Three typical load profiles are adopted in the planning, namely, weekday profile, weekend day profile, and peak day profile. For a typical year characterized by the three load profiles, the time step equals the Number of Months × Hours × Types of load profile, which is 12 × 24 × 3 = 864.

The objective function of planning is to minimize the overall microgrid investment and operation cost including emission cost in the typical year aforementioned. The objective function is formulated as follows (Eq. 1): C = C I n v + C P u r + C D e + C E x + C G + C F M + C C O 2 + C C u r , (1) where C _Inv is the annualized investment cost of various technologies, C _Pur is the total cost of electricity purchase with CO₂ taxation, C _De is the demand charge fee, C_Ex is the electricity export revenue, C _G is the generation cost of various technologies including variable maintenance costs, C _FM is the fixed maintenance cost, C _CO2 is the CO₂ taxation on local generations, and C _Cur is the load curtailment costs.

The annualized investment cost, including the capital cost of discrete technology (Diesel Generator, DG) and capital cost of continuous technology (BESS and PV), is formulated as follows: C I n v = ∑ n , g I n v n , g ⋅ P R a t e , g ⋅ C T u r n , g ⋅ r A n n , g + ∑ n , k C F X , k ⋅ P u r n , k + C V a r , k ⋅ C a p n , k ⋅ r A n n , k , (2) where Inv _n,g is the integer units of discrete generation technology g at node n, P _Rate,g is the power rating of discrete generation technology g (kW), and C _Turn,g is the turnkey capital cost of discrete generation technology g ($/kW). C_FX,k is the fixed capital cost of continuous technology k ($), C_var,k is the variable capital cost of continuous technology k ($/kW), Pur _n,k is the binary installation decision for continuous technology k, Cap _n,k is the installed capacity of continuous technology k at node n, and r _Ann,i is the annuity rate for the technology i at node n. As observed, the investment costs are decided by the investment decisions of technology, which are Inv _n,g , Pur _n,k and the installed capacity Cap _n,k .

The purchase cost of microgrids is shown in (Eq. 3) C P u r = ∑ n , t P u t n , t ⋅ P g t + C T a x ⋅ M C R T t , (3) where P _gt is the utility electricity purchasing price at time t, C _Tax is the tax on CO₂ emissions, MCRT_t is the marginal carbon emissions from marketplace generation, and Put _n,t is the electricity purchased from the utility.

The demand charge cost is as follows: C D e = ∑ n , m , p D R t m , p ⋅ M P u r n , m , p , (4) where DRt _m,p is the power demand charge for month m and period p, ($/kW) and MPur _n,m,p is the maximal electricity purchased from the utility during period p of month m at node n.

The electricity export revenues are as follows: C E x = − ∑ n , t E x R t t ⋅ E x P n , t , (5) where ExRt _t is the energy rate for electricity export ($/kWh) and ExP _n,t is the electricity exported to the utility at node n. C G = ∑ n , j , t G e n n , j , t G C s t j + M v a r , j , (6) where Gen _n,j,t is the output of technology j to meet energy use u at node n and GCst _j and M _var,j are the generation cost of technology j ($/kWh) and variable annual operation and maintenance cost of technology j ($/kWh), respectively. C F M = ∑ n , g I n v n , g ⋅ P R a t e , g ⋅ M F g + ∑ n , k C a p n , k ⋅ M F k , (7) where MF _g is the fixed annual operation and maintenance cost of technology g, $/kW capacity.

In addition, the carbon taxation on local generation is formulated as follows: C C O 2 = ∑ n , j , t G e n n , j , t ⋅ 1 η j ⋅ G C R t j ⋅ C T a x , (8) where GCRt _j is the carbon emission rate from generation technology j (kg/kWh) and η _j is the electrical efficiency of generation technology j. C C u r = ∑ n , u , t P L c u r n , u , t ⋅ C u r P r n , u , (9) where PLcur _n,u,t is the customer load not met in energy consumption u at node n (kW) and CurPr _n,u is the load curtailment cost for energy use u at node n ($/kWh).

As described in Eqs 2–9, the total cost objective function includes 1) annualized investment costs of discrete and continuous technologies; 2) total cost of electricity purchase inclusive of carbon taxation; 3) demand charges; 4) electricity export revenues; 5) generation cost for electrical, heating, or cooling technologies inclusive of their variable maintenance costs; 6) fixed maintenance cost of discrete and continuous technologies; 7) carbon taxation on local generation; and 8) load curtailment costs. The optimization variables include X = [Inv _n,g, Pur_n,k, Cap_n,k, Put _n,t , MPur _n,m,p , ExP _n,t , Gen _n,j,t, and PLcur _n,u,t ], which are composed of continuous and binary variables. Parameter Y = [ P_Rate,g, C_Turn,g, C_FX,k, C_var,k, r_Ann,i, P_gt, C_Tax, MCRT_t, DRt _m,p , ExRt _t , GCst _j , MF_g, GCRt_j, η _j , and CurPr _n,u ] is the constant associated with the planning, which should be determined before solving the optimization objective.

The constraints include energy balance constraints, power flow constraints, storage constraints, cable current constraints, and energy import/export constraints.

The power flow constraints include current and voltage constraints for multi-node microgrids. However, for single-node microgrids, power flow constraints can be ignored. In this paper, a linear power flow model is considered for a balanced multi-node microgrid. It is assumed that the slack bus of microgrids is denoted by N, which means that the voltage of node N is V N = V 0 ∠ 0 .

The power flow is represented as follows: P g n , t = P u t n , t − E x P n , t + ∑ j ∈ P V , I C E , M T , F C , W T G e n n , j , t − P L n , u = E L , t − P L c u r n , u = E L , t + P d i s , n , s = E S , t ⋅ η d i , s = E S − 1 η c h , s = E S ⋅ P c h , n , S = E S , t − 1 c o 1 ⋅ G e n n , c = E C , t , (10) Q g n , t = P g n , t ⋅ tan acos ϕ ;   n ≠ N , (11) r e V n , t = V 0 + 1 V 0 ∑ Z r n , n ′ ⋅ P g n , t + Z i n , n ′ ⋅ Q g n , t ;   n , n ′ ≠ N I m V n , t = V 0 + 1 V 0 ∑ Z i n n , n ′ ⋅ P g n , t − Z r n , n ′ ⋅ Q g n , t ;   n , n ′ ≠ N r e V n , t = V 0 , I m V n , t = 0 ;   n = N , (12) P l o s s t = 1 2 ∑ n , n ′ r n , n ′ ⋅ I r n , n ′ , t 2 + I i n , n ′ , t 2 ≈ 1 2 ∑ n , n ′ r n , n ′ ⋅ e I r n , n ′ , t + e I i n , n ′ , t Q l o s s t = 1 2 ∑ n , n ′ x n , n ′ ⋅ I r n , n ′ , t 2 + I i n , n ′ , t 2 ≈ 1 2 ∑ n , n ′ x n , n ′ ⋅ e I r n , n ′ , t + e I i n , n ′ , t , (13) where active power outputs from node n Pg _n,t are related to the exported/imported power to/from the utility, power generated from the installed energy resources (PV, DG, FC, and WT), load demand and curtailed loads, consumed power by electric chiller, and the discharged/charged power from energy storage systems. Parameter co ₁ is the coefficient of the electric chiller, and η _dis /η _ch is the discharge/charge efficiency of BESSs. Moreover, each node has the constant power factor ϕ. The nodal voltages V _n,t shown in Eqs 11, 12 are calculated by the nodal active/reactive power injection and network impedance matrix Z without the slack bus row and column. Equation 13 is the power loss of the network, which is used to decide the placements of DERs. In addition, r _n,n′ and x _n,n′ are the resistance and inductance of line impedance between nodes n and n′, respectively; eIr _n,n′t and eIi _n,n′t are the linearized real current Ir ² and image current Ii ² of line (n, n′) (Mashayekh et al., 2017), respectively; and reVn,t and ImVn,t are the real and imaginary part of the voltage amplitude of node n at time t, respectively.

The operation constraints contain the nodal voltage constraints, generation capacity constraints, storage constraints, and energy import/export constraints. The constraints of energy storage are formulated as follows: S o C n , s , t = 1 − ϕ s ⋅ S o C n , t − t + P c h , n , s , t − P d i s , n , s , t S o C min ≤ S o C n , s , t ≤ S o C max P c h , n , s , t ≤ P c h , max ⁡ , n , s P d i s , n , s , t ≤ P d i s , max ⁡ , n , s . (14)

The generation constraints are formulated as follows G e n n , c , t ⩽ C a p n , c ⋅ η e f f ⋅ S o l a r t ;   c ∈ P V , S T G e n n , g , t ⩽ I n v n , g ⋅ P R a t e , g C a p n , k ⩽ P u r n , k ⋅ M G e n n , c , t ⩽ C a p n , c , (15) where η _eff is the solar radiation conversion efficiency of generation technology c ϵ (PV, ST), Solar _t is the average fraction of maximum solar insolation received during time t (%), and Pur _n,k is the binary purchase decision for continuous technology k at node n. M is a very large positive constant which decides the upper limits of the capacity of the continuous technology. Gen _n,g,t is the DG power generation of node n at time t. Gen _n,c,t is the power generation of continuous technology of node n at time t. Cap _n,k is the capacity of technology k of node n.

For the gird-connected mode, microgrids may import or export energy from/to the utility by the point of common coupling (PCC) node. However, the energy transferred by the PCC node is normally limited, which is as follows: P u t n , t ⩽ p s b n , t ⋅ g r d ⋅ M , n = N , s l a c k b u s E x P n , t ⩽ 1 − p s b n , t ⋅ g r d ⋅ m E x P , n = N s l a c k b u s , (16) where psb _n,t is the binary electricity purchase/sell decision at node n, M is the maximal energy purchased from the utility, and mExP is the maximal energy exported to the grid.

The planning model of community microgrids is described by Eqs 1–16, where the total investment cost, operation cost, emission cost, energy balance, and operation constraints are introduced. The aforementioned optimization problem is a mixed-integer linear optimization problem, which is an NP-hard problem, but can be solved by mature optimization solvers such as Gurobi and Cplex. Before solving the planning problem, one should first initialize the parameters of the problem, such as to define the value of vector Y = [P_Rate,g, C_Turn,g, C_FX,k, C_var,k, r_Ann,i, P_gt, C_Tax, MCRT_t, DRt _m,p , ExRt _t , GCst _j , MF_g, GCRt_j, η _j , and CurPr _n,u ] according to the demand, energy policy, specific technologies, and tariffs.

Second, the basic load profile of the microgrids should be collected and input into the optimization problem. In addition, solar radiations and wind speed data should also be collected for the planning. Then, with the given parameters and data input, the proposed optimization problem can be solved. In addition, the optimization variables X = [ Inv _n,g , Pur _n,k , Cap _n,k , Put _n,t , MPur _n,m,p , ExP _n,t , Gen _n,j,t , and PLcur _n,u,t ] will be obtained. Finally, with the optimal solutions, the capacities and placements of energy resources will be given. The diagram of the planning of community microgrids is illustrated in Figure 2.

The basic data needed for the planning include the load demand for peak day, solar radiations, and electricity rates. The yearly load profiles for nodes 2, 3, and 4 are shown in Figures 3A–C, which are based on the real measured load profile of community microgrids (MGs) in Lombok, Indonesia. Figure 3 shows that the load demand varies from about 200–550 kW from 0 h to 24th hour for node 2. In addition, the load valley is around noon. For node 3, the load peak appears at 18:00, reaching 430 kW for node 3, and the load valley is about 180 kW. For village 1, the load peak comes at 18–19:00, reaching 330 kW. These load profiles are obtained by transferring the practical 5-min loads into a yearly load profile using the DER-CAM. It can be seen the maximal load deviation among months is larger than 100 kW for each node. However, the basic load profiles are similar because Indonesia’s climate is almost entirely tropical, and the temperatures do not vary much from season to season.

The solar radiation data of Lombok (Indonesia) Island are obtained from the photovoltaic geographical information system. The solar radiation is shown in Figure 4A, from which it can be observed that the maximal power generated is about 0.68 kW/m². Generally, the PV power output is higher in summer days than in winter days. The electricity price of community microgrids, estimated by the real price in Indonesia, is shown in Figure 4B, where the peak price is 0.4 $/kWh and off-peak price is 0.11 $/kWh. The hours of Time of Use (ToU) rates for summer days are from 12:00 to 18:00 during a day. The PV power sale price is the same as the purchase price in the planning parameter setup.

For the single-node case, the power flow equation is not considered; therefore, the corresponding constraints, such as current constraints and voltage constraints, are neglected in the planning. However, for multiple-node microgrids, the power constraints need to be considered. The planning objectives contain cost minimization and CO₂ emission reduction with the same weights, namely, equal to 0.5. The discount rate is set as 3%, and the maximal payback period of microgrids is 20 years. The voltage level is 12 kV, and the maximal capacity of the transformer connected to the upper grid is set as 5 MVA.

The investment cost of PV systems includes fixed investment cost, variable cost, maintenance cost, and inverter cost. In this work, the fixed cost is 2,500 $, and the variable cost is 2,500 $/kW. The lifetime is assumed to be 30 years, and the maintenance cost is 0.005 $/(kW × month). The inverter cost is 500 $/kW-cap for an inverter with a capacity of 100 kW. The investment cost of the BESS includes the fixed cost, variable cost, maintenance cost, and inverter cost. The investment cost is estimated according to the following equation: Investment Cost = (FixedCost + VariableCost × Capacity) × Investment Decision. In this study, the fixed cost is set as 500 $, variable cost is set as 300 $/kW-cap, and variable maintenance cost is set as 0.005 $/(kW × month). The inverter cost of the BESS is set as 200 $/kW-cap for the 100 kVA capacity. The lifetime of the BESS is set as 15 years, while the lifetime of the inverter is 20 years. The battery degradation parameters are shown in Table 1. The cost of diesel generators includes the variable cost and maintenance cost. The variable cost is set as 5761.4074 $/kW. The variable maintenance cost is set as 0.0128 $/kWh, which is dependent on its energy production. Its maximal capacity is 75 kW, with efficiency 0.0238. The other two kinds of DGs are listed in Table 2. The NoXRate is 0.0001 kgNOx/kWh, where NOx emissions are resulted from fuel usage. Its maximum ramp up and ramp down rate is 0.5. The starting time is 20 min, and the time needed to ramp up the generation facility to full capacity is 10 min, which are default parameters in DER-CAM software (Phase, 2018; Heleno et al., 2017)^.

The utility outages contain scheduled outages for scheduled maintenance and unscheduled outages caused by natural disasters or faults. The scheduled outage is defined to occur on the peak day of June of each year, and its duration is 24 h. The unscheduled outage is assumed to occur on the weekdays of December for 24 h. There are three types of loads for load shedding. The first type is low critical loads, which can be cut down for 20% of total loads for 24 h with the cost 0.15 $/kWh. The second type is the middle critical load. In the planning part, middle critical and high critical loads are not chosen to be cut down. The costs of curtailing load are shown in Table 3.

This case study focuses on the multi-node community MG, in which the topology constraints, namely, the power flow equations, are considered. In this case, the community MG has four nodes. Node 1 is Tanjung station, node 2 is Mina Hotel, node 3 is RSUD (hospital), and node 4 is a village nearby. The topology of this community MG is shown in Figure 5, Figure 5A shows the topology in the DER-CAM, and Figure 5B shows the geographical positions of various nodes.

This case study aims to investigate the capacities and locations of DER for the four-node community MG. The main procedure of this planning work is similar with that of the single-node community MG. The difference between the single-node MG and the multi-node MG planning is that in the multi-node MG planning, the power flow equations and the constraints of voltage and current magnitudes should be considered. During the planning, the N-1 contingency is also considered.

The utility outages for multi-node MG include scheduled outages for scheduled maintenance and unscheduled outages caused by natural disasters or faults. The scheduled outage is defined to occur on the weekdays of July of each year. Its duration is 24 h. In addition, the unscheduled outage occurs on the weekends of December for 24 h. There are three types of loads for load shedding in the DER-CAM. The first type is low critical loads, which can be cut down by 20% of the total consumption for 24 h and the cost is 0.15 $/kWh. The second type is the middle critical load. In the planning part, middle critical and high critical loads are not chosen to be cut down.

With the input data and system setup, the planning results can be obtained with the optimized capacities and locations of various energy sources, costs and revenues, and CO₂ emissions. Table 4 shows the costs of four-node community MG. With the installation of the PV, DG, and BESS, the total annual energy cost for the MG is 789 k$, which means that the MG earns money by selling energy to the utility each year. Compared with the original case (reference case), the total savings are 22.12%. The CO₂ emissions decreased to 1,420 tons per year, with a reduction rate of 25.25%.

The optimal placement and combination of technologies are shown in Figure 6A, where node 2 installs two kinds of DG with capacities being 130 and 150 kW, respectively, and one PV with 120 kW capacity, as well as a BESS with 4,539 kWh. For node 3,two DGs with capacities being 65 and 75 kW and 180 kW PV and 3,581 kWh BESS are installed, respectively. Meanwhile, for node 4, only a PV with capacity 748 kW is installed. In the planning, the area constraints for installing PV panels are considered for each node,which are, respectively, 800, 1,200, and 5,000 m². Therefore, node 2 connects only 120 kW PV. The capital and annualized investment costs of two kinds of DGs are shown in Figure 6B for various capacities.

The electricity dispatch in July of each year is obtained in Figure 7, where on a peak day, the surplus PV power is exported to the utility, as shown by a gray curve in Figure 7A. In addition, the BESS also discharges during the daylight, shown by dark red area, and during the nights, the BESS is charged by the utility, shown by blue areas. Because during the daylight (from 12:00 to 18:00), the utility price is using on-peak price, shown in Figure 4B, PV sells power to the utility to gain the revenue. In addition, the BESS discharges for local load consumption and during the night, when electricity price is low, the BESS purchases power from utility. During utility outages, the PV and BESS can also provide electricity to the local consumers, as shown in Figure 7B. At most 20% of low critical loads are curtailed in order to keep the system power balance during the utility outages, shown by a red curve.

For the electricity power interaction among nodes in July on the emergent day, the results are shown in Figure 8. From Figure 8A, it can be observed that the DGs at nodes 2 and 3 start generating power to the MG during the utility outages, where the maximal DG output power at nodes 2 and 3 is 280 and 130 kW, and the minimal output power at nodes 2 and 3 is 75 and 0 kW, respectively. The low critical loads at nodes 2 and 4 also curtail their demand during the outages. The maximal curtailed power of nodes 2 and 4 is 95 and 43 kW, respectively, shown in Figure 8B. The PV outputs and load demands are shown in Figure 8C, where PV power outputs are all consumed by local loads. The BESSs at nodes 2 and 3 provide power to the MG when the PV radiation is low (nights) and absorb power from the MG when the PV output power is high, which is shown in Figure 8D.

Figure 9A shows the electricity purchased from the utility during the normal operation, where the peak electricity purchase happens in October and that of valley electricity in March. The difference between peak and valley value is 180,703 kWh. In summer days, solar radiation is high such that the peak PV power is in May, reaching 230,534 kWh/month, while the valley PV power is in February in winter days, shown in Figure 9B. Accordingly, as shown in Figure 9C, during summer days, the PV sources sell power to the utility according to the ToU price illustrated in Figure 4.

The nodal voltages of community MG during the utility outages are shown in Figure 10A. With the power flow constraints, the nodal voltages are all varying in the normal range, i.e., [0.95 1.05] p.u., even with the fluctuation of PV power generation and outages. In the planning, node 2 becomes the slack bus providing voltage support. However, during the peak day, the nodal voltages are varying in the normal time, most of the time, except in conditions of heavy load demand. However, the nodal voltages are very close to the lower voltage limit. In the planning, only the active power dispatch is considered, and the voltage will be recovered into the normal range if reactive power dispatch is taken into account.

This section elaborates on the sensitivity analysis when different discrete capital costs are considered. As shown in Figure 11, the optimal operation costs vary from 768 to 800 k$, and the total annual CO₂ reduction emission costs vary from 1,420 to 1,422 tons with the variation of capital costs. In addition, the total cost saving is at least above 20% and CO₂ emission reduction is at least above 25%. Even with the variation of capital costs, the capacity of PV panels remains unchanged as 1,048 kW. However, the total DER capacity of each node varies due to different combinations of technologies. Interestingly, the total capacity of the BESS varies in a very small range, e.g., from 8,102 to 8,119 kWh. The total capacity of DG remains unchanged (420 kW) even with the variation of capital costs because the discrete technology is insensitive to the planning results.