A Three-Hybrid Treatment Method of the Compressor's Charateristi Line in Performane Predition of Power Systems A Three-Hybrid Treatment Method of the Compressor's Charateristi Line in Performane Predition of Power Systems 1 Yulong Zhang, Ren Yang, 3 Hongtao Zheng, 4 Fumin Pan 1, First Author,Corresponding Author College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, Heilongjiang, P.R. China, yangrenheu@163.om College of Power and Energy Engineering, Harbin Engineering University, Harbin 150001, Heilongjiang, P.R. China, yangrenheu@163.om 3 College of Power and Energy Engineering, Harbin Engineering University zhenghongtao@hrbeu.edu.n 4 College of Power and Energy Engineering, Harbin Engineering University panfumin@hrbeu.edu.n Abstrat The omplete ompressor's harateristi line is important for performane simulation of the power systems in the design and off-design onditions, suh as gas turbine, turboharged unit and so on. Thus, a three-hybrid treatment method of ompressor harateristis was introdued in this paper, whih was firstly used the numerial simulation method (CFD - Computational Fluid Dynamis) to obtain some design and off-design performane data instead of the experimental researh, then used the least square method (LSM) to inrease the performane data in eah harateristi line, and finally used the BP-artifiial neural network method to establish the ompressor's omputational model. With this method, a dynami simulation model was built for the turboharged unit power system. The pratial appliation shows that it not only an satisfy the preision and smooth requirements of the ompressor harateristis in the performane analysis, but also an get fast alulation speed. Keywords: Three-Hybrid Treatment Method, Compressor Charateristis, Performane Predition 1. Introdution Compressor is one of the most important omponents of some thermal power equipment. Thus, the omplete ompressor s harateristi line is also important for performane analysis of the power plants in the design and off-design onditions, whih have a ompressor omponent. For example, the gas turbine, the airraft engine, the turboharged boiler and so on. Generally, the ompressor s harateristi data is obtained by the experiment, but the ost is expensive. For various reasons, the experimental data of the ompressor s harateristis grasped by researhers an not be enough to satisfy the need of power plant simulation. Therefore, how to use the limited data to obtain an aurate alulate model for dynami simulation, is one of the key points to analysis the performane of variable onditions performane, rapidly and exatly. The main treatment method of the ompressor harateristi is the fitting method. The ore idea of this method is use some reasonable mathematial methods to inrease and optimize the performane data, whih an meet the simulate requirements of the smoothness, the auray and the wide sope appliation, on the basis of a small amount of ompressor operation data. The ommon mathematial treatments are urve fitting method [1-3] (inluding partial least squares and moving least squares, et.) and neural network method [4-7] (inluding the BP neural network and RBF neural network, et.). R.Tirnovan and S.Giurgea[3] disussed the aspets of the numerial modeling of a ompressor used on fuel ell appliations, inluding the semi-empirial approah, the moving least squares algorithm method and the hybrid method based on moving least squares, and the researh shows that the hybrid method desribes better the global behavior of the ompressor and an be uses for the on-line and off-line identifiation of the ompressor. Youhong Yu and Lingen Chen [5] disussed a three-layer bak propagation neural network to predit the ompressor s harateristi performane map, and the result delared that this method an be used for the development of an off-design model or overall dynami simulation of the behavior of a gas turbine. Journal of Convergene Information Tehnology(JCIT) Volume 7, Number 18, Ot 01 doi : 10.4156/jit.vol7.issue18.66 549
A Three-Hybrid Treatment Method of the Compressor's Charateristi Line in Performane Predition of Power Systems The theoretial analysis and pratial appliation show that: when the experimental data points are small, either urve fitting method or neural network method, annot meet the requirements of the preision and smoothness for simulation. Based on the above analyses, this paper presents a omprehensive treatment for the ompressor harateristi performane, whih used the numerial simulation (CFD) method to get a small amount of the design and off-design performane data instead of the experimental researh firstly, and then used the least square method (LSM) to inrease the numerial simulation data, finally used the BP neural networks method to establish the ompressor harateristi urve omputational model for ertain ompressor omponents. With this method, the author built a alulation model, and analyzed the variable onditions performane of this devie.. Treatment for the ompressor harateristis A ompressor is a rotary thermal devie, whih pressurizes the working medium. One the ompressor geometry has been fixed at the design point, the ompressor harateristi map may be generated to define its performane under all the off-design onditions. Pressure ratio and isentropi effiieny are plotted vs. orreted mass flow for a series of lines of onstant orreted speed. In pratial appliation, the most redible method to get one ertain ompressor s harateristi map is the experimental study. However, the ost is expensive and the time onsumption is long. With the development of omputer tehnology and the CFD tehnology (Computational Fluid Dynamis), the reliability of numerial simulation results is inreasing, whih makes the numerial simulation more and more attention than experimental researh on the method of performane analysis omponents. The ompressor harateristi data used in this artile is obtained by numerial simulation. In the numerial simulation proess, firstly drew the six-stage ompressor s three-dimensional geometry model based on atual size, then generated the omputational mesh, and finally set the boundary onditions aording to pratial situation. In the numerial simulation proess, it is very important to set ompressor at the standard onditions (the pressure is 0.101MPa, the temperature is 303.15K). In atual operation, in order to take Inlet onditions on the performane of power plants, ompressor harateristi line is usually treated as non-dimensional form. G T n f 1 1, p 1 T1 (1) G T n f 1, p 1 T1 () Where, is the ompressor pressure ratio on the line of atual operation; effiient on the ompressor surge boundaries; of atual operation; n is the ompressor rotation speed. is the G is the ompressor equivalent flow on the line 550
A Three-Hybrid Treatment Method of the Compressor's Charateristi Line in Performane Predition of Power Systems Pressure Ratio n=0.7 n=0.9 n=0.8 n=1.0 n=1.1 Correted Mass Flow Effiieny n=0.7 n=0.8 n=0.9 n=1.0 n=1.1 Correted Mass Flow Figure 1. Compressor performane urve of numerial simulation method The above hart shows that the ompressor performane data obtained by numerial simulation is little, and the span of data points is large. When used to fit harateristis, it an not meet the requirements of preision and smoothness. Therefore, we should use urve fitting method to enrypt the data point. Curve fitting method is a way to searh smooth urves funtion to approximate the expression of a group of ontaining data. In this paper, we take least square method for the same speed-line fitness. Literature shows that: For the axial flow ompressor, it an be regarded that there is a square relationship between pressure ratio and effiieny and equivalent flow under equivalent speed. Therefore, based on the data of numerial simulation, the author fit the square relationships of six ompression ratio-equivalent flow and effiieny-equivalent traffi. And on the basis of the relation of equivalent, the date points on the urve are inreased., f ng ag bg (3) 3 1 1 1, f ng a G bg (4) 4 Where, a, b and are the oeffiients of the eah ompressor harateristi line. 551
A Three-Hybrid Treatment Method of the Compressor's Charateristi Line in Performane Predition of Power Systems Pressure Ratio n=0.9 n=0.7 n=0.8 n=1.0 n=1.1 Correted Mass Flow Effiieny n=0.7 n=0.8 n=0.9 n=1.0 n=1.1 Correted Mass Flow Figure. Compressor performane urve of fitting method Using the urve fitting method, the performane data of the eah orreted speed is inreased enough to meet the performane simulation s requirement, though the number of the known orreted speed is too small to satisfy the off-design simulation request. Thus, the following work is to solve this question. A large number of the literatures studies have shown that the artifiial neural network method is a terrifi method to solve the problem. Artifiial Neural Networks (ANN), whih is based on the imitation of the brain networks struture and funtion, is a useful method for the data proessing. In this pratie, the multi-layer bak propagation network method (BP-Network) is widely used in the funtion approximation and fitting. The internal struture of the BP model was showed [1]. Figure 3. The internal struture of the BP model A neural network has a natural propensity for storing experimental knowledge and for making it available for use. It s made up of simple proessing units. That is, the neural networks are omposed of simple elements operating in parallel. These elements are inspired by biologial nervous systems. And the network funtion is ontated with the elements, whih an train a neural network to perform a partiular funtion by regulating the values of the onnetions between elements [8]. The transfer funtion of the BP-network inludes the linear funtion (purelin) and the nonlinear funtion (logsig and tansig). In this paper, the author used the logarithmi transfer (logsig) transfer funtion to alulate it. 1 1 a n e n (5) 55
A Three-Hybrid Treatment Method of the Compressor's Charateristi Line in Performane Predition of Power Systems Commonly a neural network is only through training, that an lead a partiular input to a speifi target output and only have a ertain generalization (the generalization is the non-input neural network training data to generate a reasonable sample of the output value). A large number of literatures show that: under the neural network training proess, there may be "too fit" problem, that is, when the error is small for training data, the non-training data errors is expanded. Therefore, it needs to hoose the right training methods to improve generalization. The independent training methods of improving the generalization ability of BP network inlude normalization method and the early termination of the law. Literature indiates that: the effet of the Bayesian normalization method for funtion approximation is good, and the early termination of the method is good for pattern reognition. Therefore, this paper used Bayesian normalization algorithm for network training. In the BP neural network was trained on the ourse, you also need to manually adjust the law to effetively ontrol the size of the network, so that the degree of onvergene speed and generalization meet the requirement. The appliation shows that: the network size and training level and training of non-linear objets onerning auray; training objets nonlinear higher the degree of auray to meet the same premise, the larger the network; and the network size is larger, the onvergene more slowly, or even reah the onvergene preision. On the basis of the above neural network method, the harateristis data is trained after it was enrypted. Now we illustrate the Speifi steps. First, through the network training, we get the generalization of intermediate data between the adjaent speeds. Then, we add the new generalization of data into the sample spae and do the next training. One again, we get new data and add into the sample spae. Analogially, the data is trained by this way until the data meet the required preision. The required preision in the training is 3 10-5. Figure 3 shows the harateristi urve of ompressor whih is got by the BP neural network method. For the multistage axial ompressors, the surge margin is an important aerodynami parameter. When the ompressor surge appeared, the thermal engine is in danger. Thus, this inident should be avoided. Compressor surge margin is defined as: G s G n Z 1 1 Gs G s s n (6) Where, is the ompressor pressure ratio on the line of atual operation; orreted mass flow on the line of atual operation; G is the ompressor s is the pressure ratio on the ompressor surge boundaries; G is the equivalent flow on the ompressor surge boundaries. s To failitate the alulation of surge margin, the ratio of orreted mass flow and pressure ratio on the ompressor surge boundaries is defined as a oeffiient. Through it, we an get the algebrai relationship between s and orreted speed ( n r ). s s r i r s i0 s 6 G i f n a n (7) Where, the subsript s stands for the point of the ompressor surge boundary; the subsript r stands for the orreted parameter; is a oeffiient. s 553
A Three-Hybrid Treatment Method of the Compressor's Charateristi Line in Performane Predition of Power Systems Pressure Ratio n=0.7 n=0.9 n=0.8 n=1.0 n=1.1 Correted Mass Flow Effiieny n=0.7 n=0.8 n=0.9 n=1.0 n=1.1 Correted Mass Flow Figure 4. Compressor performane urve of BP-network method From the above hart, we an see that the ompressor harateristi line, proessed by this method, has got high auray of alulation and better slikness of equivalent speed line. 3. Simulation model of the turboharged unit power system In order to verify the feasibility of the treatment method, a turboharged unit dynami simulation model has been built, whih an been used to analysis the power system s performane under the different working onditions. The turboharged unit dynami simulation model inludes the mathematial model of the working fluid s thermodynami properties, the alulation model of omponents (inlude ompressor, turbine, boiler and auxiliary steam turbine) and the inertia model of rotor and volume. 1) Mathematial model of Thermodynami Properties of working fluid The hemial formula of fuel assumed is C 8 H 16. Firstly, the orresponding molar onentration of gas omponents is obtained by the hemial equilibrium equation in the fuel fator β; then, thermodynami properties of every omponent are alulated by fitting formulae; finally, the thermodynami properties of gas mixture are obtained in aordane with the priniples of an ideal gas. When alulating the temperature by thermodynami properties, the author uses dihotomy in iteration to solve it. ) Mathematial model of ompressor and turbine The model mainly inludes the resistane alulation module of intake and exhaust airway modules for inquiring harateristi of omponents and modules for alulating thermal harateristis of omponents. Among them, the feature query module is obtained on the basis of trained BP neural network funtions and the thermodynami alulation module is established by variable speifi heat method on the basis of the model for alulating properties of working fluid. And the pressure loss of intake and exhaust airway is assumed to satisfy the following relationship. p G (8) Where, is the drag oeffiient, obtained by the value of a given design point parameters. 3) Boiler Model Volume inertia and thermal inertia are strong in boiler, and resistane loss of smoke an not be ignored. To simplify alulation, volume inertia and thermal inertia of boiler are embodied in the volume between ompressor modules and turbine modules. Appliation shows that: The proposed method affets dynami response of variable onditions, and does not affet the 554
A Three-Hybrid Treatment Method of the Compressor's Charateristi Line in Performane Predition of Power Systems steady-state ondition results. The following equation an be obtained by the onservation of mass and energy onservation: Gh Gf Hu W Gg hg (9) p G (10) B g Where, W is the absorption heat of boiler; G, G f and G g are respetively the mass flow of air, fuel and gas mass flow; is drag oeffiient, obtained by the value of a given design point parameters; H u is the low alorifi value of fuel; h and h g is the enthalpy of the inlet air and the)as of the boiler, respetively. Based on the simultaneous equations, we an obtain outlet temperature and outlet pressure values of boiler in different onditions of the gas boiler. h g G h G H W f u (11) G g Where, W is the absorption heat of boiler; G, G f and G g are respetively the mass flow of air, fuel and gas mass flow; is drag oeffiient, obtained by the value of a given design point parameters; H u is the low alorifi value of fuel; h and h g is the enthalpy of the inlet air and the)as of the boiler, respetively. 4) Auxiliary steam turbine model The effet of auxiliary steam turbine is simplified as additional power of ompressor - turbine rotor balane power. That is, when the turbine annot provide the ompressor s need of the power, we have to introdue the part of the overheated steam whih was produed by the boiler to another auxiliary steam turbine. 5) Rotor inertia model For the ompressor - turbine rotor, the following equation an be obtained by the law of angular momentum: dn 900 N N N dt Jn t s (1) Where, n is the rotor speed; J is the rotor inertia; N t, Ns and N are respetively power of turbine, auxiliary steam turbine and ompressor. 6) Volume Inertia Model For the turbo unit, volume inertia between ompressor and turbine is very large (mainly beause of large boiler apaity), so the volume inertia annot be ignored. The following equation an be obtained by the law of onservation of mass. Where, V is the volume; G and in dp RT ( G in G out ) (13) dt V G out are respetively the mass flow of import and export. In order to improve the effiieny of simulation, VC language is employed to finish thermodynami properties program, and C-MEX interfae is employed too. It shows that: in the dynami model, the inertia variable (referring to the rotor, the volume and thermal inertia) only 555
A Three-Hybrid Treatment Method of the Compressor's Charateristi Line in Performane Predition of Power Systems affets the dynami response, and does not affet the steady response. Therefore, the dynami model is employed to finish the steady-state alulation of Variable Conditions. 4. Results and disussion In order to verify the auray of the turboharged unit dynami simulation model, the power system performane at design ondition has been heked under the standard atmospheri ondition. Table 1. The differene between the alulated value and the referene value at design ondition parameters Unit Calulated Value Referene value Mass flow rate of the air Kg/s 45.38 45.00 Effiient of ompressor - 0.835 0.845 The hek data shows that the treatment method of ompressor harateristis whih had been used in the turboharged unit dynami simulation model is aurate. So we an use this dynami simulation model to predit the off-design performane of the power system. n=1.1 Pressure Ratio n=0.7 n=0.9 n=0.8 n=1.0 Correted Mass Flow Effiieny n=0.7 n=0.8 n=0.9 n=1.0 n=1.1 Correted Mass Flow 30 Surge Margin (%) 5 0 15 Correted Mass Flow Figure 5. The design and off-design performane of the power system The above harts show the running line of turboharged unit under the same exess air ratio (α value of 1.088). The running line is formed of the steady-state points of different onditions (power range 0.5 to 1.0). the results show that the ompressor an meet the requirements of anti-surge when the exess air ratio of the boiler remains unhanged. And in order to improve the seurity of the turboharged unit power system under the low onditions, we an inrease the 556
A Three-Hybrid Treatment Method of the Compressor's Charateristi Line in Performane Predition of Power Systems amount of work done by the auxiliary steam to adjust the auxiliary steam turbine. 5. Conlusion This paper presents a omprehensive treatment for the ompressor harateristi simulation. The method is based on the performane data, whih was firstly obtained by numerial simulation method, then densified by least square method, and finally simulated by BP-neural network method. Based on this method, a dynami simulation model was built for the turboharged unit power system in the MATLAB platform. And then, use this simulation model to hek the design performane of one ertain turboharged unit, and predit the off-design performane of the power system. The pratial appliation shows that this method not only an satisfy the preision and smooth requirements of the ompressor harateristis in the performane analysis, but also an get fast alulation speed. 6. Referene [1] Yang Xinyi, Shen Wei, Liu Haifeng, Compressor harateristis generation method using moving least square, Journal of Aerospae Power, Vol. 4, No. 8, pp. 1741-1746, 009. [] Liu Xihao, Tang Shengli. Mathematial model of ompressor hrateristi map based on the patial least square theory, Tubine Tehnology, Vol.48, No. 5, pp. 37-39, 006. [3] R. Tirnovan, S. Giurgea, A. Miraoui, Modelling the harateristis of turboompressors for fuel ell systems using hybrid method based on moving least squares, Applied Energy, Vol.86, No. 7-8, pp. 183-189, 009. [4] R. Tirnovan, S.Giurgea, A.Miraoui, Surrogate modeling of ompressor harateristis for fuel-ell appliations, Applied Energy, Vol.85, No. 5, pp. 394-403, 008. [5] Youhong Yu, Lingen Chen, Fengrui Sun, Chih Wu, Neural-network based analysis and predition of a ompressor s harateristi performane map, Applied Energy, Vol.84, No. 1, pp. 48-55, 007. [6] Chen Ce, LI Jun, A Study of Turbofan Component Charateristis Based on Bak-Propagation Network, Journal of Aerospae Power, Vol.19, No. 1, pp. 61-64, 004. [7] O.Cortés, G.Urquiza, J.A.Hernández. Optimization of operating onditions for ompressor performane by means of neural network inverse, Applied Energy, Vol.86, No. 11, pp. 487-493, 009. [8] Shifei Ding, Weikuan Jia, Chunyang Su, Xiaoliang Liu, Jinrong Chen, An Improved BP Neural Network Algorithm Based on Fator Analysis, JCIT: Journal of Convergene Information Tehnology, Vol. 5, No. 4, pp. 103-108, 010. [9] Cai Guoqiang, Jia Limin, Yang Jianwei, Liu Haibo. Improved Wavelet Neural Network Based on Hybrid Geneti Algorithm Appliationin on Fault Diagnosis of Railway Rolling Bearing, JDCTA: International Journal of Digital Content Tehnology and its Appliations, Vol. 4, No., pp. 135-141, 010 557