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DC microgrid
CHAPTER 11
Stochastic-based energy management of hybrid AC/DC microgrid Hamed Pashaei-Didani1, Hamed Ahmadi-Nezamabad1, Arash Mohammadi1 and Sayyad Nojavan2 1 Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran Department of Electrical Engineering, University of Bonab, Bonab, Iran
2
Contents 11.1 Introduction 11.2 Stochastic formulation of the hybrid AC/DC microgrid 11.2.1 Objective function 11.2.2 Network model 11.2.3 Constraints of DC subgrid 11.2.4 Constraints of AC subgrid 11.3 Stochastic simulation results 11.3.1 Generated scenarios 11.3.2 Total operating cost 11.3.3 Power generation of renewable energy source in the AC subgrid 11.3.4 Scheduled reserve and load reduction of industrial loads 11.3.5 Scheduled reserve and load reduction of demand response providers 11.3.6 Purchased energy from the upstream grid 11.3.7 Voltage profile 11.3.8 Scheduling of distributed generation units in AC subgrid 11.3.9 Battery storage systems in the AC subgrid 11.3.10 Power generation of renewable energy sources in the DC subgrid 11.3.11 DC load 11.3.12 Battery storage system in the DC subgrid 11.3.13 Power generation of distributed generation unit in the DC subgrid 11.3.14 Exchanged power between AC and DC subgrids 11.4 Conclusion References
Risk-based Energy Management DOI: https://doi.org/10.1016/B978-0-12-817491-3.00011-8
© 2020 Elsevier Inc. All rights reserved.
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11.1 Introduction Among different developed methods to model uncertainty in a system, the stochastic programming method is utilized in this chapter to get optimal energy management of a hybrid AC/DC microgrid (MG). Modeling multiple uncertain parameters through generating different scenarios are the main advantages of the stochastic programming method [1] in comparison with the robust optimization approach [2] and information gap decision theory [36]; however, the method suffers from the high computational burden, which requires scenario reduction approaches [7]. In this chapter, optimal energy management of hybrid AC/DC MG is carried out under uncertainties of power price, load demand, wind speed, and solar irradiation considering 10 discrete scenarios. In the first stage, scenario generation is implemented using the normal and Weibull distributions in which the former is utilized to generate scenarios of power price, load demand, and solar irradiation and the latter is used to generate wind speed scenarios. Then, in the second stage, optimal energy management of the hybrid AC/DC MG is carried out using the stochastic method. The case study developed in Chapter 10, Deterministic-based energy management of hybrid AC/ DC microgrid, is utilized to evaluate the performance of the proposed method. In the considered case study, which was detailed in the previous chapter, different generation units including wind turbines (WTs) [8], photovoltaic systems (PVs) [9], microturbines (MTs), and battery storage systems (BSSs) are optimally located in both DC and AC subgrids to increase the system efficiency and reduce the total operating cost of the system. In addition, different time-based and incentivebased demand response (DR) programs [10,11] including time-of-use (TOU) rate, load reduction of industrial loads (ILs), and demand response providers (DRPs) are implemented to reduce operating cost of the system. To cope with the power price and load uncertainties, it is assumed that AC and DC subgrids can exchange the excessive generation of renewable energy sources (RESs). Finally, it should be noted that the stochastic-based energy management of hybrid AC/DC MGs is formulated as mixed-integer nonlinear programming method (MINLP) and solved using the GAMS optimization software under the DICOPT solver.
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11.2 Stochastic formulation of the hybrid AC/DC microgrid To solve the optimal energy management problem of a hybrid AC/DC MG, the stochastic formulation of the problem should be developed based on the deterministic case formulation that was developed in Chapter 10, Deterministic-based energy management of hybrid AC/DC microgrid. In the following subsections the stochastic formulation of the problem is provided in detail. To get more information about the concept of the stochastic programming, please refer to Chapter 3, Stochastic-based energy management of DC microgrids, and Chapter 7, Stochastic-based energy management of AC microgrids.
11.2.1 Objective function As said previously, 10 discrete scenarios are developed to model the mentioned uncertainties in the system with different possibilities. Eq. (11.1) provides the objective function of the system considering different scenarios. 2 NDG X E CEDG ðj; t; sÞ 1 CSDG ðj; t; sÞ 1 CRDG ðj; t; sÞ 1 6 Pgrid ðt; sÞ 3 λgrid ðt; sÞ 1 CostDC 1 BX N T 6 B j51 6 πs 3 B 6 NIL B DRP NX @ t51 4 X CEIL ði; t; sÞ 1 CRIL ði; t; sÞ 1 CEDRP ðd; t; sÞ 1 CRDRP ðd; t; sÞ 0
min
Ns X s51
i51
31 7C 7C 7C 7C 5A
d51
(11.1)
where πs is the probability scenario s and CostDC is the stochastic-based operating cost of the DC subgrid, which is introduced in following subsections. Different parts of Eq. (11.1) have been detailed in Chapter 7, Stochastic-based energy management of AC microgrids.
11.2.2 Network model In each scenario s and time t, the balance between demand and supply should be provided at each bus i. Eqs. (11.2) and (11.3) present the network model of the hybrid AC/DC MG. X
Pgrid ði; t; sÞ 1 PDG ði; t; sÞ 1 PWT ði; t; sÞ 1 PPV ði; t; sÞ
iANbus 5 1 E E ði; t; sÞ 1 PIL ði; t; sÞ 2 PD ði; t; sÞ 1 PSd ði; t; sÞ 2 PSc ði; t; sÞ 1 PDRP
1 PDC=AC ðt; sÞ 3 ηDC=AC 5 PAC=DC ðt; sÞ 1
Nbus X V ði; t; sÞ 3 V ðj; t; sÞ j
3 yline ði; jÞ 3 cosðθði; jÞ 1 δðj; tÞ 2 δði; tÞÞ;
’i; t; s
(11.2)
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X
Nbus X
Qgrid ði; t; sÞ 2 QD ði; t; sÞ 5
iANbus 5 1
V ði; t; sÞ 3 V ðj; t; sÞ 3 yline ði; jÞ
j51
3 sinðθði; jÞ 1 δði; tÞ 2 δðj; tÞÞ;
’i; t; s (11.3)
11.2.3 Constraints of DC subgrid The system model and operational constraints and requirements of the DC subgrid in the stochastic form are developed based on the deterministic case model. ! Ns T X I X X CostDC 5 πs CDG ðiÞ 3 PDG ði; t; sÞ (11.4) t
s51
i
PAC=DC ðt; sÞ 3 ηAC=DC 1 PDG ðt; sÞ 1 PPV ðt; sÞ 1 PWind ðt; sÞ 3 ηAC=DC 1 Pdis ðt; sÞ DR 5 PLoad ðt; sÞ 1 Pch ðt; sÞ 1 PDC=AC ðt; sÞ
(11.5) DR ðt; sÞ 5 Pload ðt; sÞ 1 DRðt; sÞ PLoad
2DRmax 3 Pload ðt; sÞ # DRðt; sÞ # 1 DRmax 3 Pload ðt; sÞ 24 X
DRðt; sÞ 5 0
(11.6) (11.7)
(11.8)
t51
PchDC ðt; sÞ # XchDC ðt; sÞ 3 PchDC max
(11.9)
DC DC DC max ðt; sÞ # Xdis ðt; sÞ 3 Pdis Pdis
(11.10)
DC ðt; sÞ , 1 XchDC ðt; sÞ 1 Xdis
(11.11)
DC DC SOCDC ðt; sÞ 5 SOCDC ðt 2 1; sÞ 1 PchDC ðt; sÞ 3 ηDG ch 2 Pdis ðt; sÞ=ηdis (11.12)
Stochastic-based energy management of hybrid AC/DC microgrid
M ;max PDC ðt; sÞ 5
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DC DC SOCmin , SOCDC ðt; sÞ , SOCmax
(11.13)
DC DC max DC ðt; sÞ , PDG 3 UDG ðt; sÞ PDG
(11.14)
DC min DC DC PDG 3 UDG ðt; sÞ , PDG ðt; sÞ
(11.15)
G a ðtÞ NOCT 2 20 M 3 PMax;0 1 μP max 3 T a ðt; sÞ 1 G a ðt; sÞ 3 2 TM ;0 Ga0 800
(11.16) DC DC ðt; sÞ # PM PPV ;max ðt; sÞ;
’t; s
8 0 Vtw , Vci > > > 3 > > > < p 3 V w ðt;sÞ2Vci V , V w ðt; sÞ , V r ci cr DC Vr 2Vci Pwind;max ðt; sÞ 5 > > > pr Vr , V w ðt; sÞ , Vc0 > > > : 0 Vtw . Vc0 DC DC ðt; sÞ # Pwind;max ðt; sÞ; Pwind
’t; s
(11.17)
(11.18)
(11.19)
max PDC=AC ðt; sÞ , XDC=AC ðt; sÞ 3 Pcon
(11.20)
max PAC=DC ðt; sÞ , XAC=DC 3 Pcon
(11.21)
XAC=DC ðt; sÞ 1 XDC=AC ðt; sÞ , 1
(11.22)
In these equations, Eq. (11.4) models the stochastic operation cost of the DC subgrid, Eq. (11.5) balances active power demand and supply, Eqs. (11.6)(11.8) provide the TOU rate of the DR model, Eqs. (11.9) (11.13) present the BSS model in the DC subgrid, Eqs. (11.14) and (11.15) model operational constraints of the MT, Eqs. (11.16) and (11.17) and Eqs. (11.18) and (11.19) present the PV and WT systems in the DC subgrid, respectively, and finally, Eqs. (11.20)(11.22) model the power exchange between AC and DC subgrids.
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11.2.4 Constraints of AC subgrid The system model and operational constraints and requirements of the AC subgrid are provided by Eqs. (11.23)(11.55), each of which has been detailed in Chapter 7, Stochastic-based energy management of AC microgrids. Iðm; n; t; sÞ # Iðm; nÞ
(11.23)
V ðnÞ # V ðn; t; sÞ # V ðnÞ
(11.24)
V ðn; t; sÞ 5 1 5 Constant; n 5 Substation bus;
’t; s
Iðm; n; t; sÞ # Isub m 5 1; n 5 Substation bus;
’t; s
(11.26)
’i; t; s
(11.27)
RIL ði; t; sÞ 1 RDRP ði; t; sÞ 1 RDG ði; t; sÞ 5 0:2 3 PWT ði; t; sÞ 1 0:1 3 PD ði; t; sÞ; d # od1 # O1d Omin d 0 # odk # ðOk11 2 Okd Þ
(11.28)
’k 5 2; 3; . . .; k
PDRP ðd; t; sÞ 5
X
(11.25)
Okd
(11.29) (11.30)
k
CEDRP ðd; t; sÞ 5
X
πdk 3 odk
(11.31)
k
PDRP ðd; t; sÞ 1 RDRP ðd; t; sÞ # PDRP ðd; t; sÞ
(11.32)
CRDRP ðd; t; sÞ 5 RDRP ðd; t; sÞ 3 KRDRP ðd; t; sÞ
(11.33)
PIL ði; t; sÞ 1 RIL ði; t; sÞ # PIL ði; t; sÞ
(11.34)
CEIL ði; t; sÞ 5 PIL ði; t; sÞ 3 KEIL ði; t; sÞ
(11.35)
Stochastic-based energy management of hybrid AC/DC microgrid
CRIL ði; t; sÞ 5 RIL ði; t; sÞ 3 KRIL ði; t; sÞ
PWT ðvÞ 5
8 ðv 2 vci Þ > > Pr 3 > < ðvr 2 vci Þ > Pr > > : 0
(11.36)
vci # v # vr (11.37)
vr # v # vco otherwise
PWT ðw; t; sÞ # Pw ðvðt; sÞÞ ’w; t; s bsc ðb; t; sÞ 1 bsd ðb; t; sÞ # 1;
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bsc ; bsd Af0; 1g;
(11.38) ’t; s
(11.39)
SOCðb; t; sÞ 5 SOCðb; t 2 1; sÞ 1 ηc 3 PSc ðb; t; sÞ 2 ηd 3 PSd ðb; t; sÞ (11.40) SOCðbÞ # SOCðb; t; sÞ # SOCðbÞ
(11.41)
0 # PSc ðb; t; sÞ # PSc 3 bsc ðb; t; sÞ
(11.42)
0 # PSd ðb; t; sÞ # PSd 3 bsd ðb; t; sÞ
(11.43)
2 ðj; t; sÞ CEDG ðj; t; sÞ 5 aj 3 uðj; t; sÞ 1 bj 3 PDG ðj; t; sÞ 1 cj 3 PDG
(11.44)
CSDG ðj; t; sÞ 5 SUCðj; sÞ 3 ðuðj; t; sÞ 2 Uðj; t 2 1; sÞÞ ’j; t; s
(11.45)
CSDG ðj; t; sÞ $ 0;
’j; t; s
(11.46)
CRDG ðj; t; sÞ 5 KRDG 3 ðbj 1 2 3 cj 3 PDG ðj; t; sÞÞ 3 RDG ðj; t; sÞ ’j; t; s (11.47) PDG ðjÞ 3 uðj; t; sÞ # PDG ðj; t; sÞ # PDG ðjÞ 3 uðj; t; sÞ
’j; t; s
PDG ðj; t; sÞ 1 RDG ðj; t; sÞ # PDG ðjÞ 3 uðj; t; sÞ ’j; t; s
(11.48) (11.49)
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PDG ðj; t; sÞ 2 PDG ðj; t 2 1; sÞ # URðj; sÞ 3 ð1 2 yðj; t; sÞÞ 1 PDG ðjÞ 3 yðj; t; sÞ
’j; t; s
PDG ðj; t 2 1; sÞ 2 PDG ðj; t; sÞ # DRðj; sÞ 3 ð1 2 zðj; t; sÞÞ 1 PDG ðjÞ 3 zðj; t; sÞ t1UT ðjÞ21 X
’j; t; s
uðj; h; sÞ $ UT ðj; sÞ 3 yðj; t; sÞ
’j; t; s
(11.50)
(11.51)
(11.52)
h5t t1DT ðjÞ21 X
ð1 2 uðj; hÞÞ $ DT ðjÞ 3 zðj; t; sÞ
’j; t; s
(11.53)
h5t
yðj; t; sÞ 2 zðj; t; sÞ 5 uðj; t; sÞ 2 uðj; t 2 1; sÞ yðj; t; sÞ 1 zðj; t; sÞ # 1
’j; t; s
’j; t; s
(11.54) (11.55)
11.3 Stochastic simulation results Obtained results of the stochastic programming method on the developed case study in Chapter 10, Deterministic-based energy management of hybrid AC/DC microgrid, are presented in the following subsections. As said previously, the optimal energy management problem of a hybrid AC/DC MG under different uncertainties formulated as MINLP is solved using the DICOPT [12] solver in GAMS [13] optimization software. Note that among the 10 generated discrete scenarios, the results of Scenario 3 are presented in all sections. In each scenario, the problem is solved in two cases, with- and without-DR programs, to show the impact of the DR program on operating cost and operation of the system. It is worth mentioning that in the with-DR case, load reduction of ILs and DRPs is carried out in the AC subgrid and the TOU rate of DR is implemented in the DC subgrid.
11.3.1 Generated scenarios To model the impact of uncertainties of power price, load demand, wind speed, and solar irradiation using stochastic programming, discrete
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Figure 11.1 Scenarios of load in the hybrid AC/DC system. 500
Upstream grid price ($/MWh)
450 400 350 300 250 200 150 100 50 0
2
4
6
8
10
12
14
16
18
20
22
24
Time (h) Figure 11.2 Scenarios of power price in the upstream grid in the hybrid AC/DC system.
scenarios for each parameter should be generated. In this chapter, normal distribution is used to generate power price, load demand, and solar irradiation scenarios and the Weibull distribution is used to produce wind speed scenarios. Generated scenarios for load demand, power price, and wind speed are depicted in Figs. 11.111.3, respectively. It should be noted that 10 discrete scenarios are generated to model each uncertain
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Figure 11.3 Wind speed scenarios in the upstream grid in the hybrid AC/DC system.
parameter and the results are provided for Scenario 3. As it can be seen in Figs. 11.111.3, generated scenarios for each uncertain parameter almost follow the same pattern.
11.3.2 Total operating cost The total operating cost of the hybrid AC/DC MG under power price, load demand, solar irradiation, and wind speed uncertainties are obtained as $69,628.078 and $62,742.121 for without- and with-DR cases, respectively. In the stochastic energy management of the hybrid AC/DC system, it is seen that implementing DR programs has reduced total operation cost of the system by about 9.88%. In this case, the operating cost of the DC subgrid is equal to $1471.710 and $1361.138 for withoutand with-DR cases, indicating a 7.13% reduction because of using the TOU rate of DR in the DC subgrid. To provide the required reserve capacity of the system in the AC subgrid, different sources are utilized including MTs in the without-DR case and ILs, DRPs, and MTs in the with-DR case, with the total reserve cost of $1408.069 and $1585.813 for with- and without-DR cases, respectively. It is seen that although implementing DR programs has reduced total operating cost of the system significantly, it has increased reserve cost about by $177.44, which is negligible. Table 11.1 provides a summary of stochastic-based optimization results.
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Table 11.1 A summary of stochastic-based optimization results. Without DR
AC subgrid DC subgrid
With DR
Total cost ($)
Energy cost ($)
Reserve cost ($)
Total cost ($)
Energy cost ($)
Reserve cost ($)
69,628.078 1471.710
68,220.009 1471.710
1408.069
62,742.12 1361.138
61,156.309 1361.138
1585.813
Figure 11.4 Generated power by the photovoltaics in the AC subgrid.
11.3.3 Power generation of renewable energy source in the AC subgrid In the AC subgrid multiple WT and PV units are used to harness solar and wind energies. Aggregation of generated power by the PVs in Scenario 3 is depicted in Fig. 11.4. The PV systems in the start generate power from hour 5 to 18. Generated power by the PV system reaches its highest level at hour 11, recording 0.33 MW. Fig. 11.5 illustrated the generated power by the WTs in Scenario 3. Power generation of the WTs is related to the wind speed, in which it should be higher than the cut-in speed of the WT. For example, turning to Fig. 11.3, the wind speed in Scenario 3 at hour 12 is 2.254 m/s, which is less than 3 m/s as the cut-in speed of the WT; therefore, WTs did not generate power at this hour. The highest level of the generated power by the WTs is equal to 8.17 MW at hour 4. A sharp decrease is seen between hours 5 and 12 in generated power by the WTs because of wind speed reduction. Then, there is an increasing trend during hours 1315.
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Figure 11.5 Generated power by the wind turbines in the AC subgrid.
Figure 11.6 Load reduction of industrial loads in Scenario 3.
11.3.4 Scheduled reserve and load reduction of industrial loads Load reduction of ILs is depicted in Fig. 11.6 in Scenario 3 for a 24-hour time horizon of the study. In the with-DR case, it is assumed that the ILs offered to get paid instead of reducing their load in required periods. Based on provided information about offered price and demand in Chapter 6,
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Figure 11.7 Scheduled reserve of industrial loads in Scenario 3.
Deterministic-based energy management of AC microgrids, the ILs reduce their load only during hours 923. According to Fig. 11.6, the maximum offered load is curtailed at hours 9, 14, 19, and 22 in Scenario 3. Fig. 11.7 presents the scheduled resereve capacity of the ILs. It is assumed that at each hour, scheduled reserve should be equal or greater than the sum of 20% of PV generation and 10% of load demand. In addition, the sum of load reduction and scheduled reserve should be equal or less than maximum capacity of the ILs. For instance, scheduled reserve load reduction of ILs at hour 10 are equal to 0.9 and 0.4 MW, respectively, where aggreation of them is equal to 1.3 MW, which is the maximum offered amount by the ILs.
11.3.5 Scheduled reserve and load reduction of demand response providers Load reduction of ILs is depicted in Fig. 11.8. Considering the power price in the market and cost of load reduction of DRPs, results show that it is not economic to cut the load of DRPs. Although DRPs do not participate in load reduction, according to Fig. 11.9, which depict the scheduled reserve of DRPs in the system, a remarkable part of required reserve capacity of the system is provided by the DRPs, especially during hours 19. The DRPs take part in reserve provision of the hybrid AC/DC MG with the maximum capacity at hours 5, 7, 15, and 1721.
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Scheduled reserve of demand response providers (MW)
Figure 11.8 Load reduction of demand response providers in Scenario 3. 3.5 3 2.5 2 1.5 1 0.5 0
2
4
6
8
10
12
14
16
18
20
22
24
Time (h)
Figure 11.9 Scheduled reserve of demand response providers in Scenario 3.
11.3.6 Purchased energy from the upstream grid In order to supply both active and reactive load demands, the upstream grid is utilized. Purchased active power is depicted in Fig. 11.10 for withand without-DR cases. As it can be seen, obtained results in with- and without-DR cases are very close to each other. However, there is a
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Figure 11.10 Purchased active power from the upstream grid in Scenario 3.
remarkable difference in imported power from the upstream grid at hours 1423, which are in accordance with the high price periods. In this period, after applying DR programs, purchased active power is significantly reduced. As an example, imported power at hour 14 in the without-DR case is equal to 23.88 MW, which has been reduced to 18.98 MW in the with-DR case. Fig. 11.11 illustrates the purchased reactive power from the upstream grid. Obtained results in this case are the same in both with- and withoutDR cases because the upstream grid is the only source to supply load demand of the system. In addition, it should be noted that DR programs are implemented on just the active load of the hybrid AC/DC MG.
11.3.7 Voltage profile The voltage profile of bus 17 in the hybrid AC/DC system is depicted in Fig. 11.12. As expected after implementing load reduction of ILs and DRPs in the with-DR case, the voltage profile is considerably improved because purchased active power from the upstream grid is reduced, which reduces energy loss in the system.
11.3.8 Scheduling of distributed generation units in AC subgrid In the AC subgrid, the distributed generation (DG) units supply load and provide reserve capacity. Generated power and scheduled reserve of DGs
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Figure 11.11 Purchased active power from the upstream grid in Scenario 3.
Figure 11.12 Voltage profile of bus 17 in Scenario 3.
in the AC subgrid is presented in Figs. 11.13 and 11.14, respectively. According to Fig. 11.13, active power generation of the DGs is increased remarkably between hours 10 and 23 in both cases in comparison with hours 19. It is obvious that the generation of active power by the DGs is increased because, turning to Fig. 11.2, the power price in the upstream gird is absolutely high between hours 9 and 23.
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Figure 11.13 Active power generation of distributed generation units in AC subgrid in Scenario 3.
Figure 11.14 Provided reserve capacity of distributed generation units in the AC subgrid.
Also, in the with-DR case, generated power of DGs is increased in comparison with the without-DR counterpart because by applying DR programs, purchased power from the upstream grid is reduced, and to make balance between load and supply, it is necessary to increase generation of DGs. On the other hand, a remarkable part of the capacity of DGs is dedicated to provide reserve capacity in without-DR cases.
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Provided reserve capacity of the DGs is presented in Fig. 11.14. There are significant results between obtained results of with- and without-DR cases. The reason for such difference lies in the fact that in the withoutDR case, DGs are the only source of providing reserve capacity, while in the with-DR case other sources such as ILs and DRPs are added to DGs in which in the with-DR case, the majority amount of reserve capacity is provided by ILs and DRPs.
11.3.9 Battery storage systems in the AC subgrid Stored energy in the battery during the time horizon of the study is depicted in Fig. 11.15. According to Fig. 11.15, there is a steady increase in state-of-charge (SOC) of the battery during hours 36, indicating the battery is charged, while there is steady decrease during hours 1518, which shows that the battery is discharged. The lowest level of SOC in the battery is equal to 0.1 MW and the highest level of SOC is equal to 0.4 MW. Fig. 11.16 presents the charging and discharging states of the battery storage, which is in accordance with the SOC of the battery. In Fig. 11.16, positive numbers represent battery charging and negative numbers show battery discharging.
Figure 11.15 State-of-charge of the battery in the AC subgrid in Scenario 3.
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Figure 11.16 Charging and discharging states of the battery in the AC subgrid in Scenario 3.
Figure 11.17 Generated power by the wind turbines in the DC subgrid.
11.3.10 Power generation of renewable energy sources in the DC subgrid Power generation of PV and WT systems in the DC subgrid are depicted in Figs. 11.17 and 11.18, respectively. As wind speed and solar irradiation is the same in the location of the hybrid AC/DC MG, generated power by the RESs follows same pattern. It should be noted that the operational
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Figure 11.18 Generated power by the photovoltaics in the DC subgrid.
requirements of WTs and PVs are considered the same in AC and DC subgrids although they differ in system capacities. The maximum power generation of WTs in DC subgrids is equal to 0.27 MW. In addition, the highest level of generated power by the PV systems in the DC subgrid is equal to 0.15 MW.
11.3.11 DC load Load demand of the DC subgrid is shown in Fig. 11.19. To reduce the total operating cost of the system, the TOU rate of DR is implemented, which shifts the load from high price period to low price period. In this case, as Fig. 11.19 shows, the load has transferred from hours 9 to 23, which is the highest price period, to hours 19, which is the lowest price period.
11.3.12 Battery storage system in the DC subgrid The SOC of the BSS is depicted in Fig. 11.20. The highest amount of stored energy in the battery is equal to 0.35 MW and the lowest amount is equal to 0.1. In Fig. 11.20, as said previously, the SOC of the battery is increased when the battery is charged and conversely, the SOC is reduced when the battery is discharged. The charging and discharging states of the battery in the DC subgrid is shown in Fig. 11.21. In Fig. 11.21, positive numbers represent battery charging and negative numbers show battery discharging.
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Figure 11.19 DC load in Scenario 3 for with- and without-DR cases.
Figure 11.20 State-of-charge of the battery in the DC subgrid in Scenario 3.
11.3.13 Power generation of distributed generation unit in the DC subgrid Fig. 11.22 presents the generated power by the DG unit in the DC subgrid. The DG unit is utilized to generate power during high price periods to reduce the purchased power from the upstream grid and to compensate for lack of power generation of PV units between hours 20 and 24. As
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Figure 11.21 Charging and discharging states of the battery in the DC subgrid in Scenario 3.
Figure 11.22 Power generation of DG unit in Scenario 3 for with- and without-DR cases.
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Figure 11.23 Transferred power from the AC subgrid to DC subgrid.
TOU has transferred load from high price period to the low price period, generated power by the DG is reduced in the with-DR case in comparison with the without-DR case.
11.3.14 Exchanged power between AC and DC subgrids Fig. 11.23 presents the injected power to the DC subgrid by the AC subgrid. As expected, the active power is transferred from the AC subgrid to the DC subgrid. In addition, as TOU has increased the load demand between hours 1 and 9, transferred power to the DC subgrid increased after implementing DR programs in the with-DR case. Injected power to the AC subgrid by the DC subgrid is depicted in Fig. 11.24. According to Fig. 11.24 and turning to Fig. 11.2, in the high price period, active power is transferred from the DC subgrid to the AC counterpart.
11.4 Conclusion In this chapter, the optimal energy management of a hybrid AC/DC MG is carried out using stochastic programming in the presence of different uncertain parameters as solar irradiation, wind speed, power price, and load demand. To do so, 10 discrete scenarios are generated using the normal and Weibull distributions. At each scenario, optimal energy and reserve
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Figure 11.24 Transferred power from the DC subgrid to AC subgrid.
scheduling of the system is carried amount simultaneously, and optimal operation of different units of the system is determined. In order to reduce total operating cost of the system, different DR programs including load reduction of ILs, DRPs, and TOU rate of DR programs are implemented. Based on the obtained results, the stochastic operating cost of the system was obtained as $69,628.078 and $62,742.121 for without- and with-DR cases, respectively, indicating a 9.88% reduction of total cost because of DR programs. In addition, the operating cost of the DC subgrid is equal to $1471.710 and $1361.138 for without- and with-DR cases, where in this case DR programs reduced the cost by about 7.13%. The total reserve cost of the system for the with- and without-DR cases were obtained as $1408.069 and $1585.813. In this case, it is seen that the reserve cost increased by about $177.44. Finally, it should be noted that the system operator should choose the best scenario among different provided results considering the characteristics of the system and power market.
References [1] S. Nojavan, H. Allah Aalami, Stochastic energy procurement of large electricity consumer considering photovoltaic, wind-turbine, micro-turbines, energy storage system in the presence of demand response program, Energy Convers. Manag. 103 (2015) 10081018. [2] F. Jabari, B. Mohammadi-Ivatloo, M.B. Bannae Sharifian, S. Nojavan, Design and robust optimization of a novel industrial continuous heat treatment furnace, Energy 142 (2018) 896910.
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[3] S. Nojavan, K. Zare, B. Mohammadi-Ivatloo, Risk-based framework for supplying electricity from renewable generation-owning retailers to price-sensitive customers using information gap decision theory, Int. J. Electr. Power Energy Syst. 93 (2017) 156170. [4] S. Nojavan, K. Zare, B. Mohammadi-Ivatloo, Information gap decision theory-based risk-constrained bidding strategy of price-taker GenCo in joint energy and reserve markets, Electr. Power Components Syst. 45 (1) (2017) 4962. [5] F. Jabari, S. Nojavan, B. Mohammadi-Ivatloo, H. Ghaebi, H. Mehrjerdi, Riskconstrained scheduling of solar Stirling engine based industrial continuous heat treatment furnace, Appl. Therm. Eng. 128 (2018) 940955. [6] S. Nojavan, K. Zare, M.A. Ashpazi, A hybrid approach based on IGDTMPSO method for optimal bidding strategy of price-taker generation station in day-ahead electricity market, Int. J. Electr. Power Energy Syst. 69 (2015) 335343. [7] S. Nojavan, K. Zare, B. Mohammadi-Ivatloo, Robust bidding and offering strategies of electricity retailer under multi-tariff pricing, Energy Econ. 68 (2017) 359372. [8] S. Nojavan, K. Zare, Interval optimization based performance of photovoltaic/wind/ FC/electrolyzer/electric vehicles in energy price determination for customers by electricity retailer, Sol. Energy 171 (2018) 580592. [9] S. Nojavan, K. Zare, Optimal energy pricing for consumers by electricity retailer, Int. J. Electr. Power Energy Syst. 102 (2018) 401412. [10] H.A. Aalami, H. Pashaei-Didani, S. Nojavan, Deriving nonlinear models for incentive-based demand response programs, Int. J. Electr. Power Energy Syst. 106 (2019) 223231. [11] S. Nojavan, R. Nourollahi, H. Pashaei-Didani, K. Zare, Uncertainty-based electricity procurement by retailer using robust optimization approach in the presence of demand response exchange, Int. J. Electr. Power Energy Syst. 105 (2019) 237248. [12] “DICOPT.” [Online]. Available ,https://www.gams.com/24.8/docs/solvers/ dicopt/index.html. (accessed 23.09.18). [13] A. Brooke, D. Kendrick, A. Meeraus, R. Raman, GAMS-A User’s Guide, GAMS Development Corporation, Washington, DC, 2008.
Stochastic-based energy management of hybrid AC/DC microgrid Hamed Pashaei-Didani1, Hamed Ahmadi-Nezamabad1, Arash Mohammadi1 and Sayyad Nojavan2 1 Faculty of Electrical and Computer Engineering, University of Tabriz, Tabriz, Iran Department of Electrical Engineering, University of Bonab, Bonab, Iran
2
Contents 11.1 Introduction 11.2 Stochastic formulation of the hybrid AC/DC microgrid 11.2.1 Objective function 11.2.2 Network model 11.2.3 Constraints of DC subgrid 11.2.4 Constraints of AC subgrid 11.3 Stochastic simulation results 11.3.1 Generated scenarios 11.3.2 Total operating cost 11.3.3 Power generation of renewable energy source in the AC subgrid 11.3.4 Scheduled reserve and load reduction of industrial loads 11.3.5 Scheduled reserve and load reduction of demand response providers 11.3.6 Purchased energy from the upstream grid 11.3.7 Voltage profile 11.3.8 Scheduling of distributed generation units in AC subgrid 11.3.9 Battery storage systems in the AC subgrid 11.3.10 Power generation of renewable energy sources in the DC subgrid 11.3.11 DC load 11.3.12 Battery storage system in the DC subgrid 11.3.13 Power generation of distributed generation unit in the DC subgrid 11.3.14 Exchanged power between AC and DC subgrids 11.4 Conclusion References
Risk-based Energy Management DOI: https://doi.org/10.1016/B978-0-12-817491-3.00011-8
© 2020 Elsevier Inc. All rights reserved.
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11.1 Introduction Among different developed methods to model uncertainty in a system, the stochastic programming method is utilized in this chapter to get optimal energy management of a hybrid AC/DC microgrid (MG). Modeling multiple uncertain parameters through generating different scenarios are the main advantages of the stochastic programming method [1] in comparison with the robust optimization approach [2] and information gap decision theory [36]; however, the method suffers from the high computational burden, which requires scenario reduction approaches [7]. In this chapter, optimal energy management of hybrid AC/DC MG is carried out under uncertainties of power price, load demand, wind speed, and solar irradiation considering 10 discrete scenarios. In the first stage, scenario generation is implemented using the normal and Weibull distributions in which the former is utilized to generate scenarios of power price, load demand, and solar irradiation and the latter is used to generate wind speed scenarios. Then, in the second stage, optimal energy management of the hybrid AC/DC MG is carried out using the stochastic method. The case study developed in Chapter 10, Deterministic-based energy management of hybrid AC/ DC microgrid, is utilized to evaluate the performance of the proposed method. In the considered case study, which was detailed in the previous chapter, different generation units including wind turbines (WTs) [8], photovoltaic systems (PVs) [9], microturbines (MTs), and battery storage systems (BSSs) are optimally located in both DC and AC subgrids to increase the system efficiency and reduce the total operating cost of the system. In addition, different time-based and incentivebased demand response (DR) programs [10,11] including time-of-use (TOU) rate, load reduction of industrial loads (ILs), and demand response providers (DRPs) are implemented to reduce operating cost of the system. To cope with the power price and load uncertainties, it is assumed that AC and DC subgrids can exchange the excessive generation of renewable energy sources (RESs). Finally, it should be noted that the stochastic-based energy management of hybrid AC/DC MGs is formulated as mixed-integer nonlinear programming method (MINLP) and solved using the GAMS optimization software under the DICOPT solver.
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11.2 Stochastic formulation of the hybrid AC/DC microgrid To solve the optimal energy management problem of a hybrid AC/DC MG, the stochastic formulation of the problem should be developed based on the deterministic case formulation that was developed in Chapter 10, Deterministic-based energy management of hybrid AC/DC microgrid. In the following subsections the stochastic formulation of the problem is provided in detail. To get more information about the concept of the stochastic programming, please refer to Chapter 3, Stochastic-based energy management of DC microgrids, and Chapter 7, Stochastic-based energy management of AC microgrids.
11.2.1 Objective function As said previously, 10 discrete scenarios are developed to model the mentioned uncertainties in the system with different possibilities. Eq. (11.1) provides the objective function of the system considering different scenarios. 2 NDG X E CEDG ðj; t; sÞ 1 CSDG ðj; t; sÞ 1 CRDG ðj; t; sÞ 1 6 Pgrid ðt; sÞ 3 λgrid ðt; sÞ 1 CostDC 1 BX N T 6 B j51 6 πs 3 B 6 NIL B DRP NX @ t51 4 X CEIL ði; t; sÞ 1 CRIL ði; t; sÞ 1 CEDRP ðd; t; sÞ 1 CRDRP ðd; t; sÞ 0
min
Ns X s51
i51
31 7C 7C 7C 7C 5A
d51
(11.1)
where πs is the probability scenario s and CostDC is the stochastic-based operating cost of the DC subgrid, which is introduced in following subsections. Different parts of Eq. (11.1) have been detailed in Chapter 7, Stochastic-based energy management of AC microgrids.
11.2.2 Network model In each scenario s and time t, the balance between demand and supply should be provided at each bus i. Eqs. (11.2) and (11.3) present the network model of the hybrid AC/DC MG. X
Pgrid ði; t; sÞ 1 PDG ði; t; sÞ 1 PWT ði; t; sÞ 1 PPV ði; t; sÞ
iANbus 5 1 E E ði; t; sÞ 1 PIL ði; t; sÞ 2 PD ði; t; sÞ 1 PSd ði; t; sÞ 2 PSc ði; t; sÞ 1 PDRP
1 PDC=AC ðt; sÞ 3 ηDC=AC 5 PAC=DC ðt; sÞ 1
Nbus X V ði; t; sÞ 3 V ðj; t; sÞ j
3 yline ði; jÞ 3 cosðθði; jÞ 1 δðj; tÞ 2 δði; tÞÞ;
’i; t; s
(11.2)
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X
Nbus X
Qgrid ði; t; sÞ 2 QD ði; t; sÞ 5
iANbus 5 1
V ði; t; sÞ 3 V ðj; t; sÞ 3 yline ði; jÞ
j51
3 sinðθði; jÞ 1 δði; tÞ 2 δðj; tÞÞ;
’i; t; s (11.3)
11.2.3 Constraints of DC subgrid The system model and operational constraints and requirements of the DC subgrid in the stochastic form are developed based on the deterministic case model. ! Ns T X I X X CostDC 5 πs CDG ðiÞ 3 PDG ði; t; sÞ (11.4) t
s51
i
PAC=DC ðt; sÞ 3 ηAC=DC 1 PDG ðt; sÞ 1 PPV ðt; sÞ 1 PWind ðt; sÞ 3 ηAC=DC 1 Pdis ðt; sÞ DR 5 PLoad ðt; sÞ 1 Pch ðt; sÞ 1 PDC=AC ðt; sÞ
(11.5) DR ðt; sÞ 5 Pload ðt; sÞ 1 DRðt; sÞ PLoad
2DRmax 3 Pload ðt; sÞ # DRðt; sÞ # 1 DRmax 3 Pload ðt; sÞ 24 X
DRðt; sÞ 5 0
(11.6) (11.7)
(11.8)
t51
PchDC ðt; sÞ # XchDC ðt; sÞ 3 PchDC max
(11.9)
DC DC DC max ðt; sÞ # Xdis ðt; sÞ 3 Pdis Pdis
(11.10)
DC ðt; sÞ , 1 XchDC ðt; sÞ 1 Xdis
(11.11)
DC DC SOCDC ðt; sÞ 5 SOCDC ðt 2 1; sÞ 1 PchDC ðt; sÞ 3 ηDG ch 2 Pdis ðt; sÞ=ηdis (11.12)
Stochastic-based energy management of hybrid AC/DC microgrid
M ;max PDC ðt; sÞ 5
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DC DC SOCmin , SOCDC ðt; sÞ , SOCmax
(11.13)
DC DC max DC ðt; sÞ , PDG 3 UDG ðt; sÞ PDG
(11.14)
DC min DC DC PDG 3 UDG ðt; sÞ , PDG ðt; sÞ
(11.15)
G a ðtÞ NOCT 2 20 M 3 PMax;0 1 μP max 3 T a ðt; sÞ 1 G a ðt; sÞ 3 2 TM ;0 Ga0 800
(11.16) DC DC ðt; sÞ # PM PPV ;max ðt; sÞ;
’t; s
8 0 Vtw , Vci > > > 3 > > > < p 3 V w ðt;sÞ2Vci V , V w ðt; sÞ , V r ci cr DC Vr 2Vci Pwind;max ðt; sÞ 5 > > > pr Vr , V w ðt; sÞ , Vc0 > > > : 0 Vtw . Vc0 DC DC ðt; sÞ # Pwind;max ðt; sÞ; Pwind
’t; s
(11.17)
(11.18)
(11.19)
max PDC=AC ðt; sÞ , XDC=AC ðt; sÞ 3 Pcon
(11.20)
max PAC=DC ðt; sÞ , XAC=DC 3 Pcon
(11.21)
XAC=DC ðt; sÞ 1 XDC=AC ðt; sÞ , 1
(11.22)
In these equations, Eq. (11.4) models the stochastic operation cost of the DC subgrid, Eq. (11.5) balances active power demand and supply, Eqs. (11.6)(11.8) provide the TOU rate of the DR model, Eqs. (11.9) (11.13) present the BSS model in the DC subgrid, Eqs. (11.14) and (11.15) model operational constraints of the MT, Eqs. (11.16) and (11.17) and Eqs. (11.18) and (11.19) present the PV and WT systems in the DC subgrid, respectively, and finally, Eqs. (11.20)(11.22) model the power exchange between AC and DC subgrids.
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11.2.4 Constraints of AC subgrid The system model and operational constraints and requirements of the AC subgrid are provided by Eqs. (11.23)(11.55), each of which has been detailed in Chapter 7, Stochastic-based energy management of AC microgrids. Iðm; n; t; sÞ # Iðm; nÞ
(11.23)
V ðnÞ # V ðn; t; sÞ # V ðnÞ
(11.24)
V ðn; t; sÞ 5 1 5 Constant; n 5 Substation bus;
’t; s
Iðm; n; t; sÞ # Isub m 5 1; n 5 Substation bus;
’t; s
(11.26)
’i; t; s
(11.27)
RIL ði; t; sÞ 1 RDRP ði; t; sÞ 1 RDG ði; t; sÞ 5 0:2 3 PWT ði; t; sÞ 1 0:1 3 PD ði; t; sÞ; d # od1 # O1d Omin d 0 # odk # ðOk11 2 Okd Þ
(11.28)
’k 5 2; 3; . . .; k
PDRP ðd; t; sÞ 5
X
(11.25)
Okd
(11.29) (11.30)
k
CEDRP ðd; t; sÞ 5
X
πdk 3 odk
(11.31)
k
PDRP ðd; t; sÞ 1 RDRP ðd; t; sÞ # PDRP ðd; t; sÞ
(11.32)
CRDRP ðd; t; sÞ 5 RDRP ðd; t; sÞ 3 KRDRP ðd; t; sÞ
(11.33)
PIL ði; t; sÞ 1 RIL ði; t; sÞ # PIL ði; t; sÞ
(11.34)
CEIL ði; t; sÞ 5 PIL ði; t; sÞ 3 KEIL ði; t; sÞ
(11.35)
Stochastic-based energy management of hybrid AC/DC microgrid
CRIL ði; t; sÞ 5 RIL ði; t; sÞ 3 KRIL ði; t; sÞ
PWT ðvÞ 5
8 ðv 2 vci Þ > > Pr 3 > < ðvr 2 vci Þ > Pr > > : 0
(11.36)
vci # v # vr (11.37)
vr # v # vco otherwise
PWT ðw; t; sÞ # Pw ðvðt; sÞÞ ’w; t; s bsc ðb; t; sÞ 1 bsd ðb; t; sÞ # 1;
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bsc ; bsd Af0; 1g;
(11.38) ’t; s
(11.39)
SOCðb; t; sÞ 5 SOCðb; t 2 1; sÞ 1 ηc 3 PSc ðb; t; sÞ 2 ηd 3 PSd ðb; t; sÞ (11.40) SOCðbÞ # SOCðb; t; sÞ # SOCðbÞ
(11.41)
0 # PSc ðb; t; sÞ # PSc 3 bsc ðb; t; sÞ
(11.42)
0 # PSd ðb; t; sÞ # PSd 3 bsd ðb; t; sÞ
(11.43)
2 ðj; t; sÞ CEDG ðj; t; sÞ 5 aj 3 uðj; t; sÞ 1 bj 3 PDG ðj; t; sÞ 1 cj 3 PDG
(11.44)
CSDG ðj; t; sÞ 5 SUCðj; sÞ 3 ðuðj; t; sÞ 2 Uðj; t 2 1; sÞÞ ’j; t; s
(11.45)
CSDG ðj; t; sÞ $ 0;
’j; t; s
(11.46)
CRDG ðj; t; sÞ 5 KRDG 3 ðbj 1 2 3 cj 3 PDG ðj; t; sÞÞ 3 RDG ðj; t; sÞ ’j; t; s (11.47) PDG ðjÞ 3 uðj; t; sÞ # PDG ðj; t; sÞ # PDG ðjÞ 3 uðj; t; sÞ
’j; t; s
PDG ðj; t; sÞ 1 RDG ðj; t; sÞ # PDG ðjÞ 3 uðj; t; sÞ ’j; t; s
(11.48) (11.49)
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PDG ðj; t; sÞ 2 PDG ðj; t 2 1; sÞ # URðj; sÞ 3 ð1 2 yðj; t; sÞÞ 1 PDG ðjÞ 3 yðj; t; sÞ
’j; t; s
PDG ðj; t 2 1; sÞ 2 PDG ðj; t; sÞ # DRðj; sÞ 3 ð1 2 zðj; t; sÞÞ 1 PDG ðjÞ 3 zðj; t; sÞ t1UT ðjÞ21 X
’j; t; s
uðj; h; sÞ $ UT ðj; sÞ 3 yðj; t; sÞ
’j; t; s
(11.50)
(11.51)
(11.52)
h5t t1DT ðjÞ21 X
ð1 2 uðj; hÞÞ $ DT ðjÞ 3 zðj; t; sÞ
’j; t; s
(11.53)
h5t
yðj; t; sÞ 2 zðj; t; sÞ 5 uðj; t; sÞ 2 uðj; t 2 1; sÞ yðj; t; sÞ 1 zðj; t; sÞ # 1
’j; t; s
’j; t; s
(11.54) (11.55)
11.3 Stochastic simulation results Obtained results of the stochastic programming method on the developed case study in Chapter 10, Deterministic-based energy management of hybrid AC/DC microgrid, are presented in the following subsections. As said previously, the optimal energy management problem of a hybrid AC/DC MG under different uncertainties formulated as MINLP is solved using the DICOPT [12] solver in GAMS [13] optimization software. Note that among the 10 generated discrete scenarios, the results of Scenario 3 are presented in all sections. In each scenario, the problem is solved in two cases, with- and without-DR programs, to show the impact of the DR program on operating cost and operation of the system. It is worth mentioning that in the with-DR case, load reduction of ILs and DRPs is carried out in the AC subgrid and the TOU rate of DR is implemented in the DC subgrid.
11.3.1 Generated scenarios To model the impact of uncertainties of power price, load demand, wind speed, and solar irradiation using stochastic programming, discrete
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Figure 11.1 Scenarios of load in the hybrid AC/DC system. 500
Upstream grid price ($/MWh)
450 400 350 300 250 200 150 100 50 0
2
4
6
8
10
12
14
16
18
20
22
24
Time (h) Figure 11.2 Scenarios of power price in the upstream grid in the hybrid AC/DC system.
scenarios for each parameter should be generated. In this chapter, normal distribution is used to generate power price, load demand, and solar irradiation scenarios and the Weibull distribution is used to produce wind speed scenarios. Generated scenarios for load demand, power price, and wind speed are depicted in Figs. 11.111.3, respectively. It should be noted that 10 discrete scenarios are generated to model each uncertain
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Figure 11.3 Wind speed scenarios in the upstream grid in the hybrid AC/DC system.
parameter and the results are provided for Scenario 3. As it can be seen in Figs. 11.111.3, generated scenarios for each uncertain parameter almost follow the same pattern.
11.3.2 Total operating cost The total operating cost of the hybrid AC/DC MG under power price, load demand, solar irradiation, and wind speed uncertainties are obtained as $69,628.078 and $62,742.121 for without- and with-DR cases, respectively. In the stochastic energy management of the hybrid AC/DC system, it is seen that implementing DR programs has reduced total operation cost of the system by about 9.88%. In this case, the operating cost of the DC subgrid is equal to $1471.710 and $1361.138 for withoutand with-DR cases, indicating a 7.13% reduction because of using the TOU rate of DR in the DC subgrid. To provide the required reserve capacity of the system in the AC subgrid, different sources are utilized including MTs in the without-DR case and ILs, DRPs, and MTs in the with-DR case, with the total reserve cost of $1408.069 and $1585.813 for with- and without-DR cases, respectively. It is seen that although implementing DR programs has reduced total operating cost of the system significantly, it has increased reserve cost about by $177.44, which is negligible. Table 11.1 provides a summary of stochastic-based optimization results.
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Table 11.1 A summary of stochastic-based optimization results. Without DR
AC subgrid DC subgrid
With DR
Total cost ($)
Energy cost ($)
Reserve cost ($)
Total cost ($)
Energy cost ($)
Reserve cost ($)
69,628.078 1471.710
68,220.009 1471.710
1408.069
62,742.12 1361.138
61,156.309 1361.138
1585.813
Figure 11.4 Generated power by the photovoltaics in the AC subgrid.
11.3.3 Power generation of renewable energy source in the AC subgrid In the AC subgrid multiple WT and PV units are used to harness solar and wind energies. Aggregation of generated power by the PVs in Scenario 3 is depicted in Fig. 11.4. The PV systems in the start generate power from hour 5 to 18. Generated power by the PV system reaches its highest level at hour 11, recording 0.33 MW. Fig. 11.5 illustrated the generated power by the WTs in Scenario 3. Power generation of the WTs is related to the wind speed, in which it should be higher than the cut-in speed of the WT. For example, turning to Fig. 11.3, the wind speed in Scenario 3 at hour 12 is 2.254 m/s, which is less than 3 m/s as the cut-in speed of the WT; therefore, WTs did not generate power at this hour. The highest level of the generated power by the WTs is equal to 8.17 MW at hour 4. A sharp decrease is seen between hours 5 and 12 in generated power by the WTs because of wind speed reduction. Then, there is an increasing trend during hours 1315.
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Figure 11.5 Generated power by the wind turbines in the AC subgrid.
Figure 11.6 Load reduction of industrial loads in Scenario 3.
11.3.4 Scheduled reserve and load reduction of industrial loads Load reduction of ILs is depicted in Fig. 11.6 in Scenario 3 for a 24-hour time horizon of the study. In the with-DR case, it is assumed that the ILs offered to get paid instead of reducing their load in required periods. Based on provided information about offered price and demand in Chapter 6,
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Figure 11.7 Scheduled reserve of industrial loads in Scenario 3.
Deterministic-based energy management of AC microgrids, the ILs reduce their load only during hours 923. According to Fig. 11.6, the maximum offered load is curtailed at hours 9, 14, 19, and 22 in Scenario 3. Fig. 11.7 presents the scheduled resereve capacity of the ILs. It is assumed that at each hour, scheduled reserve should be equal or greater than the sum of 20% of PV generation and 10% of load demand. In addition, the sum of load reduction and scheduled reserve should be equal or less than maximum capacity of the ILs. For instance, scheduled reserve load reduction of ILs at hour 10 are equal to 0.9 and 0.4 MW, respectively, where aggreation of them is equal to 1.3 MW, which is the maximum offered amount by the ILs.
11.3.5 Scheduled reserve and load reduction of demand response providers Load reduction of ILs is depicted in Fig. 11.8. Considering the power price in the market and cost of load reduction of DRPs, results show that it is not economic to cut the load of DRPs. Although DRPs do not participate in load reduction, according to Fig. 11.9, which depict the scheduled reserve of DRPs in the system, a remarkable part of required reserve capacity of the system is provided by the DRPs, especially during hours 19. The DRPs take part in reserve provision of the hybrid AC/DC MG with the maximum capacity at hours 5, 7, 15, and 1721.
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Scheduled reserve of demand response providers (MW)
Figure 11.8 Load reduction of demand response providers in Scenario 3. 3.5 3 2.5 2 1.5 1 0.5 0
2
4
6
8
10
12
14
16
18
20
22
24
Time (h)
Figure 11.9 Scheduled reserve of demand response providers in Scenario 3.
11.3.6 Purchased energy from the upstream grid In order to supply both active and reactive load demands, the upstream grid is utilized. Purchased active power is depicted in Fig. 11.10 for withand without-DR cases. As it can be seen, obtained results in with- and without-DR cases are very close to each other. However, there is a
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Figure 11.10 Purchased active power from the upstream grid in Scenario 3.
remarkable difference in imported power from the upstream grid at hours 1423, which are in accordance with the high price periods. In this period, after applying DR programs, purchased active power is significantly reduced. As an example, imported power at hour 14 in the without-DR case is equal to 23.88 MW, which has been reduced to 18.98 MW in the with-DR case. Fig. 11.11 illustrates the purchased reactive power from the upstream grid. Obtained results in this case are the same in both with- and withoutDR cases because the upstream grid is the only source to supply load demand of the system. In addition, it should be noted that DR programs are implemented on just the active load of the hybrid AC/DC MG.
11.3.7 Voltage profile The voltage profile of bus 17 in the hybrid AC/DC system is depicted in Fig. 11.12. As expected after implementing load reduction of ILs and DRPs in the with-DR case, the voltage profile is considerably improved because purchased active power from the upstream grid is reduced, which reduces energy loss in the system.
11.3.8 Scheduling of distributed generation units in AC subgrid In the AC subgrid, the distributed generation (DG) units supply load and provide reserve capacity. Generated power and scheduled reserve of DGs
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Figure 11.11 Purchased active power from the upstream grid in Scenario 3.
Figure 11.12 Voltage profile of bus 17 in Scenario 3.
in the AC subgrid is presented in Figs. 11.13 and 11.14, respectively. According to Fig. 11.13, active power generation of the DGs is increased remarkably between hours 10 and 23 in both cases in comparison with hours 19. It is obvious that the generation of active power by the DGs is increased because, turning to Fig. 11.2, the power price in the upstream gird is absolutely high between hours 9 and 23.
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Figure 11.13 Active power generation of distributed generation units in AC subgrid in Scenario 3.
Figure 11.14 Provided reserve capacity of distributed generation units in the AC subgrid.
Also, in the with-DR case, generated power of DGs is increased in comparison with the without-DR counterpart because by applying DR programs, purchased power from the upstream grid is reduced, and to make balance between load and supply, it is necessary to increase generation of DGs. On the other hand, a remarkable part of the capacity of DGs is dedicated to provide reserve capacity in without-DR cases.
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Provided reserve capacity of the DGs is presented in Fig. 11.14. There are significant results between obtained results of with- and without-DR cases. The reason for such difference lies in the fact that in the withoutDR case, DGs are the only source of providing reserve capacity, while in the with-DR case other sources such as ILs and DRPs are added to DGs in which in the with-DR case, the majority amount of reserve capacity is provided by ILs and DRPs.
11.3.9 Battery storage systems in the AC subgrid Stored energy in the battery during the time horizon of the study is depicted in Fig. 11.15. According to Fig. 11.15, there is a steady increase in state-of-charge (SOC) of the battery during hours 36, indicating the battery is charged, while there is steady decrease during hours 1518, which shows that the battery is discharged. The lowest level of SOC in the battery is equal to 0.1 MW and the highest level of SOC is equal to 0.4 MW. Fig. 11.16 presents the charging and discharging states of the battery storage, which is in accordance with the SOC of the battery. In Fig. 11.16, positive numbers represent battery charging and negative numbers show battery discharging.
Figure 11.15 State-of-charge of the battery in the AC subgrid in Scenario 3.
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Figure 11.16 Charging and discharging states of the battery in the AC subgrid in Scenario 3.
Figure 11.17 Generated power by the wind turbines in the DC subgrid.
11.3.10 Power generation of renewable energy sources in the DC subgrid Power generation of PV and WT systems in the DC subgrid are depicted in Figs. 11.17 and 11.18, respectively. As wind speed and solar irradiation is the same in the location of the hybrid AC/DC MG, generated power by the RESs follows same pattern. It should be noted that the operational
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Figure 11.18 Generated power by the photovoltaics in the DC subgrid.
requirements of WTs and PVs are considered the same in AC and DC subgrids although they differ in system capacities. The maximum power generation of WTs in DC subgrids is equal to 0.27 MW. In addition, the highest level of generated power by the PV systems in the DC subgrid is equal to 0.15 MW.
11.3.11 DC load Load demand of the DC subgrid is shown in Fig. 11.19. To reduce the total operating cost of the system, the TOU rate of DR is implemented, which shifts the load from high price period to low price period. In this case, as Fig. 11.19 shows, the load has transferred from hours 9 to 23, which is the highest price period, to hours 19, which is the lowest price period.
11.3.12 Battery storage system in the DC subgrid The SOC of the BSS is depicted in Fig. 11.20. The highest amount of stored energy in the battery is equal to 0.35 MW and the lowest amount is equal to 0.1. In Fig. 11.20, as said previously, the SOC of the battery is increased when the battery is charged and conversely, the SOC is reduced when the battery is discharged. The charging and discharging states of the battery in the DC subgrid is shown in Fig. 11.21. In Fig. 11.21, positive numbers represent battery charging and negative numbers show battery discharging.
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Figure 11.19 DC load in Scenario 3 for with- and without-DR cases.
Figure 11.20 State-of-charge of the battery in the DC subgrid in Scenario 3.
11.3.13 Power generation of distributed generation unit in the DC subgrid Fig. 11.22 presents the generated power by the DG unit in the DC subgrid. The DG unit is utilized to generate power during high price periods to reduce the purchased power from the upstream grid and to compensate for lack of power generation of PV units between hours 20 and 24. As
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Figure 11.21 Charging and discharging states of the battery in the DC subgrid in Scenario 3.
Figure 11.22 Power generation of DG unit in Scenario 3 for with- and without-DR cases.
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Figure 11.23 Transferred power from the AC subgrid to DC subgrid.
TOU has transferred load from high price period to the low price period, generated power by the DG is reduced in the with-DR case in comparison with the without-DR case.
11.3.14 Exchanged power between AC and DC subgrids Fig. 11.23 presents the injected power to the DC subgrid by the AC subgrid. As expected, the active power is transferred from the AC subgrid to the DC subgrid. In addition, as TOU has increased the load demand between hours 1 and 9, transferred power to the DC subgrid increased after implementing DR programs in the with-DR case. Injected power to the AC subgrid by the DC subgrid is depicted in Fig. 11.24. According to Fig. 11.24 and turning to Fig. 11.2, in the high price period, active power is transferred from the DC subgrid to the AC counterpart.
11.4 Conclusion In this chapter, the optimal energy management of a hybrid AC/DC MG is carried out using stochastic programming in the presence of different uncertain parameters as solar irradiation, wind speed, power price, and load demand. To do so, 10 discrete scenarios are generated using the normal and Weibull distributions. At each scenario, optimal energy and reserve
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Figure 11.24 Transferred power from the DC subgrid to AC subgrid.
scheduling of the system is carried amount simultaneously, and optimal operation of different units of the system is determined. In order to reduce total operating cost of the system, different DR programs including load reduction of ILs, DRPs, and TOU rate of DR programs are implemented. Based on the obtained results, the stochastic operating cost of the system was obtained as $69,628.078 and $62,742.121 for without- and with-DR cases, respectively, indicating a 9.88% reduction of total cost because of DR programs. In addition, the operating cost of the DC subgrid is equal to $1471.710 and $1361.138 for without- and with-DR cases, where in this case DR programs reduced the cost by about 7.13%. The total reserve cost of the system for the with- and without-DR cases were obtained as $1408.069 and $1585.813. In this case, it is seen that the reserve cost increased by about $177.44. Finally, it should be noted that the system operator should choose the best scenario among different provided results considering the characteristics of the system and power market.
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