WT sizing by putting constraints on the GA solver and forcing it

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to find optimal solutions which utilize integer numbers of WTs. This approach provides an

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improved estimation of the costs involved if the modeled project was to be commercially

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realized. Consequently, a similar approach to modeling is adopted in the present work, since

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limiting the system component sizing as modular is computationally efficient while

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maintaining a reasonable accuracy of the final obtained results (in terms of costs and sizing).

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3. Methodology

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Modeling concept

The hybrid stand-alone micro grid consists of three sources of electricity generation, one

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electrical load and one energy storage device, all connected via an AC bus and a DC bus, and

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communicated through a bi-directional inverter/rectifier. An additional load dump was

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added to manage any excess load when storage was full and generation exceeded demand.

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Solar and wind were designed to be the primary source of energy generation, whereas diesel

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generator was installed as a boost generator to smooth the variable nature of renewable

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generation. Battery storage was also installed to reduce excess electricity and to assist other

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generation sources in adverse supply-demand conditions. The load controller would

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calculate the optimal scheduling of both battery storage system and demand management,

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to maximize the effectiveness of renewable generation and minimize cost. The time-series

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electricity demand data was a synthetized representation of costal islands near Sydney area,

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generated from the local electricity consumption and usage behavior. TMY (Typical

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Meteorological Year) data was selected for weather related inputs. We were aware that the

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final outcome, we felt TMY data was still the most representative of the local climate and

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most suitable for this study, as it focuses on the feasibility analysis instead of sensitivity test.

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Figure 1 presents an illustration of the connectivity of the various system components

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modeled in the present work.

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3.2. Mathematical modeling and optimization of stand-alone hybrid systems

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Figure 1. Illustration of the problem being modeled in the present work.

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Figure 2. Schematic of the two-staged optimization model used in the present work.

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The formulation of the problem consists of two nested mixed-integer linear programming

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(MILP) optimization models, adopting similar concept but to fulfil different purposes. Due to

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the nature of MILP formulation, decision variables are only allowed to have linear

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relationships with other variables. Unfortunately most system components have non-

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linearity in their operational profile, so to accurately model these behaviors, piece-wise

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linearization techniques were utilized for several components in the system, mainly

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generator efficiency and battery charging/discharging energy loss. Due to the uncertainties

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in component sizing, piece-wise linearization had to be dynamically performed for every

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time-series point on every component sizing alternation. The computational complexity was

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increased by the large number of integer and Boolean variables required to perform piece-

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wise linearization. With hourly time-series resolution and modeling length being a whole

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year, the amount of slack variables generated during problem solving not only required very

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large amount of system memory, it also greatly increased the run time. To populate a multi-

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dimensional matrix consisting of permutations of different load deferring and loss of

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electricity parameters, the model had to be run many times under different settings. On low

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tolerance gap allowance setting, solving every point in the matrix could be highly time

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consuming and unpractical.

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et al. [10] focused on optimal scheduling of units in an energy management system over a

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particular time horizon, and by Chen et al. [11] to quantitatively examine the optimal size for

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both grid-connected and isolated micro-grids. Morais et al. [12] proposed a constrained

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MILP model for a time-series problem on optimal scheduling of a renewable micro-grid in an

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isolated load area, with pre-determined component sizing and evaluation of the generation

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cost. The model objective function was formulated to minimize the overall generation cost

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over the modeled interval. Dai et al. [13] formulated a model featuring electricity demands

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being pre-determined then managed by a controller to make best use of the electricity

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generation from renewable sources. Depending on the energy supply condition, the load

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would be either fulfilled or curtailed. A priority load control algorithm was developed by

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Faxas-Guzmán et al.[14], in which demand was tagged with different priority levels, and

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during adverse generation conditions, loads with higher priority would be fulfilled first.

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The concept of load deferring has been considered in other researches. Bekele et al. [15]

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[16]used the software tool Hybrid Optimization Model for Electric Renewables (HOMER) to

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perform feasibility study for renewable energy focused system in Ethiopia. Deferrable load

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in the form of water pumping was considered.

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A two-stage configuration was proposed to resolve this issue and speed up the process,

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without sacrificing model accuracy. The model was split into the initial sizing and feasibility

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stage, and then followed by the operational scheduling stage. First stage was constructed to

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run on a much shorter time, effectively solving a much smaller problem. In addition, a large

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relative gap was implemented for the first stage modeling, meaning that the termination

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condition of the solving was relaxed, as an optimizer solver will attempt to approach the

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solution from both sides, finding improvements to the current best solution, and estimating

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the currently unknown global optimal solution. By allowing a larger gap between these two

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points, the solving was sped up significantly because for NP hard mix integer problems, the

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final convergence could often be computationally heavy. With the problem size and

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termination condition relaxed, the first stage modeling worked out the general direction of a

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global optimal solution, providing information on

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information was then fed to the second stage problem, so it could utilize better variable

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bound ranges and search spaces to solve a bigger problem. Finally an iterative approach was

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conducted as a search for global optimum solution, iterating on permutations of different

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component sizes based on the estimation given by stage one. As a result, stage two of the

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optimization process would calculate the optimal system scheduling and running costs, and

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decision variables estimations. This

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could be computed.

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Although the decision vector of stage two was 12 times as long as stage one (the whole year

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instead of a typical month), and the iterative approach required multiple runs of stage two

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for the local search, stage two optimization benefited largely from the fixed component

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sizing, making bound setting and variable relationship generation significantly more efficient.

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In addition, the fixed sizing component allowed better utilization of equality constraints,

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compared to inequality constraints, they were overall much easier to optimize due to the

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absence of slack variables. As a result, the solving of stage two problems greatly reduced the

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overall memory requirement and significantly improved overall problem solving time.

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3.2.1. Impact of loss of power supply probability (LPSP) on system sizing Nafeh [9] discussed on an additional aspect in his study, the loss of power supply probability.

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This variable is set at the start of the optimization run, indicating the maximum allowed

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intervals where the load was not met. Whereas Nafeh qualitatively discussed the potential

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influence of LPSP, the actual impact was not quantified. This paper attempted to quantify

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the impact of LPSP, along with other demand management strategies, through a

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computationally light algorithm.

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Ould Bilal et al. [17] modeled a PV-WT-BA system with similar constraints and the

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minimization on system annualized cost, while maintaining a maximum LPSP level. Three

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vastly different load profiles were applied to the model and the resulting annualized costs

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were compared. It was shown that the profile with the least amount of fluctuation was best

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handled by the hybrid system, requiring least amount of batteries and had the lowest

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annualized cost.

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To improve the performance and compensate the drawback of supply intermittency in

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renewable energy systems, multiple layers of load with different supply priorities could be

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implemented. Similar to load sensitive facilities such as a hospital, a critical load layer

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represents the highest priority, where it should be fulfilled immediately without any delay. A

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secondary layer of load represents demand of a less importance, where lower levels of LPSP

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could be incorporated and allowed up to a certain degree. The third and last layer

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represents the least critical demand type that allows load shifting or demand response. An

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example of the lowest priority load is an electric storage hot water system, ideally the water

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storage tank would consume electricity during midnight and have a full tank of water ready

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the system has freedom to choose the optimized heating intervals that are most suitable

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and economical. This concept would make the load model more flexible, giving the hybrid

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system more leverage in meeting the demands, at the same time improve the overall energy

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availability factor and overall system cost.

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3.2.2. Model construction and solver software

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The model described above was constructed in MATLAB 2017a, attempted to be solved with

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the MATLAB Global Optimization Toolbox, however the both solvers could not return

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converged results in reasonable time, with each scenario run taking more than twelve hours

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to converge when run on a PC with Intel Core i5-4570 CPU, 8GB RAM and 64-bit Windows 7

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operation system. IBM ILOG CPLEX Optimization Studio 12.7.0 and Gurobi Optimizer 7.0

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were introduced to the model in speeding up the solving. After many trials Gurobi optimizer

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7.0 was select to be the optimization solver for the models discussed in this paper, due to its

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superior speed and compatibility with MATLAB 2017a for this specific optimization problem.

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A tolerance level of 0.5% was set to be a termination condition for both solvers, meaning

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that the solving for problems would terminate if a feasible solution is found to be within 0.5%

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difference in objective value to the theoretical optimum.

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Solar energy is the first renewable generation source used in the model. Traditionally, the

detailed modeling of PV systems uses short circuit current I and open circuit voltage V ,

like described by Zhou et al. [18]. To convert solar irradiance to electricity generation, a

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photovoltaic model was needed, we used the California Energy Commission (CEC) 6

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parameter Photovoltaic module model for its solar output calculation[19], with maximum

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power point tracking system was considered to be operating at all times in the system in

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order to provide the maximum electricity generation.

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The electrical behavior of the equivalent circuit is described as

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 =  −    

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Where  is the output current,  is the Light current,  is the diode reverse saturation

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is the number of cells in series. For detailed model specifications, we adopted the

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specification of LG300N1-B3 panel module was selected for the model as it is one of the

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highly regarded panel in the Australian market.

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3.2.4. Wind turbine modeling Wind energy is the second renewable generation source in the model, it is included to give

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the optimizer more freedom in selecting the appropriate system combination for the

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electrical demand, also to supplement the lack of PV generation during night time. The

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power output and electricity generation from wind turbines is a function of the blade shape,

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pitch angle, blade swept radius and the rotational speed of the rotor unit [20].

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Figure 3. Typical power curve of wind energy conversion system [20]

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For the model discussed in this paper, the specification parameters from Pitchwind 14m

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30kW modeules were utilized, where the energy generation is mainly defined by four key

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 & − '& WT" = #$% &  − '&

parameters, the cut-in wind speed, V( ,, the rated wind speed  ,, the cut-out wind speed

+ and the rated power output P-.

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Figure 4Pitchwind 14m 30kW generation curve

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Similar to PV configurations, a MPPT process was also proposed for the wind turbine output

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power generation [21]. The load dump included in the system schematic allowed generation

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to exceed demand, therefore wind turbines were configured to generate maximum power at

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all times. This practice avoided the additional operational control required on power

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generation, reducing the complexity of the modeling problem and sped up optimal solution

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finding.

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3.2.5. Diesel generator modeling

A diesel generator was included in the model to assist in peak demand times and periods

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without renewable power generation. It was selected due to its portability and

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independency on energy infrastructure. In addition, as a back-power application, diesel

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generators are responsive to accept and supply electrical loads, making them good power

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supply candidates in peak demand conditions. This component was therefore considered in

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the model, with the purpose of preventing renewable energy system and battery

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components from being oversized and underutilized due to peak demands requirements.

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Diesel generators are more fuel efficient at higher loads, so in this model the diesel

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generator is set to have a maximum generation efficiency of 32% at full load [22]. Similar to

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most other fuel combustion engines, the part load engine efficiency are worse than rated. At

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40% load the generation capacity decreased significantly to 27%. Although it is possible to

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run diesel generators at even lower engine loads, the high fuel consumption makes it a poor

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option in most scenarios. Moreover, due to the drastic change in efficiency between start-up

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efficiency characteristics, further slowing down the optimization solving process. Therefore

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it was set in the model that diesel generators would not be utilized below 40% rated output.

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Figure 5. Typical 50kW diesel generator efficiency with output.

3.2.6. Inverter modeling

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Commercial inverters usually have a consistent efficiency throughout partial loads.

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Nowadays, a Pulse Width Modulation (PWM) controller is often present in a power

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converter to supply the AC load supply from a DC sources (DC to AC inverter) and also to

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supply AC load from the DC bus (AC to DC rectifier) [23] The minor change in output

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efficiency was insignificant towards the model, but also added unnecessary programming

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complexity. Therefore in this paper the SMA Sunny Boy inverter was utilized, with a

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weighted overall efficiency of 96%, and for conservative purposes, a fixed efficiency of 95%

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was adopted in the model[24].

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Figure 6. Power converter efficiency for the commercial SMA Sunny Boy inverter [24].

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battery storage system), an AC to DC rectifier would be required. Like the inverters,

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commercial rectifiers have stable performance on output efficiency. The model in this paper

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assumed the rectifier to perform similarly to the commercially available product GE

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CAR3012TE rectifier [25], with a fixed efficiency of 93% when outputting 230 VAC.

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Figure 7GE CAR3012 TE Rectifier electrical specification

3.2.8. Battery modeling

Considering the nature of the problem, stand-alone systems are generally designed for rural

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and areas outside electricity infrastructure, a well-studied energy storage device with

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minimum maintenance should be selected. Compared to other battery technologies, Li-ion

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batteries have high output voltage, and long cycle life [26]. These properties are highly

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desirable for the stand-alone micro-grid, as high power output could assist in solving the

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problems caused by renewable generation intermittency and long cycle life would be highly

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beneficial during frequent charging and discharging events scheduled by the controller.

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Being a well-developed technology Lithium-ion batteries were selected as the energy

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storage device in the model, for its low maintenance and slow self-discharging. System

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maintenance on the micro-grid system in rural areas is often expensive due to

366

inconvenience in logistics and transportation, low maintenance translated to a sizable saving

367

in operational expenditure. Similarly, in remote areas, batteries play an important role in

368

supporting renewable generation sources in fulfilling the local electricity demand. Therefore

369

battery cells that have fast and efficient charging/discharging cycles are more suited for the

370

task. Lithium-ion batteries are ideal for stand-alone systems that utilize renewable energy

371

sources [27] [28], because they could be fast discharged and charged without sacrificing

372

much efficiency, compensating the intermittent and volatile nature of renewable energy

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ACCEPTED MANUSCRIPT availability. The commercially available product BMZ ESS 7.0 Li-Ion NMC battery was used as

374

a reference.

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375 Figure 8 BMZ ESS 7.0 Li-Ion system specification

377

However, some of the specifications of BMZ ESS 7.0 were not strictly enforced, such as the

378

max discharge current and max discharge power. The battery storage unit in the model was

379

allowed to rapidly charge and discharge, in order to assist the dire electricity condition seen

380

by the micro grid in extreme events. However, heavy efficiency penalty was applied to rapid

381

charge/discharge action to discourage such act as much as possible. The detailed

382

formulation is outlined in the piece wise linearization section later in this paper.

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3.2.9. Load modeling

The impact of LPSP on levelized system cost indicated an interesting issue from a difference

385

perspective, where the marginal cost associated in boosting the availability of renewable

386

energy systems with battery storage. Unlike fossil fuel based generators, renewable energy

387

systems have a lower availability index, even with the assistance of battery storage devices,

388

and full availability is often translated to system over-sizing under nominal operational

389

conditions. By implementing the LPSP index, the model was transformed into an effective

390

sensitivity testing tool that evaluated the marginal investment return on different levels of

391

LPSP. Yang’s model [5] provided a good insight for real world applications and economic

392

sensitive projects, that under certain scenarios it might be more desirable to compromise

393

full availability for lower overall system cost.

394

Trading electricity availability for reduced system cost is an attractive approach, but there

395

could be a potential incomprehensible aspect during loss of power supply periods. It was

396

likely that yang’s model compared the electricity supply and demand for each time-series

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ACCEPTED MANUSCRIPT data point, flagging loss of power supply if the demand was greater than the supply. With no

398

other control parameters on loss of power supply periods, it was likely that the GA solver

399

assigned zero electricity supply for those periods since from the optimizer’s perspective, any

400

supplied electricity supply during time points that failed to meet the demand could be better

401

used in other time points. Following the same logic, the intermittently generated electricity

402

from PV and WT would be directed towards the battery instead of serving the load. For

403

example, discussed by Yang et al. [5], a telecommunication tower was set as the energy

404

consumer, therefore it was reasonable for the GA optimizer to fully blackout the load under

405

allowed LPSP intervals. However, depending on the actual scenario this could potentially

406

generate problems, because full black out for every consumer could be extremely risky and

407

undesired (e.g. power failure to telecommunication and life supporting medical equipment).

408

In addition, it could be a wasteful act to charge the battery when immediate loads were

409

present, due to the extra losses incurred in the charging process (battery charging loss,

410

inverter loss if the battery charges from AC instead of DC, etc). Yang’s proposed method was

411

applied to a rural telecommunication tower project design [29], where a continuous 1.5 kW

412

electricity consumption was assumed as the demand. Although compromises were made

413

due to insufficient roof area for the PV panels, and the sub-optimal WT installation height

414

due to the prevention from potential natural disaster, the hybrid system operated well with

415

battery SoC above 50% at 90% of the time. The project data was monitored for one year and

416

over-discharge situations seldom occurred.

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3.3. Problem formulation

The model was constructed to include decision variables for both component sizing and

419

operational scheduling, see the Nomenclature section for abbreviations.

421 422 423

Let variable /0% denote the diesel generator generation in kWh, during time 1. When turned

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on, the output generation was limited to be at least 40% of the rated capacity, for better

efficiency and easier model construction. Therefore /0% was set as a semi-continuous variable that could take a value between a set range, or zero. /0% = 2

424 425 426

0.4dgs ≤ /0% ≤ dgs, :ℎ  <:=1>ℎ / ? 0 , ?1ℎ @:=<

(1)

Let variable //%,A% denote the deferrable demand segmentation of deferrable electrical

demand BB% . //%,A% was set to be a special ordered set one for every 1, only allowing up to one variable to be non-zero.

17

ACCEPTED MANUSCRIPT EF

∀1, BB% = D //%,A% A%GH

∀1, ?IJ K 1? ? //%,A% >L M ?N @?

(2)

The unmet demand is formulated as the sum of instances where the electrical demand was

428

not fully fulfilled (LPSP hours). The maximum allowance of LPSP hours were set in the model

429

to reflect the minimum reliability of the microgrid.

Let variable =K/% denote the supply status of non-deferrable electrical demand /% .

431 432

1, 0,

:ℎ  /% =< KOKIO=II / ?1ℎ @:=<

SC

=K/% = 2

allowance PB.

F

D =K/% ≤ PB %GH

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≤ B% ∗ =K/% , = 0,

=K/" = 1 =K/" = 0

(5)

Let variable % denote the battery state of charge at time t, the battery state of charge

cannot exceed the boundaries of 0 and Q, where Q is the maximum battery capacity.

EP

435

(4)

In addition, variable K/% denotes the actual value of unfulfilled non-deferrable demand ∀1, K/% → 2

434

(3)

The total instances of unmet non-deferrable demand has to be smaller than the maximum

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∀1, 0 ≤ % ≤ U

(6)

In addition, the battery was assumed to have 50% state of charging during initialization, this

437

would make the battery useful from the start of the model instead of only coming into effect

438

after being charged. However the energy during initialization was also requested at the end

439

of the time-series analysis, making sure no extra resource was given to the model.

440 441 442

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1 qW ≤ U 2 1 q. ≤ U 2

(7) (8)

Let variable />% denote the change in state of charge at time 1. The change in state of

change was calculated as the difference in state of charge between the previous hour

(1 − 1) and present hour. Therefore, the change in state of charge is seen as an energy

18

ACCEPTED MANUSCRIPT 443

supply in the model, as positive figures reflect battery discharging and negative figures

444

reflect battery charging

1≠1 1=1

(9)

Let variable I% denote the electrical energy loss during battery charging and discharging ∀1, ql" = ^

/% ∗ (1 − _>`a ), /% ∗ (1 − _/`a ),

ML11 @J >ℎL@0=0 battery discharging

RI PT

445

 − % , ∀1, /% = 2 %[H 0,

(10)

446

Total energy supply at all time-series point must greater than or equal to the total demand

447

of the same hour EF

SC

∀1, /0% + _k' ∗ (/% + #% ) + l% + D //%,A% A%GH

448

3.4. Piece-wise linearization

(11)

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≥ B% + BB% + I% − K/% ∗ =K/%

Two of the main components in the model, namely the diesel generator and the lithium-ion

450

battery storage system have non-linear characteristics that have to be addressed. Due to the

451

limitations of a linear model, piece-wise linearization of non-linear functions and

452

relationships were performed to enable them being accepted by the linear solver.

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3.4.1. Diesel generator

The diesel generator operating efficiency curve was cut into three segments, each segment

455

had a unique efficiency, the overall fuel consumption used in the objective function was

456

calculated as the sum of fuel generation all segments, which was formulated as a special

457

ordered set 1, where constraints were set to only allow up to one segment to be non-zero,

458

in order to avoid the conceptual error of diesel generator operating on multiple output

459

efficiencies

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_`n

27%, = o30%, 32%,

∀1, O% =

/0% _`n

0.4/0< ≤ /0 < 0.6/0< 0.6/0< ≤ /0 < 0.8/0< 0.8/0< ≤ /0 ≤ /0<

(12)

(13)

460

The efficiency of diesel generator was cut into three segments, namely between 40% and 60%

461

load, between 60% and 80% and above 80% load. Segment under 40% load was avoided 19

ACCEPTED MANUSCRIPT from the system design, due to the inefficient operation. This was achieved by assigning a

463

heavy penalty for operational segment below 40%, achieved by an unrealistic low output

464

efficiency. This act made low load generation strictly worse than higher load (generating

465

little electricity while consuming equal or greater amount of diesel), hence eliminating the

466

potential of low load generation scenarios.

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467 Figure 9 Diesel generator efficiency linearization

469

The model formulation of the piece-wise linearization on the diesel generator involved

470

auxiliary parameters and utilized the concept of big-M method.

471

Two constraints govern the behavior of each of the three linear segments for diesel

472

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generator, on every time-series point 1. Let /0%, denote the electricity generation from the

474

diesel generator segment < at time 1, Boolean variable =vw%, denote the operating status of

475

be a positive value that is much larger than the upper-bound of all the variables in the model.

the diesel generator segment < at time <, where 1 represents on and 0 represents off, and x

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/0%,H ≥ 0.4/0< − z1 − =vw%,H { ∗ x

y/0%,& ≥ 0.6/0< − z1 − =vw%,& { ∗ x /0%,| ≥ 0.8/0< − z1 − =vw%,| { ∗ x

477

478 479

480 481

(15)

/0%,H ≥ 0.4/0< − x

(16)

EP

∀<, /0%, ≤ =vw%, ∗ x

Variable set =vw limits the value of the segment output, taking the first segment as an

example, when =vw%,H = 0, the constraints above become:

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(14)

/0%,H ≤ 0

(17)

Due to the large number nature of variable x, 0.4/0< − x will become a negative number and these constraints limit the value of /0%,H to be:

0.4/0< − x ≤ /0%,H ≤ 0

(18)

Since the value range of generator output is set to be non-negative in the bound setting, the

only feasible value for /0%,H would be 0. On the other hand, when =vw%,H = 1,

20

ACCEPTED MANUSCRIPT /0%,H ≥ 0.4/0<

(19)

/0%,H ≤ x

(20)

483

The segment output /0%,H has the freedom to select any value between 40% of the rated

484

generator output and large number x. Since the range setting also forbids the segment generation output to be greater than the rated diesel generator output, therefore the

485

effective variable range is:

488 489

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487

(21)

Under the same principle, the variable range for the second and third segments, when their

corresponding =vw variable is 1, are:

0.6/0< ≤ /0%,& ≤ /0< 0.8/0< ≤ /0%,| ≤ /0<

SC

486

0.4/0< ≤ /0%,H ≤ /0<

(22) (23)

Few extra constraints were needed to connect the three segmented pieces together. Firstly the special ordered set 1 constraints on =vw variables prevents generation double counting:

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∀1, =vw%,H + =vw%,& + =vw%,| ≤ 1

Next, the total

diesel fuel consumption for time t were expressed

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as:

/0% = /0%,H + /0%,& + /0%,|

EP

and total

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generator

O>% =

/0%,H /0%,& /0%,| + + _`n,H _`n,& _`n,|

(24)

(25)

(26)

490

It is worth noting that, in constraints 27 to 28, the upper limit of each segment was not

491

enforced onto the output variables. This was done intetionally to reduce the number of

492

constraints in the model, although eneration output variables in segment one could

493

technically have a value greater than 60% of the rated capacity, but this would be a strictly

494

worse solution compared to using the second segment to generate equal amount, due to

495

the improved fuel efficiency in the later segments. Since the objective of the model is to

496

minimize overall system cost, the optimization solver will always prioritize segments with

21

ACCEPTED MANUSCRIPT 497

higher fuel efficiency, and only use segments with lower efficiency when small amount of

498

electricity is required.

499

3.4.2. Battery storage system The construction of the battery storage system used the same principle as the diesel

501

generator constraint setting, with the exception of the batteries can have bi-directional flow

502

with different efficiencies. Therefore battery charging and discharging efficiency were split

503

into two parts and done separately. Four segments were created to represent charging

504

efficiencies and another four segments for discharging. Therefore a total of 8 segments were

505

applied for linearizing the battery performance. The model was constructed using hourly

modeling time-series resolution, therefore the c-rate of batteries could not go beyond } at

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506

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500

any interval.

508

For formulation purposes, we only considered the useful battery capacity to simplify the

509

model construction, however the full component cost was included and normalized to the

510

effective battery capacity for cost calculations. The battery module in this model used the

511

popular Panasonic NCR18650 series for the performance benchmark. The battery would

512

perform better and last longer with longer charging and discharging time, we transformed

513

these characteristics into charging and discharging efficiency to encourage slow

514

charge/discharge [30], due to the fact the one year time-span in this model was not enough

515

to reflect the long term capacity degradation. The discharging efficiency of the battery could

516

be represented as

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517 518 519

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85%,  87%,

_/`a =

€90%,   ~93%,

}` < / ≤ }` 1.5 }` }` < / ≤ 2 1.5 }` }` < / ≤ 2.5 2 }` 0 ≤ / ≤ 2.5

(29)



The negative of / was taken during charging loss calculations, this was due to the charging

aspect of the battery would have / take negative values

22

ACCEPTED MANUSCRIPT

520 521

€90%,   ~93%,

*charts of real vs linearized segments

} < −/ ≤ } 1.5 } } < −/ ≤ 2 1.5 } } < −/ ≤ 2.5 2 } 0 ≤ −/ ≤ 2.5

3.5. Residential electrical demand

(30)

RI PT

_>`a =

85%,  87%,

Isolated islands do not have the sophistication of detailed infrastructure control and

523

monitoring as large scale electricity network. The hourly electricity demand profile was

524

difficult to obtain. Considering the difficulties, the residential electrical demand profile used

525

In the model referenced, the average electricity demand of an urban residential precinct,

526

mainly in the Greater Sydney region in New South Wales, Australia.

527

To determine the deferrable electricity demand, the household electrical demand was

528

disaggregated down to individual appliances, where their electricity consumptions and

529

usage profiles were mapped out. In the end, several appliances were given the flexibility of

530

load deferring, namely the washing machine, cloth dryer, dish washer and the hot water

531

system. Other appliances that return an immediate amenity, such as lighting and air-

532

conditioning systems were not allowed from load deferring and have their demands delayed,

533

in order to maintain the resident comfort level.

534

The load profile of simulated household appliance usage on a 24 hour period was generated

535

using the methodologies listed by Richardson et al. [31] and benchmarked using the

536

commercial software CCAP Precinct [32]. The nature of stand-alone micro-grids being

537

disconnected to the well monitored electricity infrastructure, it was difficult for us to obtain

538

all the necessary parameters for simulating the electricity demand generated on the islands.

539

As an alternative, synthetic energy use behaviors of coastal Sydney areas were instead

540

applied into the modeling of demand profiles the Eastern Australian islands.

541

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3.6. Economic criteria and cost accounting

542

The modeling of MILP on minimizing the overall system cost requires each system

543

component to have levelized costs. In this paper, cost parameter comprises capital cost,

544

maintenance cost, component lifespan and operational fuel cost [33]. Since the analysis

545

performed in this paper did not extend to the full lifetime of each system component, it was

23

ACCEPTED MANUSCRIPT 546

important to normalize the component cost to a leveled platform. As a result, each

547

component cost was reduced down to an annual figure, effectively the cost of an annual

costs, taking into account the Consumer Price Index of Australia in recent years. P„……†„‡ = #'ˆk‰%ˆŠ

550

@(1 + @)‹ + #Aˆ‰Œ%ŒˆŒ' (1 + @)‹ − 1

(31)

RI PT

549

repayment of the component. The annual i rate @ of 5% [34] was considered for all system

The unit price of each of the components modeled in this study is shown in Table 1 Technology

Cost ($/kW, $/kWh or $/L) 1,800 3,800 800 1,333 1.25

(Years)

20 20 20 (assuming minimal usage) 5 -

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Photovoltaic Panel Wind Turbine Diesel Generator Battery Diesel (fuel)

Lifetime

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548

Table 1: Technology component pricing

552

4. Results and Discussion

553

Programmable household appliance loads (e.g. hot water system, washing machine, dish

554

washer and water pumping) with the ability to have the operation delayed with minimal

555

interference to the everyday life of the residents were extracted from the total electricity

556

demand and modeled as a second demand layer. A deferrable time allowance was applied

557

to the load and the optimal system configuration was then optimized on minimal levelized

558

electricity cost.

559

To explore the potential of load deferring, two scenarios were firstly modeled and compared;

560

one without any freedom of load deferring and the other with up to 10 hours of load

561

deferring allowance. Under normal residential use, appliance loads reach their peak during

562

night-time, between dusk and dawn of the next day. In addition, commercially available

563

electric hot water systems are also programmed to operate overnight, where a large amount

564

of electricity would be consumed. In contrast, to PV generation characteristics where all the

565

generations happen during the day, the big misalignment between appliances and

566

photovoltaic often make the photovoltaic generation utilization much more difficult. By

567

allowing the load to be deferred by up to 10 hours in the load deferring scenario, a

568

significant portion of the deferrable load was delayed and fulfilled the next morning, when

569

PV generation was directly available. This act of load deferring minimized the reliance on

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ACCEPTED MANUSCRIPT battery storage systems by shifting blocks of electrical demand towards generation, it

571

created better alignment between the consumption and generation profile, hence

572

enhancing the effectiveness and utilization of renewable generation sources with little

573

hardware investments needed, yielding a noticeable reduction in overall system cost.

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Electricity demand - kW

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570

574

Figure 10 Original and rescheduled average electricity demand profile

576

Observing the electricity demand profile result in Figure 10, load deferring was seen to have

577

a major impact in rescheduling the electrical demand for other system components. We

578

computed and compared the original daily average demand profile against the rescheduled

579

demand profile in the load deferring controller

580

The original demand profile had high night time demand, mainly due to the consumer

581

electronics consumption outside working hours and the overnight water heating from an

582

electric hot water system.

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Electricity demand - kW

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584 585

Figure 11 Original deferrable demand profile vs. Rescheduled deferrable demand profile

25

ACCEPTED MANUSCRIPT Shown in Figure 11, 10 hours of load deferring was allowed for this scenario run, the night

587

time demand was heavily shifted until the next morning, to better align with the expected

588

electricity generation from PV. Furthermore, a sizable average peak demand reduction of 30%

589

was also observed in the results, which indicated the successful attempt of load

590

management in the form of demand smoothing, as well as the potential in hardware sizing

591

reduction and improved network resilience.

592

Next, the deferrable load, representing approximately 48% of the overall electricity demand

593

were extracted and studied. Comparing the two figures, deferrable demands were shifted

594

and redistributed towards the middle of the day to best utilize the PV generation. In addition,

595

the deferred electrical demand resembled the PV generation profile during periods with

596

solar irradiation, indicating the deferrable load controller and system optimizer attempting

597

to restructure demands to best follow the PV generation profile, in order to reduce reliance

598

on battery storage systems and diesel generators.

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4.1. New establishment / Component replacement

After validating the significance of load deferring on electricity demand profiles, the model

601

was run on several scenarios, attempting to investigate the effectiveness of load deferring,

602

when coupled with programmed LPSP, one of the most commonly adopted demand

603

management strategies. Sizing composition of the optimal system configuration under

604

different parameter settings was graphed. Diesel generator as an electricity generation

605

source was sized smaller and not favored when the demand profiles got relaxed and

606

smoothed. The strength of diesel generators lies in dealing with spiky and intermittent loads,

607

where it also has its obvious drawback of fossil fuel reliance, hence its high operating cost.

608

The steady decrease of diesel generator component utilization was observed as both

609

demand management strategies strengthened and the electricity demand profile were

610

increasingly smoothed and rescheduled to better fit the renewable energy generation

611

profile. In other words, demand management strategies covered the strength of diesel

612

generators, where its drawbacks were left unchanged. As a result, as load deferring and LPSP

613

gained more control in demand rescheduling, diesel generator became less and less

614

attractive as a electricity generator component, hence getting its sized reduced to only

615

provide assistance in adverse situations.

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26

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Diesel/PV/Wind - kW Battery - kWh

ACCEPTED MANUSCRIPT

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Figure 12 Component sizing comparison on new precinct establishment

618

It was also shown in the results that whereas wind was the dominant component in the

619

system, its size was relatively unchanged in scenarios with higher loss of electricity and

620

deferrable load. Although on a unit pricing basis, wind is more than twice the cost than solar

621

PV, but its less fluctuating generation profile still benefited more to a shifted and relaxed

622

residential load, it could be seen from the graph that wind turbines were heavily sized in all

623

optimal system configuration setups.

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ACCEPTED MANUSCRIPT

624

Figure 13.System cost reduction against scenario without any LPSP and load deferring.

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626 627

Figure 14 Levelized electricity cost reduction comparison for different scenarios

28

ACCEPTED MANUSCRIPT The levelized system cost reduction was then calculated. Demand management strategies

629

achieved an overall reduction up to 27%, when 5% LPSP was scheduled and up to 10 hours

630

of load deferring were allowed. From the comparison in Figure 14, the demand side

631

strategies were more effective in their initial take ups, and suffered diminishing returns

632

when both strategies were granted more control over the demand profile. Therefore it was

633

clearly concluded that the impact of demand management strategies would quickly

634

converge, where additional freedom and power granted to the demand management

635

strategies might not be a good investment, especially taking into account resident amenity.

636

However, demand management strategies proved to be extremely effective at low values,

637

when the original electricity demand profile provided the most opportunities for demand

638

rescheduling.

639

The surface plot in Figure 14 presented a clear view of the system cost reduction at different

640

levels of LPSP and load deferring. Such surface plots have been presented and discussed in

641

previous literatures to illustrate system performances on multi parameter configurations

642

[35].

643

Reading from the graph, LPSP shown a stronger total system cost reduction, without the

644

assistance of load deferring, 5% of LPSP could reduce the overall system cost by 16%.

645

However, viewing from the residents’ perspective, high LPSP is very undesirable and it will

646

severely affect residents’ amenity and productivity. At 5% LPSP, a typical resident could

647

expect up to 438 hours of electricity blackout each year, heavily impacting their living quality

648

and productivity. Therefore, a less disruptive alternate solution to reduce levelized energy

649

cost would be much preferred by the consumers.

650

The other key parameter in the analysis was load deferring. At 10 hours allowance alone,

651

load deferring provided 11% system cost reduction against the reference scenario. While

652

being less effective than LPSP, load deferring was a much less disruptive load management

653

strategy than LPSP, as it only involved the non-critical residential electricity loads being

654

potentially delayed, examples being pressing the start button on the washing machine and

655

have the laundries done after 5 hours, or having the daily water heating schedule moved

656

away from midnight hours.

657

The overall surface had a gradual reduction in slope towards high values of both LPSP and

658

load deferring allowance, however the excess interference in resident amenity could create

659

bigger social problems. Thus we suggest the most effective approach could be found in a

660

combination of LPSP and deferrable load, both capped at relatively low values, this

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29

ACCEPTED MANUSCRIPT configuration would provide a relaxed generation and battery operation environment for

662

the stand-alone hybrid systems, hence reducing the total system cost without too much

663

performance loss and resident discomfort.

664

The optimal solutions obtained by MILP to minimize the levelized electricity cost in a normal

665

operation year. Each point of the graph is associated with a set of input decision variables

666

including PV sizing, wind turbine sizing, diesel generator sizing, battery sizing and optimal

667

battery management. It is shown that allowing loads to be deferred had a significant impact

668

on the system, without any compromise on the total demand. However the savings from

669

deferrable load shown a diminishing return, allowing loads to be deferred for long time (10+

670

hours) did not show significant improvement over a small deferrable hour (e.g. 2 hrs).

671

Observing the plotted results, there were non-smooth points on the surface, typically along

672

the lines of 2.5% LPSP allowance. Multiple runs of the model were performed with different

673

parameters, such as adjusting the frequency of heuristic guesses and utilizing different linear

674

programming methods (simplex, interior point etc.) to yield the same result. This could be

675

the result of the model solution trapped in a local optimum or the absence of feasible

676

solutions close to the set tolerance limit.

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This section simulated network upgrade of an existing stand-alone micro-grid, whereas

679

diesel generator was the sole electricity supplier. Hence the diesel generator was sized big

680

enough to supply the electrical demand without any other assistance. A network upgrade

681

was then proposed to reduce the system cost of the micro grid by introducing renewable

682

energy sources and energy storage systems.

683

The diesel generator capable of supplying all electricity demands was set to be present in

684

every scenario, with no capital cost associated. Similar optimization runs were performed to

685

explore the system cost saving opportunities in load deferring and allowed loss of electricity.

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30

686 Figure 15 Component sizing comparison for network upgrade scenario

688

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Diesel/PV/Wind - kW Battery - kWh

ACCEPTED MANUSCRIPT

689

Figure 16 Levelized electricity cost reduction on various scenarios on network upgrade

690

The difference in the levelized electricity cost reduction across all modeled scenarios in the

691

network upgrade scenario were observed to be much smaller than the new development

692

establishment scenario. Given the presence of the diesel generator, demand side

693

management strategies were shown to be less influencing in capital cost saving from system

31

ACCEPTED MANUSCRIPT 694

component sizing reductions. The existing diesel plant proved to be a reliable backbone for

695

the electricity system, where adding new RES components became less cost effective

696

compared to the new establishment scenario modeled in the previous section. The

697

additional operational cost saving mainly came from the reduction of fuel usage, which was

698

only a modest piece in influencing the overall levelized electricity price. 4.3. Compare to previous studies and relevant references

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Compared to studies in other literatures that constructed non-linear models and solved with

701

evolution based algorithms, the approach described in this paper achieved similar results

702

with linearized constraints. Non-linear models described in other studies [36] [37] utilize a

703

bottom-up approach where the optimization model would only cover a short period of time

704

(hourly resolution for 24 hours to a week), and then the results are post-analysed to reflect

705

the likely annual behavior. This paper took the approach of parameter linearization,

706

sacrificing non-linear relationship accuracy for better computational speed to afford longer

707

time interval simulations, which could be the preferable approach to support decision

708

making for areas located in high latitude zones, such as Sydney, Australia discussed in this

709

paper. The annual coverage in time-series points reduces the error in finding the global

710

optimum configuration that rely on post-anlaysing short time interval results into annual

711

levelized cost. For most non-linear models, the post-model-analyse on week-long

712

optimization results to predict the optimum for the annual optimum could be relatively

713

straight forward in areas with a stable climate, such as countries near the equator, however

714

the same analyse becomes difficult and challenging, due to the high seasonal variability in

715

daylight hours and temperature in other areas around the globe.

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4.4. Future research

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Component degradation was not modeled in details for the system and could be

718

investigated further. (e.g. diesel generator and battery were utilized less as load deferring

719

and loss of electricity increased, this could potentially translate to a reduced maintenance

720

cost and longer life time)

721

Impact of component pricing fluctuation on the system configuration, were not factored in

722

the analysis, however it would be another determining factor in component sizing, economic

723

sensitivity analysis could be undertaken to describe the likelihood of sizing differences when

724

capital costs change.

32

ACCEPTED MANUSCRIPT The impact of greenhouse gas emission was not discussed in the model, with the

726

introduction of RES, the fossil fuel usage in electricity generation would drop by a significant

727

amount, which would directly lower the greenhouse gas emission. As carbon emission

728

getting more attention globally, along with the increase in fuel price, most countries have

729

been considering a greener future development strategy, where the excess emission of

730

greenhouse gas would be penalized, where the use of RES gets incentivized. This shift in

731

government policies, although not quantitatively implemented in this model, would give RES

732

an even bigger advantage in economic terms, than traditional fossil fuel burning systems for

733

electricity generation.

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5. Conclusions

736

A two stage mixed-integer linear programming model was constructed and used to explore

737

the possibilities in optimizing the reduction of stand-alone renewable system costs with

738

diesel and energy storage. The results obtained reveal that load deferring is a cost-effective

739

and non-disruptive method of demand side control strategy for managing and adapting

740

residential electricity demand profiles to better align with renewable generation profiles. In

741

addition, the introduction of load deferring greatly reduced the battery capacity required in

742

the system, which was the biggest contributor towards lowering annual system costs.

743

Sizing composition charts were also developed to show the usefulness of wind turbines in

744

this particular stand-alone system, which allow load deferring and loss of power supply

745

probability. For the island scenario proposed in this paper, the nature of high latitude

746

created big seasonal variance in PV generation, coupled with the high wind speeds in coastal

747

regions, wind turbines have better capacity factors and availability than PV for the context of

748

this study, hence allowing them to be less reliant on batteries. This reliance reduction is

749

sufficient to overcome the drawback of high capital prices for wind turbines. It is expected

750

that this work will complement concurrent efforts in the field to improve the robustness and

751

computational cost-effectiveness of scheduling and sizing investigations.

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Nomenclature

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References

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