A generic framework for distributed multi-generation and multi-storage energy systems

Energy 114 (2016) 798e813

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A generic framework for distributed multi-generation and multi-storage energy systems Kaveh Rajab Khalilpour*, Anthony Vassallo School of Chemical and Biomolecular Engineering, The University of Sydney, Sydney, Australia

a r t i c l e i n f o

a b s t r a c t

Article history: Received 12 February 2016 Received in revised form 6 July 2016 Accepted 10 August 2016

We have introduced a generic decision support tool for concurrent optimal selection, sizing, and operation scheduling of grid-connected or off-grid multi-generation/multi-storage distributed generation and storage (DGS) systems with respect to the dynamics of historical/projected periodical weather data, electricity price, DGS system cost, DGS aging, and the major critical design and operational parameters. This decision support program enables the consumer (ranging from a small house to large-scale industrial plants) to implement the most efficient electricity management strategy while achieving the goal of minimizing the electricity bill. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Distributed generation and storage (DGS) Polygeneration Multi-energy systems (MES) Energy storage Nanogrid Microgrid Smart grid

1. Introduction Before the Industrial Revolution, food, water, and energy supply chains were decentralized and scattered. In other words, the producers were consumers of their products (farms and agriculture), and the redundancies were supplied to neighbourhood community markets. The Industrial Revolution transformed the lifestyle by centralizing production systems in order to benefit from the economy of scale. This resulted in the development of complex supply chain systems to link the now distant producers to their customers. Similar issues occurred for energy networks as the small scale suburban power generators moved out of cities in order to improve safety and reduce the levelized cost of energy (LCOE). In recent years, however, it seems that distributed [renewable] energy resources (DERs) are “moving the energy network forward to the past!” by recommending network decentralization. DERs have a few critical advantages, including abundance and relatively scattered geographic distribution. As such, exploring the utilization of local (renewable) energy sources has been a matter of economic benefit and security for energy-importing societies. Furthermore, the possibility of generating energy on the demand

* Corresponding author. E-mail addresses: [email protected] (K.R. Khalilpour), anthony. [email protected] (A. Vassallo). http://dx.doi.org/10.1016/j.energy.2016.08.029 0360-5442/© 2016 Elsevier Ltd. All rights reserved.

side has many advantages in terms of energy efficiency, as it can reduce the power loss due to network transmission, the network footprint, reserve generation capacity, etc. All these features have stimulated the idea of moving from traditional, often lowefficiency, and centralized macrogrids to a decentralized form with numerous small but smart grids fueled using local resources (Fig. 1). The concept of a microgrid seems to have been introduced by the electrical equipment company ABB Ltd. in an energy forum in the 2000 [1]. Lasseter [2] argued that, although the application of individual distributed generations (DG) is advantageous from many aspects, it generates many new problems. Therefore, Lasseter and Paigi [3] reasoned that “a better way to realize the emerging potential of distributed generation is to take a system approach which views generation and associated loads as a subsystem or a microgrid”. According to ABB, for microgrids “the investment, maintenance, and operating costs are low and the renewable energy sources have a large share in the mix with correspondingly positive effects on the environment” [1]. Especially, decentralizing the grid seems to be environmentally and economically a viable option at resourced but remote locations, as generally the cost of building a network in a rural area with low population density is much higher than that for high-density urban area. For instance, the South Australia Power Networks company has spent 70% of its investment towards meeting just 30% of its customers' demand at rural locations. For such a scenario the company has projected that with

K.R. Khalilpour, A. Vassallo / Energy 114 (2016) 798e813

Abbreviations CAPEX CC DER DG DGS DOD DSM EES FOM

capital expenditure charge controller distributed [renewable] energy resources distributed generation distributed generation and storage (Here DGS means: “distributed generation, or storage, or both”) depth of discharge demand side management Electrical energy storage fixed operation and maintenance cost

GHG GHI MILP MINLP NPV OPEX PR PV SOC ToU LLP UN

799

greenhouse gas global horizontal irradiation mixed integer linear program mixed integer nonlinear program net present value operational expenditure performance ratio photovoltaic state of charge time-of-use loss of load probability United Nations

Fig. 1. Centralization versus decentralization (G: Generator).

renewable technologies (wind and solar) along with storage, the rural communities could build microgrids and quit the connection to a macrogrid [4]. Therefore, grid decentralization with the development of microgrids appears a “practically” viable option for locations with suitable resources. There has been an increasing rate of research into microgrids with mixes of various power generating technologies, both renewable and nonrenewable. A search with keywords of “micro grid” or “microgrid” or “micro-grid” and “electricity” brings 881

documents in Scopus citations, the oldest of which was published in 2000 [1] (see Fig. 2). Over 10 “review” papers on microgrids have appeared in the past few years [5e17], reflecting the high level of academic attention. Huang et al. [5] reviewed microgrid architectures with distributed energy resources and storage. They analyzed emergency control of microgrids with respect to energy sources and inverters. They concluded that the microgrid technology was not mature at the time and there were various steps to be taken until putting the

Fig. 2. Trend of publications relevant to microgrids.

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K.R. Khalilpour, A. Vassallo / Energy 114 (2016) 798e813

technology safely in the market. Similarly, a review by Mu et al. [7] concluded that new strategies for communication and control are urgently needed in future power grids. Yang et al. [11] highlighted the requirement of a well-designed and controlled power management systems. According to their review, the widely used power management system was hierarchical structure with three layers: primary control, secondary control and tertiary control (optimization). However, the authors argued that the centralized structure is good for planning, but faces difficulty to support Plug & Play in real operation, as any damage of central controller can affect the whole system. As such, the suitable alternative is multi-agent system (MAS) based method with fully decentralized control structure to improve reliability of the power management, especially when it is managed by multiple operators. A similar survey, carried out by Olivares et al. [16], emphasized that robustness and adaptiveness remain as an issue in most of the existing control strategies. Huang et al. [8] reviewed microgrid studies on isolated or gridconnected mode of operation and the transfer between the two operation modes. They also emphasized the need for smart frequency and voltage control strategies in both modes. Mariam [14] focused their review on AC or DC types of microgrid. According to the study, most of the systems are AC type due to ease of integration with macrogrid and also availability of AC loads. However, DC systems have less power quality problems and thus require less additional control or components. Jamil et al. [6] reviewed the state of the art of power electric converters used in microgrids with respect to their topologies, and control and modulation strategies. They highlighted the cost and size of converter as a key future challenge, and concluded that designing a converter requires overall system approach rather than doing it in isolation. Likewise, the review by Basak et al. [10] revealed the importance of integrated view to the microgrid management with consideration of operation and control, protection and stability issues, collectively. Gu et al. [17] reviewed the modeling, planning and energy management of combined cooling, heating and power (CCHP) microgrid. They discussed that technoeconomical and environmental performance of a CCHP microgrid are dependent on its design and energy management. According to the authors, an accurate modeling is the first and most important challenge for planning and energy management of the CCHP microgrid. Narkhede et al. [9] reviewed the publications on microgrid operation and control and observed a trend of shift towards computational alternatives from the traditional iterative techniques (gradient based methods) due to the need of deriving rigorous results in short periods of time. According to the authors, there were high adoption of multi-objective optimization approaches. Xu et al. [12] also reviewed microgrid optimization studies and highlighted the importance of weather forecast for wind and solar generation for optimal microgrid operation. Tan et al. [13] reviewed the features and benefits of energy storage systems within the microgrid and analyzed their configuration and topologies, power electronics interfaces, control schemes for charging/discharging, control strategy of hybrid storage, and also their integrated optimization with distributed generators. The authors highlighted the need for smart energy storage configuration and operation, especially in hybrid form. The decentralization has not stopped at microgrid level (a small network with multiple consumers), and it has been moving towards nanogrids defined as standalone hybrid generation systems that use distributed renewable and non-renewable resources, with or without energy storage, to supply power to a local load (single user) [18]. We consider some difference between nanogrid and microgrid. In a microgrid, there are various users, each with certain constraints (demand, reliability, etc.) and also with freedom of managing their

demand from the microgrid. Nanogrid, however, refers to a single ownership with centralized management. In fact, nanogrid can be considered as an especial case of microgrid. When all users have similar constraints and cooperate with the microgrid management, then they could be considered similar. Fig. 3 illustrates a nanogrid with a DGS system. Various combinations of energy generation and storage technologies have been studied for nanogrid and microgrid applications (see Table 1 for a summary). For obvious reasons, solar systems have been of the highest interest for small-scale demand-side applications. The earliest simple configurations were PV-grid, PVdiesel [19], and PV-battery. The configurations have diversified over time with the inclusion of various hybrid DGS systems such as PVhydrogen, PV-diesel-battery, PV-wind-battery [20], PV-wind-diesel [21], PV-wind-diesel-battery [22], and PV-wind-diesel-hydrogenbattery [23]. The list of configurations could be much longer if other generation types (e.g. bioenergy, hydro, gas turbine) and storage (e.g. hydro, compressed air, flywheel, capacitance, chemical conversions) are included [24]. Obviously, a key issue to the success of nanogrids (likewise for microgrids) is the market price parity of electricity generated by DER versus centralized power plants. Traditionally, nanogrids, in simple forms such as PV-diesel or PV-battery (Fig. 4-right), have been used in remote locations without grid access. The recent rapid decline in PV prices has brought grid parity for PV to many countries. There has been an unexpected rate of increase in residential level uptake of PV systems in many countries, including Germany and Australia. Interest in DG has increased even at locations with grid connection (Fig. 4-left). Interestingly, the prices of battery storage systems have also shown a notable declining trend and it is anticipated that battery technology may follow the price trajectory of PV [25]. In off-grid applications, electricity storage is an inseparable part of PV generation if 100% reliability is sought. However, a storage system can provide flexibility for a nanogrid even when grid is available (by shifting the load to the least expensive tariff periods). As such, the third configuration, the grid-connected DGS system (Fig. 5), has received notable attention both commercially and academically. The current trend of innovative academic research is towards the modeling of grid-connected DGS systems which are relatively more complex than the former configurations [26e29]. Adding to this complexity is the projected rapid uptake of electric vehicles. When such vehicles also join the nanogrids of small-scale prosumers, the combination of static and mobile storage system will provide better flexibility for operation of the grid, though with considerably increased complexity. Thus, whereas the conventional grid was a one-directional network of producers to consumers, the future grid looks to be a

Fig. 3. Schematic of a nanogrid with DGS system.

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801

Fig. 4. Schematic of two DG configurations: grid-connected DG (left) and off-grid (stand-alone) DG with storage (right).

2. Problem statement and formulation 2.1. DGS system sizing

Fig. 5. Illustration of a grid-connected DGS system.

bidirectional network of nanogrids which are now “prosumers”: sometimes producers and at other times consumers. A grid-connected DGS system is much more complex than its predecessors (off-grid DGS or grid-connected DG). The complexity applies both to the operation of an individual nanogrid and to the macrogrid. The primary goal of any demand side management (DSM) program is to influence consumers to use electricity with higher efficiency and with a schedule that guarantees security of supply. DSM is expected to have a more complex structure and to play a much more critical role in robust operation of bidirectional networks with a large proportion of prosuming members (nanogrids). Castillo-Cagigal et al. [30] stated that DSM faces notable challenges due to the increased complexity of DGS systems that require monitoring, communication, and control systems. They highlighted the requirement of active DSM (ADSM) with a combination of DSM and automatic control at residential demand loads. This was also considered by Strbac [31]. A similar requirement was discussed by Tan et al. [32] from Sandia National Laboratories as SEGIS-ES (solar energy grid integration systemseenergy storage). Though some network operators perceive nanogrids as business competitors and behave passively, others have initiated activities toward the management of grids with nanogrids [33]. Such examples shed light on the thinking about how diverse and complex operation of the future electricity network is likely to be. The goal of the research reported here is to develop a generic integrated decision support tool for concurrent optimal selection, sizing, and operation scheduling of grid-connected or off-grid multi-generation/multi-storage distributed generation and storage (DGS) systems with respect to the dynamics of historical/projected periodical weather data, electricity price, DGS system cost, DGS aging, and the major critical design and operational parameters.

Consider an end-user electricity consumer (“the consumer”) analyzing electricity usage for a planning horizon of H segments (weeks, months, years) with P0 multiple periods of a given fixed length (minute, hour, etc.). Thus, the planning horizon consists of total P ¼ H  P0 periods (p: 1, 2, …, P). The current optimization study is occurring in the base period (p ¼ 0). The consumer expects the aggregated electricity demand to be Lp kWh during period p. The grid electricity price is a function of the time-of-use, with occasional price modifications. The long-term electricity price can be a function of various parameters (economic growth, carbon tax, etc.). Given the current retail electricity price and all other possible parameters, the consumer anticipates that the electricity price, and the connection fee (or supply charge) will be EPp and CFp in period p. The consumer is interested to investigate the feasibility of DG systems and/or storage systems to reduce electricity costs over the planning horizon. Fig. 6 provides a schematic of the decision problem. The DG systems can generate electricity to use locally, to sell to the grid, or to store in the storage system for later used. The storage can receive electricity from the DG system and/or the grid. The storage system charge can be used locally and/or sold to the grid. The consumer is indifferent to the two options of off-grid or grid connection and leaves it to the program to select the best option with the least cost. The problem is illustrated in Fig. 7. There are many DGS suppliers in the market, with a wide range of cost, size, efficiency, and operational performance. The consumer is considering I (i: 1, 2, …, I) number of DG systems, each with capital cost of CXiDG to ultimately select the best one(s). Each DG has a design specification of SDG kW with nominal (standard) design efficiency of hDG and i i occupying an area of Ai with volume Vi. The real DG efficiency in any period p is taken as hDG ip , which might be function of several parameters (weather condition, aging, etc.). The term “performance ratio” is sometimes used to address the real efficiency [34]. The performance ratio is obtained by dividing the real DG efficiency by the nominal efficiency. Likewise, the consumer also considers J (j: 1, 2, …, J) number of storage systems with capital cost of CXiS to select the best one(s). Each storage system has a nominal size of SSj kWh, with nominal charge and discharge efficiency of hCj and hD j ; respectively. Storage j occupies area of Aj with the volume of Vj. The real storage charge and discharge efficiency are functions of many parameters and are taken as hCjp and hD jp , respectively, during period p with consideration of influential factors such as ambient temperature and aging. The storage system also self-discharges at the rate of bjp in any

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Fig. 6. Illustration of a grid-connected DGS system with static and mobile (electric vehicle) storage system.

Fig. 7. Schematic of a multi-generation/multi-storage nanogrid system of a prosumer with DG system and energy storage.

K.R. Khalilpour, A. Vassallo / Energy 114 (2016) 798e813

803

4.5

Electricity demand (kWh)

4 3.5 3 2.5 2 1.5 1 0.5 0 0

2000

4000

6000

8000

10000 12000 14000 16000 18000

Periods of 30-min block

Fig. 8. The consumer's load profile during the base year.

period p. Each storage system has a lower bound and upper bound to its state of charge (SOC), SOCjL and SOCjU . As such, the storage system needs a charge controller with the efficiency of hCC for j regulation of the input/output power. Storage systems also have limitations on their rate of charge/discharge. We take CRj and DRj as the maximum possible charge and discharge rates of the storage system, respectively, per period. The inverter's nominal efficiency is taken as hDGin and hSin for DG and storage system, respectively. As i j usual, the inverter’ s efficiency is taken as a nonlinear (quadratic) function of input power [35], so it can be taken as a variable (a function of input power flow) in each period p, for DG and storage system, hDGin and hSin ip jp , respectively. However, this will convert the linear program formulation into a nonlinear program. It is possible that the consumer has a space limitation that precludes installation of DGS systems with total area or volume greater than Am and Vm, respectively. Also, one system might be considered as more than one agent. For instance, an electric vehicle could be considered as one storage unit and one load unit or a hydro plant could be considered as one generation unit and one storage unit. The feed-in-tariff (FiT) for selling the electricity to the grid is highly policy-related and the consumer projects the value of FiTp during period p over the planning horizon (p: 1, 2, …, P). Having the capex of DG system i with CXiDG $/kW and capex of

Fig. 10. Annual weather profile (JulyeJune); ambient temperature (top), GHI (lower); Please note the seasonal differences of southern hemisphere.

storage system j with CXjS $/kWh, this problem can now be stated as follows: Given: (1) a multi-period planning horizon; (2) the forecast electricity demand in each period;

Retail electricity price ($/kWh)

0.55 0.5 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0

20

40

60

80

Period (p)

100

120

140

160

Fig. 9. Grid electricity price over one week (MondayeSunday) with three ToU tariffs of off-peak, shoulder, and on-peak.

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K.R. Khalilpour, A. Vassallo / Energy 114 (2016) 798e813

(3) available sizes of DG and storage systems and specification for each size; (4) the forecast grid electricity price in each period; (5) the forecast FiT in each period; (6) the forecast weather data in each period;

size, but also it is related to weather conditions. As such, we define a DG to indicate the maximum generation (precisely new parameter Cip “generatable”) capacity of DG unit i during period p. Hence, we have DG DG:G DG:L Xip ¼ Xip þ Xip þ

J X

DG:S DG Xijp  yi Cip

1  i  I; 1  p  P

j¼1

determine:

(5) (1) (2) (3) (4)

whether to install DG and/or storage systems; the size of DGS systems if they are feasible to install; whether it is profitable to sell electricity to grid; the periodical operation schedule of the DG system (if selected); (5) the periodical operation schedule of the storage system (if selected); (6) the total net present value of the electricity system of the consumer; assuming that: process lengths are multiples of the given period length; aiming to: identify the best investment plan in the DGS system to build a nanogrid and minimize the electricity cost over the planning horizon. This is a planning problem that involves some decisions at different periods over the planning horizon. We define the following binary variable for each candidate DG system i:


yi ¼

1;

if DG system i is selected 1iI 0; otherwise

To limit the number of selected DG systems, NDG, we use: I X

yi  N DG

(1)

i¼1

The “” also includes the scenario that the program might not select any DG and might suggest buying all electricity from the grid (with or a without storage system). Similarly, we define the binary variable y0j for candidate storage systems given by

y0j ¼ J P j¼1




1;

if storage system j is selected 1jI 0; otherwise

y0j  N S

yi Ai þ

i¼1 I X i¼1

J X

J X

denotes the DC energy sent from the DG system i to storage j (j: 1, 2, …, J) during period p. For instance, we will have PV ¼ y $A $GHI $hPV Cip for a PV system or p ip i i Wind ¼ y $SWind $WS $hWind for a wind turbine (GHI: global horiCip p ip i i

zontal irradiation; WS: wind speed). For DGs of the AC type, the inverter efficiency will be taken as one. The local load in any period p can be supplied from three sources, DG, storage, or grid. This is expressed as

XpG:L þ

I X

DG:L hDGin þ ip Xip

i¼1

J X

S:L Xjp  Lp

1pP

(6)

j¼1

S:L are the AC energy received by the consumer's where XpG:L and Xip appliances in period p. Here we introduce two benchmarking variables, reliability and independence. Reliability measures the fraction of load that is served (by any source of supply). This is the complement of LLP (loss of load probability) i.e. R ¼ 1-LLP. Of course, when the customer is connected to a reliable grid, a reliability value of 100% is expected. In other conditions (e.g. off-grid), however, the consumer may set a reliability limit of RL over the planning horizon, reflecting the fraction of the demand load that “must” be satisfied. As such, the reliability constraint is given by

hP 0 X

*

R ¼

00 @@X G:L þ

I  X

DG:L hDGin ip Xip

p

p¼ðh1ÞP 0 þ1



þ

i¼1

J  X

S:L Xjp

1, 1  A Lp A

j¼1

(7) (2)

y0j Aj  Am

(3)

y0j Vj  V m

(4)

j¼1

yi Vi þ

DG:S system i to the grid and/or load, respectively, during period p. Xijp

 RL

where NS denotes the maximum number of storage system selections. Again the “” includes the scenario that the program might not select any storage system installation. The installation area (Am) and volume (Vm) limitations are given by I X

DG:G and X DG:L refer to the DC energy sent from the DG where Xip ip

j¼1

The generated electricity from the DG system i during period p, DG , will have three possible destinations: meeting the local load, Xip charging the storage system, or exporting to the grid. The total generation of a DG system cannot exceed a certain value. For a nonrenewable DG system i, the maximum generation capacity is its installed size ðSDG i Þ: For renewable generators, not only is the maximum generation capacity less than or equal to the installed

where the parameter RL and the variable R* are the “required” and “occurred” reliabilities for the customer. For obvious reasons, 0  RL   1 and 0  R*  1. For 100% reliability expectation (RL ¼ 1), Eq. (7) should be expressed with an equality sign. The constraint of Eq. (7) is not applicable for off-grid prosumers. If the selected DGS system can supply the entire required load at the desired reliability, the prosumer will not need to pay for connection fees (supply charges); otherwise they are payable. This brings us to the second benchmark, independence, which measures the fraction of load that the DGS system could supply over the planning horizon if there was no grid connection. This is given by

InD ¼

hP 0 X

00 @@

p¼ðh1ÞP 0 þ1

I  X i¼1

DG:L hDGin ip Xip



þ

J  X

S:L Xjp



1, 1 A Lp A

j¼1

(8) G:S ¼ 0: This is required as it is possible that the grid provided that Xip charges the storage system and results indirectly in a higher value S:L in Eq. (7) and thus overestimation of the independence of Xjp value. Therefore, when InDR* is satisfied, no grid connection (and thus no connection fee) is required. However, decisions about

K.R. Khalilpour, A. Vassallo / Energy 114 (2016) 798e813

maintaining connection with the grid depend on the overall economics of the system (represented in the objective function). For instance, there might be a condition that InDR* is satisfied but there is still economic benefit in maintaining the connection with the grid to sell the unused energy (UUE) to the grid. To address this, we define grid connectivity (GCh) as the sum of all inputs and outputs to and from the grid, over the timeframe of h. This is given by

0

hP 0 X

GCh ¼

@X G:L þ ip

p¼ðh1ÞP 0 þ1

I  X

DG:G Xip



1 J   X S:G G:S A þ Xjp þ Xjp

i¼1




(9)

SOCjp ¼

00

1hH

(10)

where M is a large-enough constant number (big-M method [36]). If DG system i uses fuel for power generation, its fuel cost in any period p is given by

. DG FCip ¼ Xip Fip hDG ip

p X

Bjp0

1  j  J; 1  p  P

1  i  I; 1  p  P

(11)

As discussed, the SOC should always be controlled during operation within a certain upper (SOCU) and lower (SOCL) bound. This is given by

DG:S Xijp  M$ySjp

1  i  I; 1  j  J; 1  p  P

  S:G Xjp  M$ 1  ySjp

. DG Eip ¼ Xip CIip hDG ip

  S:L Xjp  M$ 1  ySjp

(12)

Given the carbon tax/penalty of CPp in period p, the incurred GHG cost for DG i would be

GHCip ¼ Eip CPp

1  i  I; 1  p  P

(13)

The storage j, if selected, can receive DC power from the DG (after passing through the charge controller CC), or from the grid (after passing through the inverter and charge controller). When needed, the stored DC electricity can be sent to the customer's appliances or to the grid, also through the inverter. The storage system input-output balance in period p is given by

 .  C DG:S Sin CC C G:S S:G Bjp ¼ 1  bjp hCC j hjp Xijp þ hjp hj hjp Xjp  Xjp   .  CC D S:L CC D  hSin hSin jp hj hjp  Xjp jp hj hjp

(14)

where bjp is self-discharges of battery system j during period p. A DG:S , i.e. the energy from DG i to storage j, is lost by fraction of Xijp charge controller

ðhCC j Þ

and battery conversion

G:S  M$ySjp Xjp

ðhCjp Þ.

Therefore, the

C DG:S quantity of stored energy from DG i to storage j is hCC j hjp Xijp : A G:S Þ is lost in three fraction of the energy from the grid to storage j ðXjp

stages i.e. inverter, charge controller, and conversion within the CC C G:S storage j, with ultimate stored energy being hSin jp hj hjp Xjp : The

(16,17)

1  j  J; 1  p  P 1  j  J; 1  p  P 1  j  J; 1  p  P

(18) (19) (20)

(21)

Additionally, the storage system cannot be charged or discharged above a certain rate (CRj, DRj) during any period p. This is given by

Bjp  ySjp CRj

1  j  J; 1  p  P

  Bjp  1  1  ySjp DRj

1  j  J; 1  p  P

(22) (23)

For obvious reasons, the storage and/or the DG should not send electricity to the grid in period p when electricity is being received from the grid for local consumption. This is addressed by the g introduction of binary variable yp having the value of 1 when electricity is received from the grid. This is given by

XpG:L  M$yG p

1  j  J; 1  p  P

1  j  J; 1  p  P

In any period p, the storage system can either send electricity to the grid or receive charge from there. More generally, the storage system cannot be simultaneously discharged and charged. To address these constraints, we introduce the binary variable ySjp ðySjp  y0j Þ to have a value of 1 when the storage system is charged by the DG or grid. This is given by

where Fip is the fuel cost of DG i per unit of energy during period p. This value is zero for renewable DGs such as PV and wind. The CO2equivalent GHG emission of the fuel for DG i is CIi per unit of fuel (carbon intensity). Therefore, the GHG emission of DG i in period p is given by

1  i  I; 1  p  P

(15)

p0 ¼1

y0j SOCjL  SOCjp  y0j SOCjU

Therefore, we have

GCh  M$yh

losses through inverter, charge controller, and battery conversion. S:L from storage j to the load, X S:L =ðhSin hCC hD Þ Likewise, to supply Xjp jp jp j jp

1

if GCh > 0 if GCh ¼ 0

1; 0;

supply this quantity of energy to the grid, an energy amount of S:G =ðhSin hCC hD Þ is discharged from the storage j to compensate the Xjp jp j jp

j¼1

Now, we can define the following binary variable for identifying the condition at which a loss penalty should be included: 00

S:G : However, to exported energy from storage j to the grid is Xjp

amount of energy is discharged from the storage j. It is obvious that the storage system balance, Bjp, takes a positive value when the storage system is being charged and is negative during discharging. With this, the storage system's state of charge for the scenario with DG system i and storage system j is given by

hH

yh ¼

805

I X

1pP

  DG:G Xip  M$ 1  yG p

(24)

1pP

(25)

i¼1 J X

  S:G Xjp  M$ 1  yG p

1pP

(26)

j¼1

Each DG and storage technology has periodical fixed operation

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DG and FOM S , respectively, and maintenance costs given by FOMip jp during period p. With these, all the required variables and constraints have been defined for calculation of the economic objective function, that is either the minimum net present value of costs (NPVC) or the maximum net present value of overall savings in electricity costs (NPVS) over the planning horizon (h). The minimization and maximization objectives are, respectively, given by

NPVC ¼ H P

"

h¼1

I  X

yi CXiDG



þ

J  X

i¼1



j¼1

hP 0 P

00

p¼ðh1ÞP 0 þ1

2 H X 4 NPVS ¼ h¼1

y0j CXjS

XpG:L EPp þ yh CFp þ

2 H X 4 þ

hP 0 X

h¼1

p¼ðh1ÞP 0 þ1

J  X

0 @

I  X

hP 0 X



DG yi FOMip

i¼1



þ

J  X

S y0j FOMjp



13, A5

ð1 þ rÞh þ

j¼1



G:S S:G Xjp EPp  Xjp FITp 

j¼1

and maintenance costs for the selected DG and storage systems, respectively. The remaining terms are the cash costs under the selected DGS system(s). This includes the electricity purchased from the grid by load and/or storage plus the fuel and GHG cost of fossil-fuel-based DG system(s) plus the supply charge (when the grid is connected) minus the electricity sold to the grid by the DG and/or storage systems. The first term of Eq. (28) represents the

I  X i¼1

3,  Lp EPp þ CFp 5 ð1 þ rÞh  NPVC

p¼ðh1ÞP 0 þ1

(28) where r is the discount rate over h. The first and second terms in Eq. (27) are the total capital expenditures of the DG and storage systems, respectively. The third and fourth terms are fixed operation



DG:G hDGin FITp þ ip Xip

I  X



13,

FCip þ GHCip A5

(27)

ð1 þ rÞh

i¼1

baseline cost of grid electricity and grid supply charges, respectively (LpEPp þ CFp). This completes the mixed integer nonlinear program (MILP), when inverter efficiency is constant, or mixed integer linear program (MINLP), when inverter efficiency is a function of input power, for the DGS planning problem. It consists of Eqs. (1e26) with the objective of minimizing NPVC (Eq. (27)) or maximizing NPVS (Eq. (28)). It is noteworthy that a storage-only system or DG-only system is a subset of the introduced formulation. When the system under study does not include either DG or storage, the relevant

Table 1 Illustrative list of some generator/storage configurations for nanogrid and microgrid. Configuration

Grid dependence Comment

Sample reference

PV

 √ , √ 

[44] [45] [19] [46,47]

PV/diesel PV/hydrogen-fuel cell PV/battery PV/diesel/battery PV/battery/hydrogen-fuel cell Wind/diesel Wind/pumped hydro

 √     

Wind/diesel/pumped hydro Wind/diesel/battery PV/wind/diesel

, √

PV/wind/biogas

, √

PV/wind/battery

 (with enough battery size)  √

PV/wind/diesel/battery PV/wind/hydro

PV/solarthermal/wind/ hydro PV/wind/hydro/battery PV/wind/hydrogen-fuel cell/battery/diesel PV/wind/hydrogen-fuel cell/battery/hydro

   

Unable to provide 100% reliability Surplus electricity sent to grid or curtailed Diesel generally used in the absence of grid. But it could be also used during peak grid tariffs. Surplus PV generation used for hydrolysis of water and hydrogen generation to later generate electricity in a fuel cell Surplus PV output saved in battery for later consumption Battery used to shift consumer load. Economic benefit for the user and DSM benefits for network operator Surplus PV output saved in battery for later consumption. Shortfall supplied by diesel generator. Surplus PV generation saved in battery or used for electrolysis of water and hydrogen generation. Hydrogen generates electricity in fuel cell during high demand periods. Surplus wind generation curtailed. Demand shortfall supplied by diesel generator. Surplus wind generation stored in water by pumping to higher elevation. When wind unavailable, water directed to lower elevation and generates electricity. As above, except that diesel generator used when water storage insufficient to supply demand shortfall.

[48] [26] [49,50] [51,52] [53] [54] [55]

Surplus wind output saved in battery for later consumption. Shortfall supplied by diesel generator. Electricity generated with PV and wind when available. Shortfall supplied by diesel generator. When generator not operating as a base-load, possible reliability issue without grid connection. Electricity generated with PV, wind, and biogas from sewage treatment, etc. When biogas generator not operating as a base-load, possible reliability issue without gridconnection. Surplus PV/wind generation saved in battery. Demand shortfall still possible.

[56] [21]

Surplus PV/wind generation saved in battery. Possible demand shortfall supplied with diesel generator. Surplus PV/wind generation stored in water by pumping it to higher elevation. When PV/wind output insufficient, water directed to lower elevation and generates electricity. As pumped hydro cannot follow load with multiple on/off, reliability issue possible unless there is grid connection. Surplus PV/wind/solar-thermal generation stored in water by pumping to higher elevation. When PV/wind/ solar-thermal output insufficient, water directed to lower elevation and generates electricity. As above, but battery helps for faster response to load change compared with hydro. Surplus PV/wind generation s converted to hydrogen by water electrolysis and stored in battery. When PV/ wind output insufficient, fuel cell or battery used. Remaining shortfall supplied by diesel generator. Surplus PV/wind generation converted to hydrogen by water electrolysis, stored in water by pumping, and stored in battery. When PV/wind output insufficient, one or combination of the three storage sources utilized.

[22,59,60] [61]

[57] [20,58]

[62] [63] [23] [64]

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807

Table 2 Techno-economic specifications of candidate batteries for the house (parameters mainly from Ref. [43]). Battery type

Manufacturing round-trip efficiency

Annual efficiency loss factor due to aging

Dis/charge duration (hours)

Base capex ($2012/kWh)

Advanced lead acid A Advanced lead-acid B Valve-regulated lead acid A Valve-regulated lead acid B Li-ion high energy Li-ion high power

0.800 0.900 0.680 0.780 0.920 0.910

0.960 0.960 0.955 0.955 0.970 0.970

2 5 2 4 2 1

1100 870 800 625 875 1200

equations can be removed from the list and the program executed with the remaining equations. It is also noteworthy that the constraints depicted by Eqs. (2) and (18)e(21)4-26) can be unnecessary (redundant in optimization terminology) for certain problems.

2.2. Operation scheduling of DGS system In the previous section we introduced a methodology to help the customer identify whether a DGS system is a feasible investment option and, if so, to define the best DGS configuration which can return the maximum economic benefits over the planning horizon. Here, we address the scenario where the customer has installed a DGS system (or either of them) and wants to operate the integrated system so that the local electricity is always supplied with the desired reliability, while it provides the maximum economic benefit (minimum bill) over the planning horizon. The formulation of this problem is similar to that in the previous section with some differences: here the DGS are installed and their sizes and characteristics are known. The formulation in most cases is similar to that in the previous scenario, with the difference that now the technology selection variables (y0j and yi) should be removed or treated as parameters with value of 1. For instance, Eq. (5) is now given by DG DG:G DG:L Xip ¼ Xip þ Xip þ

J X

DG:S DG Xijp  Cip

Fig. 11. Annual average daily profile of the house's load by supply sources.

1  p  P; 1  i  I

j¼1

(5a) Also, given that operation is generally scheduled for shorter timeframes, H is taken as 1. The economic objective function, i.e., minimum costs (C*) or maximum dollar saving in the electricity bill (S*) over the planning horizon, is given respectively by

1 0 0 J  P I  P  X  X X X DG S @ @X G:L EPp FOMip þ FOMjp A þ C ¼ p *

p¼1

i¼1 00

þ y1 CFp þ



G:S S:G Xjp EPp  Xjp FITp 

j¼1

þ

p¼1

j¼1 J  X

1  FCip þ GHCip A

I  X

DG:G hDGin FITp ip Xip



i¼1

I  X i¼1

(29) S* ¼

P  X  Lp EPp þ CFp  NPVC

(30)

p¼1

This completes the MILP (for constant inverter efficiency) or MINLP (for inverter efficiency as a function of input power) for the DGS scheduling problem. It consists of Eqs. (5)e(26) with the objective of minimizing C* (Eq. (29)) or maximizing S* (Eq. (30)).

Fig. 12. Consumer's load profile during the base year; hourly (top), and daily average (lower).

808

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Fig. 13. Annual wind speed profile (JulyeJune).

3. Base case: optimal investment decision for a house A house in Sydney, Australia, has consumed within one year (July 1 to June 30) about 6.1 MWh of electricity, which is in the range of Sydney's average household electricity consumption. The

consumer's half-hourly load profile during the base year is illustrated in Fig. 8 [37]. The current electricity price consists of three ToU tariffs: offpeak, shoulder, and on-peak (See Fig. 9). Off-peak (13 c/kWh) includes 10:00 p.m. to 7:00 a.m. Shoulder (21 c/kWh) is during 7:00 a.m. to 2:00 p.m. and 8:00 p.m. to 10:00 p.m. on weekdays, and 7:00 a.m. to 10:00 p.m. during weekend/public holidays. The onpeak (52 c/kWh) period is during 2:00 p.m. to 8:00 p.m. on weekdays [38]. There is also a daily connection fee (supply charge) of $0.87. Under this electricity pricing scheme the house has spent $1974.35 for its electricity bill over one year. The consumer is interested to investigate the feasibility of installing a PV-battery system to curb the electricity bill. When feasible, it is of interest to find the best mix of PV/battery, with or without grid, which results in the minimum electricity cost. The candidate PV panels have the standard efficiency of 0.17 and are available in various sizes within the house's area limitation for a maximum 10 kW PV system. The periodical PV panels' efficiency ðhPV ip Þ is affected by ambient temperature with a function of 1.09036  Tp [39]. The PV output also decreases by 0.5% annually (due to aging). The annual ambient temperature and GHI profiles are illustrated in Fig. 10. The prices of PV systems are considered to be $2700 for a 1.0 kW system that follows a power-law economy of scale with power constant of 0.76 [40]. The house owner is interested to investigate the feasibility of six battery types, each with different capacity and techno-economic

Fig. 14. Schematic of the shopping center's DGS system.

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809

Table 3 Summary of the annual operation schedule for the shopping center with the installed DGS system.

Load received from

Battery 1 charge received from

Battery 2 charge received from

PV output dispatched to

Wind output dispatched to

Source/destination

kWh p.a.

%

Grid PV Wind Battery 1 Battery 2 Diesel Sum (total Grid PV Wind Sum (total Grid PV Wind Sum (total Grid Battery 1 Battery 2 Load Sum (total Grid Battery 1 Battery 2 Load Sum (total

936,481.3 160,649.8 989,02.8 59,598.35 114,829.5 140,242.7 1,510,703.7 15,116.3 3934.2 4,4662.5 63,713.02 107,147.4 1670.3 22,526.3 131,344.0 0.0 3934.2 1670.3 163,928.3 169,532.8 0.0 44,662.5 22,526.3 100,921.2 168,110.0

70.0 10.6 6.5 4.0 7.6 9.3 100.0 23.7 6.2 70.1 100.0 81.6 1.3 17.1 100.0 0.0 2.3 1.0 96.7 100.0 0.0 26.6 13.4 60.0 100.0

demand)

energy received)

energy received)

PV energy)

wind energy)

parameters. Table 2 lists the specification of the candidate batteries. The selected batteries will operate at a maximum DOD of 85%. The charge controllers and inverters have an assumed efficiency of 98%. The annual maintenance cost of the PV system is 0.5% of its capex, while it is 1.0% for batteries. The unit cost of batteries ($/kWh) during 2012 is given in Table 2. These prices have since fallen by 30% and also follow a power-law economy of scale similar to PV systems. The solar FiT is 8.0 c/kWh during the base year [41]. The annual price escalation factor is 3% with a discount rate of 7% [42]. The consumer projects that the electricity consumption will increase by 0.5% annually over the next 10 years and wants to assess whether it is economical to install PV and/or battery systems. If yes, what are the specifications of the selected system(s) and how should the

systems be operated? The problem is solved for 10 years of operation using CPLEX 12.4.0.1 on a desktop PC with 16 GB RAM. The optimization program suggests that it is more economical to invest in a PV-battery system than to buy electricity completely from the grid. The optimum decision is identified as a 2.0 kW PV system with a high energy Li-ion battery of 5.5 kWh size. Fig. 11 illustrates the annual-average daily profile of the house's electricity supply obtained from the program results. It is evident that this integrated PV-battery system has reduced the house's direct dependence on the grid to 45.7% during the first year of operation. Under this condition, the house receives 2801.2 kWh of electricity directly from the grid within the first year. The remaining demand is satisfied by the PV system (1554.2 kWh, i.e. 25.4%) and

Fig. 15. Annual-average daily profile of shopping center's load by supply sources.

810

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battery (1773.55 kWh, 28.9%). The PV output is mainly allocated for local use, providing for the local load (46.8%) and battery charge (38.3%). The small surplus PV generation (504.6 kWh, i.e. 14.9%) is dispatched to the grid. The battery does not dispatch electricity to the grid during any period B:G ¼ 0Þ. Within the first year, the battery receives 598.8 kWh ðXip (31.5%) of electricity from the grid, mainly during off-peak periods, and its remaining charge (1300.1 kWh, 68.5%) is supplied by the PV system. The selected 5.5 kWh battery never operates below 15% SOC, i.e. 0.83 kWh charge, and its average annual SOC is 2.79 kWh. In summary, without the PV-battery installation, the average annual electricity demand is 0.70 kW. With installation of the PVbattery system, the average demand from the grid decreases to 0.39 kW (0.32 kW for load and 0.07 kW for battery charge). Under the given conditions, this investment can save $949.50 (NPV of cash flow) in the electricity bill over the next 10 years. 4. Case study of a grid-connected shopping center A shopping center in rural area out of Sydney, New South Wales,

has consumed within one year (January 1 to December 31) about 1,503,187.7 kWh of electricity with hourly profiles as per Fig. 12. The electricity tariff is similar to the previous example (Fig. 9). As a large-scale customer, however, the shopping center receives 10% discount on its electricity bill. Given this electricity pricing scheme, the shopping center has spent $404171.70 for its electricity bill over one year. The building has a 150 kW diesel generator as a backup for emergency uses. The generator has a fuel-to-power efficiency of 30% and fuel price of 12 c/kWh. The building management has decided to install a 100 kW PV system together with a 50 kW wind turbine. The PV system has standard efficiency of 0.17, but the periodical PV panel's efficiency ðhDG ip Þ is affected by the ambient temperature with a function of 1.09036  Tp [39]. The PV output also decreases by 0.5% annually (due to aging). The annual ambient temperature, GHI are given in Fig. 10 and wind speed profiles are illustrated in Fig. 13. The management has also decided to install two battery systems, a 200 kWh li-ion high energy system (j1: round trip efficiency: 92%; dis/charge duration: 2 h; annual efficiency loss factor

Fig. 16. Annual-average daily generation and dispatch profiles of wind (top) and PV (lower) generators for the shopping center.

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811

Fig. 17. The annual-average daily SOC profile of the installed battery systems 1 and 2 during the first year of operation.

due to aging: 0.97) and a 400 kWh sodium nickel chloride system (j2: round trip efficiency: 87%; dis/charge duration: 4 h; annual efficiency loss factor due to aging: 0.965) [43]. The batteries will operate at a maximum depth of discharge (DOD) of 85%. The charge controllers and inverters have an assumed efficiency of 98%. The annual maintenance cost of the PV system is 0.5% of its capex and is 1.0% for batteries. The solar FiT is $0.08/kWh during the base year [41]. The annual price escalation factor is 3%, with q discount rate of 7% [42]. The overall schematic of the shopping center's DGS system is illustrated in Fig. 14. Under the new operating arrangements, the diesel generator can generate whenever it is needed, enforced by the reliability constraints and/or economic objectives. The shopping center management predict that the electricity consumption will increase by 0.5% annually over the next few years and want to assess the amount of savings in electricity bill that this new integrated DGS system could cause if it is scheduled and operated optimally. The model contains 131,403 equations and 210,243 variables. The problem is solved for one year of operation using CPLEX 12.4.0.1 with an execution time of 3.3 s using a desktop PC with 16 GB RAM. The optimization program suggests that with the given DGS system, the building could reduce its next year's electricity bill by about $133,874.40 (~32% reduction). A summary of the operation schedule that enables such a saving is given in Table 3. Fig. 15 illustrates the annual-average daily profile of the shopping center's load by supply sources obtained from the program results. It is evident that this integrated DGS system has reduced the building's direct dependence on the grid down to 62% during the first year of operation. The remaining 38% demand of the building is supplied by PV (10.6%), wind (6.5%), diesel generator (9.3%), battery 1 (4.0%) and battery 2 (7.6%). It is also evident from Fig. 15 that the diesel generator operates only during peak periods (2e8 pm). The annual-average daily generation and dispatch profiles of wind (top) and PV (lower) generators for the shopping center are illustrated in Fig. 16. As shown, the main fraction of both PV and wind generation goes directly to the load and none of the generators dispatches electricity to the grid. For wind, 60% of generation goes to the load and from the remaining 40%, around two thirds (26.6%) goes to battery 1 and one third (13.4%) is stored in battery 2. For PV, the share of direct local consumption is much higher, around 96.7%, with only a very small fraction (3.3%) stored in

batteries 1 and 2. Like the generators, the batteries do not dispatch electricity to the S:G ¼ 0Þ. Within this year, battery 1 regrid during any period ðXip ceives 63.7 MWh of energy for storage, the majority of which comes from wind turbine (70.1%). The remaining energy comes from the grid (23.7%) and the PV system (6.2%). Battery 2 receives 131.3 MWh of energy from the grid (81.6%), wind generator (17.1%) and PV (1.3%). The reason that both PV and battery dispatch more energy to battery 1 than to battery 2 could be the s charging time of battery 1. The SOCs of the two battery systems are illustrated in Fig. 17. It is evident that both batteries have identical SOC profiles. During late evenings (around 10 p.m.) the batteries have their lowest SOC. From that time, they charge overnight until around 7 a.m. the following day when they reach their full SOC. From around 8e10 a.m., they gradually discharge their energy to supply part of the local load, until reaching their lowest SOC in the late evening (~10 p.m.). 5. Conclusion With the fast development in DGS technologies and introduction of various products with diverse specifications, it becomes a complex problem to decide if and what DGS system to install. We developed a generic multi-period mixed-integer program to help end-users in this decision making process. The model is capable of identifying the feasibility of an investment in DG and/or storage systems, and the specifications of the optimal system. All these decision variables are identified concurrently with finding the optimal operation schedule of the DGS systems at each period over the planning horizon. These variables include power flows of gridto-load, DG-to-load, storage-to-load, storage-to-grid, grid-tostorage, DG-to-storage, DG-to-grid as well as SOC of storage. This decision support program enables the consumer (ranging from a small house to large-scale industrial plants) to implement the most efficient electricity management strategy while achieving the goal of minimizing the electricity bill. Nomenclature

Symbols Ai area of DG system i

812

Am Bjp CRj DRj CXjS CXiDG FiTp EPp S FOMjp DG FOMip

GHIp H I J Lp LLP M NDG NB NPV P0 R r S

SSj SDG i SOCjp SOCjL SOCjU Tp Wp S:L Xjp S:G Xjp G:S Xjp XpG:L DG:S Xijp DG:G Xip DG:L Xip yi y0j yBjp

yG p

bjp hCj hDj hCjp hDjp

hDG i hDG ip hCC j hDGin i hSin j

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maximum acceptable area of all selected DG systems input-output balance of storage system j in period p maximum possible charge rate of storage system j maximum possible discharge rate of storage system j capex of storage system i capex of DG system i FiT in period p electricity price in period p fixed operation and maintenance costs for storage system j in period p fixed operation and maintenance costs for DG system i in period p GHI in period p segments of planning horizon number of candidate DG systems number of candidate storage systems electricity demand in period p loss of load probability Big-M value maximum number of selected DG systems maximum number of selected storage systems net present value number of periods per h reliability discount rate saving over the planning horizon size of storage system j size of DG system i SOC for storage system j in period p lower bound of SOC for storage system j upper bound of SOC for storage system j weather temperature in period p wind speed in period p AC power sent from storage system j to load in period p AC power sent from storage system j to grid in period p AC power sent from grid to storage system j in period p AC power sent from grid to load in period p DC power sent from DG system i to storage system j in period p DC power sent from DG system i to grid in period p DC power sent from DG system i to load in period p binary variable to indicate if DG system i is selected binary variable to indicate if storage system j is selected binary variable to indicate if storage system j is charged by DG systems or grid in period p binary variable to indicate if electricity is received from the grid in period p self-discharges of storage system j in period p nominal charge efficiency of storage system j nominal discharge efficiency of storage system j storage charge efficiency of system i in period p nominal discharge efficiency of storage system i in period p nominal (standard) design efficiency of DG system i efficiency of DG system i in period p efficiency of charge controller for storage system j inverter nominal efficiency for DG system i inverter nominal efficiency for storage system j

Subscripts h indicator p indicator i indicator j indicator

of of of of

time segment period DG system storage system

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