Cheng Yuanchu and
Liu Yongqian
Dept. Of Hydro Power and Automation Engineering
Huazhong University of Science and Technology
Wuhan,
430074 China
Abstract:
A universal approach is proposed to simulate the water transients in the
hydropower plants with all sort of penstock topologies, surge tanks, water
turbines, etc. Using this approach, a Windows-based and visualized software
platform is developed. The simulation results of a hydropower plant show the
effectiveness of this approach and platform.
Keywords: fluid transient, digital simulation, hydro power plant
The digital simulation for the transient process is one of the important tasks for the designing of hydro power plants. In order to design the water inflow system, and select the proper measures to limit the speed raise and water pressure surge caused by water hammer, transient process simulation is a necessary step. The traditional methods for the transient process calculation are diagrammatic and approximate analytical methods that can produce the maximum values of turbine speed and water pressure rises. The stability of the hydraulic system plays an important rule in the stability of speed regulation systems for the hydroelectric generating units, and even effects the stability of the whole power system. Therefore, not only these two maximum values but also the whole transient process must be understood clearly.
Digital simulation is a very effective way to study the hydraulic transient process and the coupled transient process of hydraulic, mechanic, and electric systems[1,2,3]. However, the individualities of the penstock systems, hydro turbines and other components in the hydraulic system, make the simulation codes only applicable to specific hydropower plant. For each plant, a new code needs to be developed according to its own condition. This makes the simulation difficult and time-consuming. [Cheng 1997] proposed a universal approach to develop the simulation code for transient process in hydropower plant, and the computer code DSTFTP(Digital Simulation of Transient Flow in Turbines and Penstock) was developed. In this paper, the method is discussed and modified, and a Windows-based simulation software platform is developed for the simulation of transient process in hydropower plants. This platform has features of visualize environment, flexible module configuration, abundant output formats, so it’s very convenient to use.
The flow pattern in the penstock is relatively complex. In the elastic water hammer theory[1], the continuous equation that derived from quality conservation law is:
From Newtonian second
law, the motion equetion is:
These two equetions are the qusi-linear,hyperbolic partial differential equations.The most common approach to solve them is converting them into four normal differential equations, and solve these equations along the character lines. The algebraic appraoch is the most quick one.
As shown in Fig. 1, the differenceequations along the character lines are:
Fig. 1,
(3)
(4)
If the relative values are used, then：
Here：
——character
coefficient of pipelines;
——resistance
coefficient of the piplines;
A——section area of the
pipe;
D——diameter of the
pipe;
f——darcy-weisbach
friction factor;
a——tranmission speed
of pressure waves;
——the
relative flow rate at A,B,P;
——the
relative water head at A,B,p;
——initial
velocity.
Combining the equations (5),(6), and the boundary conditions at section 1 and section N+1, qP and hP at any time can be obtained. In the fowllowing discussion, the capitalized latters represent the relative values used in simulation code. For the algebraic approach along the character lines, it is not necessary to calculate the transients at the middle sections of the pipeline. So the algebraic approach is utilized in this paper.
Fig. 2 shows a pipeline system. In the figure, the lines represent the pipeline; the blocks represent the boundary conditions, like the nodes in network theory.
|
|
IC2 is the output port at node I－2；
IC3 is the output port at node I－3；
ID1 is the input port at node I－1；
ID2 is the input port at node I－2；
ID3 is the input port at node I－3；
Δt
is the time augment value，kk1=Δt1/Δt，kk2=Δt2/Δt,kk3=Δt3/Δt,kk4=Δt4/Δt, kk5=Δt5/Δt,kk6=Δt6/Δt.
Here：
HI（I,K）——the
input water head of node I at time K;
HO（I–1,K–kk1）——the
output water head of node I-1 at time K-kk1;
Q（I,1,K）——the
input flow rate of node I at time K;
Q（I–1,IC1,K–kk1）——the output water
head of node I-1 at time K-kk1.
Suppose:
(8)
(9)
Then：
Similarly：
From equation (6), the
following formula can be obtained ：
Here:
HO（I,K）——the
output water head of node I at time K;
HI（I+1,K–kk4）——the
intput water head of node I+1 at time K-kk4;
Q（I,4,K）——the
output flow rate of pipe 4 in unit 4water head of node I at time K;
Q（I+1,ID1,K–kk4）——the input flow
rate of pipe ID1 in unit I+1 at time K-kk4.
Suppose
(14)
(15)
Then：
(16)
Similarly：
(17)
(18)
Here：
HI——inoput
water head, HO——output water head.
similar notations are applied in the following equations.
Until
here, the fundamental equation group to solve the complex water hammer problems
has been established. The connection relations among IC1, IC2, IC3, ID1, ID2,
ID3 can be obtained using a searching programme to search these relations in the
simulation diagram of the module configuration. Combined with the boundary
conditions, the water head and the flow rate of the boundary at any momemts can
be calculated.
The
main boundary conditions are turbines, upper and down stream reservoirs,
branched pipelines, surge tanks, valves and blind
pipe. Among them the most important boundaries are hydro turbines. Next is the
calculation algorethms for the hydro turbines. For the other boundary
conditions, please refer to p[1,2,4,5,6].
For
the hydro turbines, following equations hold:
if the rigid water
hammer equations is employed, equatin (23) can be changed into：
Here：
α——the
opening of wicket gate;
β——speed
raise of the hydroelectric generating unit;
TW——the inertia time constant of the water flow;
Ta——the inertia time constant of hydroelectric generating uni;t
x0——initial speed;
——unit
flow, unit speed, unit torque;
M（K）——the
relative torque of hydro turbine;
Q（I,K）——the
relative flow rate of hydro turbine.
The visualized environment of Windows operation system brings much convenience the users, and this operation system has become dominant in the OS market. Windows has the strong interactive and graphic functions. If the transient simulation software is based on Windows, the abundant windows resources will make the simulation interface more friendly, simulation and data process more convenient. The entire simulation platform is developed using Borland C++ Builder, the main menu is shown in Fig. 3.
Fig. 3 Main Menu & simulation configuration file
The commands of File submenu are also shown in
Fig. 3. The Print command is to output the simulation files. The submenus of
Edit, Simulate, and Tools are shown in Fig. 4. “Open
Library”
under “Tools” is used to open the component library. Currently, the
following components are available in this library: Turbines (draft tube is not
considered), Turbines (draft tube is considered), Branched pipes, Upper stream
reservoirs, Down stream reservoirs, Blind pipe, Simple surge tanks, Resistance
surge tanks, Valves in the pipelines, and Terminal valves. “Add turbine”
command under “Tools” submenu is to input the new turbine characteristic
curves . “Probe Marker” command under “Tools” submenu is to mark the
points to be drawn in the simulation files. “Place” command under “Edit”
submenu is to copy the components from the component library to the simulating
configuration files. “Wire” command under “Edit” submenu is used to
connnect the components.
Under Simulate submenu, “Probe Setup” is to
set the drawing, “Probe Print” is to print the simulation curves,
“Setup” is to congigure the simulation parameters，such
as theoretical model of water hammer, calculation steps, convergence tolerance.
When the elastic water hammer model is applied, the selection of the calculation
step must be payed extra attention. The step should be the greatest common
divisor of the
pressure wave transmission times of all pipes. If it is too small, must
be adjusted.
Using the
simulation platform, it is not necessary to develop the code. In order to
simulate the transient proccess in a hydropower plant, the only task is to form
a configured file in the platform according to the characters of this plant.
Next , is an example to show this process.
Fig. 5 shows the layout of a hydropower station. The parameters of the penstock are shown in table 1. There is a sgure tank of cylinder type at point D, which section area is 135.8m2. Based on the initial flow, Tj=238.7 second. There is a turbine at point A, which type is HL702A and parameters are D1＝2m, nr=300rpm, GD2=600, Qr=33m3/s, Hr=58m, Pr=17.35MW, Yr＝0.9，100% load rejection. The greatest common divisor of the pressure wave transmission times of all pipes is too small, must be adjusted. Here, Δt1＝0.025, Δt2＝0.025, Δt3＝0.075, Δt1＝0.15, and ρ1＝5.21, ρ2＝4.73ρ3＝2.49, ρ4＝0.761; k1=0.0276, k2=0.0276, k3=0.0041, k4=0 respectively. The simulation configuration file is shown in Fig.3
Table 1 The parameter of the penstock
|
Num |
Name |
Length(m) |
Diameter(m) |
Δt |
ρ |
|
1 |
BA |
27.64 |
2.8 |
0.0218 |
5.97 |
|
2 |
BC |
25 |
2.8 |
0.0198 |
5.97 |
|
3 |
DB |
106.8 |
4.6 |
0.0844 |
2.21 |
|
4 |
ED |
173.80 |
7.5 |
0.165 |
0.692 |
First, double click eack node (boundary) and
input its parameter in turn. Then, setting the simulation parameters, marking
the plot variable and strating the simulation.
Results of simulation study shown in Fig. 6 is well coincide with field test. The maximum values of turbine speed and water pressure rises are 1.24 and 1.309 respectively in field, and there are 1.241 and 1.303 respectively for simulation calculation. The difference of speed in transient is a result of different turbine that is HL220 in simulation and HL702A in field respectively
Fig. 6
Load rejection transient in a hydropower station
A universal simulation approach and a Windows-based software platform are presented in this paper. This simulation platform has following features:
(1) Can be applied to simulate the water transients in the hydropower plants with all sort of penstock topologies, surge tanks, water turbines, etc.
(2) Without code development.
(3) Interactive and visualized interfaces makes the expression and input of the plants data and configuration much more convenient, and the output of simulation results more flexible and understandable.
The effectiveness of this approach and platform has been verified by many examples. Now, we are trying to develop the simulation code in environment of MATLAB and design more simulation module for various boundaries.
References
[1]
G.B.wylie
V.L.streter: Fluid Transient, MCGAN-HILL, 1978.
[2]
M.
Hanif. Chaudhry: Applied Hydraulic Transients, Litton Educational Publishing,
Inc, 1979.
[3]
C.S.
Martin & H.C. Jackson: Combined Surge tank and Water-hammer Analysis by
Digital Computer, Watwe Power, 1972.
[4] CHENG Yuanchu: A General Method On Calculated Turbine Transients, Design of Hydroelectric Power Station, 1997.2. (in Chinese)
[5]
CHANG
Jinshi: Transient in water turbine, Machine Industry Press, Beijing, 1991. (in
Chinese)
[6] WANG shuren: Hydraulic Calculation and method of Surge Tank. Tsinghua University Press, 1976. (in Chinese)
