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Short-term peak shaving operation for multiple power grids with pumped storage power plants
Electrical Power and Energy Systems 67 (2015) 570–581
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Short-term peak shaving operation for multiple power grids with pumped storage power plants Chun-Tian Cheng ⇑, Xiong Cheng, Jian-Jian Shen, Xin-Yu Wu Institute of Hydropower and Hydroinformatics, Dalian University of Technology, Dalian 116024, China
a r t i c l e
i n f o
Article history: Received 5 April 2014 Received in revised form 7 December 2014 Accepted 9 December 2014 Available online 27 December 2014 Keywords: Pumped storage Peak shaving Multiple power grids Fuzzy sets
a b s t r a c t The East China Power Grid (ECPG) is the biggest regional power grid in China. It has the biggest installed capacity of pumped storage power plants (PSPPs) and is responsible to coordinate the operation of its five provincial power grids. A recent challenge of coordinating operations is using PSPPs to absorb surplus energy during off-peak periods and generate power during peak periods. Differing from the traditional operations of single power grids, however, the PSPPs are required to respond to load demands from multiple provincial power grids simultaneously. This paper develops a three-step hybrid algorithm for the day-ahead quarter-hourly schedules of PSPPs to meet load demands of multiple provincial power grids. A normalization method is first proposed to reconstruct a total load curve to deal with the load differences of multiple provincial power grids, and to reflect the effect of specified electricity contract ratio on multiple provincial power grids. Secondly, a heuristic search method is presented to determine the generating and pumping powers of PSPP. Thirdly, a combination optimization method is used to allocate the determined generating and pumping powers among multiple provincial power grids to smooth the individual remaining load curve for their thermal systems. Two case studies with greatly different load demands are used to test the proposed algorithm. The simulation results show that the presented method can effectively achieve the goal of shaving the peak load and filling the off-peak load for multiple provincial power grids. Ó 2014 Elsevier Ltd. All rights reserved.
Introduction China’s electricity demand has a huge expansion during the past three decades with its growing economy. The East China Power Grid (ECPG), which is the biggest regional power grid in China, consists of five provincial power grids in eastern China, in Fig. 1. Its maximum electricity load exceeded 184.5 GW in 2012, about 26 times larger than in 1982. Its maximum load difference between peak and off-peak has also largely increased by about 4.59 times, from 11.96 GW in 2002 to 54.86 GW in 2012. Fig. 2 shows the total load demand of ECPG, and individual load demands of multiple provincial power grids on December 24, 2012. The maximum load difference of ECPG between peak and off-peak has reached 54.86 GW (29.7% of maximum electricity load). This expansion of load demands brings significant challenges to the ECPG, since over 84.8% of its total installed capacity (about 178.9 GW) is thermal power that has low effective capacity of regulating peak loads. ⇑ Corresponding author. Tel.: +86 0411 84708768. E-mail addresses: [email protected] (C.-T. Cheng), [email protected] (X. Cheng), [email protected] (J.-J. Shen), [email protected] (X.-Y. Wu). http://dx.doi.org/10.1016/j.ijepes.2014.12.043 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved.
Hydropower plants are unevenly distributed among multiple provincial power grids in ECPG. From the provincial energy structures in Fig. 3, the Fujian Power Grid has 32.4% of hydropower and little pressure on peak power demand, while the other four provincial power grids face severe power shortages for peak demand. The pressing demand for peak power resulted in a rapid establishment of pumped storage power plants (PSPPs) [1,2] in the ECPG. The PSPPs owned by the ECPG are the biggest in China [3], with a total installed capacity of 7.12 GW (35.6% of nation’s total PSPPs capacity). Table 1 shows the details of PSPPs in the ECPG. Among the established PSPPs, the four bigger plants including Tianhuangping, Xiangshuijian, Langyashan and Tongbai are directly operated by the dispatching center of the ECPG to absorb surplus energy from four provincial power grids (SHPG, JSPG, ZJPG and AHPG) and then provide peak power for these power grids. The other PSPPs are operated by different provincial power grids for meeting their local load demands respectively. This paper focuses on the former one of operating the four bigger PSPPs. A system-wide practical problem is how to determine the day-ahead quarter-hourly schedules for these PSPPs to coordinate extremely different peak and off-peak load demands among multiple provincial power grids.
C.-T. Cheng et al. / Electrical Power and Energy Systems 67 (2015) 570–581
571
Nomenclature E0koutput
specified total energy generation target (MW h)
A. Acronyms ECPG East China Power Grid PSPPs pumped storage power plants PSPP a pumped storage power plant SHPG Shanghai Power Grid JSPG Jiangsu Power Grid ZJPG Zhejiang Power Grid AHPG Anhui Power Grid FJPG Fujian Power Grid
Rk,g
specified electricity contract ratio
tgk
minimum duration periods of operation
tsk
minimum duration periods of shutdown
Tr
extreme point duration periods
wag
weight coefficient
B. Indices k g t j n1 n2 K G T J
Cg,t
remaining load demand (MW)
Cg
mean of the remaining load (MW)
C max g
maximum remaining load (MW)
C min g C total k;t
maximum remaining load (MW)
Nk,t Nk,t
generating power (positive values, MW) pumping power (negative values, MW)
Ngk;t
supply power for gird (positive values, MW)
Ngk;t Dg Dg,j
absorb power from grid (negative values, MW) variance of the remaining load candidate solution
Dmax g
maximum candidate solutions minimum candidate solutions
D. Variables Lg,t original load demand (MW)
PSPP or upper reservoir index provincial power grid index time period index candidate solution index iteration index iteration index number of PSPPs number of provincial power grids scheduling horizon number of candidate solutions
C. Parameters and constants Dt time period duration (=0.25 h).
total remaining load (MW)
qoutput k;t qoutput k;t qinput k;t qinput k;t V up k;t V up k;t
maximum water discharge limits (m /s)
Dmin g
minimum water discharge limits (m3/s)
W ag
weight coefficient
V up k;t V low k;t
water storage of upper reservoir (m3)
qk,t
water discharge (positive values, m3/s)
qk,t
pumping flow (negative values, m3/s) water level of upper reservoir (m)
V low k;t
maximum storage of lower reservoir (m3)
V low k;t
minimum storage of lower reservoir (m3)
Z up k;t Z low k;t Ht;tþ1 k
V 0up k;T
final storage target of upper reservoir (m3)
maximum extreme point duration periods
Noutput k;t Noutput k;t Ninput k;t
maximum generating power (MW)
sk;t sk,t
minimum generating power (MW)
foutput() generating power function
maximum pumping power (MW)
finput()
pumping power function
up f zm ðÞ low f zm ðÞ
water level and storage function of upper reservoir
3
maximum pumping flow limits (m3/s) minimum pumping flow limits (m3/s) maximum storage of upper reservoir (m3) 3
minimum storage of upper reservoir (m )
Ninput k;t
minimum pumping power (MW)
DN output k DN input k
maximum ramping capacity in generating model (MW)
water storage of lower reservoir (m3)
water level of lower reservoir (m) average gross head minimum extreme point duration periods
water level and storage function of lower reservoir
maximum ramping capacity in pumping model (MW)
Different from the traditional operations of PSPPs for a single power grid [4–7], the PSPPs in ECPG are usually required to shave the peak load and fill the off-peak load (Fig. 4) for multiple provincial power grids according to multilateral electricity contracts. It is difficult to coordinate generating power and pumping power of PSPPs to respond promptly to different load demands because of the strong electrical coupling, inconsistent load demand with largely varying magnitude and peak and off-peak periods among multiple provincial power grids. Besides, the traditional reservoir and hydropower plant constraints and multilateral electricity contracts are coupled across the entire scheduling horizon, which make it more difficult to find rational and efficient operational schedules for PSPPs. Optimization of PSPP scheduling is an important area that has attracted many researches. Various methods have been developed to resolve the problem, including Linear Programming (LP) [6],
Mixed Integer Programming (MIP) [8,9], Dynamic Programming (DP) [10–12], Lagrangian Relaxation algorithm (LR) [9], Artificial intelligence algorithm [13–15], practical operation strategies [16–19] and commercial software [20,21]. However, these methods have some limits. For instance, LP, MIP and commercial software may not guarantee the accuracy of optimized results due to the linearization or piecewise linearization of nonlinear objective functions and constraints. DP is not an efficient method for solving short-term operation of multiple PSPPs among multiple power grids because of the acknowledged curse of dimensionality [22,23]. A similar study has confirmed the inefficiency of DP [10] that uses DP method to obtain the optimal scheduling of one PSPP in combination with several interconnected power systems. LR is not applicable to deal with dynamic transition among operating states (generating, pumping and idle) and optimizing multipliers, and is not an effective method for our problem. Furthermore, many
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this reason, this paper develops a three-step hybrid algorithm to optimize day-ahead quarter-hourly operation of PSPPs among multiple provincial power grids. The three-step hybrid algorithm is carried out for each PSPP one after another repeatedly, until the termination condition is satisfied. Two case studies with significantly different load demands are used to test the proposed method. Such simulation results show that the presented method can effectively achieve the goal of shaving the peak load and filling the off-peak load for multiple provincial power grids. Problem formulations Objective function
Fig. 1. The geographical distribution of the five subsidiary power grids in eastern China, and schematic representation of the PSPP providing to and absorbing energy from the MPPG.
constraints in quarter-hourly PSPP scheduling are not considered in previous literatures that have considerably discussion on hourly PSPP scheduling only. Complex constraints and requirements of PSPPs operation pose a real challenge for most optimization methods to solve this practical engineering problem. In recent years, heuristic methods have been widely applied to complex real-world engineering problems which are difficult to be solved by classical optimization methods [7,24,25]. Although heuristic methods cannot guarantee convergence to the global optimal solution, they are usually capable of searching acceptable and practical solutions depended on rules-of-thumb, experience, rules information in real world’s engineering problems [26]. Compared with traditional technical methods, the heuristic method is promising, particularly well suited for industrial applications. For
11:15
Load(MW) 170500
ECPG
Load(MW) 23500
As mentioned above, the PSPPs in the ECPG are directly operated by the dispatching center of the ECPG and mainly used to shave the peak load and fill the off-peak load (Fig. 4) for multiple provincial power grids. Generally, A PSPP is typically equipped with reversible pumps/generators connecting upper and lower reservoirs. The pumps typically operate during off-peak periods, pumping water from the lower reservoir to the upper one to absorb surplus energy. During periods of high electricity demand (peak periods), water is released from the upper reservoir to generate peak power. In mathematical terms, a variance function of remaining load series of each power grid can be utilized to describe the optimization objective as following:
8 T h i2 X > > > min Dg ¼ C g;t C g > < t¼1 ! g ¼ 1; 2 G K > X > g > > C g;t ¼ Lg;t Nk;t : k¼1
Eq. (1) is aimed to ensure the equivalence of the remaining load of each provincial power grid at every period to the greatest extent and to smooth the remaining loads for respective thermal systems [27]. N gk;t represents power supply (positive values) or to power absorption (negative values) at period t, in MW. If N gk;t > 0, the power flow is transferred from the kth PSPP to the gth power grid to shave the peak load. Otherwise, the power flow is transferred from the gth power grid to the kth PSPP to absorb surplus energy during off-peak periods. Lg,t and Cg,t are the original and remaining load for the gth power grid at period t, in MW. C g and Dg are the mean and variance of remaining load Cg,t for the gth power grid. K
10:45
Shanghai
21500
160500
140500
17500
54,857 MW
130500
15500
120500
13500
110500 3:15
6:15
Load(MW)
9:15 12:15 15:15 18:15 21:15 Time
11:10
46100
Zhejiang
55000
15,641 MW 50000
0:15
Load(MW) 20200
3:15
6:15
Anhui
9:15 12:15 15:15 18:15 21:15 Time
18:30
19200
18,134 MW
6,173 MW
16200 15200
31100
13200 0:15
3:15
6:15
9:15 12:15 15:15 18:15 21:15 Time
Load(MW) 24000
3:15
6:15
Fujian
9:15 12:15 15:15 18:15 21:15 Time
18:15
18000
8,060 MW
16000
14200
26100
0:15
20000
17200
36100
45000
22000
18200
41100
Jiangsu
11:00
9,480 MW
11500 0:15
Load(MW) 65000 60000
19500
150500
ð1Þ
14000 0:15
3:15
6:15
9:15 12:15 15:15 18:15 21:15 Time
0:15
3:15
Fig. 2. The total load demand of ECPG, and load demand of MPPG on December 24, 2012.
6:15
9:15 12:15 15:15 18:15 21:15 Time
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Installed Capacity (MW) Thermal Hydropower Nuclear Wind Pump Other Total
SHPG
JSPG
ZJPG
AHPG
FJPG
21205.7
64159
22535.5 474
24855 11348
269.35
2000 1946 1100
38524 1649 320 140
295.5 80
40633
23385
1132 1200 174 38709
0 21475.05
69205
Dispatching Center(DCECPG) 7580 1207.2 4077 4600 17464.2
ECPG 178859.2 14678.2 6397 3642.85 7120 174 210871.25
Note: The above power sources are only operated by central or provincial dispatch centers. Don’t include the power sources operated by municipal dispatch centers. Fig. 3. Electric power structure of different dispatching sectors in ECPG, 2012. Table 1 All PSPPs in the ECPG by the end of 2012. Plant
Dispatching sector
Turbine capacity (MW) (single capacity units)
Pump capacity (MW) (single capacity units)
Type
Tianhuangping Xiangshuijian Langyashan Tongbai Shahe Yixing Xianghongdian Xikou Xikou II Xianyou
Dispatching Dispatching Dispatching Dispatching JSPG JSPG AHPG ZJPG ZJPG FJPG
300 6 = 1800 230 4 = 920 147 4 = 588 300 4 = 1200 51 2 = 102 250 4 = 1000 40 2 = 80 40 2 = 80 30 2 = 60 300 4 = 1200
315 6 = 1890 275 4 = 1100 165 4 = 660 312 4 = 1248 58 2 = 116 250 4 = 1000 40 2 = 80 40 2 = 80 30 2 = 60 300 4 = 1200
Pure/daily Pure/daily Pure/daily Pure/daily Pure/daily Pure/daily Mixed/multi-yearly Pure/daily Pure/daily Mixed/weekly
center center center center
and G are the total number of PSPPs and power grids, respectively. T is the scheduling horizon. Constraints The problem here involves reservoirs, plant operations and system control. Below are the specific constraints regarding each component. (1) The operational reservoir constraints:
8 up up up > < V k;t ¼ f zm Z k;t > : V low ¼ f low Z low zm k;t k;t 0 up V up k;T ¼ V k;T
ð4Þ
ð5Þ
up up up where V up k;t ,V k;tþ1 ,V k;t ,V k;t are the beginning, ending, minimum and maximum water storage of the upper reservoir in the kth PSPP at
Eq. (2) is water balance of the upper and lower reservoirs. Eq. (3) shows the maximum and minimum storages of the upper and lower reservoirs. Eq. (4) illustrates the relation between water level and storage for upper and lower reservoirs. And Eq. (5) is the specified demand target for the upper reservoir storage at the final period.
8 up up < V k;tþ1 ¼ V k;t qk;t Dt :
low V low k;tþ1 ¼ V k;t þ qk;t Dt
8 up up up < V k;t 6 V k;t 6 V k;t :
low low V low k;t 6 V k;t 6 V k;t
ð2Þ
ð3Þ Fig. 4. Schematic diagram of shaving the peak load and filling the off-peak load with PSPP.
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low low low period t, respectively, in m3. V low k;t ,V k;tþ1 ,V k;t ,V k;t are the beginning, ending, minimum and maximum water storage of the lower reserlow voir in the kth PSPP at period t, respectively, in m3. Z up k;t ,Z k;t are the water level of upper and lower reservoir in the kth PSPP at period t, respectively. qk,t is the water discharge (positive values) or pumping up flow (negative values) in the kth PSPP at period t, in m3/s. f zv ðÞ, low f zv ðÞ are the functional relationship of water storage and water up level. V 0k;T is the required water storage target of the upper reservoir in the kth PSPP at the final period. Duration of each time period in this study is Dt = 0.25 h. (2) The operational plant constraints Eq. (6) calculates the average gross water head of the upper and lower reservoirs. Eq. (7) shows the generating power (namely output) or pumping power (namely input) in the kth PSPP, which can be expressed as a function of the discharge or pumping water flow and average water head. The coupling relationship is very complex and should not simply be assumed as linear or piecewise linear function in modeling [28]. Particularly in pure PSPP with a small available storage capacity, operating efficiency is very sensitive to water head [22]. The minimum and maximum power capacities are in Eq. (8). The minimum and maximum discharge and pumping water inflows are in Eq. (9). Specified total energy demand over the entire scheduling horizon is in Eq. (10). This constraint is hardly satisfied in this paper. The maximum ramping capacity is in Eq. (11). The minimum duration between operation and shutdown is required in Eq. (12). The minimum lasting durations for local maximum and minimum powers are in Eq. (13) and in Fig. 5. This requirement on generating power and pumping power of the kth plant is to avoid frequent power fluctuation.
Ht;tþ1 ¼ k
Z up k;t
2
( N k;t ¼ (
(
þ
Z up k;tþ1
Z low k;t
þ 2
Z low k;tþ1
f output ðHt;tþ1 ; qk;t Þ; k
if
f input ðHkt;tþ1 ; qk;t Þ;
ð6Þ
qk;t P 0 if
ð7Þ
qk;t < 0
Noutput 6 Nk;t 6 Noutput ; if N k;t > 0 k;t k;t input input Nk;t 6 Nk;t 6 Nk;t ; if Nk;t < 0 qoutput k;t qinput k;t
qoutput ; k;t
6 qk;t 6 6 qk;t 6 qinput ; k;t
if
qk;t > 0
if
qk;t < 0
ð8Þ
ð9Þ
Eoutput ¼ E0koutput k
if Nk;ttsk > 0; Nk;t > 0 if Nk;ttgk ¼ 0; Nk;t ¼ 0
sk;t P T r sk;t P T r
ð12Þ
ð13Þ
where Hkt;tþ1 is the average gross water head between the upper and lower reservoirs in the kth PSPP at period t. Nk,t is the generating power (positive values) or pumping power (negative values) in the kth PSPP at period t, in MW. N output ,Noutput are the generating k;t k;t input power limits in the kth PSPP at period t, in MW. N input are k;t ,N k;t the pumping power limits in the kth PSPP at period t, in MW. input qoutput ,qoutput are the water discharge limits, in (m3/s). qinput k;t k;t k;t ,qk;t output 3 are the pumping water flow limits, in (m /s) DNk is the maximum ramping capacity in generating mode in the kth PSPP at period t, in MW; DN input is the maximum ramping capacity in pumping k mode in the kth PSPP at period t, in MW. tgk, tsk are the minimum duration periods of operation and shutdown in the kth PSPP. sk;t , sk,t are the minimum duration periods requirement in local maximum and minimum powers in the kth PSPP. (3) The operational power system constraints For any time period, the power balance between the kth PSPP and multiple provincial power grids is in Eq. (14). G X Ngk;t ¼ Nk;t ; 0 6 t < T
ð14Þ
g¼1
For the entire scheduling horizon, the energy balance between the kth PSPP and multiple provincial power grids is in Eq. (15). Rk,g is the electricity contract ratio between the kth PSPP and the gth power grid.
8 PT P Ng Dt ¼ Rk;g Tt¼0 Nk;t Dt; Ngk;t > 0; Nk;t > 0 > > < Pt¼0 k;t PT T g g t¼0 N k;t Dt ¼ Rk;g t¼0 N k;t Dt; N k;t < 0; N k;t < 0 > > : PG g¼1 Rk;g ¼ 1
ð15Þ
Eqs. (14) and (15) are hard constraints to guarantee the power and energy balance between PSPPs and multiple provincial power grids. In this paper, tie-line maximum and minimum available transfer capability limit, frequency, voltage stability and transmission losses issues of are not considered.
ð10Þ Solution methodologies
*HQHUDWLQJ SRZHU 0:
( Nk;t Nk;t1 6 DNoutput ; if Nk;t > 0; Nk;t1 > 0 k Nk;t Nk;t1 6 DNinput ; if Nk;t < 0; Nk;t1 < 0 k
3XPSLQJ SRZHU 0:
(
ð11Þ
/RFDOPD[LPXP JHQHUDWLQJSRZHU
/RFDOPD[LPXP JHQHUDWLQJSRZHU
τ ktmax ,
τ ktmax ,
τ ktmin ,
τ ktmax ,
/RFDOPLQLPXP JHQHUDWLQJSRZHU
/RFDOPD[LPXP SXPSLQJSRZHU
3HULRGV Fig. 5. The explanation of minimum duration periods requirements of extreme points.
Different from the conventional operations of PSPPs for a single power grid [4,6,7,13,19,29]. The PSPPs in this paper are required to simultaneously shave the peak loads and fill the light loads for multiple provincial power grids according to multilateral electricity contracts. The primary characteristic of this problem is that each PSPP is not facing a single load curve, but multiple load curves with huge differences in magnitude, peak and off-peak periods. The difference of load demands adds challenges for determining feasible generating and pumping schedules for each PSPP. In addition, satisfying the multilateral electricity contracts in the process of electric power distribution among multiple provincial power grids makes it more difficult to solve problem. Due to the complexity of the present problem, a three-step hybrid algorithm is prosed in this paper to optimize day-ahead quarter-hourly operation of PSPPs among multiple provincial power grids. This hybrid algorithm consists of three components: a normalization method, a heuristic search method and a combination optimization method. The whole procedure of the three-step hybrid algorithm is in Fig. 6 (see more details in the following subsections).
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C.-T. Cheng et al. / Electrical Power and Energy Systems 67 (2015) 570–581
Start The iteration n1=0 The plant k=1
Cktotal ,t
Section 3.1: Reconstructing a total load curve, Fig.(a) Section 3.2: Establishing the kth PSPP schedules
(a)
The iteration n2=0
Generating power
Pumping power
Searching the optimal Pumping power in the total load curve, Fig. (b) ΔN koutput
Searching the optimal generating power In the total load curve, Fig. (c) Using the Eq.(2)-(4), (6)-(9) to calculate the water balance
n2=n2+1
1R
WaW
ΔN kinput
Z Z
( c )a
(b)
Next optimal generating periods
Conform to the Eq.(5) and (10) Next optimal pumping periods
(d)
(e)
Section 3.3: Allocating the kth PSPP schedules Generating power or pumping one is divided into a series of electricity equal piece, Fig.(f) these small pieces are allocated to each power grid subject to electricity contracts, Fig.(g)
(f)
exchange the allocating combination of these small pieces 1R
the optimal combination?
k=k+1
1R
(g)
N!."
n1=n1+1
1R
The remaining load of each grid is the same with the previous calculation ?
Normalization method for reconstructing a total load curve In general, the PSPPs should generate power during peak periods and pump water to absorb surplus energy during off-peak periods. For a single power grid, the daily load curve can easily determine PSPPs operations. However, for multiple provincial power grids, determining optimal schedules of PSPPs are difficult because these PSPPs are required to respond simultaneously to multiple load demands. These multiple daily load curves are not generally synchronous in magnitude and occurring time of peak and off-peak loads. A normal idea is to merge all individual load curves into one load curve and determine the optimal generating
and pumping powers similar to that for a single power grid. However, if accumulated total load curve is dominated by the power grid with the biggest load value that could not reflect the characteristics of peak and off-peak load of other power grids. Furthermore, specified electricity contract ratios of each PSPP would affect multiple power grids. So a normalization method is proposed to reconstruct a reasonable total load curve from multiple load curves:
8 C g;t C min > g < C total ¼ PG C R g k;g k;t g¼1 C max C min g
> : PG R ¼ 1 g¼1 k;g
g
; 1 6 k 6 K; 0 6 t < T
ð16Þ
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Table 2 Reservoir constraint parameters of the four PSPPs. Plant
Tianhuangping Xiangshuijian Langyashan Tongbai
Storage limits of lower reservoir (104 m3)
Storage limits of upper reservoir (104 m3)
Begin storage of lower reservoir (104 m3)
Begin storage of upper reservoir (104 m3)
Specified final storage of upper reservoir (104 m3)
V low k;t
V low k;t
V up k;t
V up k;t
V low k;0
V up k;0
up V 0k;T
57.5 138.5 650.0 418.7
848.3 1402.2 4400.0 1283.8
30.3 302.7 508.6 104.9
871.1 1612.2 1746.8 1147.5
836.7 1338.1 2260 1230.5
246.4 561.1 685.7 220.1
246.4 561.1 685.7 220.1
Table 3 Plant constraint parameters of the four PSPPs. Plant
N output k;t
N output k;t
N input k;t
N input k;t
qoutput k;t
qoutput k;t
qinput k;t
qinput k;t
DN output k
DN input k
tgk
tsk
Tr
E0koutput
Tianhuangping Xiangshuijian Langyashan Tongbai
300 230 147 300
1800 920 588 1200
315 275 165 312
1890 1100 660 1248
142.3 137.4 130 142.3
853.8 549.6 520 569.2
118.4 143.0 127 118.4
710.4 572 508 473.6
300 230 147 300
315 275 165 312
4 4 4 4
4 4 4 4
4 4 4 4
725 200 155 435
where C max ,C min g g ,C g are the maximum, minimum and mean value of the remaining load Cg,t of the gth power grid, respectively. C total is k;t the total remaining load for the kth PSPP. Eq. (16) aims to minimize the effect of load magnitude to retain the load characteristics in the peak and off-peak periods for multiple provincial power grids. Heuristic search method for determining generating and pumping power of PSPP After a total load curve for the kth PSPP is created, the schedules of this PSPP could be determined similar to that for a singer power. This section is primarily to determine the optimal generating and pumping powers for the kth PSPP. As mentioned above, a PSPP should generate power during peak periods and pump water during off-peak periods. So the optimal generating and pumping powers of the kth PSPP could be determined by the following heuristic method. Detailed procedures of the heuristic method. Step 1: Set the iteration index n2 = 0. Step 2: Determine the optimal pumping power. Search the minP v k total imum sum of vk consecutive load points f ¼ min ð tþ t¼t C k;t Þ. vk 06t
is the minimum durations between operation and shutdown as in the Eqs. (11) and (12), which is 4 periods in this paper. So the total total minimum sum of four consecutive load points (C total k;t 1 , C k;t 2 , C k;t 3 ,
C total k;t 4 ) needs to be selected in the total load curve, where t1, t2, t3, t4 represent period numbers. Next, the initial pumping power of the kth PSPP during these periods is increased by a Table 4 The specified electricity contracts ratio Rk,g for different power grids. Plantnpower gird
SHPG
JSPG
ZJPG
AHPG
FJPG
Tianhuangping Xiangshuijian Langyashan Tongbai
0.34 0.5 0.5 0.42
0.27 0 0 0
0.27 0 0 0.58
0.12 0.5 0.5 0
0 0 0 0
specified step DN input and the remaining total load curve is k 8 input < N k;t ¼ N k;t þ ðDN k Þ; N k;t < 0 total total input updated, namely , as shown : C k;t ¼ C k;t þ DN k t ¼ t1 ; t2 ; t3 ; t4 in Fig. 6(b). Step 3: Similarly, search the maximum sum of four consecutive load points in the total load curve. Then initial generating power of the kth PSPP in these periods is increased by a specified step DN output and the remaining total load curve is updated, 8 k output ; N k;t > 0 < N k;t ¼ N k;t þ DN k total output namely C total , as shown in Fig. 6(c). : k;t ¼ C k;t DN k t ¼ w1 ; w2 ; w3 ; w4 Step 4: Calculate the water balance in upper and lower reservoirs using the Eqs. (2)–(4), (6)–(9). Step 5: If the PSPP k satisfies the constraints in Eqs. (5) and (10), the iteration procedure is terminated. Otherwise, set n2 = n2 + 1 and search again the optimal pumping and generating periods in the remaining total load curve as shown in Fig. 6(d), repeating from Step 2. Combination optimization method for allocating generating and pumping powers among multiple provincial power grids When a feasible power schedule is obtained (Fig. 6(e)), it should be allocated among multiple provincial power grids subject to multilateral electricity contracts. The objective is to minimize the system-wide load differences between peak and off-peak to smooth the remaining load curves for thermal systems. Mathematically, this complex nonlinear multiobjective optimization problem is minimizing the variance of the remaining loads as defined in Eq. (1). Here, a combination optimization method is presented to address the problem. For a selected PSPP k, its generating power or pumping power are first divided into a series of electricity equal pieces, as shown in Fig. 6(f). These small pieces are numbered and allocated to the associated power grid subject to electricity contracts. The initial allocating results are shown in Fig. 6(g). Then
Table 5 The rest parameters. Rest parameters
K
G
J
T
Dt
wag
t1, t2, t3, t4
w1, w2, w3, w4
Values
4
4
24
96(¼ 24 h)
1(¼ 0:25 h)
1/4
Only symbols
Only symbols
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Fig. 7. A comparison of remaining loads from the optimization model and real data of a typical daily load in the summer, case 1.
all the possible allocating combinations of these small pieces are evaluated to find the best performed combination based on the Eq. (1). Allocating pumping power of the kth PSPP among multiple provincial power grids is similar. Two problems exist in the combination method. Firstly, it is not feasible to list all possible combinations at the same time. This paper exchanges only some selected pieces among multiple provincial power grids in each iteration. For example, the four power grids are included, single piece for each power grid is selected to exchange. According to permutation and combination principle, there are A44 ¼ 24 different combinations. Secondly, it is difficult to evaluate the advantages and limitations of each combination because Eq. (1) includes G measures which minimize the variance of the remaining loads for G power grids. The above procedure is an evaluation problem with limited alternatives and multiple objectives. In this paper, a fuzzy optimal method [30–32] which can obtain the optimal rank of alternatives by the membership degree of alternatives, is employed to deal with Eq. (1) [33–35]. The objective function in this step is expressed as:
8 2 91 G X > > max > > a 1 Dg Dg;j > > > > w max min g > > D D < = g g g¼1 F ¼ Max 1 þ 2 G > 16j6J > X > > Dmax Dg;j g > > > > wag Dmax min > > D : ; g g
ð17Þ
g¼1
where F is the maximum membership degree among J alternatives, Dg,j is the variance of the remaining load Cg,t in the gth power grid for the candidate solution j. Dmax , Dmin are the maximum and ming g imum Dg,j in all candidate solutions. wag is the weight coefficient. To maintain the same importance of shaving peak for any power grid, we choose the equal weight coefficient wag ¼ 1=G. By sorting the values of membership degree of J alternatives in descending order, the optimal order of alternatives can be obtained. Consequently, a better combination can be obtained with an exchange being completed. Replacing different pieces of combination and repeating the above procedure, we can finally get an overall optimal allocating schedules.
Numerical results The proposed approach has been applied to the four PSPPs in order to shave the peak load and fill the off-peak load for four provincial power grids in the ECPG. Our model has been implemented in a decision support software which was developed for ECPG’s dispatching center and used to suggest schedules each day. Input data Table 1 shows the basic information of the four PSPPs. Table 2 shows the upper and lower reservoirs constraint parameters of
Table 6 The results comparison from the optimization model and real data of a typical day in the summer, case 1. Scenario
– Optimize Real
Load
Original Remaining (MW) Decrease (%) Remaining (MW) Decrease (%)
Mean squared deviation
Load differences between peak and off-peak
SHPG
JSPG
ZJPG
AHPG
SHPG
JSPG
ZJPG
AHPG
3632 2830 22.1 2887 20.5
3828 3580 6.5 3597 6.0
3958 3300 16.6 3387 14.4
1909 1505 21.2 1526 20.1
10,491 7623 27.3 8454 19.4
12,041 10,976 8.8 11,381 5.5
13,062 10,130 22.4 11,409 12.7
6125 4900 20.0 5327 13.0
Note: Decrease (%) = (Original-Remaining)/Original.
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Fig. 8. Water level and generating and pumping power profile of PSPPs from the optimization model, case 1.
the four PSPPs for Eqs. (2)–(5). Table 3 shows the plant constraint parameters of the four PSPPs for Eqs. (6)–(13) and Section ‘Heuristic search method for determining generating and pumping power of PSPP’. Table 4 shows specified electricity contract ratio Rk,g param-
eters of the four PSPPs for Eqs. (15), (16) and Section ‘Heuristic search method for determining generating and pumping power of PSPP’. Table 5 shows the rest parameters for this numerical study.
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The time horizon is 96 quarter-hourly intervals (one day). Two different daily load curves are used to test the algorithm. One is the typical quarter-hourly load curve in summer where load demands of different power grids largely differ in magnitude and occurring times of the peak and off-peak loads. Another is the typical quarter-hourly load curve in winter where the peak and off-peak loads of different power grids roughly occur synchronously. Two important statistical indicators are analyzed and discussed in the following two cases: one is the mean squared deviation of remaining loads, and other is the load difference between peak and off-peak. Here, the remaining load of FJPG is not analyzed because the four PSPPs do not provide power to it in practice. Case study 1 This case uses the typical load curve in summer, as shown in Fig. 7. The lowest values of the original loads in SHPG, JSPG, ZJPG and AHPG occur between 4:15 am and 6:15 am, but the highest values occur differently at 13:30 pm, 21:15 pm, 13.15 pm and 20:45 pm, respectively. The magnitudes of the original load values also greatly differ. The maximum load difference between peak and off-peak in SHPG, JSPG and ZJPG are 10491 MW, 12,041 MW, and 13,062 MW, but only 6125 MW in AHPG. An overall comparison about the mean squared deviation and the difference of
remaining load between peak and off-peak is summarized in Table 6. First of all, the optimized remaining load is compared with the original load in Table 6. The mean squared deviations of the remaining load for SHPG, ZJPG and AHPG are far smaller than their respective original ones. According to statistical theory, the remaining load profiles of the three power grids are smoother than the original loads. Correspondingly, maximum differences of the remaining load between peak and off-peak are also greatly reduced for the three power grids by 27.3%, 22.4%, and 20% respectively. Statistically, the results for the JSPG in Table 6 are comparatively poor, primarily due to the low specified electricity contracts ratio. Secondly, the optimized remaining load is compared with the real data. Our model produces smaller mean squared deviation and load difference between peak and off-peak than the real data (Table 6). This indicates that the optimization model deals better with the load differences of different power grids over the entire scheduling horizon to coordinate the loads among multiple provincial power grids through the flexible regulation performances of each PSPP. In addition, Fig. 8 presents the water level profile and generating and pumping powers of each PSPP from our optimization model in one day. All constraints including reservoirs and plant operations are satisfied. This illustrates that optimization results are reasonable and acceptable.
Fig. 9. A comparison of remaining loads from the optimization model and real data of a typical daily load in the winter, case 2.
Table 7 The results comparison from the optimization model and real data of a typical day in the winter, case 2. Scenario
– Optimize Real
Load
Original Remaining (MW) Decrease (%) Remaining (MW) Decrease (%)
Mean squared deviation
Load differences between peak and off-peak
SHPG
JSPG
ZJPG
AHPG
SHPG
JSPG
ZJPG
AHPG
1476 660 55.3 680 53.9
4049 3749 7.4 3807 6.0
2460 1862 24.3 1872 23.9
1932 1445 25.2 1500 22.4
4633 2601 43.9 2591 44.1
13,776 12,878 6.5 12,950 6.0
7836 5361 31.6 5939 24.2
6602 4697 28.9 5183 21.5
Note: Decrease (%) = (Original-Remaining)/Original.
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Case study 2 This case study represents another normal situation in the winter. Fig. 9 illustrates a typical daily load curve in this season where the occurring times of the peak and off-peak load of different power grids are roughly synchronous. From Fig. 9, the maximum load differences between peak and off-peak are also greatly reduced for SHPG, ZJPG and AHPG. Correspondingly, the mean squared deviations of the remaining loads for SHPG, ZJPG and AHPG are far smaller than their respective original ones. Similar to Table 6, an overall comparison of the mean squared deviation and the load difference between peak and off-peak is summarized in Table 7. Detailed comparisons of the optimized remaining load and the real data are not included here. The validity and feasibility of the presented method are demonstrated again. In summary, although great differences exist between the typical daily load curves for different power grids in winter and summer, the developed method can effectively shave the peak loads and fill the off-peak loads for multiple provincial power grids simultaneously. So the proposed model and method can solve the practical short-term peak shaving operation problem among multiple provincial power grids. Conclusions The increasing peak load demand is a great challenge for most power grids in China, especially for the coastal regions and economic heartlands. PSPP was perceived as an important complement to other baseload power plants for providing peaking power. Many PSPPs with large capacities were established in the ECPG for such purpose. These PSPPs are directly operated by the ECPG to shave the peak load and fill the off-peak load for its provincial power grids. However, operating these PSPPs is a new problem that few researches have analyzed. The paper addresses the real demand of peak shaving operation for multiple provincial power grids with PSPPs. A three-step hybrid algorithm is presented in this paper to determine day-ahead quarter-hourly schedules and to allocate the schedules among multiple provincial power grids. Two case studies including different typical quarter-hourly load curves are used to test the algorithm. The results show that the presented model can effectively achieve the goal of shaving the peak load and filling the off-peak load for multiple provincial power grids according to different load demands. The algorithm has been embedded into a newly developed decision support system that is currently being used by operators of the ECPG to make day-ahead quarter-hourly generation and pumping schedules.
Acknowledgements This research was supported by National Science Fund for Distinguished Young Scholars (No. 51025934) and National Natural Science Foundation of major international cooperation (No. 51210014). References [1] Deane JP, Ó Gallachóir BP, McKeogh EJ. Techno-economic review of existing and new pumped hydro energy storage plant. Renew Sustain Energy Rev 2010;14(4):1293–302. [2] Yang Chi-Jen, Jackson Robert B. Opportunities and barriers to pumped-hydro energy storage in the United States. Renew Sustain Energy Rev 2011;15(1):839–44.
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Contents lists available at ScienceDirect
Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
Short-term peak shaving operation for multiple power grids with pumped storage power plants Chun-Tian Cheng ⇑, Xiong Cheng, Jian-Jian Shen, Xin-Yu Wu Institute of Hydropower and Hydroinformatics, Dalian University of Technology, Dalian 116024, China
a r t i c l e
i n f o
Article history: Received 5 April 2014 Received in revised form 7 December 2014 Accepted 9 December 2014 Available online 27 December 2014 Keywords: Pumped storage Peak shaving Multiple power grids Fuzzy sets
a b s t r a c t The East China Power Grid (ECPG) is the biggest regional power grid in China. It has the biggest installed capacity of pumped storage power plants (PSPPs) and is responsible to coordinate the operation of its five provincial power grids. A recent challenge of coordinating operations is using PSPPs to absorb surplus energy during off-peak periods and generate power during peak periods. Differing from the traditional operations of single power grids, however, the PSPPs are required to respond to load demands from multiple provincial power grids simultaneously. This paper develops a three-step hybrid algorithm for the day-ahead quarter-hourly schedules of PSPPs to meet load demands of multiple provincial power grids. A normalization method is first proposed to reconstruct a total load curve to deal with the load differences of multiple provincial power grids, and to reflect the effect of specified electricity contract ratio on multiple provincial power grids. Secondly, a heuristic search method is presented to determine the generating and pumping powers of PSPP. Thirdly, a combination optimization method is used to allocate the determined generating and pumping powers among multiple provincial power grids to smooth the individual remaining load curve for their thermal systems. Two case studies with greatly different load demands are used to test the proposed algorithm. The simulation results show that the presented method can effectively achieve the goal of shaving the peak load and filling the off-peak load for multiple provincial power grids. Ó 2014 Elsevier Ltd. All rights reserved.
Introduction China’s electricity demand has a huge expansion during the past three decades with its growing economy. The East China Power Grid (ECPG), which is the biggest regional power grid in China, consists of five provincial power grids in eastern China, in Fig. 1. Its maximum electricity load exceeded 184.5 GW in 2012, about 26 times larger than in 1982. Its maximum load difference between peak and off-peak has also largely increased by about 4.59 times, from 11.96 GW in 2002 to 54.86 GW in 2012. Fig. 2 shows the total load demand of ECPG, and individual load demands of multiple provincial power grids on December 24, 2012. The maximum load difference of ECPG between peak and off-peak has reached 54.86 GW (29.7% of maximum electricity load). This expansion of load demands brings significant challenges to the ECPG, since over 84.8% of its total installed capacity (about 178.9 GW) is thermal power that has low effective capacity of regulating peak loads. ⇑ Corresponding author. Tel.: +86 0411 84708768. E-mail addresses: [email protected] (C.-T. Cheng), [email protected] (X. Cheng), [email protected] (J.-J. Shen), [email protected] (X.-Y. Wu). http://dx.doi.org/10.1016/j.ijepes.2014.12.043 0142-0615/Ó 2014 Elsevier Ltd. All rights reserved.
Hydropower plants are unevenly distributed among multiple provincial power grids in ECPG. From the provincial energy structures in Fig. 3, the Fujian Power Grid has 32.4% of hydropower and little pressure on peak power demand, while the other four provincial power grids face severe power shortages for peak demand. The pressing demand for peak power resulted in a rapid establishment of pumped storage power plants (PSPPs) [1,2] in the ECPG. The PSPPs owned by the ECPG are the biggest in China [3], with a total installed capacity of 7.12 GW (35.6% of nation’s total PSPPs capacity). Table 1 shows the details of PSPPs in the ECPG. Among the established PSPPs, the four bigger plants including Tianhuangping, Xiangshuijian, Langyashan and Tongbai are directly operated by the dispatching center of the ECPG to absorb surplus energy from four provincial power grids (SHPG, JSPG, ZJPG and AHPG) and then provide peak power for these power grids. The other PSPPs are operated by different provincial power grids for meeting their local load demands respectively. This paper focuses on the former one of operating the four bigger PSPPs. A system-wide practical problem is how to determine the day-ahead quarter-hourly schedules for these PSPPs to coordinate extremely different peak and off-peak load demands among multiple provincial power grids.
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571
Nomenclature E0koutput
specified total energy generation target (MW h)
A. Acronyms ECPG East China Power Grid PSPPs pumped storage power plants PSPP a pumped storage power plant SHPG Shanghai Power Grid JSPG Jiangsu Power Grid ZJPG Zhejiang Power Grid AHPG Anhui Power Grid FJPG Fujian Power Grid
Rk,g
specified electricity contract ratio
tgk
minimum duration periods of operation
tsk
minimum duration periods of shutdown
Tr
extreme point duration periods
wag
weight coefficient
B. Indices k g t j n1 n2 K G T J
Cg,t
remaining load demand (MW)
Cg
mean of the remaining load (MW)
C max g
maximum remaining load (MW)
C min g C total k;t
maximum remaining load (MW)
Nk,t Nk,t
generating power (positive values, MW) pumping power (negative values, MW)
Ngk;t
supply power for gird (positive values, MW)
Ngk;t Dg Dg,j
absorb power from grid (negative values, MW) variance of the remaining load candidate solution
Dmax g
maximum candidate solutions minimum candidate solutions
D. Variables Lg,t original load demand (MW)
PSPP or upper reservoir index provincial power grid index time period index candidate solution index iteration index iteration index number of PSPPs number of provincial power grids scheduling horizon number of candidate solutions
C. Parameters and constants Dt time period duration (=0.25 h).
total remaining load (MW)
qoutput k;t qoutput k;t qinput k;t qinput k;t V up k;t V up k;t
maximum water discharge limits (m /s)
Dmin g
minimum water discharge limits (m3/s)
W ag
weight coefficient
V up k;t V low k;t
water storage of upper reservoir (m3)
qk,t
water discharge (positive values, m3/s)
qk,t
pumping flow (negative values, m3/s) water level of upper reservoir (m)
V low k;t
maximum storage of lower reservoir (m3)
V low k;t
minimum storage of lower reservoir (m3)
Z up k;t Z low k;t Ht;tþ1 k
V 0up k;T
final storage target of upper reservoir (m3)
maximum extreme point duration periods
Noutput k;t Noutput k;t Ninput k;t
maximum generating power (MW)
sk;t sk,t
minimum generating power (MW)
foutput() generating power function
maximum pumping power (MW)
finput()
pumping power function
up f zm ðÞ low f zm ðÞ
water level and storage function of upper reservoir
3
maximum pumping flow limits (m3/s) minimum pumping flow limits (m3/s) maximum storage of upper reservoir (m3) 3
minimum storage of upper reservoir (m )
Ninput k;t
minimum pumping power (MW)
DN output k DN input k
maximum ramping capacity in generating model (MW)
water storage of lower reservoir (m3)
water level of lower reservoir (m) average gross head minimum extreme point duration periods
water level and storage function of lower reservoir
maximum ramping capacity in pumping model (MW)
Different from the traditional operations of PSPPs for a single power grid [4–7], the PSPPs in ECPG are usually required to shave the peak load and fill the off-peak load (Fig. 4) for multiple provincial power grids according to multilateral electricity contracts. It is difficult to coordinate generating power and pumping power of PSPPs to respond promptly to different load demands because of the strong electrical coupling, inconsistent load demand with largely varying magnitude and peak and off-peak periods among multiple provincial power grids. Besides, the traditional reservoir and hydropower plant constraints and multilateral electricity contracts are coupled across the entire scheduling horizon, which make it more difficult to find rational and efficient operational schedules for PSPPs. Optimization of PSPP scheduling is an important area that has attracted many researches. Various methods have been developed to resolve the problem, including Linear Programming (LP) [6],
Mixed Integer Programming (MIP) [8,9], Dynamic Programming (DP) [10–12], Lagrangian Relaxation algorithm (LR) [9], Artificial intelligence algorithm [13–15], practical operation strategies [16–19] and commercial software [20,21]. However, these methods have some limits. For instance, LP, MIP and commercial software may not guarantee the accuracy of optimized results due to the linearization or piecewise linearization of nonlinear objective functions and constraints. DP is not an efficient method for solving short-term operation of multiple PSPPs among multiple power grids because of the acknowledged curse of dimensionality [22,23]. A similar study has confirmed the inefficiency of DP [10] that uses DP method to obtain the optimal scheduling of one PSPP in combination with several interconnected power systems. LR is not applicable to deal with dynamic transition among operating states (generating, pumping and idle) and optimizing multipliers, and is not an effective method for our problem. Furthermore, many
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this reason, this paper develops a three-step hybrid algorithm to optimize day-ahead quarter-hourly operation of PSPPs among multiple provincial power grids. The three-step hybrid algorithm is carried out for each PSPP one after another repeatedly, until the termination condition is satisfied. Two case studies with significantly different load demands are used to test the proposed method. Such simulation results show that the presented method can effectively achieve the goal of shaving the peak load and filling the off-peak load for multiple provincial power grids. Problem formulations Objective function
Fig. 1. The geographical distribution of the five subsidiary power grids in eastern China, and schematic representation of the PSPP providing to and absorbing energy from the MPPG.
constraints in quarter-hourly PSPP scheduling are not considered in previous literatures that have considerably discussion on hourly PSPP scheduling only. Complex constraints and requirements of PSPPs operation pose a real challenge for most optimization methods to solve this practical engineering problem. In recent years, heuristic methods have been widely applied to complex real-world engineering problems which are difficult to be solved by classical optimization methods [7,24,25]. Although heuristic methods cannot guarantee convergence to the global optimal solution, they are usually capable of searching acceptable and practical solutions depended on rules-of-thumb, experience, rules information in real world’s engineering problems [26]. Compared with traditional technical methods, the heuristic method is promising, particularly well suited for industrial applications. For
11:15
Load(MW) 170500
ECPG
Load(MW) 23500
As mentioned above, the PSPPs in the ECPG are directly operated by the dispatching center of the ECPG and mainly used to shave the peak load and fill the off-peak load (Fig. 4) for multiple provincial power grids. Generally, A PSPP is typically equipped with reversible pumps/generators connecting upper and lower reservoirs. The pumps typically operate during off-peak periods, pumping water from the lower reservoir to the upper one to absorb surplus energy. During periods of high electricity demand (peak periods), water is released from the upper reservoir to generate peak power. In mathematical terms, a variance function of remaining load series of each power grid can be utilized to describe the optimization objective as following:
8 T h i2 X > > > min Dg ¼ C g;t C g > < t¼1 ! g ¼ 1; 2 G K > X > g > > C g;t ¼ Lg;t Nk;t : k¼1
Eq. (1) is aimed to ensure the equivalence of the remaining load of each provincial power grid at every period to the greatest extent and to smooth the remaining loads for respective thermal systems [27]. N gk;t represents power supply (positive values) or to power absorption (negative values) at period t, in MW. If N gk;t > 0, the power flow is transferred from the kth PSPP to the gth power grid to shave the peak load. Otherwise, the power flow is transferred from the gth power grid to the kth PSPP to absorb surplus energy during off-peak periods. Lg,t and Cg,t are the original and remaining load for the gth power grid at period t, in MW. C g and Dg are the mean and variance of remaining load Cg,t for the gth power grid. K
10:45
Shanghai
21500
160500
140500
17500
54,857 MW
130500
15500
120500
13500
110500 3:15
6:15
Load(MW)
9:15 12:15 15:15 18:15 21:15 Time
11:10
46100
Zhejiang
55000
15,641 MW 50000
0:15
Load(MW) 20200
3:15
6:15
Anhui
9:15 12:15 15:15 18:15 21:15 Time
18:30
19200
18,134 MW
6,173 MW
16200 15200
31100
13200 0:15
3:15
6:15
9:15 12:15 15:15 18:15 21:15 Time
Load(MW) 24000
3:15
6:15
Fujian
9:15 12:15 15:15 18:15 21:15 Time
18:15
18000
8,060 MW
16000
14200
26100
0:15
20000
17200
36100
45000
22000
18200
41100
Jiangsu
11:00
9,480 MW
11500 0:15
Load(MW) 65000 60000
19500
150500
ð1Þ
14000 0:15
3:15
6:15
9:15 12:15 15:15 18:15 21:15 Time
0:15
3:15
Fig. 2. The total load demand of ECPG, and load demand of MPPG on December 24, 2012.
6:15
9:15 12:15 15:15 18:15 21:15 Time
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Installed Capacity (MW) Thermal Hydropower Nuclear Wind Pump Other Total
SHPG
JSPG
ZJPG
AHPG
FJPG
21205.7
64159
22535.5 474
24855 11348
269.35
2000 1946 1100
38524 1649 320 140
295.5 80
40633
23385
1132 1200 174 38709
0 21475.05
69205
Dispatching Center(DCECPG) 7580 1207.2 4077 4600 17464.2
ECPG 178859.2 14678.2 6397 3642.85 7120 174 210871.25
Note: The above power sources are only operated by central or provincial dispatch centers. Don’t include the power sources operated by municipal dispatch centers. Fig. 3. Electric power structure of different dispatching sectors in ECPG, 2012. Table 1 All PSPPs in the ECPG by the end of 2012. Plant
Dispatching sector
Turbine capacity (MW) (single capacity units)
Pump capacity (MW) (single capacity units)
Type
Tianhuangping Xiangshuijian Langyashan Tongbai Shahe Yixing Xianghongdian Xikou Xikou II Xianyou
Dispatching Dispatching Dispatching Dispatching JSPG JSPG AHPG ZJPG ZJPG FJPG
300 6 = 1800 230 4 = 920 147 4 = 588 300 4 = 1200 51 2 = 102 250 4 = 1000 40 2 = 80 40 2 = 80 30 2 = 60 300 4 = 1200
315 6 = 1890 275 4 = 1100 165 4 = 660 312 4 = 1248 58 2 = 116 250 4 = 1000 40 2 = 80 40 2 = 80 30 2 = 60 300 4 = 1200
Pure/daily Pure/daily Pure/daily Pure/daily Pure/daily Pure/daily Mixed/multi-yearly Pure/daily Pure/daily Mixed/weekly
center center center center
and G are the total number of PSPPs and power grids, respectively. T is the scheduling horizon. Constraints The problem here involves reservoirs, plant operations and system control. Below are the specific constraints regarding each component. (1) The operational reservoir constraints:
8 up up up > < V k;t ¼ f zm Z k;t > : V low ¼ f low Z low zm k;t k;t 0 up V up k;T ¼ V k;T
ð4Þ
ð5Þ
up up up where V up k;t ,V k;tþ1 ,V k;t ,V k;t are the beginning, ending, minimum and maximum water storage of the upper reservoir in the kth PSPP at
Eq. (2) is water balance of the upper and lower reservoirs. Eq. (3) shows the maximum and minimum storages of the upper and lower reservoirs. Eq. (4) illustrates the relation between water level and storage for upper and lower reservoirs. And Eq. (5) is the specified demand target for the upper reservoir storage at the final period.
8 up up < V k;tþ1 ¼ V k;t qk;t Dt :
low V low k;tþ1 ¼ V k;t þ qk;t Dt
8 up up up < V k;t 6 V k;t 6 V k;t :
low low V low k;t 6 V k;t 6 V k;t
ð2Þ
ð3Þ Fig. 4. Schematic diagram of shaving the peak load and filling the off-peak load with PSPP.
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low low low period t, respectively, in m3. V low k;t ,V k;tþ1 ,V k;t ,V k;t are the beginning, ending, minimum and maximum water storage of the lower reserlow voir in the kth PSPP at period t, respectively, in m3. Z up k;t ,Z k;t are the water level of upper and lower reservoir in the kth PSPP at period t, respectively. qk,t is the water discharge (positive values) or pumping up flow (negative values) in the kth PSPP at period t, in m3/s. f zv ðÞ, low f zv ðÞ are the functional relationship of water storage and water up level. V 0k;T is the required water storage target of the upper reservoir in the kth PSPP at the final period. Duration of each time period in this study is Dt = 0.25 h. (2) The operational plant constraints Eq. (6) calculates the average gross water head of the upper and lower reservoirs. Eq. (7) shows the generating power (namely output) or pumping power (namely input) in the kth PSPP, which can be expressed as a function of the discharge or pumping water flow and average water head. The coupling relationship is very complex and should not simply be assumed as linear or piecewise linear function in modeling [28]. Particularly in pure PSPP with a small available storage capacity, operating efficiency is very sensitive to water head [22]. The minimum and maximum power capacities are in Eq. (8). The minimum and maximum discharge and pumping water inflows are in Eq. (9). Specified total energy demand over the entire scheduling horizon is in Eq. (10). This constraint is hardly satisfied in this paper. The maximum ramping capacity is in Eq. (11). The minimum duration between operation and shutdown is required in Eq. (12). The minimum lasting durations for local maximum and minimum powers are in Eq. (13) and in Fig. 5. This requirement on generating power and pumping power of the kth plant is to avoid frequent power fluctuation.
Ht;tþ1 ¼ k
Z up k;t
2
( N k;t ¼ (
(
þ
Z up k;tþ1
Z low k;t
þ 2
Z low k;tþ1
f output ðHt;tþ1 ; qk;t Þ; k
if
f input ðHkt;tþ1 ; qk;t Þ;
ð6Þ
qk;t P 0 if
ð7Þ
qk;t < 0
Noutput 6 Nk;t 6 Noutput ; if N k;t > 0 k;t k;t input input Nk;t 6 Nk;t 6 Nk;t ; if Nk;t < 0 qoutput k;t qinput k;t
qoutput ; k;t
6 qk;t 6 6 qk;t 6 qinput ; k;t
if
qk;t > 0
if
qk;t < 0
ð8Þ
ð9Þ
Eoutput ¼ E0koutput k
if Nk;ttsk > 0; Nk;t > 0 if Nk;ttgk ¼ 0; Nk;t ¼ 0
sk;t P T r sk;t P T r
ð12Þ
ð13Þ
where Hkt;tþ1 is the average gross water head between the upper and lower reservoirs in the kth PSPP at period t. Nk,t is the generating power (positive values) or pumping power (negative values) in the kth PSPP at period t, in MW. N output ,Noutput are the generating k;t k;t input power limits in the kth PSPP at period t, in MW. N input are k;t ,N k;t the pumping power limits in the kth PSPP at period t, in MW. input qoutput ,qoutput are the water discharge limits, in (m3/s). qinput k;t k;t k;t ,qk;t output 3 are the pumping water flow limits, in (m /s) DNk is the maximum ramping capacity in generating mode in the kth PSPP at period t, in MW; DN input is the maximum ramping capacity in pumping k mode in the kth PSPP at period t, in MW. tgk, tsk are the minimum duration periods of operation and shutdown in the kth PSPP. sk;t , sk,t are the minimum duration periods requirement in local maximum and minimum powers in the kth PSPP. (3) The operational power system constraints For any time period, the power balance between the kth PSPP and multiple provincial power grids is in Eq. (14). G X Ngk;t ¼ Nk;t ; 0 6 t < T
ð14Þ
g¼1
For the entire scheduling horizon, the energy balance between the kth PSPP and multiple provincial power grids is in Eq. (15). Rk,g is the electricity contract ratio between the kth PSPP and the gth power grid.
8 PT P Ng Dt ¼ Rk;g Tt¼0 Nk;t Dt; Ngk;t > 0; Nk;t > 0 > > < Pt¼0 k;t PT T g g t¼0 N k;t Dt ¼ Rk;g t¼0 N k;t Dt; N k;t < 0; N k;t < 0 > > : PG g¼1 Rk;g ¼ 1
ð15Þ
Eqs. (14) and (15) are hard constraints to guarantee the power and energy balance between PSPPs and multiple provincial power grids. In this paper, tie-line maximum and minimum available transfer capability limit, frequency, voltage stability and transmission losses issues of are not considered.
ð10Þ Solution methodologies
*HQHUDWLQJ SRZHU 0:
( Nk;t Nk;t1 6 DNoutput ; if Nk;t > 0; Nk;t1 > 0 k Nk;t Nk;t1 6 DNinput ; if Nk;t < 0; Nk;t1 < 0 k
3XPSLQJ SRZHU 0:
(
ð11Þ
/RFDOPD[LPXP JHQHUDWLQJSRZHU
/RFDOPD[LPXP JHQHUDWLQJSRZHU
τ ktmax ,
τ ktmax ,
τ ktmin ,
τ ktmax ,
/RFDOPLQLPXP JHQHUDWLQJSRZHU
/RFDOPD[LPXP SXPSLQJSRZHU
3HULRGV Fig. 5. The explanation of minimum duration periods requirements of extreme points.
Different from the conventional operations of PSPPs for a single power grid [4,6,7,13,19,29]. The PSPPs in this paper are required to simultaneously shave the peak loads and fill the light loads for multiple provincial power grids according to multilateral electricity contracts. The primary characteristic of this problem is that each PSPP is not facing a single load curve, but multiple load curves with huge differences in magnitude, peak and off-peak periods. The difference of load demands adds challenges for determining feasible generating and pumping schedules for each PSPP. In addition, satisfying the multilateral electricity contracts in the process of electric power distribution among multiple provincial power grids makes it more difficult to solve problem. Due to the complexity of the present problem, a three-step hybrid algorithm is prosed in this paper to optimize day-ahead quarter-hourly operation of PSPPs among multiple provincial power grids. This hybrid algorithm consists of three components: a normalization method, a heuristic search method and a combination optimization method. The whole procedure of the three-step hybrid algorithm is in Fig. 6 (see more details in the following subsections).
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C.-T. Cheng et al. / Electrical Power and Energy Systems 67 (2015) 570–581
Start The iteration n1=0 The plant k=1
Cktotal ,t
Section 3.1: Reconstructing a total load curve, Fig.(a) Section 3.2: Establishing the kth PSPP schedules
(a)
The iteration n2=0
Generating power
Pumping power
Searching the optimal Pumping power in the total load curve, Fig. (b) ΔN koutput
Searching the optimal generating power In the total load curve, Fig. (c) Using the Eq.(2)-(4), (6)-(9) to calculate the water balance
n2=n2+1
1R
WaW
ΔN kinput
Z Z
( c )a
(b)
Next optimal generating periods
Conform to the Eq.(5) and (10) Next optimal pumping periods
(d)
(e)
Section 3.3: Allocating the kth PSPP schedules Generating power or pumping one is divided into a series of electricity equal piece, Fig.(f) these small pieces are allocated to each power grid subject to electricity contracts, Fig.(g)
(f)
exchange the allocating combination of these small pieces 1R
the optimal combination?
k=k+1
1R
(g)
N!."
n1=n1+1
1R
The remaining load of each grid is the same with the previous calculation ?
Normalization method for reconstructing a total load curve In general, the PSPPs should generate power during peak periods and pump water to absorb surplus energy during off-peak periods. For a single power grid, the daily load curve can easily determine PSPPs operations. However, for multiple provincial power grids, determining optimal schedules of PSPPs are difficult because these PSPPs are required to respond simultaneously to multiple load demands. These multiple daily load curves are not generally synchronous in magnitude and occurring time of peak and off-peak loads. A normal idea is to merge all individual load curves into one load curve and determine the optimal generating
and pumping powers similar to that for a single power grid. However, if accumulated total load curve is dominated by the power grid with the biggest load value that could not reflect the characteristics of peak and off-peak load of other power grids. Furthermore, specified electricity contract ratios of each PSPP would affect multiple power grids. So a normalization method is proposed to reconstruct a reasonable total load curve from multiple load curves:
8 C g;t C min > g < C total ¼ PG C R g k;g k;t g¼1 C max C min g
> : PG R ¼ 1 g¼1 k;g
g
; 1 6 k 6 K; 0 6 t < T
ð16Þ
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C.-T. Cheng et al. / Electrical Power and Energy Systems 67 (2015) 570–581
Table 2 Reservoir constraint parameters of the four PSPPs. Plant
Tianhuangping Xiangshuijian Langyashan Tongbai
Storage limits of lower reservoir (104 m3)
Storage limits of upper reservoir (104 m3)
Begin storage of lower reservoir (104 m3)
Begin storage of upper reservoir (104 m3)
Specified final storage of upper reservoir (104 m3)
V low k;t
V low k;t
V up k;t
V up k;t
V low k;0
V up k;0
up V 0k;T
57.5 138.5 650.0 418.7
848.3 1402.2 4400.0 1283.8
30.3 302.7 508.6 104.9
871.1 1612.2 1746.8 1147.5
836.7 1338.1 2260 1230.5
246.4 561.1 685.7 220.1
246.4 561.1 685.7 220.1
Table 3 Plant constraint parameters of the four PSPPs. Plant
N output k;t
N output k;t
N input k;t
N input k;t
qoutput k;t
qoutput k;t
qinput k;t
qinput k;t
DN output k
DN input k
tgk
tsk
Tr
E0koutput
Tianhuangping Xiangshuijian Langyashan Tongbai
300 230 147 300
1800 920 588 1200
315 275 165 312
1890 1100 660 1248
142.3 137.4 130 142.3
853.8 549.6 520 569.2
118.4 143.0 127 118.4
710.4 572 508 473.6
300 230 147 300
315 275 165 312
4 4 4 4
4 4 4 4
4 4 4 4
725 200 155 435
where C max ,C min g g ,C g are the maximum, minimum and mean value of the remaining load Cg,t of the gth power grid, respectively. C total is k;t the total remaining load for the kth PSPP. Eq. (16) aims to minimize the effect of load magnitude to retain the load characteristics in the peak and off-peak periods for multiple provincial power grids. Heuristic search method for determining generating and pumping power of PSPP After a total load curve for the kth PSPP is created, the schedules of this PSPP could be determined similar to that for a singer power. This section is primarily to determine the optimal generating and pumping powers for the kth PSPP. As mentioned above, a PSPP should generate power during peak periods and pump water during off-peak periods. So the optimal generating and pumping powers of the kth PSPP could be determined by the following heuristic method. Detailed procedures of the heuristic method. Step 1: Set the iteration index n2 = 0. Step 2: Determine the optimal pumping power. Search the minP v k total imum sum of vk consecutive load points f ¼ min ð tþ t¼t C k;t Þ. vk 06t
is the minimum durations between operation and shutdown as in the Eqs. (11) and (12), which is 4 periods in this paper. So the total total minimum sum of four consecutive load points (C total k;t 1 , C k;t 2 , C k;t 3 ,
C total k;t 4 ) needs to be selected in the total load curve, where t1, t2, t3, t4 represent period numbers. Next, the initial pumping power of the kth PSPP during these periods is increased by a Table 4 The specified electricity contracts ratio Rk,g for different power grids. Plantnpower gird
SHPG
JSPG
ZJPG
AHPG
FJPG
Tianhuangping Xiangshuijian Langyashan Tongbai
0.34 0.5 0.5 0.42
0.27 0 0 0
0.27 0 0 0.58
0.12 0.5 0.5 0
0 0 0 0
specified step DN input and the remaining total load curve is k 8 input < N k;t ¼ N k;t þ ðDN k Þ; N k;t < 0 total total input updated, namely , as shown : C k;t ¼ C k;t þ DN k t ¼ t1 ; t2 ; t3 ; t4 in Fig. 6(b). Step 3: Similarly, search the maximum sum of four consecutive load points in the total load curve. Then initial generating power of the kth PSPP in these periods is increased by a specified step DN output and the remaining total load curve is updated, 8 k output ; N k;t > 0 < N k;t ¼ N k;t þ DN k total output namely C total , as shown in Fig. 6(c). : k;t ¼ C k;t DN k t ¼ w1 ; w2 ; w3 ; w4 Step 4: Calculate the water balance in upper and lower reservoirs using the Eqs. (2)–(4), (6)–(9). Step 5: If the PSPP k satisfies the constraints in Eqs. (5) and (10), the iteration procedure is terminated. Otherwise, set n2 = n2 + 1 and search again the optimal pumping and generating periods in the remaining total load curve as shown in Fig. 6(d), repeating from Step 2. Combination optimization method for allocating generating and pumping powers among multiple provincial power grids When a feasible power schedule is obtained (Fig. 6(e)), it should be allocated among multiple provincial power grids subject to multilateral electricity contracts. The objective is to minimize the system-wide load differences between peak and off-peak to smooth the remaining load curves for thermal systems. Mathematically, this complex nonlinear multiobjective optimization problem is minimizing the variance of the remaining loads as defined in Eq. (1). Here, a combination optimization method is presented to address the problem. For a selected PSPP k, its generating power or pumping power are first divided into a series of electricity equal pieces, as shown in Fig. 6(f). These small pieces are numbered and allocated to the associated power grid subject to electricity contracts. The initial allocating results are shown in Fig. 6(g). Then
Table 5 The rest parameters. Rest parameters
K
G
J
T
Dt
wag
t1, t2, t3, t4
w1, w2, w3, w4
Values
4
4
24
96(¼ 24 h)
1(¼ 0:25 h)
1/4
Only symbols
Only symbols
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C.-T. Cheng et al. / Electrical Power and Energy Systems 67 (2015) 570–581
Fig. 7. A comparison of remaining loads from the optimization model and real data of a typical daily load in the summer, case 1.
all the possible allocating combinations of these small pieces are evaluated to find the best performed combination based on the Eq. (1). Allocating pumping power of the kth PSPP among multiple provincial power grids is similar. Two problems exist in the combination method. Firstly, it is not feasible to list all possible combinations at the same time. This paper exchanges only some selected pieces among multiple provincial power grids in each iteration. For example, the four power grids are included, single piece for each power grid is selected to exchange. According to permutation and combination principle, there are A44 ¼ 24 different combinations. Secondly, it is difficult to evaluate the advantages and limitations of each combination because Eq. (1) includes G measures which minimize the variance of the remaining loads for G power grids. The above procedure is an evaluation problem with limited alternatives and multiple objectives. In this paper, a fuzzy optimal method [30–32] which can obtain the optimal rank of alternatives by the membership degree of alternatives, is employed to deal with Eq. (1) [33–35]. The objective function in this step is expressed as:
8 2 91 G X > > max > > a 1 Dg Dg;j > > > > w max min g > > D D < = g g g¼1 F ¼ Max 1 þ 2 G > 16j6J > X > > Dmax Dg;j g > > > > wag Dmax min > > D : ; g g
ð17Þ
g¼1
where F is the maximum membership degree among J alternatives, Dg,j is the variance of the remaining load Cg,t in the gth power grid for the candidate solution j. Dmax , Dmin are the maximum and ming g imum Dg,j in all candidate solutions. wag is the weight coefficient. To maintain the same importance of shaving peak for any power grid, we choose the equal weight coefficient wag ¼ 1=G. By sorting the values of membership degree of J alternatives in descending order, the optimal order of alternatives can be obtained. Consequently, a better combination can be obtained with an exchange being completed. Replacing different pieces of combination and repeating the above procedure, we can finally get an overall optimal allocating schedules.
Numerical results The proposed approach has been applied to the four PSPPs in order to shave the peak load and fill the off-peak load for four provincial power grids in the ECPG. Our model has been implemented in a decision support software which was developed for ECPG’s dispatching center and used to suggest schedules each day. Input data Table 1 shows the basic information of the four PSPPs. Table 2 shows the upper and lower reservoirs constraint parameters of
Table 6 The results comparison from the optimization model and real data of a typical day in the summer, case 1. Scenario
– Optimize Real
Load
Original Remaining (MW) Decrease (%) Remaining (MW) Decrease (%)
Mean squared deviation
Load differences between peak and off-peak
SHPG
JSPG
ZJPG
AHPG
SHPG
JSPG
ZJPG
AHPG
3632 2830 22.1 2887 20.5
3828 3580 6.5 3597 6.0
3958 3300 16.6 3387 14.4
1909 1505 21.2 1526 20.1
10,491 7623 27.3 8454 19.4
12,041 10,976 8.8 11,381 5.5
13,062 10,130 22.4 11,409 12.7
6125 4900 20.0 5327 13.0
Note: Decrease (%) = (Original-Remaining)/Original.
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Fig. 8. Water level and generating and pumping power profile of PSPPs from the optimization model, case 1.
the four PSPPs for Eqs. (2)–(5). Table 3 shows the plant constraint parameters of the four PSPPs for Eqs. (6)–(13) and Section ‘Heuristic search method for determining generating and pumping power of PSPP’. Table 4 shows specified electricity contract ratio Rk,g param-
eters of the four PSPPs for Eqs. (15), (16) and Section ‘Heuristic search method for determining generating and pumping power of PSPP’. Table 5 shows the rest parameters for this numerical study.
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The time horizon is 96 quarter-hourly intervals (one day). Two different daily load curves are used to test the algorithm. One is the typical quarter-hourly load curve in summer where load demands of different power grids largely differ in magnitude and occurring times of the peak and off-peak loads. Another is the typical quarter-hourly load curve in winter where the peak and off-peak loads of different power grids roughly occur synchronously. Two important statistical indicators are analyzed and discussed in the following two cases: one is the mean squared deviation of remaining loads, and other is the load difference between peak and off-peak. Here, the remaining load of FJPG is not analyzed because the four PSPPs do not provide power to it in practice. Case study 1 This case uses the typical load curve in summer, as shown in Fig. 7. The lowest values of the original loads in SHPG, JSPG, ZJPG and AHPG occur between 4:15 am and 6:15 am, but the highest values occur differently at 13:30 pm, 21:15 pm, 13.15 pm and 20:45 pm, respectively. The magnitudes of the original load values also greatly differ. The maximum load difference between peak and off-peak in SHPG, JSPG and ZJPG are 10491 MW, 12,041 MW, and 13,062 MW, but only 6125 MW in AHPG. An overall comparison about the mean squared deviation and the difference of
remaining load between peak and off-peak is summarized in Table 6. First of all, the optimized remaining load is compared with the original load in Table 6. The mean squared deviations of the remaining load for SHPG, ZJPG and AHPG are far smaller than their respective original ones. According to statistical theory, the remaining load profiles of the three power grids are smoother than the original loads. Correspondingly, maximum differences of the remaining load between peak and off-peak are also greatly reduced for the three power grids by 27.3%, 22.4%, and 20% respectively. Statistically, the results for the JSPG in Table 6 are comparatively poor, primarily due to the low specified electricity contracts ratio. Secondly, the optimized remaining load is compared with the real data. Our model produces smaller mean squared deviation and load difference between peak and off-peak than the real data (Table 6). This indicates that the optimization model deals better with the load differences of different power grids over the entire scheduling horizon to coordinate the loads among multiple provincial power grids through the flexible regulation performances of each PSPP. In addition, Fig. 8 presents the water level profile and generating and pumping powers of each PSPP from our optimization model in one day. All constraints including reservoirs and plant operations are satisfied. This illustrates that optimization results are reasonable and acceptable.
Fig. 9. A comparison of remaining loads from the optimization model and real data of a typical daily load in the winter, case 2.
Table 7 The results comparison from the optimization model and real data of a typical day in the winter, case 2. Scenario
– Optimize Real
Load
Original Remaining (MW) Decrease (%) Remaining (MW) Decrease (%)
Mean squared deviation
Load differences between peak and off-peak
SHPG
JSPG
ZJPG
AHPG
SHPG
JSPG
ZJPG
AHPG
1476 660 55.3 680 53.9
4049 3749 7.4 3807 6.0
2460 1862 24.3 1872 23.9
1932 1445 25.2 1500 22.4
4633 2601 43.9 2591 44.1
13,776 12,878 6.5 12,950 6.0
7836 5361 31.6 5939 24.2
6602 4697 28.9 5183 21.5
Note: Decrease (%) = (Original-Remaining)/Original.
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Case study 2 This case study represents another normal situation in the winter. Fig. 9 illustrates a typical daily load curve in this season where the occurring times of the peak and off-peak load of different power grids are roughly synchronous. From Fig. 9, the maximum load differences between peak and off-peak are also greatly reduced for SHPG, ZJPG and AHPG. Correspondingly, the mean squared deviations of the remaining loads for SHPG, ZJPG and AHPG are far smaller than their respective original ones. Similar to Table 6, an overall comparison of the mean squared deviation and the load difference between peak and off-peak is summarized in Table 7. Detailed comparisons of the optimized remaining load and the real data are not included here. The validity and feasibility of the presented method are demonstrated again. In summary, although great differences exist between the typical daily load curves for different power grids in winter and summer, the developed method can effectively shave the peak loads and fill the off-peak loads for multiple provincial power grids simultaneously. So the proposed model and method can solve the practical short-term peak shaving operation problem among multiple provincial power grids. Conclusions The increasing peak load demand is a great challenge for most power grids in China, especially for the coastal regions and economic heartlands. PSPP was perceived as an important complement to other baseload power plants for providing peaking power. Many PSPPs with large capacities were established in the ECPG for such purpose. These PSPPs are directly operated by the ECPG to shave the peak load and fill the off-peak load for its provincial power grids. However, operating these PSPPs is a new problem that few researches have analyzed. The paper addresses the real demand of peak shaving operation for multiple provincial power grids with PSPPs. A three-step hybrid algorithm is presented in this paper to determine day-ahead quarter-hourly schedules and to allocate the schedules among multiple provincial power grids. Two case studies including different typical quarter-hourly load curves are used to test the algorithm. The results show that the presented model can effectively achieve the goal of shaving the peak load and filling the off-peak load for multiple provincial power grids according to different load demands. The algorithm has been embedded into a newly developed decision support system that is currently being used by operators of the ECPG to make day-ahead quarter-hourly generation and pumping schedules.
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