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Optimal operation scheduling of wind power integrated with compressed air energy storage (CAES)
Renewable Energy 51 (2013) 53e59
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Renewable Energy journal homepage: www.elsevier.com/locate/renene
Optimal operation scheduling of wind power integrated with compressed air energy storage (CAES) M. Abbaspour a, M. Satkin a, *, B. Mohammadi-Ivatloo b, F. Hoseinzadeh Lotfi a, Y. Noorollahi c a
Faculty of Energy and Environmental Sciences, Science and Research Branch, Islamic Azad University, Tehran, Iran Faculty of Electrical and Computer Engineering, Tabriz University, Tabriz, Iran c Department of Renewable Energy, Faculty of New Science & Technology, University of Tehran, Tehran, Iran b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 February 2012 Accepted 8 September 2012 Available online 10 October 2012
This study optimises and compares the operation of a conventional gas-fired power generation company with its operation in combination with wind power and compressed air energy storage (CAES). A mixed integer non-linear programming (MINLP) formulation is developed for the optimisation problem. Limits in ramp rate, capacity, and minimum on/off time, as well as start-up cost constraints, are considered for the modelling of conventional units. Injected and produced power constraints, storage, air balance and CAES-operation limits are considered in the CAES modelling. Two objective functions (profit maximisation and cost minimisation) are modelled. Without considering capital costs, it is found that the use of CAES results in 43% higher operational profits and 6.7% lower costs in a market environment. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Wind power Optimal operation Optimisation Compressed air energy storage
1. Introduction Intermittent renewable energy sources, such as wind power, are variable by nature. Thus, when there is insufficient wind power, the electricity demand will be provided by other sources, e.g., conventional thermal generators. One solution to the variability problem of renewable-energy resources is the use of storage systems. Accordingly, a wide range of storage systems has been proposed. A list of such methods includes pumped hydroelectric storage [1,2], compressed air energy storage [3], batteries, including lead acid, nickel cadmium and lithium ion [4], hydrogen storage [5], capacitors and super capacitors [6], flywheel [5,6] and superconducting magnetic energy storage [7]. Storage systems for renewable energy generation have been studied in Ref. [8] and a survey of energy storage options for the integration of large-scale intermittent renewable is provided in Ref. [9]. A survey of energy storage options for integration of the large scale intermittent renewable is provided in Ref. [6]. Among the many energy-storage systems, only pumped storage and CAES systems have the capability for large-scale wind energy
* Corresponding author. E-mail address: [email protected] (M. Satkin). 0960-1481/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.renene.2012.09.007
integration [6]. In the literature, a significant amount of attention has been given to the scheduling of conventional hydro systems [10,11], thermal units [12,13] and pumped storage units [14,15]. However, little focus has been given to the operation scheduling of CAES units, especially within a market environment. In this paper, short-term operation scheduling of a power generation company is formulated as an MINLP problem and solved using commercial optimisation packages. The generation company considered has three types of generation facilities, i.e., conventional thermal units, wind energy, and the CAES system. In a conventional gas turbine, approximately 2/3 of the fuel is consumed for air compression [16], resulting in a power generation efficiency of less than 40%. However, CAES systems utilise precompressed air during the generation. In such systems, low-cost power during periods of low-energy demand (off-peak) is used to pre-compress air for utilisation during higher-demand (peak load) periods. The CAES systems store the compressed air in large reservoirs, typically making use of existing geological formations and structures, such as salt caverns, aquifers, and abandoned mines. The capital cost of CAES becomes much lower compared with other storage technologies using these existing reservoirs. The capital cost of reservoir of CAES has been compared with other storage technologies in Ref. [17] and concluded that CAES is the preferable technology compared with pumped storage, lead acid batteries,
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M. Abbaspour et al. / Renewable Energy 51 (2013) 53e59
Nomenclature
aPj s(i)
the efficiency of produced power the time constant of unit i [h] Costc (t) the total cost of CAES units at time horizon t [$/h] Costt (t) the total cost of thermal generation units at time horizon t [$/h] MUT (i) the minimum on times of unit i [h] PW (k, t) the power output of wind power unit k at time horizon t [$/MW] SUC (i, t) start-up cost of thermal generation unit i if started at time t [$] uinj (j, t) binary variable, which is equal to 1 if air injected by the CAES unit j at time t, and 0 otherwise Vrated (k) the rated speed of wind turbine k [m/s] Vt(i, t) binary variable, which is equal to 1 if the thermal unit i be on at time t, and 0 otherwise Yt(i, t) binary variable, which is equal to 1 if the thermal generation unit i is started at time t, and 0 otherwise Ct0(i) the fixed start up cost of unit i [$] Ct1 the cold start up cost of unit i [$] PWGmax(k) the rated power of wind turbine k [MW] SDC(i) shut-down cost of thermal unit i if turned off at time t [$] ainj the efficiency of injected power j le(t) the forecasted energy price at time horizon t [$/MW] a(i) quadratic cost coefficient of thermal generation unit i [$/(MW)2h] A(j, t) the amount of stored energy in the storage j at time t [MWh] Amax(j) the maximum level of storage j in [MWh] Amin(j) the minimum level of storage j in [MWh] b(i) linear cost coefficient of thermal generation unit i [$/MWh] c(i) no-load cost coefficient of thermal generation f unit i [$/h] MDT(i) the minimum down times of unit i [h]
and vanadium redox batteries in terms of the capital cost incurred. The largest CAES system, a 2700-MW plant is planned for construction in an existing limestone mine in Norton, Ohio [18]. There are more geologically suitable sites for CAES than for the pumped storage system. Geological studies indicate that over 75% of the U.S. has suitable sites for consideration for underground air storage [19,20]. Currently, two CAES systems are in operation; The 290-MW Huntorf plant from 1978 near Bremen, Germany [21], and the 110-MW McIntosh plant from 1991 in Southwest Alabama [22]. CAES has high ramp rates that make it suitable for ancillary services. For instance, the McIntosh plant, which has a 134-MW generation and 110-MW compression capacity, can go from full generation to full compression in less than 5 min [6]. The energy balance effects of adding CAES to the Western Danish energy system were studied in Ref. [23]. Optimal yearly operation strategies of CAES units in an energy market have been studied in Ref. [24]. The remainder of this paper is organised as follows: In Section 2 a mathematical formulation of the operation of a wind and CAES integrated power system is provided. The system in the case study and simulation results for different scenarios are presented in Section 3. The concluding remarks are presented in Section 4.
Nc Nt Nw Pt(i, t)
the number of CAES generation units the number of thermal generation units the number of wind power generation units the power output of thermal unit i at time horizon t [MW] Ptmax ðiÞ the maximum power output of the thermal generation unit i Ptmin ðiÞ the minimum power output of the thermal generation unit i Pc,p(j, t) the power consumed by CAES unit j at time t for compressing and injecting air [MW] PC,S(j, t) the power output of CAES unit j at time horizon t that sold to market [$/MW] Pdemand(t) the total system demand at time t RD(i) the ramp down limit of unit i [MW/h] RU(i) the ramp up limit of unit i [MW/h] Td(i, t) the number of hours that unit i was off before time t up(j, t) binary variable, which is equal to 1 if air pumped by the CAES unit j at time t, and 0 otherwise Vp(j, t) the energy equivalent of pumped air to combustion chamber at time t [MWh] Vinj(j, t) the energy equivalent of injected air to storage at time t [MWh] p Vmax ðjÞ the maximum level of pumped air from storage to combustion chamber in [MW/h] inj Vmax ðjÞ the maximum level of injected air into storage in [MW/ h] p Vmin ðjÞ the minimum level of pumped air from storage to combustion chamber in [MW/h] inj Vmin ðjÞ the minimum level of injected air into storage in [MW/ h] Vcutin(k) the cut in speed of wind turbine k [m/s] Vcutout(k) the cut out speed of wind turbine k [m/s] Vws(t) the forecasted wind speed at time t [m/s] Zt(i, t) binary variable, which is equal to 1 if the thermal generation unit i is turned off at time t, and 0 otherwise
2. Problem formulation This case study involves three types of generation facilities, i.e., conventional thermal units, a wind farm, and CAES. In this section, a mathematical formulation of the optimisation problem is provided. The objective of the generation company is to maximise its profit in the energy market. The objective function can be mathematically formulated as follows:
2 Nt Nc T X X X 4 Max profit ¼ Pt ði; tÞle ðtÞ þ PC;S ðj; tÞle ðtÞ t¼1
þ
i¼1
Nw X k¼1
3
j¼1
PW ðk; tÞle ðtÞ5
T X
½Costt ðtÞ þ Costc ðtÞ
t¼1
(1) The objective function defined in Equation (1) should be maximised while considering several technical and logical constraints that are listed in the following section.
M. Abbaspour et al. / Renewable Energy 51 (2013) 53e59
2.2. Constraints for CAES units
2.1. Constraints for conventional thermal units
Costc ðtÞ ¼ Costt ðtÞ ¼
Pc;p ðj; tÞle ðtÞ
(10)
aðiÞPt ði; tÞ2 þbðiÞPt ði; tÞ þ cðiÞ þ SDCðiÞZt ði; tÞ
i þ SUCði; tÞYt ði; tÞ h
SUCði; tÞ ¼ Ct0 ðiÞ þ Ct1 ðiÞ 1 eTd ði;tÞ=sðiÞ
ð2Þ i
Ptmin ðiÞ Pt ði; tÞ Ptmax ðiÞ
Pt ði; t 1Þ RDðiÞ Pt ði; tÞ Pt ði; t 1Þ þ RUðiÞ
MUTðiÞ1 X
MDTðiÞ1 X
inj V inj ðj; tÞ ¼ aj Pc;p ðj; tÞ
(11)
PC;s ðj; tÞ ¼ aPj V p ðj; tÞ
(12)
inj inj Vmin ðjÞuinj ðj; tÞ V inj ðj; tÞ Vmax ðjÞuinj ðj; tÞ
(13)
p p ðjÞup ðj; tÞ V p ðj; tÞ Vmax ðjÞup ðj; tÞ Vmin
(14)
up ðj; tÞ þ uinj ðj; tÞ 1
(15)
Aðj; t þ 1Þ ¼ Aðj; tÞ þ V inj ðj; tÞ V p ðj; tÞ
(16)
Amin ðjÞ Aðj; tÞ Amax ðjÞ
(17)
(3)
(4)
(5)
Zt ði; t þ nÞ 1
(6)
Yt ði; t þ nÞ 1
(7)
n¼1
Zt ði; tÞ þ
Nc X j¼1
Nt h X i¼1
Yt ði; tÞ þ
55
n¼1
Production cost of CAES Equation (10) is modelled as the cost of purchased energy from the energy market [28]. Constraint (11) models the injected air in units of MW/h [29]. The produced power of CAES is modelled using constraint (12). The amounts of injected air into storage and pumped air from storage to combustion chamber are limited (depending on the valve size and pressure limits) and are modelled by constraints (13) and (14), respectively. The CAES unit can either be in the air injection or pumping state. This constraint is satisfied in Equation (15), which also precludes the CAES unit from being in the generation and consumption status at same time. The amount of the stored air is updated every hour, as
8 > > 0 Vws ðtÞVcutout ðkÞ > > < Vws ðtÞVcutin ðkÞ 3 PW ðk;tÞ ¼ PWG max ðkÞ Vcutin ðkÞVws ðtÞVrated ðkÞ > Vrated ðkÞVcutin ðkÞ > > > : PWG max ðkÞ Vrated ðkÞVws ðtÞVcutout ðkÞ
Yt ði; tÞ Zt ði; tÞ ¼ Vt ði; tÞ Vt ði; t 1Þ
(8)
Yt ði; tÞ þ Zt ði; tÞ 1
(9)
Equation (2) shows the total production cost considering startup and shut-down costs using a quadratic function [13,25]. Constraint (3) models the start-up cost using an exponential function [26]. The real power operation limit is enforced in constraint (4). The ramp rate limits are modelled in Equation (5). The minimum ON and OFF times are enforced in Equations (6) and (7), respectively. Two logical operation constraints, (8) and (9) are included [27]. Constraint (8) determines the start-up or shut-down status based on the on/off status of the unit within the last 2 h. Finally, constraint (9) prevents the illogical situation of the unit starting up and shutting down simultaneously. The ramp rate, minimum ON time, and minimum OFF time limits represent dynamic constraints (constraints that hold at different times) that complicate the optimisation problem.
(18)
dictated in Equation (16), and calculated by taking the current storage plus or minus the injected or pumped air. Constraint (17) models the capacity limit of the storage. 2.3. Wind power constraints The operation cost of the wind power is very low and is often neglected in the literature [30]. The total power generated by a wind turbine is dependent on the wind speed and can be calculated using the following equation. 3. Simulation results and discussions In this section, two scenarios are studied to assess the performance of the CAES integrated system in two different frameworks. In the first scenario, it is assumed that the generation company participates in a perfect market and that the generation company is a price taker, i.e., the generation of the company does not change the market clearing price. In this scenario, the objective of the generation company is to maximise its profit without attempting to satisfy the generation load balance or other system-wide
56
M. Abbaspour et al. / Renewable Energy 51 (2013) 53e59
constraints. In the second scenario, it is assumed that the generation company serves a special load centre (such as a micro-grid). The objective of the generation company in this case is to serve the forecasted load with the minimum cost. The optimisation problems are solved using the Generalised Algebraic Modelling Systems (GAMS) software package [31] and the SBB Mixed Integer Non-Linear Programming (MINLP) solver [32].
70 65
Price ($/MW)
60 55 50 45 40
3.1. First scenario: profit maximisation
35 30 25 20
0
5
10
15
20
Time (hour) Fig. 1. Forecasted price profile (le(t)) over the 24-h study period.
20
Wind Speed hourly Average
Wnd Spped (m/s)
18 16 14 12 10
The forecasted price profile (le(t)) is shown in Fig. 1. A geographical illustration of the Bordekhon wind measurement site and the Dashti salt dome is presented in Fig. 3.The measured wind data at the Bordekhon site (south of Iran) on 21 Feb. 2008 is shown in Fig. 2. The wind speed measurements are provided in 10-min averages, but as the time step of our scheduling problem is 1 h, hourly averaged wind speeds are used in this paper. The hourly averaged and 10-min wind speed averages are shown in Fig. 2. Data for conventional generating units are adopted from Ref. [33]. The system introduced in Ref. [33] has 54 thermal units but in this study only 6 units (units 1e6 of IEEE 118 bus test system) are used for simulation purposes. Conventional generation unit data are shown in Table 1. The simulated wind farm consists of 50 similar wind turbines. The wind turbine is a model E-70 E4 manufactured by ENERCON [34]. The parameters of the wind turbine are provided in Table 2. To evaluate the effect of CAES on the operation of the system, two different cases are studied in each scenario.
8 6 0
5
10
15
20
25
Time (Hour) Fig. 2. Wind speed profile (Vws(t)) over the 24-h study period.
3.1.1. Test system without CAES In the first case, the operation of the system is optimised without considering a CAES system. The total profit in this case is $334,700 and the optimal dispatch of thermal units and total wind generation are presented in Table 3.
Fig. 3. Geographical illustration of Bordekhon wind measurement site and Dashti salt dome.
Table 1 Conventional generating units characteristics in the case study system. Unit
Pmin
Pmax
ai
bi
ci
SUC
RU
RD
SDC
MUT
MDT
1 2 3 4 5 6
5 5 5 150 100 10
30 30 30 300 300 30
0.0697 0.0697 0.0697 0.0109 0.0109 0.0697
26.2438 26.2438 26.2438 12.8875 12.8875 26.2438
31.67 31.67 31.67 6.78 6.78 31.67
40 40 40 440 110 40
15 15 15 150 150 15
15 15 15 150 150 15
0 0 0 0 0 0
1 1 1 10 10 1
1 1 1 10 10 1
M. Abbaspour et al. / Renewable Energy 51 (2013) 53e59 Table 2 Parameters of the 2.05 MW wind turbine.
57
700
Vrated
Vcutout
PWGmax
2
14
25
2.05
Table 3 Optimal operation scheduling of scenario 1 and case 1. Time
Pt (1)
Pt (2)
Pt (3)
Pt (4)
Pt (5)
Pt (6)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0 0 0 0 0 0 0 5 15 30 30 30 30 30 15 23.788 12.599 15 30 30 30 30 30 15
0 0 0 0 0 0 0 0 15 30 30 30 30 30 15 23.789 12.599 15 30 30 30 30 30 15
0 0 0 0 0 0 0 0 15 30 30 30 30 30 15 23.788 12.599 15 30 30 30 30 30 15
150 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300
150 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300
0 0 0 0 0 0 0 0 15 30 30 30 30 30 15 23.789 12.597 15 30 30 30 30 30 15
P
Pw ðkÞ
51.394 40.884 54.137 57.847 80.396 22.604 42.764 30.181 30.943 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 83.336 49.006 7.267 8.34 9.514
Demand (MW)
650
Vcutin
600 550 500 450 400 350 0
5
Amin
Amax
inj Vmin
inj Vmax
p Vmin
p Vmax
50
500
5
50
5
50
15
Table 5 presents the obtained optimum results taking a CAES unit in consideration. The generation company’s profit in this case is $479,100, which is 43% higher compared with the case without CAES ($334,700).
3.2. Second scenario: cost minimisation In this section another scenario is studied. Here, the objective of the generation company is to minimise the total load serving cost. The objective function can be defined as follows: T P
½Costt ðtÞ þ Costc ðtÞ
(19)
t¼1
Another equality constraint should be added to the constraints of the problem defined in Section 2. This constraint enforces the balance between total power generation and total load and can be expressed in the following mathematical form: Nc X
Nw X
Nt X
Table 5 Optimal operation scheduling of scenario 1 and case 2.
Table 6 Optimal operation scheduling of scenario 2 and case 1.
Pt (1)
Pt (2)
Pt (3)
Pt (4)
Pt (5)
Pt (6)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0 0 0 0 0 0 0 0 15 30 30 30 30 30 15 23.789 12.598 15 30 30 30 30 30 15
0 0 0 0 0 0 0 0 15 30 30 30 30 30 15 23.789 12.598 15 30 30 30 30 30 15
0 0 0 0 0 0 0 0 15 30 30 30 30 30 15 23.789 12.598 15 30 30 30 30 30 15
150 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300
150 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300
0 0 0 0 0 0 0 0 15 30 30 30 30 30 15 23.789 12.598 15 30 30 30 30 30 15
P
Pw ðkÞ
51.394 40.884 54.137 57.847 80.396 22.604 42.764 30.181 30.943 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 83.336 49.006 7.267 8.34 9.514
25
Fig. 4. Forecasted load profile (Pdemand(t)) over the 24-h study period.
3.1.2. Test system with CAES In the second test case constraints of CAES are added to the optimisation problem. Parameters of the CAES system are adopted from Ref. [29] and presented in Table 4.
Time
20
Time (hour)
Min cost ¼
Table 4 Parameters of the CAES system.
10
Pt ði;tÞþ
i¼1
PC;S ðj;tÞþ
j¼1
PW ðk;tÞ ¼ Pdemand ðtÞþ
Nc X
Pc;p ðj;tÞ
j¼1
k¼1
(20)
PC,S
Pc,p
Time
Pt (1)
Pt (2)
Pt (3)
Pt (4)
Pt (5)
Pt (6)
50 0 5 10 0 0 0 0 0 50 50 50 50 50 0 50 0 0 50 50 50 50 50 50
0 50 0 0 5 23.33 5 0 0 0 0 0 0 0 50 0 50 0 0 0 0 0 0 0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
11.202 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 18.733 5 0
11.202 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 5 0
11.202 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 5 0
150 159.058 162.681 158.076 157.802 164.698 165.618 166.41 166.028 196.25 207.25 212.75 221 223.75 223.75 223.75 234.75 237.5 245.75 277.332 297.997 300 296.33 297.743
150 159.058 162.681 158.076 157.802 164.698 165.618 166.41 166.028 196.25 207.25 212.75 221 223.75 223.75 223.75 234.75 237.5 245.75 277.332 297.997 300 296.33 297.743
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 15 0 0
P
Pw ðkÞ
51.394 40.884 54.137 57.847 80.396 22.604 42.764 30.181 30.943 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 83.336 49.006 7.267 8.34 9.514
58
M. Abbaspour et al. / Renewable Energy 51 (2013) 53e59
Table 7 Optimal operation scheduling of scenario 2 and case 2. Time
Pt (1)
Pt (2)
Pt (3)
Pt (4)
Pt (5)
Pt (6)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 13.733 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
150 164.058 160.181 167.46 167.46 167.46 165.618 166.41 166.028 196.25 207.25 207.875 223.5 207.875 207.875 207.875 209.75 212.5 220.75 252.332 277.997 300 278.83 272.743
150 164.058 160.181 167.46 167.46 167.46 165.618 166.41 166.028 196.25 207.25 207.875 223.5 207.875 207.875 207.875 209.75 212.5 220.75 252.332 277.997 300 278.83 272.743
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
The demand data for the duration of the study is depicted in Fig. 4. Two cases are also studied in this scenario in the analysis of the effect of CAES. 3.2.1. Test system without CAES The total cost in case 1 (without considering CAES units) is $163,500. The optimal operation scheduling is provided in Table 6. 3.2.2. Test system with CAES In this case, in addition to wind generation and conventional units, CAES participates in satisfying the power demand. The resulting total cost is $152,500, which is 6.7% lower than the case without CAES. The optimal operation scheduling is presented in Table 7. It can be observed that to minimise cost, no power is generated by the more expensive units 2, 3 and 6. 4. Conclusion A short-term optimal operation scheduling of a power generation company with integrated wind and storage is studied in this paper. The daily scheduling problem is formulated as a mixed integer non-linear programming problem and solved using commercial optimisation software. Two different frameworks are studied in this paper. In the first framework, the generation company is assumed to be participating in a liberalised power market. In this scenario, the objective of the generation company is to maximise its total profit. In the second framework, the classic power system is studied, wherein the objective of the generation company is to supply the power demand with minimal cost. The effects and benefits of the compressed-air energy storage system are studied in each framework, indicating that CAES has a considerable effect in increasing profits in the first scenario while decreasing total costs in the second scenario. Simulation results show that in the profit-maximisation scenario, using CAES results in a 43% higher profit compared with the case without CAES. CAES also leads to a 6.7% total cost reduction in the cost-minimisation scenario. It should be noted that the numerical results are provided for a typical market day with a wind profile close to its annual average.
P
Pw ðkÞ
51.394 40.884 54.137 57.847 80.396 22.604 42.764 30.181 30.943 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 83.336 49.006 7.267 8.34 9.514
PC,S
Pc,p
33.606 5 5 0 0 0 0 0 0 0 0 9.75 0 31.75 31.75 31.75 50 50 50 50 50 50 50 50
0 0 0 18.767 19.316 10.924 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0
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M. Abbaspour et al. / Renewable Energy 51 (2013) 53e59 [17] Nyamdash B, Denny E, OMalley M. The viability of balancing wind generation with large scale energy storage. Energy Policy 2010;38(11):7200e8. [18] Pesola A, Hagstrm M, Vanhanen J. Study on distributed energy options in Skaftkrr testbed [Online]. Available from: http://www.stok.fi/pdf_t/Gaian raportti yhtenaisena STOKin julkaisuna.pdf; 2011. accessed October 2011. [19] Allen K. CAES: the underground portion. IEEE Transactions on Power Apparatus and Systems 1985;104(4):809e12. [20] Mehta B. CAES geology. EPRI Journal 1992;17:38e41. [21] Crotogino F, Mohmeyer KU, Scharf R. Huntorf caes: more than 20 years of successful operation. In: Solution mining research institute meeting Orlando, Florida, USA, 2001; 2001. [22] Davis L, Schainker R. Compressed air energy storage (caes): Alabama electric cooperative Mcintosh plant e overview and operational history. In: Electricity storage association meeting 2006: energy storage in Action Knoxville, Tenn. Energy Storage Association; 2006. [23] System behaviour of compressed-air energy-storage in Denmark with a high penetration of renewable energy sources. Applied Energy 2008;85(4):182e9. [24] Optimal operation strategies of compressed air energy storage (caes) on electricity spot markets with fluctuating prices. Applied Thermal Engineering 2009;29(5e6):799e806. [25] Bisanovic S, Hajro M, Dlakic M. Hydrothermal self-scheduling problem in a day-ahead electricity market. Electric Power Systems Research 2008;78(9): 1579e96.
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[26] Shahidehpour M, Yamin H, Li Z. Market operations in electric power systems: forecasting, scheduling, and risk management. John Wiley & Sons; 2002. [27] Diaz FJ, Contreras J, Munoz JI, Pozo D. Optimal scheduling of a price-taker cascaded reservoir system in a pool-based electricity market. IEEE Transactions on Power Systems 2011;26:604e15. [28] Daneshi H, Srivastava A, Daneshi A. Generation scheduling with integration of wind power and compressed air energy storage. In: 2010 IEEE PES transmission and distribution conference and exposition; 2010. p. 1e6. [29] Daneshi H, Daneshi A, Tabari NM, Jahromi AN. Security-constrained unit commitment in a system with wind generation and compressed air energy storage. In: 2009 6th international conference on the European energy market; 2009. p. 1e6. [30] Morais H, Kadar P, Faria P, Vale ZA, Khodr H. Optimal scheduling of a renewable micro-grid in an isolated load area using mixed-integer linear programming. Renewable Energy 2010;32:151eV156. [31] Brooke A, Kendrick D, Meeraus A, Roman R. GAMS: a user’s guide. GAMS Development Corporation; 1998. [32] Bussieck MR, Drud AS. BB: a new solver for mixed integer nonlinear programming. GAMS Development Corp; 2001. [33] [Online]. Available from: motor.ece.iit.edu/data/SCUC_118test.xls, accessed February 2011. [34] [Online]. Available from: http://www.enercon.de/p/downloads/ENProduktue bersicht0710.pdf, accessed February 2011.
Contents lists available at SciVerse ScienceDirect
Renewable Energy journal homepage: www.elsevier.com/locate/renene
Optimal operation scheduling of wind power integrated with compressed air energy storage (CAES) M. Abbaspour a, M. Satkin a, *, B. Mohammadi-Ivatloo b, F. Hoseinzadeh Lotfi a, Y. Noorollahi c a
Faculty of Energy and Environmental Sciences, Science and Research Branch, Islamic Azad University, Tehran, Iran Faculty of Electrical and Computer Engineering, Tabriz University, Tabriz, Iran c Department of Renewable Energy, Faculty of New Science & Technology, University of Tehran, Tehran, Iran b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 19 February 2012 Accepted 8 September 2012 Available online 10 October 2012
This study optimises and compares the operation of a conventional gas-fired power generation company with its operation in combination with wind power and compressed air energy storage (CAES). A mixed integer non-linear programming (MINLP) formulation is developed for the optimisation problem. Limits in ramp rate, capacity, and minimum on/off time, as well as start-up cost constraints, are considered for the modelling of conventional units. Injected and produced power constraints, storage, air balance and CAES-operation limits are considered in the CAES modelling. Two objective functions (profit maximisation and cost minimisation) are modelled. Without considering capital costs, it is found that the use of CAES results in 43% higher operational profits and 6.7% lower costs in a market environment. Ó 2012 Elsevier Ltd. All rights reserved.
Keywords: Wind power Optimal operation Optimisation Compressed air energy storage
1. Introduction Intermittent renewable energy sources, such as wind power, are variable by nature. Thus, when there is insufficient wind power, the electricity demand will be provided by other sources, e.g., conventional thermal generators. One solution to the variability problem of renewable-energy resources is the use of storage systems. Accordingly, a wide range of storage systems has been proposed. A list of such methods includes pumped hydroelectric storage [1,2], compressed air energy storage [3], batteries, including lead acid, nickel cadmium and lithium ion [4], hydrogen storage [5], capacitors and super capacitors [6], flywheel [5,6] and superconducting magnetic energy storage [7]. Storage systems for renewable energy generation have been studied in Ref. [8] and a survey of energy storage options for the integration of large-scale intermittent renewable is provided in Ref. [9]. A survey of energy storage options for integration of the large scale intermittent renewable is provided in Ref. [6]. Among the many energy-storage systems, only pumped storage and CAES systems have the capability for large-scale wind energy
* Corresponding author. E-mail address: [email protected] (M. Satkin). 0960-1481/$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.renene.2012.09.007
integration [6]. In the literature, a significant amount of attention has been given to the scheduling of conventional hydro systems [10,11], thermal units [12,13] and pumped storage units [14,15]. However, little focus has been given to the operation scheduling of CAES units, especially within a market environment. In this paper, short-term operation scheduling of a power generation company is formulated as an MINLP problem and solved using commercial optimisation packages. The generation company considered has three types of generation facilities, i.e., conventional thermal units, wind energy, and the CAES system. In a conventional gas turbine, approximately 2/3 of the fuel is consumed for air compression [16], resulting in a power generation efficiency of less than 40%. However, CAES systems utilise precompressed air during the generation. In such systems, low-cost power during periods of low-energy demand (off-peak) is used to pre-compress air for utilisation during higher-demand (peak load) periods. The CAES systems store the compressed air in large reservoirs, typically making use of existing geological formations and structures, such as salt caverns, aquifers, and abandoned mines. The capital cost of CAES becomes much lower compared with other storage technologies using these existing reservoirs. The capital cost of reservoir of CAES has been compared with other storage technologies in Ref. [17] and concluded that CAES is the preferable technology compared with pumped storage, lead acid batteries,
54
M. Abbaspour et al. / Renewable Energy 51 (2013) 53e59
Nomenclature
aPj s(i)
the efficiency of produced power the time constant of unit i [h] Costc (t) the total cost of CAES units at time horizon t [$/h] Costt (t) the total cost of thermal generation units at time horizon t [$/h] MUT (i) the minimum on times of unit i [h] PW (k, t) the power output of wind power unit k at time horizon t [$/MW] SUC (i, t) start-up cost of thermal generation unit i if started at time t [$] uinj (j, t) binary variable, which is equal to 1 if air injected by the CAES unit j at time t, and 0 otherwise Vrated (k) the rated speed of wind turbine k [m/s] Vt(i, t) binary variable, which is equal to 1 if the thermal unit i be on at time t, and 0 otherwise Yt(i, t) binary variable, which is equal to 1 if the thermal generation unit i is started at time t, and 0 otherwise Ct0(i) the fixed start up cost of unit i [$] Ct1 the cold start up cost of unit i [$] PWGmax(k) the rated power of wind turbine k [MW] SDC(i) shut-down cost of thermal unit i if turned off at time t [$] ainj the efficiency of injected power j le(t) the forecasted energy price at time horizon t [$/MW] a(i) quadratic cost coefficient of thermal generation unit i [$/(MW)2h] A(j, t) the amount of stored energy in the storage j at time t [MWh] Amax(j) the maximum level of storage j in [MWh] Amin(j) the minimum level of storage j in [MWh] b(i) linear cost coefficient of thermal generation unit i [$/MWh] c(i) no-load cost coefficient of thermal generation f unit i [$/h] MDT(i) the minimum down times of unit i [h]
and vanadium redox batteries in terms of the capital cost incurred. The largest CAES system, a 2700-MW plant is planned for construction in an existing limestone mine in Norton, Ohio [18]. There are more geologically suitable sites for CAES than for the pumped storage system. Geological studies indicate that over 75% of the U.S. has suitable sites for consideration for underground air storage [19,20]. Currently, two CAES systems are in operation; The 290-MW Huntorf plant from 1978 near Bremen, Germany [21], and the 110-MW McIntosh plant from 1991 in Southwest Alabama [22]. CAES has high ramp rates that make it suitable for ancillary services. For instance, the McIntosh plant, which has a 134-MW generation and 110-MW compression capacity, can go from full generation to full compression in less than 5 min [6]. The energy balance effects of adding CAES to the Western Danish energy system were studied in Ref. [23]. Optimal yearly operation strategies of CAES units in an energy market have been studied in Ref. [24]. The remainder of this paper is organised as follows: In Section 2 a mathematical formulation of the operation of a wind and CAES integrated power system is provided. The system in the case study and simulation results for different scenarios are presented in Section 3. The concluding remarks are presented in Section 4.
Nc Nt Nw Pt(i, t)
the number of CAES generation units the number of thermal generation units the number of wind power generation units the power output of thermal unit i at time horizon t [MW] Ptmax ðiÞ the maximum power output of the thermal generation unit i Ptmin ðiÞ the minimum power output of the thermal generation unit i Pc,p(j, t) the power consumed by CAES unit j at time t for compressing and injecting air [MW] PC,S(j, t) the power output of CAES unit j at time horizon t that sold to market [$/MW] Pdemand(t) the total system demand at time t RD(i) the ramp down limit of unit i [MW/h] RU(i) the ramp up limit of unit i [MW/h] Td(i, t) the number of hours that unit i was off before time t up(j, t) binary variable, which is equal to 1 if air pumped by the CAES unit j at time t, and 0 otherwise Vp(j, t) the energy equivalent of pumped air to combustion chamber at time t [MWh] Vinj(j, t) the energy equivalent of injected air to storage at time t [MWh] p Vmax ðjÞ the maximum level of pumped air from storage to combustion chamber in [MW/h] inj Vmax ðjÞ the maximum level of injected air into storage in [MW/ h] p Vmin ðjÞ the minimum level of pumped air from storage to combustion chamber in [MW/h] inj Vmin ðjÞ the minimum level of injected air into storage in [MW/ h] Vcutin(k) the cut in speed of wind turbine k [m/s] Vcutout(k) the cut out speed of wind turbine k [m/s] Vws(t) the forecasted wind speed at time t [m/s] Zt(i, t) binary variable, which is equal to 1 if the thermal generation unit i is turned off at time t, and 0 otherwise
2. Problem formulation This case study involves three types of generation facilities, i.e., conventional thermal units, a wind farm, and CAES. In this section, a mathematical formulation of the optimisation problem is provided. The objective of the generation company is to maximise its profit in the energy market. The objective function can be mathematically formulated as follows:
2 Nt Nc T X X X 4 Max profit ¼ Pt ði; tÞle ðtÞ þ PC;S ðj; tÞle ðtÞ t¼1
þ
i¼1
Nw X k¼1
3
j¼1
PW ðk; tÞle ðtÞ5
T X
½Costt ðtÞ þ Costc ðtÞ
t¼1
(1) The objective function defined in Equation (1) should be maximised while considering several technical and logical constraints that are listed in the following section.
M. Abbaspour et al. / Renewable Energy 51 (2013) 53e59
2.2. Constraints for CAES units
2.1. Constraints for conventional thermal units
Costc ðtÞ ¼ Costt ðtÞ ¼
Pc;p ðj; tÞle ðtÞ
(10)
aðiÞPt ði; tÞ2 þbðiÞPt ði; tÞ þ cðiÞ þ SDCðiÞZt ði; tÞ
i þ SUCði; tÞYt ði; tÞ h
SUCði; tÞ ¼ Ct0 ðiÞ þ Ct1 ðiÞ 1 eTd ði;tÞ=sðiÞ
ð2Þ i
Ptmin ðiÞ Pt ði; tÞ Ptmax ðiÞ
Pt ði; t 1Þ RDðiÞ Pt ði; tÞ Pt ði; t 1Þ þ RUðiÞ
MUTðiÞ1 X
MDTðiÞ1 X
inj V inj ðj; tÞ ¼ aj Pc;p ðj; tÞ
(11)
PC;s ðj; tÞ ¼ aPj V p ðj; tÞ
(12)
inj inj Vmin ðjÞuinj ðj; tÞ V inj ðj; tÞ Vmax ðjÞuinj ðj; tÞ
(13)
p p ðjÞup ðj; tÞ V p ðj; tÞ Vmax ðjÞup ðj; tÞ Vmin
(14)
up ðj; tÞ þ uinj ðj; tÞ 1
(15)
Aðj; t þ 1Þ ¼ Aðj; tÞ þ V inj ðj; tÞ V p ðj; tÞ
(16)
Amin ðjÞ Aðj; tÞ Amax ðjÞ
(17)
(3)
(4)
(5)
Zt ði; t þ nÞ 1
(6)
Yt ði; t þ nÞ 1
(7)
n¼1
Zt ði; tÞ þ
Nc X j¼1
Nt h X i¼1
Yt ði; tÞ þ
55
n¼1
Production cost of CAES Equation (10) is modelled as the cost of purchased energy from the energy market [28]. Constraint (11) models the injected air in units of MW/h [29]. The produced power of CAES is modelled using constraint (12). The amounts of injected air into storage and pumped air from storage to combustion chamber are limited (depending on the valve size and pressure limits) and are modelled by constraints (13) and (14), respectively. The CAES unit can either be in the air injection or pumping state. This constraint is satisfied in Equation (15), which also precludes the CAES unit from being in the generation and consumption status at same time. The amount of the stored air is updated every hour, as
8 > > 0 Vws ðtÞ
Yt ði; tÞ Zt ði; tÞ ¼ Vt ði; tÞ Vt ði; t 1Þ
(8)
Yt ði; tÞ þ Zt ði; tÞ 1
(9)
Equation (2) shows the total production cost considering startup and shut-down costs using a quadratic function [13,25]. Constraint (3) models the start-up cost using an exponential function [26]. The real power operation limit is enforced in constraint (4). The ramp rate limits are modelled in Equation (5). The minimum ON and OFF times are enforced in Equations (6) and (7), respectively. Two logical operation constraints, (8) and (9) are included [27]. Constraint (8) determines the start-up or shut-down status based on the on/off status of the unit within the last 2 h. Finally, constraint (9) prevents the illogical situation of the unit starting up and shutting down simultaneously. The ramp rate, minimum ON time, and minimum OFF time limits represent dynamic constraints (constraints that hold at different times) that complicate the optimisation problem.
(18)
dictated in Equation (16), and calculated by taking the current storage plus or minus the injected or pumped air. Constraint (17) models the capacity limit of the storage. 2.3. Wind power constraints The operation cost of the wind power is very low and is often neglected in the literature [30]. The total power generated by a wind turbine is dependent on the wind speed and can be calculated using the following equation. 3. Simulation results and discussions In this section, two scenarios are studied to assess the performance of the CAES integrated system in two different frameworks. In the first scenario, it is assumed that the generation company participates in a perfect market and that the generation company is a price taker, i.e., the generation of the company does not change the market clearing price. In this scenario, the objective of the generation company is to maximise its profit without attempting to satisfy the generation load balance or other system-wide
56
M. Abbaspour et al. / Renewable Energy 51 (2013) 53e59
constraints. In the second scenario, it is assumed that the generation company serves a special load centre (such as a micro-grid). The objective of the generation company in this case is to serve the forecasted load with the minimum cost. The optimisation problems are solved using the Generalised Algebraic Modelling Systems (GAMS) software package [31] and the SBB Mixed Integer Non-Linear Programming (MINLP) solver [32].
70 65
Price ($/MW)
60 55 50 45 40
3.1. First scenario: profit maximisation
35 30 25 20
0
5
10
15
20
Time (hour) Fig. 1. Forecasted price profile (le(t)) over the 24-h study period.
20
Wind Speed hourly Average
Wnd Spped (m/s)
18 16 14 12 10
The forecasted price profile (le(t)) is shown in Fig. 1. A geographical illustration of the Bordekhon wind measurement site and the Dashti salt dome is presented in Fig. 3.The measured wind data at the Bordekhon site (south of Iran) on 21 Feb. 2008 is shown in Fig. 2. The wind speed measurements are provided in 10-min averages, but as the time step of our scheduling problem is 1 h, hourly averaged wind speeds are used in this paper. The hourly averaged and 10-min wind speed averages are shown in Fig. 2. Data for conventional generating units are adopted from Ref. [33]. The system introduced in Ref. [33] has 54 thermal units but in this study only 6 units (units 1e6 of IEEE 118 bus test system) are used for simulation purposes. Conventional generation unit data are shown in Table 1. The simulated wind farm consists of 50 similar wind turbines. The wind turbine is a model E-70 E4 manufactured by ENERCON [34]. The parameters of the wind turbine are provided in Table 2. To evaluate the effect of CAES on the operation of the system, two different cases are studied in each scenario.
8 6 0
5
10
15
20
25
Time (Hour) Fig. 2. Wind speed profile (Vws(t)) over the 24-h study period.
3.1.1. Test system without CAES In the first case, the operation of the system is optimised without considering a CAES system. The total profit in this case is $334,700 and the optimal dispatch of thermal units and total wind generation are presented in Table 3.
Fig. 3. Geographical illustration of Bordekhon wind measurement site and Dashti salt dome.
Table 1 Conventional generating units characteristics in the case study system. Unit
Pmin
Pmax
ai
bi
ci
SUC
RU
RD
SDC
MUT
MDT
1 2 3 4 5 6
5 5 5 150 100 10
30 30 30 300 300 30
0.0697 0.0697 0.0697 0.0109 0.0109 0.0697
26.2438 26.2438 26.2438 12.8875 12.8875 26.2438
31.67 31.67 31.67 6.78 6.78 31.67
40 40 40 440 110 40
15 15 15 150 150 15
15 15 15 150 150 15
0 0 0 0 0 0
1 1 1 10 10 1
1 1 1 10 10 1
M. Abbaspour et al. / Renewable Energy 51 (2013) 53e59 Table 2 Parameters of the 2.05 MW wind turbine.
57
700
Vrated
Vcutout
PWGmax
2
14
25
2.05
Table 3 Optimal operation scheduling of scenario 1 and case 1. Time
Pt (1)
Pt (2)
Pt (3)
Pt (4)
Pt (5)
Pt (6)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0 0 0 0 0 0 0 5 15 30 30 30 30 30 15 23.788 12.599 15 30 30 30 30 30 15
0 0 0 0 0 0 0 0 15 30 30 30 30 30 15 23.789 12.599 15 30 30 30 30 30 15
0 0 0 0 0 0 0 0 15 30 30 30 30 30 15 23.788 12.599 15 30 30 30 30 30 15
150 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300
150 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300
0 0 0 0 0 0 0 0 15 30 30 30 30 30 15 23.789 12.597 15 30 30 30 30 30 15
P
Pw ðkÞ
51.394 40.884 54.137 57.847 80.396 22.604 42.764 30.181 30.943 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 83.336 49.006 7.267 8.34 9.514
Demand (MW)
650
Vcutin
600 550 500 450 400 350 0
5
Amin
Amax
inj Vmin
inj Vmax
p Vmin
p Vmax
50
500
5
50
5
50
15
Table 5 presents the obtained optimum results taking a CAES unit in consideration. The generation company’s profit in this case is $479,100, which is 43% higher compared with the case without CAES ($334,700).
3.2. Second scenario: cost minimisation In this section another scenario is studied. Here, the objective of the generation company is to minimise the total load serving cost. The objective function can be defined as follows: T P
½Costt ðtÞ þ Costc ðtÞ
(19)
t¼1
Another equality constraint should be added to the constraints of the problem defined in Section 2. This constraint enforces the balance between total power generation and total load and can be expressed in the following mathematical form: Nc X
Nw X
Nt X
Table 5 Optimal operation scheduling of scenario 1 and case 2.
Table 6 Optimal operation scheduling of scenario 2 and case 1.
Pt (1)
Pt (2)
Pt (3)
Pt (4)
Pt (5)
Pt (6)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0 0 0 0 0 0 0 0 15 30 30 30 30 30 15 23.789 12.598 15 30 30 30 30 30 15
0 0 0 0 0 0 0 0 15 30 30 30 30 30 15 23.789 12.598 15 30 30 30 30 30 15
0 0 0 0 0 0 0 0 15 30 30 30 30 30 15 23.789 12.598 15 30 30 30 30 30 15
150 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300
150 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300 300
0 0 0 0 0 0 0 0 15 30 30 30 30 30 15 23.789 12.598 15 30 30 30 30 30 15
P
Pw ðkÞ
51.394 40.884 54.137 57.847 80.396 22.604 42.764 30.181 30.943 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 83.336 49.006 7.267 8.34 9.514
25
Fig. 4. Forecasted load profile (Pdemand(t)) over the 24-h study period.
3.1.2. Test system with CAES In the second test case constraints of CAES are added to the optimisation problem. Parameters of the CAES system are adopted from Ref. [29] and presented in Table 4.
Time
20
Time (hour)
Min cost ¼
Table 4 Parameters of the CAES system.
10
Pt ði;tÞþ
i¼1
PC;S ðj;tÞþ
j¼1
PW ðk;tÞ ¼ Pdemand ðtÞþ
Nc X
Pc;p ðj;tÞ
j¼1
k¼1
(20)
PC,S
Pc,p
Time
Pt (1)
Pt (2)
Pt (3)
Pt (4)
Pt (5)
Pt (6)
50 0 5 10 0 0 0 0 0 50 50 50 50 50 0 50 0 0 50 50 50 50 50 50
0 50 0 0 5 23.33 5 0 0 0 0 0 0 0 50 0 50 0 0 0 0 0 0 0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
11.202 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 18.733 5 0
11.202 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 5 0
11.202 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 5 0
150 159.058 162.681 158.076 157.802 164.698 165.618 166.41 166.028 196.25 207.25 212.75 221 223.75 223.75 223.75 234.75 237.5 245.75 277.332 297.997 300 296.33 297.743
150 159.058 162.681 158.076 157.802 164.698 165.618 166.41 166.028 196.25 207.25 212.75 221 223.75 223.75 223.75 234.75 237.5 245.75 277.332 297.997 300 296.33 297.743
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 15 0 0
P
Pw ðkÞ
51.394 40.884 54.137 57.847 80.396 22.604 42.764 30.181 30.943 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 83.336 49.006 7.267 8.34 9.514
58
M. Abbaspour et al. / Renewable Energy 51 (2013) 53e59
Table 7 Optimal operation scheduling of scenario 2 and case 2. Time
Pt (1)
Pt (2)
Pt (3)
Pt (4)
Pt (5)
Pt (6)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 13.733 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
150 164.058 160.181 167.46 167.46 167.46 165.618 166.41 166.028 196.25 207.25 207.875 223.5 207.875 207.875 207.875 209.75 212.5 220.75 252.332 277.997 300 278.83 272.743
150 164.058 160.181 167.46 167.46 167.46 165.618 166.41 166.028 196.25 207.25 207.875 223.5 207.875 207.875 207.875 209.75 212.5 220.75 252.332 277.997 300 278.83 272.743
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
The demand data for the duration of the study is depicted in Fig. 4. Two cases are also studied in this scenario in the analysis of the effect of CAES. 3.2.1. Test system without CAES The total cost in case 1 (without considering CAES units) is $163,500. The optimal operation scheduling is provided in Table 6. 3.2.2. Test system with CAES In this case, in addition to wind generation and conventional units, CAES participates in satisfying the power demand. The resulting total cost is $152,500, which is 6.7% lower than the case without CAES. The optimal operation scheduling is presented in Table 7. It can be observed that to minimise cost, no power is generated by the more expensive units 2, 3 and 6. 4. Conclusion A short-term optimal operation scheduling of a power generation company with integrated wind and storage is studied in this paper. The daily scheduling problem is formulated as a mixed integer non-linear programming problem and solved using commercial optimisation software. Two different frameworks are studied in this paper. In the first framework, the generation company is assumed to be participating in a liberalised power market. In this scenario, the objective of the generation company is to maximise its total profit. In the second framework, the classic power system is studied, wherein the objective of the generation company is to supply the power demand with minimal cost. The effects and benefits of the compressed-air energy storage system are studied in each framework, indicating that CAES has a considerable effect in increasing profits in the first scenario while decreasing total costs in the second scenario. Simulation results show that in the profit-maximisation scenario, using CAES results in a 43% higher profit compared with the case without CAES. CAES also leads to a 6.7% total cost reduction in the cost-minimisation scenario. It should be noted that the numerical results are provided for a typical market day with a wind profile close to its annual average.
P
Pw ðkÞ
51.394 40.884 54.137 57.847 80.396 22.604 42.764 30.181 30.943 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 102.5 83.336 49.006 7.267 8.34 9.514
PC,S
Pc,p
33.606 5 5 0 0 0 0 0 0 0 0 9.75 0 31.75 31.75 31.75 50 50 50 50 50 50 50 50
0 0 0 18.767 19.316 10.924 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0
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