Model 3: Hydro Power Plant Pumping and Releasing Optimization Problem
Based on the previous pumping problem in Model 2, the optimization model could be further improved by
involving releasing operation in it. Figure 3 shows the pumping and releasing optimization during available
time.
Upper reservoir of the
Power grids
hydro power plant
Capacity of
Turbine and generator: releasing process p
the reservoir
00000
@@@@@@@
Initial stored
energy Ein
Turbine: Pumping process p+
Figure 3 Pumping and releasing process of a hydro power plant
The mathematical model of the pumping and releasing process of the hydro power plant is formulated as
follows:
Min
(5)
(6)
Subject to
(7)
(8)
0,
(9)
ts St

Question

Model 3: Hydro Power Plant Pumping and Releasing Optimization Problem
Based on the previous pumping problem in Model 2, the optimization model could be further improved by
involving releasing operation in it. Figure 3 shows the pumping and releasing optimization during available
time.
Upper reservoir of the
Power grids
hydro power plant
Capacity of
Turbine and generator: releasing process p
the reservoir
00000
@@@@@@@
Initial stored
energy Ein
Turbine: Pumping process p+
Figure 3 Pumping and releasing process of a hydro power plant
The mathematical model of the pumping and releasing process of the hydro power plant is formulated as
follows:
Min
(5)
(6)
Subject to
(7)
(8)
0,
(9)
ts St<te
0,
6
Module Project
EEE334 Power Generation Technologies
0<t<ts
(10)
At E [1,2, ---,T]
4,SIST
At E[[,2, ---,T]
(11)
+1
At
(12)
(13)
itand iT are integers
In model 3, pt and Pt are decision variable of the pumping power of the pump and the releasing power to
the generator (including turbine), and it and is are integer variables.
Task 3. Based on Model 2, revise your Matlab program to a pumping and releasing optimization model
based on the mathematical formulation: (5)-(13). Relevant model parameters are available in Table 1
and
Table 2.
You need to include the following contents in Section 2 Mathematical Modelling in your report:
Explain the meaning of the objective function (5), and each constraint (6)-(13).
You need to include the following contents in Section 3 Results and Discussions in your report:
Plot the optimization results: hourly pumping and releasing power of the hydro power plant, and
the total revenue or cost with proper label and units of the axis. The real-time price and total stored
energy in the upper reservoir at each hour should also be included in the figure.
Discuss and explain the obtained results: how to verify the pumping and releasing operations are
optimized? What is the profit of the hydro power plant?
Table 1 Real-time price information
4
Time
6
1
3
7
2
5
8
12.7
12.4
20.4
14.7
12.8
18.9
21.5
13.5
Price($/MWh)
14
Time
9
10
12
11
16
13
15
19.4
11.8
8.7
8.3
14.7
9.0
7.0
7.6
Price($/MWh)
Time
17
18
24
21
22
23
19
20
6.8
17.4
18.9
16.4
17.5
17.3
9.5
7.5
Price($/MWh)
Table 2 Hydro power plant information
2
Start time
ts
22
End time
te
6.4 MWh
Initial energy stored in the upper reservoir
Eini
60 MWh
Target energy stored in the upper reservoir
Etar
E
64 MWh
Capacity of the upper reservoir
P Pump
12 MW
Maximum pumping power of the pump
16 MWh
PG&T
Maximum generation power of the generator

Accepted Answer

⚹ Based on the information provided, it seems you need to revise your MATLAB program for a pumping and releasing optimization model for a hydro power plant. ⚹ ⚹ Here’s a structured approach to tackle your project: ⚹ ∻Mathematical Modelling∻ ‖ ▪ ⋮ **Objective Function (5)**: This function represents the total cost or revenue associated with the pumping and releasing operations. It should be minimized to ensure cost-effectiveness. ‖ ‖ ▪ ⋮ **Constraints (6)-(13)**: Each constraint defines the operational limits and requirements for the hydro power plant, such as energy balance, maximum pumping and releasing capacities, and time intervals. ‖ ‖ ▪ ⋮ **Variables**: Define your decision variables clearly, such as $ p^+ $ for pumping power and $ p^- $ for releasing power, ensuring they adhere to integer constraints where necessary. ‖ ∻Results and Discussions∻ ‖ ▪ ⋮ **Plotting Results**: Use MATLAB to plot the hourly pumping and releasing power, total revenue or cost, and include real-time prices and stored energy in the upper reservoir. Ensure axes are properly labeled. ‖ ‖ ▪ ⋮ **Verification of Optimization**: Discuss methods to verify that the operations are optimized, such as comparing results against benchmarks or expected outcomes. ‖ ‖ ▪ ⋮ **Profit Calculation**: Calculate the profit by subtracting total costs from total revenues, and discuss the implications of the results on the hydro power plant's operations. ‖ ⚹ Make sure to refer to Tables 1 and 2 for relevant parameters and data needed for your calculations and plots. ⚹ ⚹ If you need further assistance with specific MATLAB code or additional details on the mathematical formulation, feel free to ask! ⚹

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