Optimization of turbine cold-end system based on BP neural network and genetic algorithm

Abstract

The operation condition of the cold-end system of a steam turbine has a direct impact on the economy and security of the unit as it is an indispensible auxiliary system of the thermal power unit. Many factors influence the cold-end operation of a steam turbine; therefore, the operation mode needs to be optimized. The optimization analysis of a 1000 MW ultra-supercritical (USC) unit, the turbine cold-end system, was performed utilizing the back propagation (BP) neural network method with genetic algorithm (GA) optimization analysis. The optimized condenser pressure under different conditions was obtained, and it turned out that the optimized parameters were of significance to the performance and economic operation of the system.

Keywords

optimization / turbine / cold-end system / BP neural network / genetic algorithm

Introduction

Nowadays energy conservation and emission reduction of the power system become very important. The operation of the cold-end system, an important part of the thermal power plant, has a direct impact on the output of the unit and auxiliary power. The cold-end system of a 1000 MW ultra-supercritical (USC) unit, including the condenser, the circulating pump, the vacuum pump, the condensate pump and accessories, has many adjustable factors and there is a great potential of energy saving in it [ 1]. Hence it is necessary to optimize these parameters by selecting and defining the optimal target value and the optimization programs of the whole conditions according to the designed value of the parameters, the configuration of system, the load rate and the operating conditions of the unit [ 2].

The traditional method to optimize the cold-end system is to establish a mathematical model between the net power of the unit and some major parameters of the cold-end system. As there are many parameters affecting the net power, and the relationships among those parameters are very complex, it is very difficult to establish the model, and the model thus established is not accurate enough as well. Back propagation (BP) neural network has a strong nonlinear mapping ability to avoid the above complex function modeling [ 3]. Therefore, this paper studied the optimization of the cold-end system of a 1000 MW USC unit using BP neural network and genetic algorithm (GA). First, it established a BP neural network model of the cold-end system. Next, the optimal condenser pressure was found by using GA. Finally, by using the data collating from the actual operating database of the unit, the BP neural network samples were trained, and the model trained by the samples could accurately reflect the actual situation of the unit. So the optimization results are more accurate than the traditional method.

Target of optimization of cold-end system

Cold-end system is a very important auxiliary system, mainly including the final stages of steam turbine, the condenser, circulating pumps, the circulating water system and the vacuum pumping system, etc.

The condenser is the core equipment of the devices in the cold-end system mentioned above, so the condenser pressure is an important operating parameter. When the initial steam condition is fixed, the output of the unit acts reversely against the condenser pressure. Within the condenser, the steam is in a saturation state. The saturation temperature ( t_{\mathrm{s}} ) is impacted by the inlet circulating water temperature, the temperature rise of the circulating water, terminal temperature difference, and the circulating water flow, as shown in Eq. (1) [ 1].

(1) t_{\mathrm{s}}=t_{\mathrm{w}\mathrm{1}}+\mathrm{\Delta }t+\delta t,

where t_{\mathrm{s}} is saturation temperature, t_{\mathrm{w}\mathrm{1}} is inlet circulating water temperature, \mathrm{\Delta }t is the temperature rise of the circulating water, \delta t is terminal temperature difference. Then the saturation pressure corresponding to t_{\mathrm{s}} is the condenser pressure, which can be obtained by querying the steam table, or using the empirical formula Eq. (2) [ 4].

(2) p_{\mathrm{c}}={\left({\displaystyle \frac{t_{\mathrm{s}}+\mathrm{100}}{\mathrm{57.66}}}\right)}^{\mathrm{7.46}}\times \mathrm{9.8}\times {\mathrm{10}}^{-\mathrm{3}}\left(\mathrm{kPa}\right),

where p_{\mathrm{c}} is condenser pressure.

Many of the above factors can be epitomized in the circulating water flow. Under certain unit load and inlet circulating water temperature, condenser pressure changes with the circulating water flow. On the other hand, the change of the circulating water flow directly affects the work of the circulating pump. Therefore, the rise of circulating water flow causes the drop in the condenser pressure, which, in turn, increases the output of the unit and the work of the circulating pump. When the difference between the output of the unit and the work of the circulating pump, which is called the net power of the unit, reaches the maximum, the current condenser pressure is defined as the optimum condenser pressure [ 5– 8]. The target of optimization of the cold-end system is to find that pressure. The cold-end system of a 1000 MW USC unit has two condensers, a low pressure condenser and a high pressure condenser.

Establishment of the BP neural network model of a cold-end system

The mathematical model of cold-end system optimization turned out to be the relationship between the net power of the unit and some parameters of the cold-end system. Because the net power is a complex result of a multiple of factors, the model should be a multi-input and single-output system. But it is difficult to find a certain mathematic equation to describe the relationship. As mentioned above, BP neural network has an outstanding ability in nonlinear fitting, this paper established the model of cold-end system optimization using BP neural network.

BP neural network was proposed in 1986 by Rumelhant and McClelland. It is one of the most successful and widely-used artificial neural networks [ 9]. A typical BP neural network is demonstrated in Fig. 1, which consists of the input layer, the output layer and the middle (hidden) layer.

The learning process of the BP algorithm can be divided into the forward computing of data stream and the backward propagation of error signals. The basic algorithm principle of BP neural network is listed as follows [ 3]:

First, during the forward propagation process, input samples from the input layer propagated to the hidden layer and finally transmitted into the output layer. Next, if the actual output does not match the desired output, the model produces error signals which are fed backward (backward propagation). The backward propagation of error signals is a process in which the output error signals are passed in the opposite direction. That is to say the error signals originate from the output layer, pass through the hidden layer, and go into input layer ultimately. During this process, they are allocated to all units averagely by some means to get the error signal of each unit of each layer. This error signal is the foundation for correction of the weight value of each unit. Eventually, the process of continuous correction of weight value is also the self learning and training process of the network. Simultaneously, this process is carried out until the output error declined to an acceptable degree or to a pre-set number of learning.

Samples of BP neural network

For the cold-end system of 1000 MW USC unit, 11 variables were taken as the input parameters of the BP neural network model. They are:

Actual generation power (P) /MW;

Water flow of circulating pump A (D_wA) /(t·h^–1);

Water flow of circulating pump B (D_wB)/ (t·h^–1);

Circulating water inlet temperature (t_w1) /°C;

Circulating water outlet temperature (t_w2) /°C;

Current of circulating pump A (I_cpA) /A;

Current of circulating pump B (I_cpB) /A;

Current of vacuum pump A (I_vpA) /A;

Current of vacuum pump B (I_vpB) /A;

Pressure of the low pressure condenser (p_cLP) /kPa;

Pressure of the high pressure condenser (p_cHP) /kPa.

The output parameter is the net power P_net (MW) of the unit. To describe different conditions of the cold-end, 31 groups of data were chosen from different operating conditions of the unit, which were taken from different loads. These 31 groups of data were used as training samples to train the network. Besides, in order to test the extrapolation ability of the neural network, other eight conditions were chosen randomly as the calibration samples. The final training samples and calibration samples are presented in Table 1. Due to space limitations, Table 1 only lists eight groups of data of the training samples.

Setting parameters of BP neural network

Before training the BP network, the structure and parameters of the network must be set. There are 11 input layer nodes and 1 output layer nodes.

The determination of the hidden layer nodes is the key point. If there are only a few hidden nodes, the network has a lower training accuracy and poorer generalization ability. On the contrary, if there are too many hidden nodes, the training time is too long while the error is not always the smallest. The empirical formula in Ref. [ 3] was used to determine the number of hidden nodes.

(3) m=\sqrt{n+l}+a,

where m is the number of hidden nodes, n is the number of input nodes, l is the number of output nodes, and a is a constant between 1 to 10. This paper selected 17 hidden nodes.

Except for the input layer nodes, the output layer nodes and the hidden nodes, other parameters should be set as follows:

Structure: three layer BP neural network;

Number of input layer nodes: 11;

Number of hidden layer nodes: 17;

Activation function of hidden layer: hyperbolic logarithm function;

Number of output layer nodes: 1;

Activation function of output layer: linear activation function;

Learning function: gradient decreasing based approach;

Goal of the network: 1.00 × 10^-8;

Learning efficiency: 0.25;

Training times: 2000.

The BP neural network set according to the above parameters is depicted in Fig. 2.

Training result

Using MATLAB neural network toolbox [ 10], the BP neural network of cold-end system established above was trained by the training samples. The calculating result is displayed in Fig. 3.

As can be seen, for the training samples, the outputs of the network are very close to the operating data, which were collected from the operating database of the unit, the maximum error is less than 0.19%. The maximum error of the calibration sample is controlled at 0.14%, which could meet the needs of engineering calculations.

Determination of optimal condenser pressure

Based on the BP neural network model established, some parameters of the cold-end system, mainly including the pressure of low pressure condenser (p_c,LP) and high pressure condenser (p_c,HP), can be optimized. Because of the nonlinearity between the input and output in the BP neural network model, it is hard to directly find the optimal condenser pressure. The algorithm can handle any form of mathematic models [ 11]; therefore, this paper found the objective condenser pressure using GA proposed by the American professor J. Holland. It is a kind of randomized search method learned by natural selection and genetic law. There are four basic elements of GA shown as follows [ 12]:

Fitness function design: The probability of its choice is determined by the fitness value;

Set initial population: So the population can be made large enough to have a certain randomness;

Parameter coding: Some kind of coding rules are used to map the variables in practical problems to the corresponding gene at chromosome;

Genetic manipulation: Genetic manipulation includes the selection operator, crossover operator and mutation operator.

The basic steps of GA are shown as follows [ 13, 14]:

1) Initialization. Initially many individual solutions are usually randomly generated to form an initial population. The population size depends on the nature of the problem. Traditionally, the population is generated randomly, allowing the entire range of possible solutions.

2) Selection. During each successive generation, a proportion of the existing population is selected to breed a new generation. Individual solutions are selected through a fitness-based process, where fitter solutions (as measured by a fitness function) are typically more likely to be selected. Certain selection methods rate the fitness of each solution and preferentially select the best solutions. Other methods rate only a random sample of the population, as the former process may be very time-consuming.

3) Crossover and mutation. By producing a “child” solution using the methods of crossover and mutation, a new solution is created which typically shares many of the characteristics of its “parents”. New parents are selected for each new child, and the process continues until a new population of solutions of appropriate size is generated. These processes ultimately result in the next generation population of chromosomes that is different from the initial generation. Generally, the average fitness value will have increased by this procedure for the population.

Under given conditions, when the net power of the unit reaches the highest, the pressure p_c,LP and the pressure p_c,HP are the optimal ones. To find out the optimal condenser pressure, the parameters of GA with binary encoding are set as

Hereditary algebra T = 50;

Population size m = 20;

Crossover probability P_c = 0.8

Mutation probability P_m = 0.08.

Using MATLAB GA toolbox [ 15, 16], the optimal condenser pressure under different conditions could be found. To take one condition (100%THA condition of steam turbine unit) as an example, the fitness value and the current best individual are obtained (exhibited in Fig. 4). As it can be seen, after the 10th generation (Fig. 4(a)), in the whole population, fitness value of the best individual and the mean fitness value of all individuals tend to be consistent and stable. Now the variable 10 (p_c,LP) and variable 11 (p_c,HP) are the final optimal condenser pressure. The same method is used to find the optimal pressure of other conditions. Table 2 tabulates the optimal condenser pressures for 7 conditions with the load changing from 40% to 100% THA (turbine heat acceptance) conditions.

Concluding remarks

This paper discussed the optimization of the cold-end system by taking advantage of BP neural network and GA. A BP neural network model for the cold-end system of a 1000 MW USC unit were established, in which the training samples and the calibration samples were collected from the actual operating data of the unit. The training result shows that, for the training samples, the outputs of the network are very close to the operating data, the maximum error is less than 0.19%, while for the calibration sample, the maximum error is controlled at 0.14%. The method proves to be effective and accurate.

Based on this, this paper obtained the corresponding optimal condenser pressure on 13 different conditions by GA instead of by complex mathematical calculation. The operation optimization can be realized on the unit.

This analysis mode can also be used on the optimization of the cold-end system of other units. But it should be noted that the BP neural network model is different from different units. Besides, the models should be trained according to their operating data. The analysis mode mentioned in this paper provides a new method for optimization of the cold-end system of large units.

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