Optimal siting and sizing of tri-generation equipment for developing an autonomous community microgrid considering uncertainties

Accepted Manuscript Title: Optimal siting and sizing of tri-generation equipment for developing an autonomous community microgrid considering uncertainties Authors: Akhtar Hussain, Syed Muhammad Arif, Muhammad Aslam, Syed Danial Ali Shah PII: DOI: Reference:

S2210-6707(16)30394-8 http://dx.doi.org/doi:10.1016/j.scs.2017.04.004 SCS 629

To appear in: Received date: Revised date: Accepted date:

20-9-2016 5-4-2017 5-4-2017

Please cite this article as: Hussain, Akhtar., Arif, Syed Muhammad., Aslam, Muhammad., & Shah, Syed Danial Ali., Optimal siting and sizing of tri-generation equipment for developing an autonomous community microgrid considering uncertainties.Sustainable Cities and Society http://dx.doi.org/10.1016/j.scs.2017.04.004 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.

Optimal Siting and Sizing of Tri-Generation Equipment for Developing an Autonomous Community Microgrid Considering Uncertainties Akhtar Hussain a, ∗, Syed Muhammad Arif b, Muhammad Aslamc, Syed Danial Ali Shahd a

Department of Electrical Engineering, Incheon National University, 119 Academy-ro, Yeonsu-gu, Incheon, Korea

b College

of Information & Communication Engineering, Sungkyunkwan University, 2066 Seobu-ro, Jangan-gu, Suwon, Korea

c

Department of Electrical Engineering, Myongji University, 116 Myongji-ro, Cheoin-gu, Yongin, Korea

d

Department of Electronics Engineering, Incheon National University, 119 Academy-ro, Yeonsu-gu, Incheon, Korea

Highlights     

Development of sustainable community microgrid has been proposed. Total network losses are considered for siting of tri-generation equipment. Uncertainties in energy demands are considered for sizing of tri-generation equipment. Seasonal energy demand variations are considered in the siting and sizing phases. Particle swarm optimization is used for siting and sizing of energy hub.

Abstract- Community microgrids are central pillars of the modern clean and efficient infrastructures, due to their deployment in municipalities. Community energy mangers are responsible for fulfilling the energy demands of inhabitants, especially during outages of the main grid. Determination of optimal sizes of generation sources and optimal site for deployment of these sources is a key issue. Therefore, in this paper, development of an autonomous community microgrid is suggested through optimal sizing and siting of tri-generation equipment. Total network losses (thermal and electrical) for different seasons of the year are considered for determining the optimal site of the energy hub. Thermal losses are computed through modified Dijkstra algorithm and electrical losses are computed by using exact loss formula. Worst-case realization of uncertainties associated with energy demands (cooling, heat, and power) are considered for optimal sizing of tri-generation equipment to fulfil the load demands of community microgrid throughout the year. Final sizes of tri-generation equipment are determined through worst-case realization of uncertainties associated with renewable energy sources. Particle swarm optimization (PSO) is used for both sizing and siting of tri-generation equipment in the community microgrid. Standard IEEE 33-bus distribution system is transformed into a sustainable community microgrid by placing the optimally sized energy hub at the optimal location determined by PSO.

Keywords- Network transformation, particle swarm optimization, resilient microgrid network, siting and sizing, sustainable microgrids, tri-generation

1. Introduction Distributed generators (DGs) are expected to play a vital role in the transformation of the conventional passive distribution system to an active distribution network [1]. DGs have the potential to offer several benefits to both the utilities and the customers, which includes economic, technical, and environmental (if renewable) benefits. Installation of DGs at non-optimal locations can result in various issues for power systems, i.e. increase in system losses, voltage deviation, and system reliability & stability issues. Therefore, optimal deployment of DGs is required to get the above-mentioned benefits. Various studies are conducted for optimal siting and sizing of DGs in distribution systems [2]-[6]. The major objectives of the DG deployment could be categorized as minimization of power losses, cost, and voltage deviations along with maximization of DG capacity and social welfare. The major methods used by the researchers can be broadly categorized as analytical methods, artificial intelligence-based methods, and hybrid intelligent methods. Experiences during recent natural disasters around the globe have shown that microgrid can help communities and businesses to function with greater resiliency during extreme weather [7-9], especially microgrids with combined heat and power (CHP) technologies [10]. A similar report has been released by the United States Departments of Energy (DOE) Housing and Urban Development (HUD) and Environmental Protection Agency (EPA) [11] in 2013. CHP systems are of specific importance to microgrids due to their proximity to the end users [12]. Waste heat is used to fulfill the heat load demands of the consumers and thus enhances the overall system efficiency. Tri-generation, also known as combined cooling, heat and power (CCHP), technologies are becoming more desirable and are even more economical due to their ability to suffice cooling, heat, and power demands [13]. The efficiency of trigeneration systems is up to 60-80%, which is considerably higher than those of conventional power systems [14]. Due to these benefits, only in the USA more than 80% of the installed capacity of microgrids is based on CHP systems [15]. Various studies are conducted for modeling and deployment of CHP systems in microgrids [16]-[19]. Among various other microgrid types, community microgrids have a higher impact on utility grids in terms of coverage and power ratings [20]. Therefore, community microgrids are considered as central pillars of modern smart grids due to their deployment in the municipalities [21]. Community microgrids empower local leaders to serve their local energy needs in more economical, reliable, and environmentfriendly manner [22]. Community microgrids have the potential to enhance the resiliency of municipalities during high-impact low probability events [23], [24]. Therefore, various studies are conducted for energy management and deployment of community microgrids. Microgrid community as a socio-ecological system-based formulation is suggested by [25] for energy management of community microgrids. Electrification of rural communities is carried out by the [26-28] considering the

socioeconomic requirements of the targeted population. The importance of community microgrids for highlands and islands in the UK has been analyzed by [29] in partnership with Scottish government. Planned community microgrids have been analyzed by [30] as a business model for the application of the microgrid concept. The authors in [31] have analyzed the planning aspect and energy balancing of planned community microgrids. The performance of community microgrids has been analyzed by [32] due to change in environmental conditions and electric faults in the UK and China. According to DOE, microgrids are a group of interconnected loads and DRs with clearly defined electrical boundaries that act as a single controllable entity with respect to the grid [23]. Originally, the purpose of microgrids was to operate both in grid-connected and islanded modes and survive the local critical loads during grid contingencies [24]. However, recently studies on transformation of existing distribution systems into autonomous microgrids are also carried out. Optimal siting and sizing of DGs along with structural modifications are suggested by [33] for transforming an existing distribution network into an autonomous microgrid. Both particle swarm optimization (PSO) and genetic algorithms are used for the optimal placement of DGs. A double bus bar DC system is used in [34] for assessing the resilience of grid and to rebuild more efficient partitions in run-time. Service-oriented architecture is used to make an intelligent system for dynamically distributing load between the two buses to make selfsustainable microgrids. Meanwhile, recently the concept of energy hubs is being used for fulfilling the electrical, heat, and cooling requirements of the customers. Energy hubs represent an interface between different energy infrastructures and loads. They consume power at their input ports (electricity and natural gas) and prepare certain required energy services like electricity, heating, and cooling at their output ports [35]. Energy hub approach is used by [36] for optimal placement of CHP units in multi-carrier energy networks. An analytical approach is used by [37] for determining the optimal size of energy hub by using cost and benefit analysis. The energy requirement of microgrid residents significantly varies during different seasons of the year [38]. In addition, the uncertainties associated with load forecasted values and renewable generations make the optimization problem more challenging. Low carbon energy hub for decentralized, renewable energy-based energy systems has been analyzed for Oxfordshire and the U.K by [39], in order to put ownership of local power in the hands of local people. The energy research center (ERC) of the UK has published a report in 2016, where different scenarios have been analyzed for development of smart grids in the UK [40]. Energy hub concept has been opted as a feasible solution in that report. The concept of energy hub has been utilized by [41], and a general approach has been suggested to optimize the power and heat flow between residential houses. Interconnected energy hubs have been considered by [42] for multicarrier energy networks by using a goal programming

methodology. The proposed methodology has been utilized for identification of optimal operation state of the distributed energy hubs. Various researches have been conducted for managing the uncertainties in microgrids. Sensitivity analysis [43, 44], fuzzy logic-based optimization [45], stochastic optimization techniques [46], and robust optimization [47, 48] are among the noticeable techniques available in the literature for uncertainty management. Due to the ability of the robust optimization to provide immunity against the worst-case realization, it has gained popularity among the energy management research community. Most of the researches available in the literature on uncertainty management are focused on day-ahead scheduling or day of economic dispatch problems. Consideration of uncertainties and seasonal demand variations at planning phase is more desirable for fulfilling the energy demands of the network throughout the year. An attempt has been made in this paper to site and size the tri-generation equipment in a community microgrid, from the community energy manager point of view. The objective of the formulation is to minimize the reliance of microgrid community on the central grid and to develop an autonomous community microgrid. In contrast to [33], [34], where only electrical self-sufficiency of microgrids is focused, self-adequacy of CCHP is suggested in this paper. In addition, seasonal thermal energy losses are considered due to the dependence of thermal losses on ambient temperatures. Siting has been done by considering the total network losses, which includes both electrical and thermal losses. Similar to [49] and [50], exact loss formula is used to determine both active and reactive losses at each node. Modified Dijkstra algorithm is used to determine the thermal losses (heat and cooling) at each node. Uncertainties in all the loads (electrical, heat, and cooling) and renewable power generations have been considered during the sizing phase. The uncertainties are realized via a robust optimization technique. An autonomous and sustainable community microgrid has been developed by transforming the standard IEEE 33-bus distribution system. An energy hub has been placed at the optimal location determined by PSO. Optimal sizes of all the tri-generation equipment have also been determined through PSO.

2. Community microgrid network and energy management The purpose of community microgrids is to serve community’s energy needs in a more economical, reliable, and environmentally friendly manner than the conventional electricity grid [21]. A community microgrid is an energy system, which is specifically designed to meet the energy needs of a community. The responsibilities of community microgrid could be generation of electricity, heating and/or cooling, distribution of the generated energy, and energy management. More specifically, a community microgrid typically focuses on ensuring the critical services to the community members during a grid outage [22]. A community energy manager (community leader) is required to plan and manage the energy requirements of the entire community. The focus of this study is to site and size an energy hub within the community to

fulfill the energy demands of the entire community round the year. The formulation is focused on the community energy manager’s planning point of view.

2.1 Energy network A conventional distribution system, standard IEEE 33-bus radial distribution system, is shown in Fig. 1(a). The conventional distribution system contains only electrical network. However, heating and cooling networks are also considered in this study. The networking of heating and cooling networks is taken as same with the conventional electrical network, as shown in Fig. 1(b). All of the nodes have heating, cooling, and electricity demands. As mentioned earlier, the role of community microgrid is to provide energy to the community members during grid outages. Therefore, the formulation, in this study, has been targeted to minimize the grid dependency, i.e. planning to suffice the energy demands of the community autonomously.

2.2 Energy management Due to the advantages of energy hub as mentioned earlier, energy hub concept has been used in this paper to fulfill the energy demands of the microgrid community. A typical energy hub for tri-generation is shown in Fig. 2. The electricity demand of the microgrid community can be fulfilled by using CHPs or DGs. CHPs and heat only boilers (HOBs) can be used for fulfilling the heating demand and finally, cooling demand of the network can be fulfilled by using adsorption/absorption chillers (ACH) and electric heat pumps (EHPs). The consumers at each of the community microgrid could have their own local generation sources. These generation sources could be electrical (𝑃𝐷𝐺𝑖 , 𝑄𝐷𝐺𝑖 ), heat (𝐻𝑖𝐶𝑆 ), and/or cooling (𝐶𝑂𝑖𝐶𝑆 ). The objective of the microgrid community manager is to fulfil the net demand of the network. Therefore, net demand at each node can be computed by using following equations. 𝑃𝑖𝑙𝑜𝑎𝑑 = 𝑃𝐷𝐺𝑖 − 𝑃𝑖𝑙 , 𝑄𝑖𝑙𝑜𝑎𝑑 = 𝑄𝐷𝐺𝑖 − 𝑄𝑖𝑙

∀𝑖 = 1,2,3, … 𝑁

(1) 𝐻𝑖𝑙𝑜𝑎𝑑 = 𝐻𝑖𝐶𝑆 − 𝐻𝑖𝑙 , 𝐶𝑂𝑖𝑙𝑜𝑎𝑑 = 𝐶𝑂𝑖𝐶𝑆 − 𝐶𝑂𝑖𝑙

∀𝑖 = 1,2,3, … 𝑁

(2)

Where, 𝑃𝑖𝑙𝑜𝑎𝑑 , 𝑄𝑖𝑙𝑜𝑎𝑑 , 𝐻𝑖𝑙𝑜𝑎𝑑 , 𝐶𝑂𝑖𝑙𝑜𝑎𝑑 are the net active power, reactive power, heat, and cooling demands, respectively at node i. 𝑃𝑖𝑙 , 𝑄𝑖𝑙 , 𝐻𝑖𝑙 , 𝐶𝑂𝑖𝑙 are the initial active power, reactive power, heat, and cooling demands, respectively at node i. 𝑃𝐷𝐺𝑖 , 𝑄𝐷𝐺𝑖 , 𝐻𝑖𝐶𝑆 , 𝐶𝑂𝑖𝐶𝑆 are the active, reactive, heat, and cooling energies, respectively generated at node i. Fig. 3 shows the conceptual overview of the net energy at each node of the community microgrid.

Due to the presence of renewable energy sources (DGs) and unpredictable energy usage patterns of community members, the net energy demand of the consumers is highly uncertain. In addition, the thermal network losses vary during different seasons of the year due to differences in ambient temperatures. Finally, the heating and cooling demands of the community members also vary with seasons of the year, which also influence the electricity demand. Therefore, all of the above-mentioned parameters need to be considered by the community manager to assure service reliability throughout the year.

3 Siting and sizing of tri-generation equipment The siting and sizing of energy hub is decomposed into two steps in this paper, in order to reduce computation time and to avoid local trapping of PSO. In siting phase, an optimal location for the deployment of an energy hub is determined. In the siting phase, the network losses of both electrical and thermal networks are assessed and an optimal location is determined. In siting phase, forecasted values of loads and renewables are considered and a rough energy balancing is considered. However, in the sizing phase, uncertainties associated with loads and renewable generations are considered, and final solutions are determined. Therefore, sizing phase can be seen as tuning of energy generation/conversion equipment sizes under worst-case scenarios.

3.1 Siting of energy hub The first step in the proposed method for development of a sustainable community microgrid is to determine the location of energy hub, i.e. siting of energy hub. Both thermal (heat and cooling) and electrical losses of the network are determined to find the optimal location of the energy hub. Similar to [49] and [50], exact loss formulas are used for determining the active power loss of the network (𝑃𝐿 ) and reactive power loss of the network (𝑄𝐿 ), as given by equations (3) and (4), respectively. The sensitivity factors for both active (𝛼𝑖𝑗 , 𝛽𝑖𝑗 ) and reactive (𝛾𝑖𝑗 , 𝛿𝑖𝑗 ) power losses are computed by using the bus voltage, bus angle, and line impedances. Bus voltage and angle are computed at each iteration of PSO by using load flow analysis. Firstly, Y-bus of the network is computed by using the network connection information and then Newton-Raphson method is used for load flow analysis. 𝑛

𝑛

𝑃𝐿 = ∑ ∑ (𝛼𝑖𝑗 . (𝑃𝑖 . 𝑃𝑗 + 𝑄𝑖 . 𝑄𝑗 ) + 𝛽𝑖𝑗 . (𝑄𝑖 . 𝑃𝑗 − 𝑃𝑖 . 𝑄𝑗 ))

∀𝑖, 𝑗 = 1,2,3, … 𝑛

(3)

∀𝑖, 𝑗 = 1,2,3, … 𝑛

(4)

𝑖=1 𝑗=1 𝑛

𝑛

𝑄𝐿 = ∑ ∑ (𝛾𝑖𝑗 . (𝑃𝑖 . 𝑃𝑗 + 𝑄𝑖 . 𝑄𝑗 ) + 𝛿𝑖𝑗 . (𝑄𝑖 . 𝑃𝑗 − 𝑃𝑖 . 𝑄𝑗 )) 𝑖=1 𝑗=1

Where, 𝑃𝑖 = 𝑃𝐷𝐺𝑖 − 𝑃𝑖𝑙𝑜𝑎𝑑 ,

𝑄𝑖 = 𝑄𝐷𝐺𝑖 − 𝑄𝑖𝑙𝑜𝑎𝑑

∀𝑖 = 1,2,3, … 𝑛

𝛼𝑖𝑗 =

𝑟𝑖𝑗 . cos(𝜃𝑖 − 𝜃𝑗 ) , 𝑉𝑖 . 𝑉𝑗

𝛾𝑖𝑗 =

𝑥𝑖𝑗 𝑥𝑖𝑗 . cos(𝜃𝑖 − 𝜃𝑗 ), 𝛿𝑖𝑗 = . sin(𝜃𝑖 − 𝜃𝑗 ) 𝑉𝑖 . 𝑉𝑗 𝑉𝑖 . 𝑉𝑗

𝛽𝑖𝑗 =

𝑟𝑖𝑗 . sin(𝜃𝑖 − 𝜃𝑗 ) 𝑉𝑖 . 𝑉𝑗

∀𝑖, 𝑗 = 1,2,3, … 𝑛 ∀𝑖, 𝑗 = 1,2,3, … 𝑛

𝑃𝐷𝐺𝑖 , 𝑄𝐷𝐺𝑖 : Active and reactive power injected by DG units at bus i. 𝑃𝑖𝑙𝑜𝑎𝑑 , 𝑄𝑖𝑙𝑜𝑎𝑑 : Active and reactive loads at bus i. 𝑃𝑖 , 𝑄𝑖 : Net active and reactive power injected at node i. 𝑉𝑖 . 𝜃𝑖 : Voltage magnitude and angle at bus i. 𝑟𝑖𝑗 , 𝑥𝑖𝑗 : Resistance and reactance of line connecting buses i and j. The thermal conduction loss of a circular or a cylindrical pipe of known length, connecting nodes i and j, can be determined by using equation (5) [18]. 𝑙𝑜𝑠𝑠 𝑇𝐻𝑖𝑗 =

2. 𝜋. 𝐿𝑖𝑗 . (𝑡1 − 𝑡2 ). 𝑘 𝑟 ln( 2⁄𝑟1 )

∀𝑖, 𝑗 = 1,2,3, … 𝑁

(5)

Where 𝐿𝑖𝑗 is the length of pipe connecting buses i and j; 𝑡1 , 𝑡2 are the fluid and ambient temperatures, respectively; 𝑟1 , 𝑟2 are, respectively, the radius of the pipe and radius of the pipe with lagging material; 𝑘 is the thermal conductivity of lagging material in W/mK. Equation (5) has been used to determine the thermal conduction loss between each connected node pair of the network. Dijkstra algorithm [51] has been modified and used to determine the total thermal loss of the network. Dijkstra algorithm is primarily used for finding the shortest route between nodes, i.e. source and destination nodes. However, in this study, Dijkstra algorithm is used to find the thermal loss of the network. The thermal loss of a network is a function of the length of pipeline connecting two adjacent nodes and the ambient temperature of the medium, as given by Equation (5). The step-by-step process of the modified Dijkstra algorithm is as follows: a. Compute loss between each pair of nodes by using Equation (5). b. Determine the network adjacency matrix based on the connection information of the network. c. Transform the adjacency matrix to loss matrix by using losses computed in the previous step. d. Select node i and compute losses from all nodes of the network to the selected node (i). e. Accumulate all the losses and store the accumulated value for selected node. f.

Repeat steps d and e for all the nodes of the network and for all the seasons of the year.

g. Sort the data of step f and select the node with minimal value. The selected node will be the node with minimal thermal loss for the given network configuration. The overall algorithm for determining thermal loss of the network is shown in Fig. 4.

After finding the electrical and thermal losses of each node pair, PSO has been used to determine the optimal location for placing the energy hub. Unlike genetic algorithms, PSO does not change the population in each iteration, instead, updates the positions of members of the same population [52]. This results in fast convergence of PSO as compared to genetic algorithms. Instead of using a survival of the fittest approach, the members of PSO population interact and influence each other. This results in cooperation between the population members and finally, the optimal solution is achieved more rapidly as compared to other alternative methods. Therefore, PSO has been widely used for siting and sizing of DGs [49, 50, 53-55]. Due to the above-mentioned merits of PSO, it has been used in this study for optimal siting and sizing of tri-generation equipment. The objective function with related constraints for determining the optimal location of the energy hub is discussed in the following sections.

3.1.1 Objective function The objective of the optimal siting step is to find a single location for the deployment of the energy hub. It has been assumed that the maximum size (capacity) of energy hub is known in advance. The community leader needs to analyze the required capacity of energy hub for his/her community. The size of the energy hub could be very large or very small depending on the load amount of a particular community microgrid. The maximum and minimum bounds of the energy hub are taken as inputs for the optimization method. In addition, a single energy hub has following advantages over multiple energy hubs. a) If more energy hubs are deployed, separate energy networks may be required for each energy hub, which will result in an increase of deployment cost. b) Due to the presence of several energy hubs, operation and maintenance costs will increase. c) If a single community microgrid has more than one energy hubs with different ownerships, it may result in policy clash and cause administrative issues.

The objective function for optimal siting of the energy hub is given by (6). The objective function contains the cost of deployment of CHP units (𝐶𝑐𝐶𝐻𝑃 . 𝑢𝑐𝐶𝐻𝑃 ), cost of deployment of DGs (𝐶𝑑𝐷𝐺 . 𝑢𝑑𝐷𝐺 ), energy loss cost of the network (𝐶𝑖𝑗𝑙𝑜𝑠𝑠 . 𝑇𝑖𝑗𝑙𝑜𝑠𝑠 ), and penalty cost for voltage limits violation (𝐶𝑖𝑣𝑖𝑜𝑙 . 𝑣𝑖 ). The objective of the PSO is to find the location with minimal value for objective function F1. There are various types of distributed energy source, which are used either as only power generators (DGs) or as both power and thermal energy generators (CHPs). These DGs and CHPs could be gas turbines, Stirling engines, diesel generators, steam engines, photovoltaic arrays, and fuel cells. The deployment and maintenance cost for each type of energy source is different. Therefore, DG type indicator (𝑢𝑑𝐷𝐺 ) and CHP type indicator (𝑢𝑐𝐶𝐻𝑃 ) are defined and used in this paper.

𝐶

𝑚𝑖𝑛 𝐹1(𝐶

𝐶𝐻𝑃

,𝐶

𝐷𝐺

,𝐶

𝑙𝑜𝑠𝑠

,𝐶

𝑣𝑖𝑜𝑙

)=

𝐷

∑ 𝐶𝑐𝐶𝐻𝑃 . 𝑢𝑐𝐶𝐻𝑃 𝑐=1 𝑁

+ ∑ 𝐶𝑑𝐷𝐺 . 𝑢𝑑𝐷𝐺

𝑁

+ ∑ ∑ 𝐶𝑖𝑗𝑙𝑜𝑠𝑠 . 𝑇𝑖𝑗𝑙𝑜𝑠𝑠 𝑖=1 𝑗=1

𝑑=1 𝑁

+ ∑ 𝐶𝑖𝑣𝑖𝑜𝑙 . 𝑣𝑖

(6)

𝑖=1

Where, 𝑙𝑜𝑠𝑠 𝑇𝑖𝑗𝑙𝑜𝑠𝑠 = 𝑃𝑖𝑗𝑙𝑜𝑠𝑠 + 𝑇𝐻𝑖𝑗

∀𝑖, 𝑗 = 1,2,3, … 𝑁

(7)

0 𝑖𝑓 𝑉 𝑚𝑖𝑛 ≤ 𝑉𝑖 ≤ 𝑉 𝑚𝑎𝑥 𝑣𝑖 = { 1 𝑒𝑙𝑠𝑒

∀𝑖 = 1,2,3, … 𝑁

(8)

∀𝑐 = 1,2,3, … 𝐶

(9)

𝑢𝑐𝐶𝐻𝑃 = {

𝑢𝑑𝐷𝐺 = {

1 𝑖𝑓 𝑐𝑡ℎ 𝑡𝑦𝑝𝑒 𝐶𝐻𝑃 𝑖𝑠 𝑝𝑙𝑎𝑐𝑒𝑑 0

𝑒𝑙𝑠𝑒

1 𝑖𝑓 𝑑𝑡ℎ 𝑡𝑦𝑝𝑒 𝐷𝐺 𝑖𝑠 𝑝𝑙𝑎𝑐𝑒𝑑 0

∀𝑑 = 1,2,3, … 𝐷

(10)

𝑒𝑙𝑠𝑒

The totals energy loss of the network (𝑇𝑖𝑗𝑙𝑜𝑠𝑠 ) can be determined by summing the power loss (𝑃𝑖𝑗𝑙𝑜𝑠𝑠 ) 𝑙𝑜𝑠𝑠 and thermal loss (𝑇𝐻𝑖𝑗 ), as given by (7). The binary variable 𝑣𝑖 will be 1 if voltage limits are violated

and zero otherwise as given by (8). The binary variables 𝑢𝑐𝐶𝐻𝑃 and 𝑢𝑑𝐷𝐺 will be 1 if a c-type CHP unit or d-type DG unit is placed and zero otherwise as given by (9) and (10), respectively.

3.1.2 Energy balancing In the siting phase, a rough energy balancing of the network is considered to avoid penalty cost for voltage limit violations. Final energy balancing of all the three types of energies (heat, cooling, and electrical) considering uncertainties is carried out at the sizing phase (next section). The active power generated by CHP (𝑃𝑐𝐶𝐻𝑃 ) and DG (𝑃𝑑𝐷𝐺 ) units should be balanced with active power demand (𝑃𝑖𝑙𝑜𝑎𝑑 ) and active power loss (𝑃𝑖𝑗𝑙𝑜𝑠𝑠 ) as given by (11). Similarly, the reactive power generated by CHP (𝑄𝑐𝐶𝐻𝑃 ) and DG (𝑄𝑑𝐷𝐺 ) units should be balanced with reactive power demand (𝑃𝑖𝑙𝑜𝑎𝑑 ) and reactive power loss (𝑃𝑖𝑗𝑙𝑜𝑠𝑠 ) as given by (12). 𝐶

𝑁

∑ 𝑃𝑖𝑙𝑜𝑎𝑑 𝑖=1

≤

𝐶

𝑁

∑ 𝑄𝑖𝑙𝑜𝑎𝑑 𝑖=1

∑ 𝑃𝑐𝐶𝐻𝑃 𝑐=1

≤

∑ 𝑄𝑐𝐶𝐻𝑃 𝑐=1

𝐷

+∑

𝑁

𝑃𝑑𝐷𝐺

𝑑=1

𝑑=1

− ∑ ∑ 𝑃𝑖𝑗𝑙𝑜𝑠𝑠

(11)

𝑖=1 𝑗=1

𝐷

+∑

𝑁

𝑁

𝑄𝑑𝐷𝐺

𝑁

𝑙𝑜𝑠𝑠 − ∑ ∑ 𝑄𝑖𝑗 𝑖=1 𝑗=1

3.1.3 Generation and capacity related constraints

(12)

The maximum and minimum generation constraints imposed on active power generating DGs and reactive power generating DGs is given by (13). Similarly, equations (14) constrain the active and reactive power generation limits of CHP units. The maximum and minimum voltage angle deviations are constrained by equation (15). The voltage magnitude deviation constraint has been considered in the objective function therefore, it is not mentioned in this section. Finally, the current carrying limitations of lines connecting bus pair i and j are given by (16). 𝐼𝑖𝑟𝑎𝑡𝑒𝑑 is the magnitude of rated current for line connecting buses i and j. 𝑚𝑖𝑛 𝑚𝑎𝑥 𝑃𝐷𝐺 ≤ 𝑃𝑑𝐷𝐺 ≤ 𝑃𝐷𝐺 ,

𝑚𝑖𝑛 𝑚𝑎𝑥 𝑄𝐷𝐺 ≤ 𝑄𝑑𝐷𝐺 ≤ 𝑄𝐷𝐺

∀𝑑 = 1,2,3, … 𝐷

(13)

𝑚𝑖𝑛 𝑚𝑎𝑥 𝑃𝐶𝐻𝑃 ≤ 𝑃𝑐𝐶𝐻𝑃 ≤ 𝑃𝐶𝐻𝑃 ,

𝑚𝑖𝑛 𝑚𝑎𝑥 𝑄𝐶𝐻𝑃 ≤ 𝑄𝑐𝐶𝐻𝑃 ≤ 𝑄𝐶𝐻𝑃

∀𝑐 = 1,2,3, … 𝐶

(14)

∀𝑖 = 1,2,3, … 𝑁

(15)

𝜃 𝑚𝑖𝑛 ≤ 𝜃𝑖 ≤ 𝜃 𝑚𝑎𝑥 𝐼𝑖 ≤ 𝐼𝑖𝑟𝑎𝑡𝑒𝑑 ∀𝑖 ∈ {all branches of the network}

(16)

3.2 Sizing of energy hub DGs are usually renewable energy sources (wind and solar), therefore, due to the intermittent environmental conditions, the output power of these renewable DGs is uncertain. Similarly, it is very difficult to accurately predict the consumption behavior of energy consumers, which results in demand uncertainty. It has been noted in the introduction section that robust optimization technique has gained popularly in microgrid uncertainty management. If the uncertainty lies within the uncertainty bounds (upper and lower), robust optimization provides guaranteed feasible solutions as shown in Fig. 5. In this study also, worst-case uncertainty has been considered. The worst-case will occur when the load takes the upper bound of uncertainty and renewable generations take the lower bound of uncertainty. If the solution is feasible for the worst-case realization and uncertainty lies within the specified bounds, the determined size of tri-generation equipment will provide feasible solutions for all realizations of uncertainty.

3.2.1 Objective function The objective function for optimal sizing of the energy hub is given by (17). The first five terms of the objective function show the cost of deployment of HOBs (𝐶ℎ𝐻𝑂𝐵 . 𝑢ℎ𝐻𝑂𝐵 ), EHPs (𝐶𝑒𝐸𝐻𝑃 . 𝑢𝑒𝐸𝐻𝑃 ), ADCs (𝐶𝑎𝐴𝐷𝐶 . 𝑢𝑎𝐴𝐷𝐶 ), CHPs (𝐶𝑐𝐶𝐻𝑃 . 𝑢𝑐𝐶𝐻𝑃 ), and DGs (𝐶𝑑𝐷𝐺 . 𝑢𝑑𝐷𝐺 ), respectively. The last two terms show the penalty cost for load shedding (𝐶𝑖𝑠ℎ𝑒𝑑 . 𝑇𝑖𝑠ℎ𝑒𝑑 ) and voltage limits violation (𝐶𝑖𝑣𝑖𝑜𝑙 . 𝑣𝑖 ), respectively. The objective of the PSO is to find the optimal size of tri-generation equipment with minimal value for objective function F2. Similar to DGs and CHPs, there are different types of HOBs, ADCs, and EHPs. The deployment and maintenance cost for each type is different. Therefore, a type indicator is defined for each of the energy conversion equipment.

The focus of this study is to develop an autonomous community microgrid. Therefore, the penalty cost for load shedding is taken as much higher than the generation cost of the respective energy sources. Similarly, the penalty cost for voltage limits violation is also assumed as much higher in order to assure the stability of the power network. Due to theses consideration, load shedding and voltage violations will be avoided at all lost. The cost associated with each type of energy generating units and energy conversion units will be computed by the community manager. Therefore, these values are taken as input by the optimization algorithm. If these considerations in sizing objective function (F2) are analyzed in parallel with siting objective function (F1), following observations can be deduced. a) Load shedding of all types of loads will be avoided even if the deployment of most expensive energy generation and/or energy conversion equipment is required. b) Voltage violation at all buses of the network will be avoided even if the deployment of most expensive power generation units is required. c) The remaining deciding factor is the cost associated with the total loss (electricity and thermal) of the network. Therefore, siting will be mostly affected by the total loss of the network. The cost associated with the energy generation and energy conversion equipment in the objective function is required to control the size of respective units. The cost of each unit depends on its type and is also a function of the generation capacity of respective units. 𝐻

𝑚𝑖𝑛 𝐹2(𝐶

𝐻𝑂𝐵

,𝐶

𝐸𝐻𝑃

,𝐶

𝐴𝐷𝐶

,𝐶

𝑠ℎ𝑒𝑑

,𝐶

𝐶𝐻𝑃

,𝐶

𝐷𝐺

,𝐶

𝑣𝑖𝑜𝑙

)=∑

𝐾

𝐶ℎ𝐻𝑂𝐵 . 𝑢ℎ𝐻𝑂𝐵

ℎ=1 𝐶

𝐴

+ ∑ 𝐶𝑎𝐴𝐷𝐶 . 𝑢𝑎𝐴𝐷𝐶 𝑎=1

+

∑ 𝐶𝑐𝐶𝐻𝑃 . 𝑢𝑐𝐶𝐻𝑃 𝑐=1

𝐷

+

∑ 𝐶𝑑𝐷𝐺 . 𝑢𝑑𝐷𝐺 𝑑=1

+ ∑ 𝐶𝑒𝐸𝐻𝑃 . 𝑢𝑒𝐸𝐻𝑃 𝑒=1

𝑁

𝑁

+ ∑ 𝐶𝑖𝑠ℎ𝑒𝑑 . 𝑇𝑖𝑠ℎ𝑒𝑑 𝑖=1

+ ∑ 𝐶𝑖𝑣𝑖𝑜𝑙 . 𝑣𝑖

(17)

𝑖=1

Where, 𝑇𝑖𝑠ℎ𝑒𝑑 = 𝑃𝑖𝑠ℎ𝑒𝑑 + 𝐻𝑖𝑠ℎ𝑒𝑑 + 𝐶𝑂𝑖𝑠ℎ𝑒𝑑

∀𝑖 = 1,2,3, … 𝑁

(18)

1 𝑖𝑓 ℎ𝑡ℎ 𝑡𝑦𝑝𝑒 𝐻𝑂𝐵 𝑖𝑠 𝑝𝑙𝑎𝑐𝑒𝑑 𝑢ℎ𝐻𝑂𝐵 = { 0 𝑒𝑙𝑠𝑒

∀ℎ = 1,2,3, … 𝐻

(19)

1 𝑖𝑓 𝑒𝑡ℎ 𝑡𝑦𝑝𝑒 𝐸𝐻𝑃 𝑖𝑠 𝑝𝑙𝑎𝑐𝑒𝑑 𝑢𝑒𝐸𝐻𝑃 = { 0 𝑒𝑙𝑠𝑒

∀𝑒 = 1,2,3, … 𝐸

(20)

1 𝑖𝑓 𝑎𝑡ℎ 𝑡𝑦𝑝𝑒 𝐴𝐷𝐶 𝑖𝑠 𝑝𝑙𝑎𝑐𝑒𝑑 𝑢𝑎𝐴𝐷𝐶 = { 0 𝑒𝑙𝑠𝑒

∀𝑎 = 1,2,3, … 𝐴

(21)

The total load shedding (𝑇𝑖𝑠ℎ𝑒𝑑 ) at node i can be determined by summing the amount of electric load shed at i (𝑃𝑖𝑠ℎ𝑒𝑑 ), heat load shed at i (𝐻𝑖𝑠ℎ𝑒𝑑 ), and cooling load shed at i (𝐶𝑂𝑖𝑠ℎ𝑒𝑑 ), as given by (18). The binary variables 𝑢ℎ𝐻𝑂𝐵 , 𝑢𝑒𝐸𝐻𝑃 , and 𝑢𝑎𝐴𝐷𝐶 will be 1 if a h-type HOB unit, e-type EHP unit, or a-type ADC

unit is placed and zero otherwise as given by (19), (20), and (21), respectively. 𝑢𝑐𝐶𝐻𝑃 , 𝑢𝑑𝐷𝐺 , and 𝑣𝑖 are given by equations (8), (9), and (10), respectively.

3.2.2 Energy balancing In the sizing phase, uncertainty in both loads and renewable generations is considered and a worst-case realization is formulated. Upper and lower bounds have been determined for heat, cooling, and electric loads and renewable generators. The upper and lower bounds can be determined by using methods suggested by [56, 57]. The worst-case active power demand (𝑃𝑊𝐶 ) should be balanced with active power generated by CHPs (𝑃𝑐𝐶𝐻𝑃 ), amount of electric load shed (𝑃𝑖𝑠ℎ𝑒𝑑 ), amount of active power loss (𝑃𝑖𝑗𝑙𝑜𝑠𝑠 ), and amount of power required by EHPs (𝑃𝑒𝐸𝐻𝑃 ) as given by (22). Similarly, the worst-case reactive 𝑙𝑜𝑠𝑠 power demand (𝑄 𝑊𝐶 ) should be balanced with amount of reactive power loss (𝑄𝑖𝑗 ) as given by (23).

The worst-case heat demand (𝐻 𝑊𝐶 ) should be balanced with amount of heat generated by CHPs (𝑃𝑐𝐶𝐻𝑃 ), amount of heat generated by HOBs (𝐻ℎ𝐻𝑂𝐵 ), amount of heat load shed (𝐻𝑖𝑠ℎ𝑒𝑑 ), amount of heat loss (𝑇𝐻𝑖𝑗𝑙𝑜𝑠𝑠 ), and amount of heat required by ADCs (𝐻𝑐𝐴𝐷𝐶 ) as given by (24). Finally, The worst-case cooling demand (𝐶𝑂𝑊𝐶 ) should be balanced with amount of cooling energy generated by ADCs (𝐶𝑂𝑎𝐴𝐷𝐶 ), amount of cooling energy generated by EHPs (𝐶𝑂𝑒𝐸𝐻𝑃 ), amount of cooling load shed (𝐶𝑂𝑖𝑠ℎ𝑒𝑑 ), and amount of 𝑙𝑜𝑠𝑠 cooling energy loss (𝑇𝐻𝑖𝑗 ) as given by (25). The worst-case active and reactive power demand can be

computed by using (26) and worst-case heat and cooling demand can be computed by using (27). In equations (26) and (27) the bar above the load variables (𝑋𝑖𝑙𝑜𝑎𝑑 ) shows the upper bound of loads and bar below the energy source variables (𝑋𝑑𝐻𝑆 ) shows the lower bound of generation. 𝐶

𝑃

𝑊𝐶

≤

𝑁

∑ 𝑃𝑐𝐶𝐻𝑃 𝑐=1 𝑁

𝑄

𝑊𝐶

+

𝑁

∑ 𝑃𝑖𝑠ℎ𝑒𝑑 𝑖=1

−

𝑁

𝐸

∑ ∑ 𝑃𝑖𝑗𝑙𝑜𝑠𝑠 𝑖=1 𝑗=1

− ∑ 𝑃𝑒𝐸𝐻𝑃

(22)

𝑒=1

𝑁

𝑙𝑜𝑠𝑠 + ∑ ∑ 𝑄𝑖𝑗 ≤0

(23)

𝑖=1 𝑗=1 𝐶

𝐻

𝑊𝐶

≤

𝐻

∑ 𝐻𝑐𝐶𝐻𝑃 𝑐=1

+

𝐴

𝐶𝑂

𝑊𝐶

≤

𝑃

=

∑ 𝑃𝑖𝑙𝑜𝑎𝑑 𝑖=1

+

𝑁

∑ 𝐻𝑖𝑠ℎ𝑒𝑑 𝑖=1

𝐸

∑ 𝐶𝑂𝑎𝐴𝐷𝐶 𝑎=1 𝑁

𝑊𝐶

𝑁

∑ 𝐻ℎ𝐻𝑂𝐵 ℎ=1

+

𝑁

∑ 𝐶𝑂𝑖𝑠ℎ𝑒𝑑 𝑖=1

𝐷

−

,

𝑄

=

− ∑ 𝐻𝑎𝐴𝐷𝐶

(24)

𝑎=1

𝑁

𝑙𝑜𝑠𝑠 − ∑ ∑ 𝑇𝐻𝑖𝑗

(25)

𝑖=1 𝑗=1

𝑁 𝑊𝐶

𝐴

𝑙𝑜𝑠𝑠 ∑ ∑ 𝑇𝐻𝑖𝑗 𝑖=1 𝑗=1

𝑁

+ ∑ 𝐶𝑂𝑒𝐸𝐻𝑃 𝑒=1

∑ 𝑃𝑑𝐷𝐺 𝑑=1

−

𝑁

∑ 𝑄𝑖𝑙𝑜𝑎𝑑 𝑖=1

𝐷

− ∑ 𝑄𝑑𝐷𝐺 𝑑=1

(26)

𝐻𝑆

𝑁

𝐻

𝑊𝐶

=

∑ 𝐻𝑖𝑙𝑜𝑎𝑑 𝑖=1

− ∑

𝐶𝑆

𝑁 𝐻𝑆 𝐻ℎ𝑠

,

𝐶𝑂

ℎ𝑠=1

𝑊𝐶

=

∑ 𝐶𝑂𝑖𝑙𝑜𝑎𝑑 𝑖=1

𝐶𝑆 − ∑ 𝐶𝑂𝑐𝑠

(27)

𝑐𝑠=1

The energy efficiency rating of an e-type EHP unit (𝜂𝐸𝐻𝑃 ) and an a-type ADC unit (𝜂𝐴𝐷𝐶 ) is given by (28). Similarly, the electricity to heat conversion efficiency of a c-type CHP unit (𝜂𝐶𝐻𝑃 ) is given by (29). 𝐶𝑂𝑒𝐸𝐻𝑃 = 𝜂𝐸𝐻𝑃 . 𝑃𝑒𝐸𝐻𝑃 , 𝐶𝑂𝑎𝐴𝐷𝐶 = 𝜂𝐴𝐷𝐶 . 𝐻𝑎𝐴𝐷𝐶

∀𝑒 = 1,2,3, … 𝐸, ∀𝑎 = 1,2,3, … 𝐴

(28)

∀𝑖 = 1,2,3, … 𝑁

(29)

𝐻𝑐𝐶𝐻𝑃 = 𝜂𝐶𝐻𝑃 . 𝑃𝑐𝐶𝐻𝑃

3.3 Particle swarm optimization PSO has been widely used for siting and sizing of DGs with various objectives due to its benefits as described in section 3.1. Therefore, PSO has been used in the proposed algorithm also where optimal sizing and siting of tri-generation equipment is carried out for the development of sustainable community microgrids. A brief description of PSO algorithm is given in this section. In PSO technique, individuals known as particles update their positions (state) with time. The particles search around in an N-dimensional space. During the searching process, each particle updates its position in accordance with its own experience and experience of neighboring particles [49]. The own experience value (best-encountered value) is called 𝑝𝑏𝑒𝑠𝑡 and the selected neighboring particle’s experience value (best encountered value among neighboring particles) is called 𝑔𝑏𝑒𝑠𝑡. Mathematically, the position of nth particle (𝑥𝑚,𝑛 ) in an N-dimensional space vector can be represented as (30). Similarly, the velocity of nth particle (𝑣𝑚,𝑛 ) in the N-dimensional space vector can be represented as in (31). 𝑋𝑚 = (𝑥𝑚,1 , 𝑥𝑚,2 , 𝑥𝑚,2 , … 𝑥𝑚,𝑁 )

(30)

𝑉𝑚 = (𝑣𝑚,1 , 𝑣𝑚,2 , 𝑣𝑚,2 , … 𝑣𝑚,𝑁 )

(31)

𝑘 The current position (𝑆𝑖𝑝 ) of particle p can be modified according to equation (32). Similarly, the

velocity of particle p can be modified according to equation (33). The weight function used for velocity of particle i is given by (34). 𝑘+1 𝑘 𝑘+1 𝑆𝑖𝑝 = 𝑆𝑖𝑝 + 𝑣𝑖𝑝

∀𝑖 = 1,2,3, … 𝑁

(32)

∀𝑝 = 1,2,3, … 𝑚 𝑘+1 𝑘 𝑘 𝑘 𝑣𝑖𝑝 = 𝜔𝑖 . 𝑣𝑖𝑝 + 𝑐1 . 𝑟𝑎𝑛𝑑. (𝑝𝑏𝑒𝑠𝑡𝑖𝑝 − 𝑆𝑖𝑝 ) + 𝑐2 . 𝑟𝑎𝑛𝑑. (𝑔𝑏𝑒𝑠𝑡𝑖𝑝 − 𝑆𝑖𝑝 )

𝜔𝑖 = 𝜔𝑚𝑎𝑥 −

(𝜔𝑚𝑎𝑥 − 𝜔𝑚𝑖𝑛 ) .𝑘 𝑘𝑚𝑎𝑥

Where, 𝑘 𝑘 𝑆𝑖𝑝 , 𝑣𝑖𝑝 : Current position and velocity of particle p.

(33) (34)

𝑘+1 𝑘+1 𝑆𝑖𝑝 , 𝑣𝑖𝑝 : Modified position and velocity of particle p.

𝑁, 𝑚: Number of particles in a group and number of members in a particle. 𝑐1 , 𝑐2 : Self and social accelerating coefficients. 𝑝𝑏𝑒𝑠𝑡𝑖𝑝 , 𝑔𝑏𝑒𝑠𝑡𝑖𝑝 : The pbest of the particles and gbest of the group. 𝜔𝑖 : Weight function for velocity of particle i. 𝜔𝑚𝑎𝑥 , 𝜔𝑚𝑖𝑛 : Minimum and maximum weights for velocity of particles. 𝑘𝑚𝑎𝑥 , 𝑘: Maximum and current iteration number. The best position related to the lowest value objective function for each particle in the N-dimensional space is given by (35). Similarly, the global best position among all the particles is given by (36). The velocity and the position of each particle are updated after each iteration. Initial velocities and positions of the particles are random and are updated according to equations (32) and (33). The values of selfacceleration coefficients and social accelerating coefficients are taken as 2. The minimum and maximum weights for velocities of particles are taken as 0.4 and 0.9, respectively. Same parameters have been used for both siting and sizing of the energy hub. 𝑃𝑏𝑒𝑠𝑡𝑚 = (𝑝𝑏𝑒𝑠𝑡𝑚,1 , 𝑝𝑏𝑒𝑠𝑡𝑚,2 , 𝑝𝑏𝑒𝑠𝑡𝑚,2 , … 𝑝𝑏𝑒𝑠𝑡𝑚,𝑁 )

(35)

𝐺𝑏𝑒𝑠𝑡𝑚 = (𝑔𝑏𝑒𝑠𝑡𝑚,1 , 𝑔𝑏𝑒𝑠𝑡𝑚,2 , 𝑔𝑏𝑒𝑠𝑡𝑚,2 , … 𝑔𝑏𝑒𝑠𝑡𝑚,𝑁 )

(36)

In siting phase, the objective function of the PSO is set to F1 (6). Initially, 50 particles with random locations from bus 1 to bus 33 are generated. All the particles calculate the value of the objective function (F1) at their corresponding location. The best-encountered value so far, the minimum value of F1, is selected as 𝑔𝑏𝑒𝑠𝑡 and all the particles update their positions. This process is repeated until the solution converges, either value of F1 remains same for successive iterations, or maximum iterations are finished. Maximum of 100 iteration have been set as terminating criteria in this study. In sizing phase, the objective function of PSO is set to F2 (17). In this phase sizes of DGs, CHPs, HOBs, ADCs, and EHPs are decided in such a way that the existing distribution system can be transformed into a self-sufficient community microgrid. In this case, the size (upper and lower limits) of each energy source is randomly divided into 10 parts and each part is denoted by a particle. Each particle calculates the value of F2 and updates its size. The process is repeated until one of the termination criteria is met. The termination criteria and system parameters are same with the sizing phase.

3.4 Sustainable community microgrid development The step-wise summary of the proposed method for developing a sustainable community microgrid is shown in Fig. 4. Due to similar demand patterns and similar ambient temperatures, spring and autumn

seasons are taken as one case and is named as off-seasons. Therefore, three seasons i.e. summer, spring, and off-seasons are considered in this study. Voltage profile of each bus in the microgrid network has been evaluated and restricted to acceptable limits i.e. 10.5p.u. Seasonal energy demand variations have also been considered in the sizing phase.

4 Simulation results and discussion The standard IEEE 33-bus distribution system, as shown in Fig. 1(a), has been considered for evaluating the effectiveness of the proposed method. PSO has been used for both sizing and siting of trigeneration equipment in the proposed method. Total 50 particles and maximum 100 iterations have been used for the simulations. The acceptable bound for voltage deviation has been taken as 10.5 p.u. The ambient temperatures have been taken as 22, 8, and 16ºC for summer, winter, and off-seasons, respectively [58]. Demand (all electrical, heating, and cooling) variation has been taken as 10% and generation variation has been taken as 20% of the forecasted values . The data of standard IEEE 33-bus system has been used for electrical demand while heat demand for summer has been borrowed from [36] and has been scaled. Cooling demand in winter is taken as same with the heating demand in summer. In the off-seasons, both cooling and heating demands are taken as 30% of winter’s heating demand and summer’s cooling demand, respectively. The base value for complex power is 10MVA and voltage is 22.9kV. The length of pipes, for heating and cooling, between nodes has been taken in proportion to the line resistances of the electrical network. Table 1 shows the electrical and thermal loads in different seasons on the year while Table 2 shows the electrical line impedances and thermal pipe lengths used in this study.

4.1 Siting of energy hub The first step in the proposed algorithm is to find the optimal location for deploying the energy hub. The objective for siting is to minimize the total network’s power loss (heat, cooling, and electrical) throughout the year, as depicted in equation (6). The thermal loss has been computed by using equation (5) and electrical loss by using equations (1)-(4). The demand for electricity is taken as same for all the seasons of the year, therefore, only thermal losses have been computed for different seasons of the year. The iteration-wise total network loss for the summer season is given by Fig. 7(a) while Fig. 7(b) shows the total network loss for off-seasons and Fig. 7(c) shows the total network loss for the winter season. It can be observed from Fig. 7 that the in all the three cases network losses have converged to specific values. By using the input data, as shown in Tables 1 and 2, PSO has suggested node 6 as the optimal location. Electrical, heat, and cooling energy losses for different seasons of the year are tabulated in Table 3. It is

evident from Table 3 that all the losses are minimum for node 6. In addition to minimization of heat loss, voltage deviation should also be within the permitted bounds. PSO has suggested an active power generation of 4.0MW and reactive power generation of 2.39MVAr. The voltage profiles of all the 33busses of the network have been analyzed by placing the suggested sizes of generators at node 6. Fig. 8 shows the voltage profiles of all the 33-buses before and after placing the DGs at node 6. It is evident that the voltage profiles of all the buses have improved significantly and voltage deviations are within the permitted bounds, i.e. 10.5 p.u. The sizes of DGs at this stage are not finalized; they will be finalized in the sizing phase.

4.2 Sizing of tri-generation equipment After finding the optimal location for deploying the energy hub, the second step is to find the optimal sizes of different energy generating sources for fulfilling the energy demands of the community microgrid. The objective is to develop a sustainable community microgrid, which is capable of fulfilling the heating, cooling, and electrical demands of the microgrid community throughout the year. Uncertainties in load demands are considered at this step and sizes of tri-generation equipment are determined by using PSO for all the three seasons, as described in section 3. After analyzing the suggested sizes by PSO for each season, uncertainty in generation will be considered and final sizes will be determined for each of the energy-generating sources. In the winter season, only electrical and heating demands are considered. 10% of uncertainty has been considered in both of the energy demands and upper bounds have been used for simulations to provide immunity against the worst-case realization. The objective of the sizing in winter season is to mitigate the load shedding of both electrical and heating loads, which are named as total load shedding. The iterationwise load shedding for the winter season is shown in Fig. 9. It can be observed from Fig.9 that load shedding has reduced to zero after 82 iterations and PSO has converged. The suggested sizes (in MW) of CHP, DG, and HOB by PSO are 3.393+0.734j, 0.986+2.000j, and 2.000, respectively. Similarly, in the summer season, there is no heating load, i.e. only electrical and cooling loads. The uncertainty bound for the summer season is also similar with that of the winter season for both types of loads (10%). PSO has converged to zero total load shedding after 80th iteration for summer season as depicted in Fig. 10. The worst-case realization of load uncertainty has been assumed by considering upper bounds for both electrical and cooling loads. The optimal sizes (in MW) suggested by PSO for CHP, DG, ADC, and EHP are 5.000+00.998j, 0.22+2.000j, 2.000, 1.622, and 1.675, respectively. Due to the absence of heating loads, HOB size has not been considered in the summer season.

In the off-seasons (spring and autumn), all the three types of loads (electrical, cooling, and heating) are considered. The amount of electrical load is similar to the previous two cases (summer and winter) while heating and cooling load amounts are taken as 30% of the winter season’s heating load and summer season’s cooling load, respectively. The uncertainty bounds for all the three types of load are taken as 10%. Worst-case uncertainty realization has been simulated by considering upper bounds for all the three load types. It can be observed from Fig. 11 that PSO has converged to zero load shedding after 90th iteration for off-seasons scenario. The suggested sizes (in MW) of CHP, DG, HOB, ADC, and EHP for off-seasons are 4.123+1.533j, 0.734+2.000j, 0.261, 0.428 and 0.621, respectively. In order to ensure the stability of the power system, voltage deviations at each bus should be within the permitted bounds. Therefore, the suggested sizes of equipment have been placed in the energy hub, placed at node 6, and voltage profile of all the 33 busses have been analyzed. The voltage profile of the community microgrid is shown in Fig. 12. It can be observed from Fig. 12 that the voltage profile of all the buses is within the permitted bounds (10.5 p.u). Voltage profile for all the three cases was identical due to the identical location of power sources (node 6), therefore, only one figure is shown.

4.3 Sustainable community microgrid The final step is to decide the optimal sizes of different tri-generation equipment to develop a sustainable community microgrid. The size of each energy source has been analyzed for all the three seasons and maximum size among the three cases has been selected. Based on the above-mentioned rule, the selected size of each energy source is highlighted in Table 4. The uncertainty bound for generation sources has been taken as 20% and the worst-case realization has been achieved by considering lower bounds for energy sources. Therefore, the final size of each equipment is determined by adding 20% additional capacity to the selected size. The final sizes for all the tri-generation equipment, used in this study, are tabulated in the last column of Table 4. The finalized sizes of all the equipment have been placed at node 6 and voltage profiles of the busses have been analyzed again. The final voltage profile of the community microgrid network was identical to that of Fig. 12. The sustainable community grid, which has been formed by placing the selected sizes of trigeneration equipment at node 6 is shown in Fig. 13. The sustainable community grid shown in Fig. 13 has been transformed from the standard IEEE 33-bus distribution system shown in Fig. 1(a). The transformed sustainable community grid is capable of fulfilling the CCHP need of the community members throughout the year. In addition, the final sizing has the ability to provide feasible solutions even if both load and generations profiles fluctuate (within the uncertainty bounds).

5 Conclusion

The standard IEEE 33-bus distribution network has been transformed into a sustainable microgrid community. Siting of energy hub has been determined by considering total losses of the network during different seasons of the year. Sizing of tri-generation equipment has been carried out by considering demand variations during different seasons of the year and uncertainties associated with energy demands. Finally, the size of each equipment has been finalized by considering the uncertainties associated with the energy generation equipment. In this way, a sustainable microgrid community has been developed. The reliance of the developed sustainable microgrid community on the central power system has been minimized to enhance the resiliency of the community microgrid during disturbance events. The objective of the formulation is to assist the community energy managers for developing sustainable community microgrids. Through optimal siting and sizing of tri-generation equipment, the community microgrid energy managers can develop sustainable microgrids, which can suffice the energy demands (cooling, heat, and power) of the community members throughout the year. Due to the minimal reliance on the central grid, the proposed siting and sizing method can improve the resilient performance of the community microgrids during system disturbances. Simulation results have proved that the proposed method is capable of providing immunity against the worst-case realization of uncertainties, with bounded uncertainties.

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[58]The Renewable Energy site for Do-It-Yourselfers, [Available online] http://www.builditsolar.com/Projects/ Cooling/EarthTemperatures.htm.

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Fig. 1. Microgrid transformation: a) Conventional distribution system; b) Transformed community microgrid.

HOBs

Fuel

Heat load

ACHs Cooling load

Energy Hub CHPs EHPs

Fuel Flow Heat Flow

Electricity Flow

DGs

Electric load

Cooling Energy Flow

Fig. 2. A typical energy hub for tri-generation.

Vi θi Iij

𝑃𝑖 + 𝑗𝑄𝑖

Vj θj

𝑃𝑗 + 𝑗𝑄𝑗

𝑧𝑖𝑗 = 𝑟𝑖𝑗 + 𝑗𝑥𝑖𝑗

a

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𝐻𝑗𝐶𝑆

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𝑄𝐷𝐺 𝑗

𝑃𝑗𝑙𝑜𝑎𝑑 + 𝑗𝑄𝑗𝑙𝑜𝑎𝑑

Node j

𝐶𝑂𝑗𝐶𝑆

HS

𝑙𝑜𝑎𝑑i Node 𝐻𝑗𝑙𝑜𝑎𝑑 𝐶𝑂 𝑗

HS: Heating source(s)

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CS: Cooling source(s)

Fig. 3. Net energy demand at each node: a) Electrical; b) Heating; c) Cooling.

Start Read system data and set s=1 Compute loss between each node pair by using equation (5)

Determine adjacency and loss matrices using system data i=1 Compute loss from all other nodes to i using Dijkstra's algorithm Accumulate all the losses and store the result for node i in season s i=i+1 No

i
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Display the stored data of each bus for each season End

Fig. 4. Algorithm for determining thermal loss of the network.

Nominal Value

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Power or Load

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Fig. 5. Uncertainty bounds and solution feasibility.

Read network data (loads, network topology, line impedance, distance), etc and compute thermal energy loss between each node pair of the network 1 Identify the optimal location for deployment of energy hub considering thermal and electrical losses in different seasons of the year (siting through PSO) 2 Find the optimal sizes of CHPs, DGs, HOBs, EHPs, and ADCs considering uncertainties in loads (thermal and electrical) and DGs for all 3 seasons of the year (sizing through PSO) Evaluate the voltage profile of each bus in each 4 case to avoid violation of voltage limits Analyze the sizes of all equipment in different cases, and select the suitable sizes to make a zero-energy community microgrid (zero load5 shedding in all cases)

Total Loss (MW)

Fig. 6. Steps for developing a sustainable community microgrid.

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Fig. 7. Iteration-wise total energy loss: a) Summer season; b) Off-seasons; c) Winter season.

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Fig. 8. Voltage profiles of busses (nodes) before and after placing DGs.

Iteration Number

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Fig. 9. Iteration-wise total load shedding in the winter season.

Iteration Number

Total Load Shed (MW)

Fig. 10. Iteration-wise total load shedding in the summer season.

Iteration Number

Fig. 11. Iteration-wise total load shedding in off-seasons.

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Fig. 12. Voltage profiles of busses after sizing tri-generation equipment.

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Table 1. Electrical and thermal load demand throughout the year. Electric Demand Node

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Electric Demand

Summer Heating/ Winter Cooling

Off-Seasons (Cooling/ Heating)

Active

Reactive

MW

MVAr

MW

MW

0 0.1000 0.0900 0.1200 0.0600 0.0600 0.2000 0.2000 0.0600 0.0600 0.0450 0.0600 0.0600

0 0.0600 0.0400 0.0800 0.0300 0.0200 0.1000 0.1000 0.0200 0.0200 0.0300 0.0350 0.0350

0 0.0165 0.0399 0.0197 0.0101 0.0101 0.0037 0.0325 0.1010 0.0101 0.0327 0.2675 0.0101

0 0.0050 0.0120 0.0059 0.0030 0.0030 0.0011 0.0098 0.0303 0.0030 0.0098 0.0803 0.0030

Node

18 19 20 21 22 23 24 25 26 27 28 29 30

Active

Reactive

MW

MW

0.0900 0.0900 0.0900 0.0900 0.0900 0.0900 0.4200 0.4200 0.0600 0.0600 0.0600 0.1200 0.2000

0.0400 0.0400 0.0400 0.0400 0.0400 0.0500 0.2000 0.2000 0.0250 0.0250 0.0200 0.0700 0.6000

Summer Heating/ Winter Cooling

Off-Seasons (Cooling/ Heating)

0.0399 0.0649 0.0149 0.0149 0.2899 0.0149 0.0675 0.2675 0.0601 0.1851 0.0851 0.0452 0.1830

0.0120 0.0195 0.0045 0.0045 0.0870 0.0045 0.0203 0.0803 0.0180 0.0555 0.0255 0.0136 0.0549

14 15 16 17

0.1200 0.0600 0.0600 0.0600

0.0800 0.0100 0.0200 0.0200

0.0197 0.0101 0.0101 0.0101

0.0059 0.0030 0.0030 0.0030

31 32 33 -

0.1500 0.2100 0.0600 -

0.0700 0.1000 0.0400 -

0.2245 0.2090 0.3510 -

0.0673 0.0627 0.1053 -

Table 2. Impedances of electrical lines and lengths of thermal pipes. Nodes From 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

To 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Resistance Reactance Per-unit (p.u) 0.0058 0.0029 0.0308 0.0157 0.0228 0.0116 0.0238 0.0121 0.0511 0.0441 0.0117 0.0386 0.1068 0.0771 0.0643 0.0462 0.0651 0.0462 0.0123 0.0041 0.0234 0.0077 0.0916 0.0721 0.0338 0.0445 0.0369 0.0328 0.0466 0.0340 0.0804 0.1074

Pipe Length meters 58 308 228 238 511 117 1068 643 651 123 234 916 338 369 466 804

Nodes From 17 2 19 20 21 3 23 24 6 26 27 28 29 30 31 32

To 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Resistance Reactance Per-unit (p.u) 0.0457 0.0358 0.0102 0.0098 0.0939 0.0846 0.0255 0.0298 0.0442 0.0585 0.0282 0.0192 0.0560 0.0442 0.0559 0.0437 0.0127 0.0065 0.0177 0.0090 0.0661 0.0583 0.0502 0.0437 0.0317 0.0161 0.0608 0.0601 0.0194 0.0226 0.0213 0.0331

Table 3. Electrical and thermal energy losses for siting of energy hub. Node 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Electrical Energy Loss Active Reactive MW MVAr 0.1825 0.1239 0.1726 0.119 0.1306 0.0981 0.1198 0.0927 0.1113 0.0886 0.0972 0.076 0.1072 0.1108 0.2144 0.1857 0.2821 0.2327 0.3474 0.2775 0.36 0.2807 0.3844 0.2868 0.4726 0.3567 0.5016 0.4013 0.5362 0.433 0.5801 0.4636 0.645 0.5679 0.6841 0.5967 0.1866 0.133 0.3116 0.2487 0.343 0.2882

Heat Energy Loss Winter Off-Seasons MW MW 1.523 0.2547 1.492 0.2485 1.3828 0.2296 1.3334 0.2218 1.2894 0.2141 1.212 0.2015 1.23 0.2042 1.4269 0.2372 1.5673 0.2606 1.7308 0.2876 1.7665 0.2927 1.8406 0.306 2.1619 0.3606 2.293 0.3813 2.448 0.4063 2.6586 0.4414 3.0501 0.5052 3.2857 0.5455 1.5345 0.256 1.9584 0.3262 2.0831 0.3465

Cooling Energy Loss Summer Off-Seasons MW MW 0.3778 1.523 0.3716 1.492 0.3443 1.3828 0.3313 1.3334 0.3203 1.2894 0.3014 1.212 0.3059 1.23 0.3554 1.4269 0.3905 1.5673 0.431 1.7308 0.4395 1.7665 0.4585 1.8406 0.5383 2.1619 0.5705 2.293 0.608 2.448 0.6593 2.6586 0.7579 3.0501 0.8168 3.2857 0.3816 1.5345 0.4869 1.9584 0.5188 2.0831

Pipe Length meters 457 102 939 255 442 282 560 559 127 177 661 502 317 608 194 213

22 23 24 25 26 27 28 29 30 31 32 33

0.396 0.1572 0.211 0.278 0.1074 0.1225 0.1792 0.2218 0.2509 0.3213 0.344 0.3701

0.3653 0.1161 0.1591 0.212 0.0811 0.0887 0.1393 0.1768 0.1907 0.2628 0.2909 0.3365

2.3125 1.5097 1.7823 2.0737 1.2477 1.3047 1.5378 1.731 1.8635 2.1389 2.2317 2.3433

0.3837 0.2512 0.2976 0.3472 0.2083 0.2178 0.2556 0.2878 0.3103 0.3562 0.3707 0.3893

0.5746 0.3767 0.4434 0.5147 0.3099 0.3232 0.382 0.4303 0.4628 0.5303 0.5535 0.5814

2.3125 1.5097 1.7823 2.0737 1.2477 1.3047 1.5378 1.731 1.8635 2.1389 2.2317 2.3433

Table 4. Final sizing of tri-generation equipment considering uncertainties. Equipment CHP DG HOB ADC EHP

Active Reactive Active Reactive -

Siting (MW/MVAr) 2.000 0.390 2.000 2.000 -

Sizing (MW/MVAr) Winter Summer 3.393 5.000 0.734 0.998 0.986 0.622 2.000 2.000 2.000 1.622 1.675

Off-Seasons 4.123 1.533 0.734 2.000 0.261 0.482 0.621

Final Sizes (MW/MVAr) 6.000 1.840 1.183 2.400 2.400 1.947 2.010