Page 48 - Mathematical Models and Algorithms for Power System Optimization

38 Chapter 2

2.6.4 Constraints of Pumped Storage Plant and Related Conversion Calculation

(1) Initial conditions are given as follows:
4 3
Initial water storage quantity W 0 ¼310.0 10 (m )
4 3
Final water storage quantity W 24 ¼350.0 10 (m )
4 3
Maximum water storage quantity W max ¼850.0 10 (m )
3
4
Minimum water storage quantity W min ¼0.0 10 (m )
(2) Energy balance of pumped storage plant:

W H ¼ W 0 W 24 Þ=640 ¼ 40=640 104 ¼ 625 MWhð Þ
ð
If the energy is a negative value, it means that the energy consumed by pumping is larger
than that by generating.
(3) Lower limit of generated energy for pumped storage plant:

W 1 ¼ W 0 W max Þ=640 ¼ 540=640 104 ¼ 8437:5 MWhð Þ
ð
(4) Upper limit of generated energy for pumped storage plant:

W A ¼ W 0 W min Þ=640 ¼ 310=640 104 ¼ 4843:8 MWhð Þ
ð
(5) Constraint of pumped storage units for generating: the calculation condition is that four
pumped storage units are put into operation, with the output constraint of each unit as
[180MW, 300MW]. Thus, the total output constraint of four pumped storage units shall be
[180MW, 1200MW].
(6) Constraint of pumped storage units for pumping: the calculation condition is that output
constraint in water pumping is 0, 165, 330, 495, and 825MW, with integer constraint as [0,
5] and unit step size of 165MW.
(7) In the optimization calculation of reservoir capacity constraint, average water balancing
constraint of the pumped storage plant is converted into an energy balancing constraint.
However, when output it is still converted back to water quantity unit, the upper limit of
generated energy by pumped storage plant is 8500MWh, the lower limit 5000MWh, and
the energy by reservoir capacity is 3500MWh (8500–5000).

The correctness and reasonableness of the proposed mathematical model is verified by daily
economic optimization dispatch of pumped storage plant calculation using practical system
data of the province. The calculation results show that the mathematical model proposed in this
chapter can fully use the peak load regulating capacity of a pumped storage plant and
effectively adjust the load curve by peak load shifting while meeting all operational constraints.
The detailed results are shown in the following section.