Energy System Integration

Abstract

This chapter provides a solution for energy system integration (ESI) problem in GAMS. The ESI analysis refers to a class of studies which investigate the potential in different energy sectors (water, gas, and electricity) for moving toward a more environmentally friendly and efficient energy supply. The main idea is how to harvest the flexibilities in each energy carrier in a larger framework. In this chapter, the coordination between water desalination systems and power system, gas network-power network, and finally the concept of energy hub is investigated.

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This chapter provides a solution for energy system integration (ESI) problem in GAMS. The ESI analysis refers to a class of studies which investigate the potential in different energy sectors (water, gas, and electricity) for moving toward a more environmentally friendly and efficient energy supply. The main idea is how to harvest the flexibilities in each energy carrier in a larger framework. In this chapter, the coordination between water desalination systems and power system, gas network-power network, and finally the concept of energy hub is investigated.

10.1 Water-Power Nexus

The water-electricity interdependence is an undeniable issue. Water is used for cooling the power plants. On the other hand, the electricity is used for collecting, treatment, and disposal of water.

The water-energy nexus concept is shown in Fig. 10.1 [1]. The optimization is formulated as follows:

$$\displaystyle\begin{array}{rcl} \min _{\mathrm{DV}}\mathrm{OF} = \mathrm{TC} + \mathrm{CC} + \mathrm{WC}& &{}\end{array}$$

(10.1a)

$$\displaystyle\begin{array}{rcl} \mathrm{DV} = \left \{P_{g,t},P_{c,t},W_{c,t},W_{w,t}\right \}& &{}\end{array}$$

(10.1b)

$$\displaystyle\begin{array}{rcl} \mathrm{CT} =\sum _{g,t}a_{g}P_{g,t}^{2} + b_{ g}P_{g,t} + c_{g}U_{g,t}& &{}\end{array}$$

(10.1c)

$$\displaystyle\begin{array}{rcl} \mathrm{CC} =\sum _{c,t}\alpha _{c}P_{c,t}^{2} +\beta _{ c}P_{c,t}W_{c,t} +\gamma _{c}W_{c,t}^{2} +\zeta _{ c}P_{c,t} +\varsigma _{c}W_{c,t} +\xi _{c}U_{c,t}& &{}\end{array}$$

(10.1d)

$$\displaystyle\begin{array}{rcl} \mathrm{CW} =\sum _{w,t}a_{w}W_{w,t}^{2} + b_{ w}W_{w,t} + c_{w}U_{w,t}& &{}\end{array}$$

(10.1e)

$$\displaystyle\begin{array}{rcl} P_{g}^{\min }U_{ g,t} \leq P_{g,t} \leq P_{g}^{\max }U_{ g,t}& &{}\end{array}$$

(10.1f)

$$\displaystyle\begin{array}{rcl} P_{c}^{\min \nolimits }U_{ c,t} \leq P_{c,t} \leq P_{c}^{\max \nolimits }U_{ c,t}& &{}\end{array}$$

(10.1g)

$$\displaystyle\begin{array}{rcl} W_{c}^{\min \nolimits }U_{ c,t} \leq W_{c,t} \leq W_{c}^{\max \nolimits }U_{ c,t}& &{}\end{array}$$

(10.1h)

$$\displaystyle\begin{array}{rcl} W_{w}^{\min \nolimits }U_{ w,t} \leq W_{w,t} \leq W_{w}^{\max \nolimits }U_{ w,t}& &{}\end{array}$$

(10.1i)

$$\displaystyle\begin{array}{rcl} R_{c}^{\min \nolimits } \leq \frac{P_{c,t}} {W_{c,t}} \leq R_{c}^{\max \nolimits }& &{}\end{array}$$

(10.1j)

$$\displaystyle\begin{array}{rcl} \sum _{g}P_{g,t} +\sum _{c}P_{c,t} = PL_{t}& &{}\end{array}$$

(10.1k)

$$\displaystyle\begin{array}{rcl} \sum _{w}W_{w,t} +\sum _{c}W_{c,t} = WL_{t}& &{}\end{array}$$

(10.1l)

The simulation data are taken from [1] with slight modifications (Tables 10.1, 10.2, and 10.3).

Table 10.1 Technical and economical characteristics of thermal units

Table 10.2 Technical and economical characteristics of co-production units

Table 10.3 Technical and economical characteristics of water desalination units

Fig. 10.1

Water-energy nexus concept

GCode 10.1 Water-energy nexus optimization problem

Sets    t /t1 * t24 /, i  /p1 * p4/, c /c1 * c3 /, w  /w1/; Table gendata ( i, * )  generator cost  c h a r a c t e r i s t i c s  and limits    a         b       c      Pmax   Pmin p1 0.0002069 −0.1483 57.11  500    0 p2 0.0003232 −0.1854 57.11  400    0 p3 0.001065  −0.6026 126.8  400    0 p4 0.0004222 −0.2119 57.11  350    0; Table Coproduct (c, * )      Pmax Pmin Wmax  Wmin  rmin rmax A11       A12      A22       b1     b2    C c1   800  160  200  30   4    9    0.0004433 0.003546 0.007093 −1.106 −4.426 737.4 c2   600  120  150  23   4    9    0.0007881 0.006305 0.01261  −1.475 −5.901 737.4 c3   400  80   100  15   4    9    0.001773  0.01419  0.02837  −2.213 −8.851 737.4; Table waterdata (w, * )      a         b        c      Wmax    Wmin w1   1.82E −02 −7.081e−1 7.374  250    0; Table PWdata( t, * )      Pd   water t1   1250 150 t2   1125 130 t3   875  100 t4   750  150 t5   950  200 t6   1440 350 t7   1500 300 t8   1750 200 t9   2000 300 t10  2250 400 t16  2500 550 t17  2125 550 t18  2375 500 t19  2250 400 t20  1975 350 t21  1750 300 t22  1625 250 t23  1500 200 t24  1376 150; Variables  Of,  p( i, t ),TC,CC, Pc(c, t ),Wc(c, t ),Water(w, t ), WaterCost; Binary variables  Up( i, t ),Uc(c, t ),Uw(w, t ); p. up( i, t )=gendata ( i,”Pmax”);  p. lo ( i, t )=0; Pc. up(c, t )= Coproduct (c, ’Pmax ’ ); Pc. lo (c, t )=0; Wc. up(c, t )= Coproduct (c, ’Wmax’ );  Wc. lo (c, t )=0; Water. up(w, t )=waterdata (w, ’Wmax’ );  Water. lo (w, t )=0; Equations costThermal, balanceP, balanceW, costCoprodcalc, Objective, costwatercalc, ratio1, ratio2,EQ1,EQ2,EQ3,EQ4,EQ5,EQ6,EQ7,EQ8; costThermal..TC = e = sum(( t, i ), gendata ( i, ’a ’ ) * power (p( i, t ),2)+gendata ( i, ’b ’ ) * p( i, t ) +gendata ( i, ’ c ’ ) * Up( i, t ) ); balanceP ( t ) ..  sum( i, p( i, t ) )+ sum(c, Pc(c, t ) )= e = PWdata( t, ’Pd ’ ); balanceW( t ) ..  sum(w, Water(w, t ) )+ sum(c,Wc(c, t ) )= e = PWdata( t, ’ water ’ ); costCoprodcalc..  CC = e = sum(( c, t ), Coproduct (c, ’A11 ’ ) * power (Pc(c, t ),2) +2* Coproduct (c, ’A12 ’ ) * Pc(c, t ) * Wc(c, t ) + Coproduct (c, ’A22 ’ ) * power (Wc(c, t ),2) + Coproduct (c, ’B1 ’ ) * Pc(c, t )+ Coproduct (c, ’B2 ’ ) * Wc(c, t )+ Coproduct (c, ’C’ ) * Uc(c, t ) ); costwatercalc..  WaterCost = e = sum(( t,w), waterdata (w, ’a ’ ) * power (Water(w, t ),2) +waterdata (w, ’b ’ ) * Water(w, t ) +waterdata (w, ’ c ’ ) * Uw(w, t ) ); Objective ..  OF = e = TC + CC + WaterCost; ratio1 (c, t ) ..  Pc(c, t )=l= Wc(c, t ) * Coproduct (c, ’Rmax ’ ); ratio2 (c, t ) ..  Pc(c, t )= g = Wc(c, t ) * Coproduct (c, ’Rmin ’ ); eq1 (w, t )    ..  Water(w, t )=l= Uw(w, t ) * waterdata (w, ’Wmax’ ); eq2 (w, t )..  Water(w, t )= g = Uw(w, t ) * waterdata (w, ’Wmin’ ); eq3 (c, t )..  wc(c, t )=l=  Uc(c, t ) * Coproduct (c, ’Wmax’ ); eq4 (c, t )..  wc(c, t )= g =  Uc(c, t ) * Coproduct (c, ’Wmin’ ); eq5 (c, t )..  Pc(c, t )=l=  Uc(c, t ) * Coproduct (c, ’Pmax ’ ); eq6 (c, t )..  Pc(c, t )= g =  Uc(c, t ) * Coproduct (c, ’Pmin ’ ); eq7 ( i, t )..  p( i, t ) =l= Up( i, t ) * gendata ( i,”Pmax”); eq8 ( i, t )..  p( i, t ) = g = Up( i, t ) * gendata ( i,”Pmin”); Model DEDcostbased /all/;  Solve DEDcostbased us MInlp min OF;

The hourly water output of different plants in water-energy nexus problem is depicted in Fig. 10.2. The hourly power output of different plants in water-energy nexus problem is shown in Fig. 10.3.

Fig. 10.2

Hourly water output of different plants in water-energy nexus problem

Fig. 10.3

Hourly power output of different plants in water-energy nexus problem

10.2 Gas-Power Nexus

The interaction of gas network and electricity network is modeled in this section. The electrical network is IEEE RTS 24-bus network which is shown in Fig. 10.4. It is a transmission network with the voltage levels of 138 kV, 230 kV and Sbase = 100 MVA. The branch data for IEEE RTS 24-bus network is given in Table 10.4 [2]. The from bus, to bus, reactance (X), resistance (r), total line charging susceptance (b), and MVA rating (MVA) are specified in this table. The parallel lines in MATPOWER are merged and the resultants are given in Table 10.4. The generation data for IEEE RTS 24-bus network is given in Table 10.5. The data of generating units in this network is inspired by Conejo et al. [3] and Bouffard et al. [4] with some modifications. The slack bus is bus 13 in this network. The wind turbines and the capacities are also shown in Fig. 10.4.

Fig. 10.4

Gas network linkage with electricity network

Table 10.4 Branch data for IEEE RTS 24-bus network

Table 10.5 Generation data for IEEE RTS 24-bus network

The gas network is also shown in Fig. 10.4 which its data is taken from [5]. The technical and economical characteristics of gas nodes are given in Table 10.6. The technical characteristics of gas network are also provided in Table 10.7 [5]. The gas network equations are described in (10.2).

$$\displaystyle\begin{array}{rcl} \mathrm{GC} =\sum _{n,t}c_{n}\mathrm{Sg}_{n,t}& &{}\end{array}$$

(10.2a)

$$\displaystyle\begin{array}{rcl} \sum _{m}f_{n,m,t} =\sum _{m}f_{m,n,t} + \mathrm{Sg}_{n,t} -\zeta _{g,t}\mathrm{Sd}_{n} - Se_{n,t}& &{}\end{array}$$

(10.2b)

$$\displaystyle\begin{array}{rcl} f_{m,n,t} = C_{m,n}\sqrt{\mathrm{Pr } _{m,t }^{2 } - \mathrm{Pr } _{n,t }^{2}}\ \ \text{Passive arcs}& &{}\end{array}$$

(10.2c)

$$\displaystyle\begin{array}{rcl} f_{m,n,t} \geq C_{mn}\sqrt{\mathrm{Pr } _{m,t }^{2 } - \mathrm{Pr } _{n,t }^{2}}\ \ \text{Active arcs}& &{}\end{array}$$

(10.2d)

$$\displaystyle\begin{array}{rcl} \mathrm{Sg}_{n}^{\min \nolimits } \leq \mathrm{Sg}_{ n,t} \leq \mathrm{Sg}_{n}^{\max \nolimits }& &{}\end{array}$$

(10.2e)

$$\displaystyle\begin{array}{rcl} \mathrm{Pr}_{n}^{\min \nolimits } \leq \mathrm{Pr}_{ n,t} \leq \mathrm{Pr}_{n}^{\max \nolimits }& &{}\end{array}$$

(10.2f)

Table 10.6 Technical and economical characteristics of gas nodes

Table 10.7 Technical characteristics of gas network

The electrical network equations are described in (10.3).

$$\displaystyle\begin{array}{rcl} \mathrm{EC} =\sum _{g,t}a_{g}(P_{g,t})^{2} + b_{ g}P_{g,t} + c_{g} +\sum _{i,t}\mathrm{VOLL} \times \mathrm{LS}_{i,t} + \mathrm{VWC} \times P_{i,t}^{\mathrm{wc}}& &{}\end{array}$$

(10.3a)

$$\displaystyle\begin{array}{rcl} \sum _{g\in \varOmega _{G}^{i}}P_{g,t} + \mathrm{LS}_{i,t} + P_{i,t}^{w} - L_{ i,t} =\sum _{j\in \varOmega _{\ell}^{i}}P_{ij,t}:\lambda _{i,t}& &{}\end{array}$$

(10.3b)

$$\displaystyle\begin{array}{rcl} P_{ij,t} = \frac{\delta _{i,t} -\delta _{j,t}} {X_{ij}} & &{}\end{array}$$

(10.3c)

$$\displaystyle\begin{array}{rcl} -P_{ij}^{\max \nolimits } \leq P_{ ij,t} \leq P_{ij}^{\max \nolimits }& &{}\end{array}$$

(10.3d)

$$\displaystyle\begin{array}{rcl} P_{g}^{\min \nolimits } \leq P_{ g,t} \leq P_{g}^{\max \nolimits }& &{}\end{array}$$

(10.3e)

$$\displaystyle\begin{array}{rcl} P_{g,t} - P_{g,t-1} \leq \mathrm{RU}_{g}& &{}\end{array}$$

(10.3f)

$$\displaystyle\begin{array}{rcl} P_{g,t-1} - P_{g,t} \leq \mathrm{RD}_{g}& &{}\end{array}$$

(10.3g)

$$\displaystyle\begin{array}{rcl} 0 \leq \mathrm{LS}_{i,t} \leq L_{i,t}& &{}\end{array}$$

(10.3h)

$$\displaystyle\begin{array}{rcl} P_{i,t}^{\mathrm{wc}} = w_{ t}\varLambda _{i}^{w} - P_{ i,t}^{w}& &{}\end{array}$$

(10.3i)

$$\displaystyle\begin{array}{rcl} 0 \leq P_{i,t}^{w} \leq w_{ t}\varLambda _{i}^{w}& &{}\end{array}$$

(10.3j)

The overall optimization problem, constraints, and the decision variables are as follows:

$$\displaystyle\begin{array}{rcl} & & \min _{\mathrm{DV}}\mathrm{OF} = \mathrm{EC} + \mathrm{GC} \\ & & \mathrm{DV} = \left \{\begin{array}{c} \delta _{i,t},P_{g,t},P_{c,t},W_{c,t},W_{w,t} \\ \mathrm{Sg}_{n,t},f_{n,m,t},\mathrm{Pr}_{n,t} \end{array} \right \} \\ & & \ (10.2\ \mathrm{and}\ (10.3) {}\end{array}$$

(10.4)

The hourly variation pattern of wind generation, electric and gas demand is shown in Fig. 10.5.

Fig. 10.5

Hourly variation pattern of wind generation, electric and gas demand (pu)

The integrated electricity-gas problem is solved using the GCode 10.2. The total electricity cost EC is $3. 9760 × 10⁵. The total gas extraction costs are GC = $5. 1755 × 10⁵ and the total costs are $9. 1515 × 10⁵. The hourly variation pattern of wind generation, electric and gas demand is shown in Fig. 10.5.

GCode 10.2 Gas-electricity nexus optimization problem

Sets   bus  /1*24/  , slack ( bus ) /13/,Gen /g1 * g12 /, t /t1 * t24/        genD( gen ) /g1 * g2, g5, g7 * g11 /, genN( gen ) /g3, g4, g6, g12/ ; scalars  Sbase /100/  ,VOLL  /10000/, VOLW  /50/; a l i a s (bus, node ); Sets gn NODES  / Anderlues,  Antwerpen,  Arlon,  Berneau,  Blaregnies,  Brugge,  Dudzele,                Gent,  Liege,  Loenhout,  Mons,  Namur,  Petange,  Peronnes,  Sinsin,                Voeren,  Wanze,  Warnand,  Zeebrugge,  Zomergem /      a PIPES  / L1 * L24 /;  Alias (gn,gm);  set Pnm(a, gn,gm) arc description; table  Ndata(gn, * )  Node Data            slo     sup       Sd     plo  pup  c  *  Removed for saving space   ; set GElink (gn, gen ) /Loenhout     .        g12 Voeren       .         g6 Sinsin        .         g3 Petange      .         g4 /; table  AData(a, gn,gm, * )  Arc Data                                     act  C2mn; table  GD (Gen, * )   Generating units  characteristics; set GB(bus,  Gen) connectivity  index of each generating unit to each bus ; Table BusData(bus, * )  Demands of each bus in MW; Table branch (bus,  node, * )     Network technical                r       x       b     z  limit; Table DataWDL( t, * )      w                  d                 g; Parameters Wcap( bus ), conex (bus, node ),SD(gn); branch (bus, node, ’ bij ’ ) $branch (bus, node, ’ Limit ’ ) =1/branch (bus, node, ’x ’ ); conex (bus, node )$( branch (bus, node, ’ limit ’ )and branch (node, bus, ’ limit ’ ) )=1; conex (bus, node )$( conex (node, bus ) )=1; Variables f (a, gn,gm, t ), sg (gn, t ), pressure (gn, t ), EC, Pij (bus, node, t ),Pg(Gen, t ), delta (bus, t ), lsh (bus, t ),Pw(bus, t ), pc(bus, t ),Gc,OF  ; Pnm(a, gn,gm) $adata (a, gn,gm, ’c2mn ’ )=yes; Equations const1, const2, const3, const4, const5, const6,CG1,CG2,CG3,CG4, Objective; const1 (bus, node, t ) $conex (bus, node ).. Pij (bus, node, t )= e = branch (bus, node, ’ bij ’ ) * ( delta (bus, t ) −delta (node, t ) ); const2 (bus, t ).. lsh (bus, t )$BusData(bus, ’pd ’ )+ Pw(bus, t )$Wcap( bus )+ sum(Gen$GB(bus,Gen), Pg(Gen, t ) ) − DataWDL( t, ’d ’ ) * BusData(bus, ’pd ’ )/Sbase= e = + sum( node$conex (node, bus ), Pij (bus, node, t ) ); const3..EC = e = sum(( bus,GenD, t )$GB(bus,GenD),Pg(GenD, t ) * GD (GenD, ’b ’ ) * Sbase ) + sum(( bus, t ),VOLL * lsh (bus, t ) * Sbase$BusData (bus, ’pd ’ )+ VOLW* Pc(bus, t ) * sbase$Wcap( bus ) ); const4 (gen, t ) ..  pg(gen, t+1) − pg(gen, t )=l= GD (gen, ’RU’ )/Sbase; const5 (gen, t ) ..  pg(gen, t−1) − pg(gen, t )=l= GD (gen, ’RD’ )/Sbase; const6 (bus, t )$Wcap( bus ) ..  pc(bus, t )= e = DataWDL( t, ’w’ ) * Wcap( bus )/Sbase− pw(bus, t ); Pg. lo (Gen, t )= GD (Gen, ’Pmin ’ )/Sbase;  Pg. up(Gen, t )= GD (Gen, ’Pmax ’ )/Sbase; delta. up(bus, t )= pi/2; delta. lo (bus, t )=− pi/2; delta. fx ( slack, t )=0; Pij. up(bus, node, t )$ (( conex (bus, node ) ) ) =1*  branch (bus, node, ’ Limit ’ )/Sbase; Pij. lo (bus, node, t )$ (( conex (bus, node ) ) )=−1*branch (bus, node, ’ Limit ’ )/Sbase; lsh. up(bus, t )=  DataWDL( t, ’d ’ ) * BusData(bus, ’pd ’ )/Sbase;  lsh. lo (bus, t )=  0; Pw. up(bus, t )= DataWDL( t, ’w’ ) * Wcap( bus )/Sbase;  Pw. lo (bus, t )=0; Pc. up(bus, t )= DataWDL( t, ’w’ ) * Wcap( bus )/Sbase;  Pc. lo (bus, t )=0; SD(gn)= Ndata(gn, ’SD ’ ); CG1(gn, t )..  sum(Pnm(a, gn,gm), f (Pnm, t ) )= e = sum(Pnm(a,gm, gn), f (Pnm, t ) ) +sg (gn, t )$(Ndata(gn, ’Sup ’ )>0) − DataWDL( t, ’G’ ) * SD(gn) − sum((GenN) $Gelink (gn,GenN),Pg(GenN, t ) * GD (GenN, ’b ’ ) * Sbase /35315); CG2(Pnm(a, gn,gm), t )$(AData(a, gn,gm, ’C2mn ’ ) AND  AData(a, gn,gm, ’ACT’ )=0)  ..  signpower ( f (Pnm, t ),2) = e =  AData(Pnm, ’C2mn ’ ) * ( pressure (gn, t ) −pressure (gm, t ) ); CG3(Pnm(a, gn,gm), t )$(AData(a, gn,gm, ’C2mn ’ ) AND  AData(a, gn,gm, ’ACT’ )=1)   ..  −sqr ( f (Pnm, t ) ) = g =  AData(Pnm, ’C2mn ’ ) * ( pressure (gn, t ) −pressure (gm, t ) ); CG4..  Gc = e =  sum(( gn, t ), 35315* ndata (gn, ’ c ’ ) * sg (gn, t )$Ndata(gn, ’Sup ’ ) ); Objective..OF = e = EC + Gc; sg. lo (gn, t )=0; sg. up(gn, t )=  ndata (gn, ’ sup ’ ); pressure. lo (gn, t ) =  sqr ( ndata (gn, ’ plo ’ ) );  pressure. up(gn, t ) =  sqr ( ndata (gn, ’pup ’ ) ); f. lo (Pnm(a, gn,gm), t )$(AData(a, gn,gm, ’C2mn ’ ) ) = − sqrt(AData(a, gn,gm, ’C2mn ’ ) * (  pressure. up(gn, t ) −pressure. lo (gn, t ) ) ); f. up(Pnm(a, gn,gm), t )$(AData(a, gn,gm, ’C2mn ’ ) )= sqrt(AData(a, gn,gm, ’C2mn ’ ) * (  pressure. up(gn, t ) −pressure. lo (gn, t ) ) ); f. lo (Pnm(a, gn,gm), t )$(AData(a, gn,gm, ’C2mn ’ ) AND  AData(a, gn,gm, ’ACT’ )=1) =0; Model overall  /all/;  Solve overall   using nlp min OF;

Hourly variation pattern of gas generation from gas sources are shown in Fig. 10.6.

Fig. 10.6

Hourly variation pattern of gas generation from gas sources

The hourly variation pattern of electricity power generation is shown in Fig. 10.7.

Fig. 10.7

Hourly variation pattern of electricity power generation

The interaction of gas network and electricity sector has been investigated in several works. The impacts of the gas network on security constrained UC is analyzed in [6]. A unified gas and power flow analysis in natural gas and electricity coupled networks can be found in [7]. A robust scheduling model for wind-integrated energy systems with the considerations of both gas pipeline and power transmission contingencies is developed in [8]. The reliability of gas networks and their impacts on the reliability of electricity network is modeled in [9]. The impact of large penetration of wind generation on the UK gas network is analyzed in [10]. One of the recent efficient methods of electricity storage is storing the electricity as gas. This method is also called power to gas or P2G technique [11].

10.3 Energy Hub Concept

The concept of Energy Hub was introduced in [12]. Energy hub may be considered as a virtual box that can convert a set of input energy carriers into a set of energy demands. This box contains several technologies that can store, transfer, or convert different forms of energies to each other. A general example of Energy hub is shown in Fig. 10.8. Different aspects of energy hubs are investigated in the literature such as economic dispatch of energy hubs [13], demand response and energy hub [14], energy hub concept applied on car manufacturing plants [15], and wind power uncertainty modeling in energy hubs [16, 17].

Fig. 10.8

The energy hub concept

The technologies shown in Fig. 10.8 are explained as follows:

• Combined heat and power (CHP): receives the natural gas (G _t ) and converts it into heat (H _t ) and electricity (E _t ) The CHP economic dispatch problem can be modeled in (10.5) [18]:

  $$\displaystyle\begin{array}{rcl} H_{t} =\eta _{ \mathrm{ge}}^{\mathrm{chp}}G_{ t}& & {}\end{array}$$

  (10.5a)
  $$\displaystyle\begin{array}{rcl} E_{t} =\eta _{ \mathrm{gh}}^{\mathrm{chp}}G_{ t}& & {}\end{array}$$

  (10.5b)

• Electric heat pump (EHP): It is fed by electricity and generates heat demand (H _t ) or cool demand (C _t ) based on the operating mode. The operation of EHP is mathematically formulated as follows:

  $$\displaystyle\begin{array}{rcl} C_{t} + H_{t} = E_{t} \times \mathrm{COP}& & {}\end{array}$$

  (10.6a)
  $$\displaystyle\begin{array}{rcl} H_{t}^{\min \nolimits }I_{ t}^{h} \leq H_{ t} \leq H_{t}^{\max \nolimits }I_{ t}^{h}& & {}\end{array}$$

  (10.6b)
  $$\displaystyle\begin{array}{rcl} C_{t}^{\min \nolimits }I_{ t}^{c} \leq C_{ t} \leq C_{t}^{\max \nolimits }I_{ t}^{c}& & {}\end{array}$$

  (10.6c)
  $$\displaystyle\begin{array}{rcl} I_{t}^{c} + I_{ t}^{h} \leq 1& & \\ I_{t}^{c},I_{ t}^{h} \in \left \{0,1\right \}& & {}\end{array}$$

  (10.6d)

  The EHP can be in heat or cool generation mode. COP is the coefficient of performance for EHP.

• Chiller boiler (CB): It receives heat and transforms it into cool demand The chiller boiler operation is mathematically formulated as follows:

  $$\displaystyle\begin{array}{rcl} C_{t} =\eta _{hc}H_{t}& & {}\end{array}$$

  (10.7)

  The η _hc is the efficiency of heat to cooling conversion for chiller boiler.

• Electricity storage system (ESS): It can store (electricity) and then discharge electricity The ESS operation is mathematically formulated as follows:

  $$\displaystyle\begin{array}{rcl} \mathrm{SOC}_{t} = \mathrm{SOC}_{t-1} + (E_{t}^{\mathrm{ch}}\eta _{ c} - E_{t}^{\mathrm{dch}}/\eta _{ d})\varDelta _{t}& & {}\end{array}$$

  (10.8a)
  $$\displaystyle\begin{array}{rcl} E_{\min }^{\mathrm{ch}} \leq E_{ t}^{\mathrm{ch}} \leq E_{\max }^{\mathrm{dch}}& & {}\end{array}$$

  (10.8b)
  $$\displaystyle\begin{array}{rcl} E_{\min }^{\mathrm{dch}} \leq E_{ t}^{\mathrm{dch}} \leq E_{\max }^{\mathrm{dch}}& & {}\end{array}$$

  (10.8c)
  $$\displaystyle\begin{array}{rcl} \mathrm{SOC}_{\min } \leq \mathrm{SOC}_{t} \leq \mathrm{SOC}_{\max }& & {}\end{array}$$

  (10.8d)
  $$\displaystyle\begin{array}{rcl} & & I_{t}^{\mathrm{dch}} + I_{ t}^{\mathrm{ch}} \leq 1 \\ & & I_{t}^{\mathrm{ch}},I_{ t}^{\mathrm{dch}} \in \left \{0,1\right \} {}\end{array}$$

  (10.8e)

  SOC _t is the state of charge in ESS. E _t ^ch∕dch is for demonstrating the charged and discharged electricity in ESS. The binary variables I _t ^ch, I _t ^dch show the charge or discharge mode of ESS at time t.

• Transformer (Tr): It receives electricity and the output is also electricity (with different voltage level)

  $$\displaystyle\begin{array}{rcl} E_{t}^{\mathrm{out}} =\eta _{\mathrm{ ee}}E_{t}^{\mathrm{in}}& & {}\end{array}$$

  (10.9)

• Furnace (F): receives the natural gas and generates the heat demand

  $$\displaystyle\begin{array}{rcl} H_{t} =\eta _{\mathrm{gh}}G_{t}& & {}\end{array}$$

  (10.10)

Three different energy hub configurations will be analyzed to investigate the level of achievable operational flexibility.

10.3.1 Data

The energy hubs which are analyzed in this chapter would have three types of energy demands namely electric, heat, and cooling demand. Different hourly demand and electricity price data for three energy hub configurations are given in Table 10.8.

Table 10.8 Different hourly demand and electricity price data for energy hub configurations

• The charging and discharging efficiencies (η _ch∕dch) of ESS are assumed to be 0.9. The ESS capacity is SOC_max = 600 MW h and SOC_min = 120 MW h. The initial stored energy in ESS is 120 MW h. The minimum charging and discharging limits are E _min ^ch∕dch = 0 and the maximum charging and discharging limits are E _max ^ch∕dch = 120 MW.

• The transformer efficiency is η _ee = 0. 98.

• The CHP efficiencies for gas to electricity is η _ge = 0. 35 and for gas to heat is η _gh = 0. 45. The CHP capacity is 250 MW.

• For EHP, C _Max ^ehp = H _Max ^ehp = 500 MW; The COP is assumed to be 2.5.

• The furnace efficiency η _gh ^f is 0.9. The furnace capacity is 600 MW.

• The chiller boiler has a capacity equal to 500 MW and the efficiency is η _hc = 0. 95

• The natural gas price is assumed to be constant for different hours and it is equal to λ _t ^g = 12$/MW h

10.3.2 Configuration I

This configuration contains transformer, furnace, and chiller boiler as shown in Fig. 10.9.

$$\displaystyle\begin{array}{rcl} \min \mathrm{OF} =\sum _{t}\lambda _{t}^{e}E_{ t} +\lambda _{ t}^{g}G_{ t}& &{}\end{array}$$

(10.11a)

$$\displaystyle\begin{array}{rcl} \eta _{\mathrm{ee}}E_{t} = D_{t}^{e}& &{}\end{array}$$

(10.11b)

$$\displaystyle\begin{array}{rcl} \eta _{\mathrm{gh}}^{f}G_{ t} = H_{1,t} + H_{2,t}& &{}\end{array}$$

(10.11c)

$$\displaystyle\begin{array}{rcl} \eta _{\mathrm{hc}}H_{2,t} = D_{t}^{c}& &{}\end{array}$$

(10.11d)

$$\displaystyle\begin{array}{rcl} H_{1,t} = D_{t}^{h}& &{}\end{array}$$

(10.11e)

The GAMS code for solving the hub configuration I described in (10.11) is given in GCode 10.3.

Fig. 10.9

The energy hub configuration I, considering transformer, furnace, and chiller boiler

The developed model in GCode 10.3 is linear and can be solved using any lp solver. The problem is solved and the total operating costs are $1. 1327 × 10⁵. The hourly purchased electricity and natural gas in energy hub configuration I are shown in Fig. 10.10.

Fig. 10.10

The hourly purchased electricity and natural gas in energy hub configuration I

The output of furnace system will be divided into two streams. The first one will supply the chiller and the second one will directly supply the heat demand. The hourly output of furnace unit in energy hub configuration-I is shown in Fig. 10.11.

Fig. 10.11

The hourly output of furnace unit in energy hub configuration I

GCode 10.3 The optimal operation of energy hub configuration I

Set     t       hours            /t1 * t24/ Table data ( t, * )      Dh   De    Dc   lambda t1   21.4 52.1  11.5 36.7 t2   23.2 66.7  13.7 40.4 t3   26.1 72.2  16   38.5 t4   26.7 78.4  21.4 38 t5   25.6 120.2 22   40.2 t6   26.4 83.5  30.8 38.6 t7   39.5 110.4 38.9 52.3 t8   47.3 124.3 46.8 67.3 t9   52.1 143.6 51   70.5 t10  49.1 149.3 48.9 66.2 t11  69.3 154.2 34.8 73.3 t12  62   147.3 32.7 60.8 t13  68   200.7 27.8 63.2 t14  68.6 174.4 32   70.8 t15  56.4 176.5 33.2 63.1 t16  41.3 136.1 34.1 52.5 t17  37.4 108.7 40.8 57 t18  25.4 96.9  43.6 49.2 t19  25.7 89.1  51.5 47.5 t20  21.9 82.5  43.1 49.5 t21  22.4 76.9  36.5 53.1 t22  24.6 66.8  27.7 51.6 t23  22.7 47.2  19.1 50.5 t24  22.6 64.7  11   36.4  *  −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−− Variable cost; Positive  variables     E( t ),G( t ),H1( t ),H2( t ); Scalar CBmax  /500/, eta_ee /0.98/, eta_ghf /0.9/, eta_hc /0.95/; H2. up( t)= CBmax; Equations eq1, eq2, eq3, eq4, eq5; eq1      ..    cost = e = sum( t, data ( t, ’lambda ’ ) * E( t )+12*G( t ) ); eq2 ( t )   ..    eta_ee * E( t)=e =data ( t, ’E ’ ); eq3 ( t )  ..    H1( t)=e =data ( t, ’h ’ ); eq4 ( t )  ..    eta_ghf * G( t)=e = H1( t)+H2( t ); eq5 ( t )  ..    eta_hc * H2( t)=e =data ( t, ’ c ’ ); Model Hub /all/; Solve hub us lp min cost;

10.3.3 Configuration II

This configuration contains transformer, furnace, chiller boiler, CHP, and ESS as shown in Fig. 10.12.

Fig. 10.12

The energy hub configuration II, considering transformer, furnace, chiller boiler, CHP, and electric energy storage

$$\displaystyle\begin{array}{rcl} \min \mathrm{OF} =\sum _{t}\lambda _{t}^{e}E_{ t} +\lambda _{ t}^{g}G_{ t}& &{}\end{array}$$

(10.12a)

$$\displaystyle\begin{array}{rcl} \eta _{\mathrm{ee}}E_{2,t} + E_{t}^{\mathrm{dch}} +\eta _{\mathrm{ ge}}G_{1,t} = D_{t}^{e}& &{}\end{array}$$

(10.12b)

$$\displaystyle\begin{array}{rcl} E_{t} = E_{1,t} + E_{2,t}& &{}\end{array}$$

(10.12c)

$$\displaystyle\begin{array}{rcl} E_{1,t} = E_{t}^{\mathrm{ch}}& &{}\end{array}$$

(10.12d)

$$\displaystyle\begin{array}{rcl} \mathrm{SOC}_{t} = \mathrm{SOC}_{t-1} + (E_{t}^{\mathrm{ch}}\eta _{ c} - E_{t}^{\mathrm{dch}}/\eta _{ d})\varDelta _{t}& &{}\end{array}$$

(10.12e)

$$\displaystyle\begin{array}{rcl} E_{\min }^{\mathrm{ch}} \leq E_{ t}^{\mathrm{ch}} \leq E_{\max }^{\mathrm{dch}}& &{}\end{array}$$

(10.12f)

$$\displaystyle\begin{array}{rcl} E_{\min }^{\mathrm{dch}} \leq E_{ t}^{\mathrm{dch}} \leq E_{\max }^{\mathrm{dch}}& &{}\end{array}$$

(10.12g)

$$\displaystyle\begin{array}{rcl} \mathrm{SOC}_{\min } \leq \mathrm{SOC}_{t} \leq \mathrm{SOC}_{\max }& &{}\end{array}$$

(10.12h)

$$\displaystyle\begin{array}{rcl} I_{t}^{\mathrm{dch}} + I_{ t}^{\mathrm{ch}} \leq 1& &{}\end{array}$$

(10.12i)

$$\displaystyle\begin{array}{rcl} I_{t}^{\mathrm{ch}},I_{ t}^{\mathrm{dch}} \in \left \{0,1\right \}& & \\ G_{t} = G_{1,t} + G_{2,t}& &{}\end{array}$$

(10.12j)

$$\displaystyle\begin{array}{rcl} \eta _{\mathrm{gh}}^{f}G_{ 1,t} + H_{1,t} = D_{t}^{h}& &{}\end{array}$$

(10.12k)

$$\displaystyle\begin{array}{rcl} \eta _{\mathrm{gh}}G_{2,t} = H_{1,t} + H_{2,t}& &{}\end{array}$$

(10.12l)

$$\displaystyle\begin{array}{rcl} \eta _{\mathrm{hc}}H_{2,t} = D_{t}^{c}& &{}\end{array}$$

(10.12m)

The GAMS code for solving the hub configuration II described in (10.12) is given in GCode 10.4.

GCode 10.4 The optimal operation of energy hub configuration II

set     t       hours            /t1 * t24/ table  data ( t, * )      Dh   De    Dc   lambda t1   21.4 52.1  11.5 36.7 t2   23.2 66.7  13.7 40.4 t3   26.1 72.2  16   38.5 t4   26.7 78.4  21.4 38 t5   25.6 120.2 22   40.2 t6   26.4 83.5  30.8 38.6 t7   39.5 110.4 38.9 52.3 t8   47.3 124.3 46.8 67.3 t9   52.1 143.6 51   70.5 t10  49.1 149.3 48.9 66.2 t11  69.3 154.2 34.8 73.3 t12  62   147.3 32.7 60.8 t13  68   200.7 27.8 63.2 t14  68.6 174.4 32   70.8 t15  56.4 176.5 33.2 63.1 t16  41.3 136.1 34.1 52.5 t17  37.4 108.7 40.8 57 t18  25.4 96.9  43.6 49.2 t19  25.7 89.1  51.5 47.5 t20  21.9 82.5  43.1 49.5 t21  22.4 76.9  36.5 53.1 t22  24.6 66.8  27.7 51.6 t23  22.7 47.2  19.1 50.5 t24  22.6 64.7  11   36.4 Variable cost; Positive  variables E( t ),E1( t ),E2( t ),G( t ),G1( t ),G2( t ),H1( t ),H2( t ) SOC( t ),Ec( t ),Ed( t ) ; Binary variables  Idch ( t ), Ich ( t ); scalar  SOC0 /20/,SOCmax  /600/, eta_c /0.9/, eta_d /0.9/, eta_ee /0.98/, eta_ge /0.45/, eta_gh /0.35/, eta_hc /0.95/,Chpmax /250/,CBmax  /500/,Fmax /600/, eta_ghf /0.9/; SOC0 =  0. 2 * SOCmax; SOC. up( t )= SOCmax;  SOC. lo ( t ) =0.2*SOCmax;  SOC. fx ( ’ t24 ’ )= SOC0; Ec. up( t ) =0.2*SOCmax;  Ec. lo ( t )=0; Ed. up( t ) =0.2*SOCmax;  Ed. lo ( t )=0; G1. up( t )= Chpmax; G2. up( t )= Fmax; H2. up( t )= CBmax; Equations  eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9, eq10, eq11, eq12; eq1      ..    cost = e = sum( t, data ( t, ’lambda ’ ) * E( t ) +12*G( t ) ); eq2 ( t )   ..    eta_ee * E2( t )+ Ed( t )+eta_ge * G1( t )= e =data ( t, ’E ’ ); eq3 ( t )   ..    E( t )= e = E1( t )+ E2( t ); eq4 ( t )   ..    E1( t )= e = Ec( t ); eq5 ( t )   ..    SOC( t )= e = SOC0$( ord ( t )=1) +  SOC( t−1)$( ord ( t )>1) + Ec( t ) * eta_c− Ed( t )/eta_d; eq6 ( t )   ..    Ed( t )=l =0.2*SOCmax * Idch ( t ); eq7 ( t )   ..    Ec( t )=l =0.2*SOCmax * Ich ( t ); eq8 ( t )   ..    Idch ( t )+Ich ( t )=l =1; eq9 ( t )   ..    G( t )= e = G1( t )+ G2( t ); eq10 ( t )  ..    eta_gh * G1( t )+ H1( t )= e =1* data ( t, ’h ’ ); eq11 ( t )  ..    eta_ghf * G2( t )= e = H1( t )+ H2( t ); eq12 ( t )  ..    eta_hc * H2( t )= e =data ( t, ’ c ’ ); model Hub2 /all/; Solve hub2 us mip min cost;

The developed model in GCode 10.4 is linear and can be solved using any lp solver. The problem is solved, and the total operating costs are $0. 85504 × 10⁵. The hourly purchased electricity and its division between transformer and ESS in energy hub configuration-II are shown in Fig. 10.13. The output of furnace system will be divided into two streams. The first one will supply the chiller and the second one will supply the heat demand. The hourly output of furnace unit in energy hub configuration II is shown in Fig. 10.14. The hourly state of charge, charging, and discharging of ESS in energy hub configuration II is shown in Fig. 10.15.

Fig. 10.13

The hourly purchased electricity and its division between transformer and ESS in energy hub configuration II

Fig. 10.14

The hourly output of furnace unit in energy hub configuration II

Fig. 10.15

The hourly state of charge (MW h), charging, and discharging of ESS (MW) in energy hub configuration II

10.3.4 Configuration III

This configuration contains transformer, furnace, chiller boiler, CHP, and ESS as shown in Fig. 10.16.

Fig. 10.16

The energy hub configuration III, considering transformer, furnace, chiller boiler, CHP, electric energy storage, and EHP

$$\displaystyle\begin{array}{rcl} \min \mathrm{OF} =\sum _{t}\lambda _{t}^{e}E_{ t} +\lambda _{ t}^{g}G_{ t}& &{}\end{array}$$

(10.13a)

$$\displaystyle\begin{array}{rcl} \eta _{\mathrm{ee}}E_{2,t} + E_{t}^{\mathrm{dch}} +\eta _{\mathrm{ ge}}G_{1,t} = D_{t}^{e}& &{}\end{array}$$

(10.13b)

$$\displaystyle\begin{array}{rcl} E_{t} = E_{1,t} + E_{2,t} + E_{3,t}& &{}\end{array}$$

(10.13c)

$$\displaystyle\begin{array}{rcl} E_{1,t} = E_{t}^{\mathrm{ch}}& &{}\end{array}$$

(10.13d)

$$\displaystyle\begin{array}{rcl} \mathrm{SOC}_{t} = \mathrm{SOC}_{t-1} + (E_{t}^{\mathrm{ch}}\eta _{ c} - E_{t}^{\mathrm{dch}}/\eta _{ d})\varDelta _{t}& &{}\end{array}$$

(10.13e)

$$\displaystyle\begin{array}{rcl} E_{\min }^{\mathrm{ch}}I_{ t}^{\mathrm{ch}} \leq E_{ t}^{\mathrm{ch}} \leq E_{\max }^{\mathrm{ch}}I_{ t}^{\mathrm{ch}}& &{}\end{array}$$

(10.13f)

$$\displaystyle\begin{array}{rcl} E_{\min }^{\mathrm{dch}}I_{ t}^{\mathrm{dch}} \leq E_{ t}^{\mathrm{dch}} \leq E_{\max }^{\mathrm{dch}}I_{ t}^{\mathrm{dch}}& &{}\end{array}$$

(10.13g)

$$\displaystyle\begin{array}{rcl} \mathrm{SOC}_{\min } \leq \mathrm{SOC}_{t} \leq \mathrm{SOC}_{\max }& &{}\end{array}$$

(10.13h)

$$\displaystyle\begin{array}{rcl} I_{t}^{\mathrm{dch}} + I_{ t}^{\mathrm{ch}} \leq 1& &{}\end{array}$$

(10.13i)

$$\displaystyle\begin{array}{rcl} I_{t}^{\mathrm{ch}},I_{ t}^{\mathrm{dch}} \in \left \{0,1\right \}& & \\ G_{t} = G_{1,t} + G_{2,t}& &{}\end{array}$$

(10.13j)

$$\displaystyle\begin{array}{rcl} \eta _{\mathrm{gh}}G_{1,t} + H_{1,t} + H_{t}^{\mathrm{EHP}} = D_{ t}^{h}& &{}\end{array}$$

(10.13k)

$$\displaystyle\begin{array}{rcl} \eta _{\mathrm{gh}}^{f}G_{ 2,t} = H_{1,t} + H_{2,t}& &{}\end{array}$$

(10.13l)

$$\displaystyle\begin{array}{rcl} \eta _{\mathrm{hc}}H_{2,t} + C_{t}^{\mathrm{EHP}} = D_{ t}^{c}& &{}\end{array}$$

(10.13m)

$$\displaystyle\begin{array}{rcl} C_{t}^{\mathrm{EHP}} + H_{ t}^{\mathrm{EHP}} = E_{ 3,t} \times \mathrm{COP}& &{}\end{array}$$

(10.13n)

$$\displaystyle\begin{array}{rcl} H_{t}^{\min \nolimits }I_{ t}^{h} \leq H_{ t}^{\mathrm{EHP}} \leq H_{ t}^{\max \nolimits }I_{ t}^{h}& &{}\end{array}$$

(10.13o)

$$\displaystyle\begin{array}{rcl} C_{t}^{\min \nolimits }I_{ t}^{c} \leq C_{ t}^{\mathrm{EHP}} \leq C_{ t}^{\max \nolimits }I_{ t}^{c}& &{}\end{array}$$

(10.13p)

$$\displaystyle\begin{array}{rcl} I_{t}^{c} + I_{ t}^{h} \leq 1& & \\ I_{t}^{c},I_{ t}^{h} \in \left \{0,1\right \}& &{}\end{array}$$

(10.13q)

The developed model in GCode 10.5 is linear and can be solved using any lp solver.

GCode 10.5 The optimal operation of energy hub configuration III

Set     t       hours            /t1 * t24/ Table data ( t, * )           Dh   De    Dc   lambda t1   21.4 52.1  11.5 36.7 t2   23.2 66.7  13.7 40.4 t3   26.1 72.2  16   38.5 t4   26.7 78.4  21.4 38 t5   25.6 120.2 22   40.2 t6   26.4 83.5  30.8 38.6 t7   39.5 110.4 38.9 52.3 t8   47.3 124.3 46.8 67.3 t9   52.1 143.6 51   70.5 t10  49.1 149.3 48.9 66.2 t11  69.3 154.2 34.8 73.3 t12  62   147.3 32.7 60.8 t13  68   200.7 27.8 63.2 t14  68.6 174.4 32   70.8 t15  56.4 176.5 33.2 63.1 t16  41.3 136.1 34.1 52.5 t17  37.4 108.7 40.8 57 t18  25.4 96.9  43.6 49.2 t19  25.7 89.1  51.5 47.5 t20  21.9 82.5  43.1 49.5 t21  22.4 76.9  36.5 53.1 t22  24.6 66.8  27.7 51.6 t23  22.7 47.2  19.1 50.5 t24  22.6 64.7  11   36.4  ; data ( t, ’lambda ’ ) =0.6* data ( t, ’lambda ’ ); variable  cost; positive  variables  E( t ),E1( t ),E2( t ),E3( t ),G( t ),G1( t ),G2( t ),H1( t ),H2( t ) SOC( t ),Ec( t ),Ed( t ),H_ehp( t ),C_ehp( t ) ; Binary variables  Idch ( t ), Ich ( t ), Ic ( t ), Ih ( t ); scalar  SOC0 /20/, SOCmax  /600/, eta_c /0.9/, eta_d /0.9/, eta_ee /0.98/ , eta_ge /0.45/ , eta_gh /0.35/ eta_hc /0.95/, COP  /2.5/, H_ehpMax /200/, C_ehpMax /200/,Chpmax /300/, CBmax  /300/,Fmax /300/, eta_ghf /0.9/; SOC0 =  0. 2 * SOCmax;  SOC. up( t )= SOCmax;  SOC. lo ( t ) =0.2*SOCmax;  SOC. fx ( ’ t24 ’ )= SOC0; Ec. up( t ) =0.2*SOCmax;  Ec. lo ( t )=0; Ed. up( t ) =0.2*SOCmax;  Ed. lo ( t )=0; C_ehp. up( t )= C_ehpMax;  H_ehp. up( t )= H_ehpMax; G1. up( t )= Chpmax;  G2. up( t )= Fmax;  H2. up( t )= CBmax;  E. up( t ) =1000; Equations eq1, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9, eq10, eq11, eq12, eq13, eq14, eq15, eq16; eq1      ..    cost = e = sum( t, data ( t, ’lambda ’ ) * E( t ) +12*G( t ) ); eq2 ( t )   ..    eta_ee * E2( t ) + Ed( t )+eta_ge * G1( t )= e =data ( t, ’E ’ )+ E3( t ); eq3 ( t )   ..    E( t )= e = E1( t )+ E2( t ); eq4 ( t )   ..    E1( t )= e = Ec( t ); eq5 ( t )   ..    SOC( t )= e = SOC0$ ( ord ( t )=1) +  SOC( t−1)$( ord ( t )>1) + Ec( t ) * eta_c− Ed( t )/eta_d; eq6 ( t )   ..    Ed( t )=l =0.2*SOCmax * Idch ( t ); eq7 ( t )   ..    Ec( t )=l =0.2*SOCmax * Ich ( t ); eq8 ( t )   ..    Idch ( t )+Ich ( t )=l =1; eq9 ( t )   ..    G( t )= e = G1( t )+ G2( t ); eq10 ( t )  ..    eta_gh * G1( t )+ H1( t )+ H_ehp( t )= e =1* data ( t, ’h ’ ); eq11 ( t )  ..    eta_ghf * G2( t )= e = H1( t )+ H2( t ); eq12 ( t )  ..    eta_hc * H2( t )+ C_ehp( t )= e =data ( t, ’ c ’ ); eq13 ( t )  ..    C_ehp( t )+ H_ehp( t )= e = E3( t ) * cop; eq14 ( t )  ..    H_ehp( t )=l= H_ehpMax *  Ih ( t ); eq15 ( t )  ..    C_ehp( t )=l= C_ehpMax *  Ic ( t ); eq16 ( t )  ..    Ic ( t )+Ih ( t )=l =1; Model Hub /all/; Solve hub us mip min cost;

The problem is solved and the total operating costs are $0. 84430 × 10⁵. The hourly purchased electricity and its division between transformer and ESS in energy hub configuration-III are shown in Figs. 10.17, 10.18. The output of furnace system will be divided into two streams. The first one will supply the chiller and the second one will supply the heat demand. The hourly output of furnace unit in energy hub configuration II is shown in Fig. 10.14. The hourly state of charge, charging, and discharging of ESS in energy hub configuration III is shown in Fig. 10.19. The hourly output of EHP in energy hub configuration III is shown in Fig. 10.20.

Fig. 10.17

The hourly purchased electricity and its division between transformer and ESS in energy hub configuration III

Fig. 10.18

The hourly output of furnace unit in energy hub configuration III

Fig. 10.19

The hourly state of charge (MW h), charging, and discharging of ESS (MW) in energy hub configuration III

Fig. 10.20

The hourly output of EHP in energy hub configuration III