The hydroturbine generator regulating system can be considered as one system synthetically integrating water, machine, and electricity. It is a complex and nonlinear system, and its configuration and parameters are time-dependent. A one-step-ahead predictive control based on on-line trained neural networks (NNs) for hydroturbine governor with variation in gate position is described in this paper. The proposed control algorithm consists of a one-step-ahead neuropredictor that tracks the dynamic characteristics of the plant and predicts its output and a neurocontroller to generate the optimal control signal. The weights of two NNs, initially trained off-line, are updated on-line according to the scalar error. The proposed controller can thus track operating conditions in real-time and produce the optimal control signal over the wide operating range. Only the inputs and outputs of the generator are measured and there is no need to determine the other states of the generator. Simulations have been performed with varying operating conditions and different disturbances to compare the performance of the proposed controller with that of a conventional PID controller and validate the feasibility of the proposed approach.
Hydroturbine governor (HTG) provides the basic control in hydropower stations to ensure the reliability and the quality of electricity supply. The conventional hydroturbine governor adopted by most utilities is a proportional, integral, and derivative (PID) type controller based on linear control theory. It has simple structure with flexibility and is easy for implementation, and thus it has made a great contribution in enhancing the quality of electrical supply [
The hydroturbine generator regulating system can be considered as one system synthetically integrating water, machine, and electricity. It is a complex and nonlinear system, and its configuration and parameters are time-dependent [
This creates discrepancies between the mathematical linear model of the hydroturbine generator regulating system and the physical nonlinear plant. Therefore, with the conventional linear control theory based PID controller, it is difficult to realize the desired control performance over wide operating conditions of the power plant [
To meet this requirement, a large amount of research has been conducted on the hydroturbine generator regulating system. Numerous methods for PID tuning have been reported in the literature [
Neural networks (NNs) have been applied very successfully in the identification and control of dynamic systems. The universal approximation capabilities of the multilayer perceptron make it a popular choice for modeling nonlinear systems and implementing general-purpose nonlinear controllers [
The theory and algorithm of predictive control have achieved great development in the industrial process control after thirty years’ application and study. It has been introduced to the optimal control of hydroturbines by lots of experts. Jones and Mansoor [
A predictive control scheme for hydroturbine governor based on NNs is introduced in this paper. The control architecture consists of two NNs: an adaptive neuroidentifier (ANI) to track the plant and predict its output one-step-ahead and an adaptive neurocontroller (ANC) to produce the control signal. A scalar error is used in each sampling period to update the identifier and controller weights continuously in real-time. With a similar architecture, called indirect adaptive control [
The effect of different amplitude step disturbances and trapezoidal shape reference signal (turbine power) are investigated in this paper. Also, a number of studies are performed to compare the performance of the proposed controller with that of the conventional PID controller under different operating conditions.
A simple layout of a hydropower plant shown in Figure
General layout of hydropower plant.
The hydroturbine governing system consisting of the controller and the controlled plant is a complex, nonlinear, time varying, and non-minimum-phase system with fractional distributed parameters and uncertainties. The controlled plant includes a turbine, a penstock, a generator, and a load (Figure
Hydroturbine generator regulating system.
The characteristic equations of the Francis turbine are [
The six transmission coefficients (as shown below) change as the gate opening changes:
The general expression of penstock, taking rigid water hammer, is described as
The characteristic equation of the generator and the load can be written as
Neglecting small time constants, the servomechanism can be expressed with a first-order equation:
The structure of the controller is shown in Figure
Schematic of control structure.
A multilayer perceptron neural network (MLPNN) structure is developed to model the nonlinear dynamic relationship between the gate position and the turbine mechanical power. Considering it is difficult to measure the turbine mechanical power, generator output power is measured instead to obtain the turbine mechanical power by
The network transforms
Neuroidentifier.
The input vector to the ANI is scaled in the range of
Taking advantage of the recognized universal approximation properties of NN, a nonlinear plant in the MLPNN form is obtained as discussed before. Based on the neural model, a predictive control strategy is implemented by an adaptive neurocontroller. The input vector to the ANC is
Using (
The success implementation of the control algorithm presented in Section At time step Compute Calculate the error between The output of the controller Using input vector ( Based on
The flowchart of the adaptive predictive control algorithm.
In step (3) above, the training is straightforward since the error at the output of the ANI is obtained. However, in step (6) the training is difficult since the error at the output of the ANC is not provided. In this case, first, the weights of the ANI are frozen and the error between the desired and predicted plant output is back propagated through the ANI. Then, the back propagated signal at the input of the ANI is further propagated through the ANC, making necessary changes to the controller weights. In other words, for adapting weights of the controller, the identifier acts as a channel to convey the error from the output of the identifier to the output of the controller. This evaluates the need to have the identifier. The error is used to train the ANI and the ANC.
The plant model is simulated using the mathematical model given in Section
Transmission coefficients as a function of gate opening.
Operating point number | Gate opening % |
|
|
|
|
|
---|---|---|---|---|---|---|
1 | 43.74 | 2.867 | 0.526 | −0.353 | 1.674 | 0.232 |
2 | 47.52 | 2.562 | 0.679 | −0.455 | 1.541 | 0.262 |
3 | 51.26 | 2.278 | 0.814 | −0.545 | 1.416 | 0.290 |
4 | 55 | 2.016 | 0.934 | −0.626 | 1.300 | 0.315 |
5 | 58.74 | 1.766 | 1.039 | −0.696 | 1.191 | 0.338 |
6 | 62.52 | 1.654 | 1.132 | −0.759 | 1.090 | 0.360 |
7 | 66.26 | 1.333 | 1.212 | −0.813 | 0.997 | 0.380 |
8 | 70 | 1.146 | 1.281 | −0.859 | 0.913 | 0.397 |
9 | 73.74 | 0.974 | 1.340 | −0.898 | 0.837 | 0.414 |
10 | 77.52 | 0.822 | 1.391 | −0.932 | 0.768 | 0.429 |
11 | 81.26 | 0.691 | 1.433 | −0.961 | 0.708 | 0.443 |
12 | 85 | 0.578 | 1.468 | −0.984 | 0.655 | 0.455 |
13 | 88.74 | 0.484 | 1.498 | −1.000 | 0.611 | 0.467 |
14 | 92.52 | 0.409 | 1.523 | −1.020 | 0.574 | 0.478 |
15 | 96.26 | 0.353 | 1.544 | −1.030 | 0.546 | 0.489 |
16 | 100 | 0.317 | 1.563 | −1.047 | 0.526 | 0.499 |
The Simulation Toolbox SIMULINK of MATLAB is utilized to develop plant model and generate data. The absolute value of pseudorandom binary signal is applied to the input to represent the variation of gate position, and the corresponding turbine mechanical power is obtained. The data collected (input and output) are divided into two sets: one set is for training the NN and the other set is for validation.
An input-output identifier model and control strategy is established and its parameters are set as follows. The number of time delays used for the input of ANI and ANC is set to 3; that is,
The quadratic programming problem in (
As the control parameters have been determined as discussed before, the performance of the proposed adaptive neural predictive control is simulated on a large amplitude step and trapezoidal wave-shape reference signals. These reference signals may represent the nature of load changes. The turbine gate opening and power output are shown in Figures
Response to large amplitude step in turbine power reference,
Turbine power output response
Turbine gate opening response
Response to large amplitude step in turbine power reference,
Turbine power output response
Turbine gate opening response
Response to trapezoidal wave reference,
Turbine power output response
Turbine gate opening response
Response to trapezoidal wave reference,
Turbine power output response
Turbine gate opening response
The response shows a non-minimum-phase characteristic. The turbine power response on the large amplitude step signal follows more or less closely. It is evident that despite a large change in the operating conditions the controller still provides good results because of the adaptation process. However, the gate position is observed to exhibit large fluctuation on step change with
A number of studies have been performed to compare the quality of the proposed adaptive predictive controller with those of the conventional PID controller.
Generally, the conventional governors adopt a PI or PID control law. Figure
Illustration of the conventional load-change method.
Regarding the adjustments of PID parameters, the following formulas are often used by experienced engineers.
For PI controller,
According to these empirical formulae, the parameters of the conventional PID controller are chosen as below:
The proposed adaptive neuropredictive controller adopts the parameters determined as discussed above and the value of the penalty factor
Step increases of 10% and 80% in power reference are introduced and the system responses with the conventional PID controller (CPID) and the proposed adaptive neuropredictive controller (PAPC) are shown in Figures
Turbine power output response to a 10% step in reference.
Turbine power output response to an 80% step in reference.
Gate opening response to a 10% step in reference.
Gate opening response to an 80% step in reference.
It is observed from Figure
From the responses for 10% and 80% step changes in power reference, it can be seen that the conventional PID controller only provides acceptable performance for a small disturbance rather than the large disturbance. Even for a small disturbance, the proposed adaptive predictive controller is better than the conventional one regarding the speed and the overshoot of response of the process.
This is logically correct because of the existence of nonlinearities in a hydroturbine governing system. These nonlinearities can be divided into two parts. The first comes from the turbine’s nonlinear characteristics that depend on the operating point. It can be clearly seen from (
An adaptive neuropredictive control for hydroturbine governor is presented in this paper. The back propagation network with on-line learning is used in the proposed method. The controller introduced in this work inherits the general advantages of neural networks such as high speed, generalization capability, and fault tolerance as well as adaptation (learning) property. This method features the simple structure and the nonrequirement for a large number of neurons in the implementation. The learning algorithm is simplified by employing a single element error vector. The controller weights are updated directly in an on-line mode from the inputs and the outputs of the generator, and the states of the system are not necessarily determined. Simulation results for the large amplitude step and trapezoidal wave-shape reference signals show that the proposed adaptive predictive controller can adaptively improve the dynamic performance of the system. By comparing the performance of the proposed adaptive predictive controller with that of the conventional PID controller, it is found that the proposed adaptive predictive controller is not only simple but also robust, and it features strong adaptivity as well.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors acknowledge the financial supports from the National Natural Science Foundation of China under Grant no. 51379160.