Nonlinear Identification of a Gas Turbine System in Transient Operation Mode Using Neural Network

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1 Nonlinear Identification of a Gas Turbine System in Transient Operation Mode Using Neural Network 1 Mehdi Rahnama 1, Hadi Ghorbani 2, Allahyar Montazeri 3* 1 Operation Department of Montazar-Ghaem Power Plant, Karaj, Iran. mehdi.rahnama@gmail.com 2 Operation Department of Montazar-Ghaem Power Plant, Karaj, Iran. ghorbani.hadi@gmail.com 3 Ilmenau University of Technology, Ilmenau, Germany, allah-yar.montazeri@tu-ilmenau.de Abstract: In this paper ANN (Artificial Neural Network) identification techniques are developed to estimate a General Electric frame 9, 116MW combined cycle, single shaft heavy duty gas turbine dynamic behaviors during loading process based on available operational data in Montazer Ghaem power plant in Karaj. Related Input and output data are chosen based on thermodynamics and first order linear models. Electrical power and exhaust gas temperature are chosen as system main outputs which can be expressed by fuel flow, shaft speed and compressor inlet guide vanes considering the ambient temperature effects. The operating condition of the gas turbine during identification procedure is considered from full speed no load to full load. Comprehensive results perform that this model outputs is closer to the experimental data than conventional NARX models and can predict system behaviors perfectly. Keywords: Gas Turbine, System Identification, ANN, Power Plant 1. Introduction In the history of energy conversion, the gas turbine is a relatively new energy converter. Nowadays, gas turbines which run on natural gas, diesel fuel, biomass gases and etc, are natural power plant for offshore platforms because of their compactness, low weight, and multiple fuel applications. Therefore the gas turbine has found increasing service in the power industry throughout IRAN. Since gas turbine internal faults or distribution network load fluctuations may cause instabilities in the grid, it is necessary to investigate an accurate dynamical model for gas turbine system [1-5]. Mathematical models using computational techniques and thermodynamics [6, 7, 8] are unsuitable for the design of the control system or stability studies, due to their complexity and nonlinear characteristics. Thus a simplified mathematical model consists of a set of algebraic equations, simple time delays, and related temperature, speed and acceleration controllers is provided by W.I.Rowen [9], and modified by adding the influence of variable inlet guide vanes (VIGV) in [10]. This frequency-domain model validated by L.N.Hannet using some tests [11] and was developed in some fields such as fuzzy control and frequency studies [12,13]. Physically-based model for determining frequency dependency and a neural network simulator [14, 15] are examples of gas turbine other models too. The identification techniques have been concerned mainly about aircraft gas turbine engines e.g. [16, 17, 18]. As an implementation a low order linear model using Box-Jenkins algorithm of a micro-turbine is presented in [19]. Gas turbine low dimensional linear models are often accurate about operating points. Also, static nonlinear models such as Wiener-Hammerstein have constant DC gain or contain linear approximations that cause these kinds of models be heavily dependent on the selected operating points. Otherwise, NARX models can well approximate many dynamical systems with a wide range of nonlinear behaviors [20, 23, and 24]. An algorithm for identification of reduced-order dynamic models of gas turbines is presented in [26] taking account of the dependency of prediction errors. Using soft computing applications and genetic algorithms are applied for gas turbine system in order to parameter identification [27]. There have already been a few attempts to control a gas turbine with (Feed forward) neural Networks [28], [29], [30]. The combination of Recurrent Neural Networks (RNN) and Reinforcement Learning (RL) is used in [31]. In this paper ANN identification approaches are used in order to identify a GE 9001EA heavy-duty gas turbine with 116.4MW rated power and SPEED TRONIC MK IV control system which has been mounted in Montazer Ghaem power plant. Compressor, combustion and turbine dynamics are studied and I/O (Input-Output) signals are chosen according to the thermodynamic and typical W.I.Rowen models [9]. Electrical output power and exhaust temperature are estimated as main outputs and simulating results are compared with NARX model [26] and experimental data. Results show that ANN system identification are perfectly applicable to estimate gas turbine behaviors in wide range of operating points from full speed no load to full load conditions. *Allahyar Montazeri is Humboldt Research Fellow with the Control Engineering Group at Ilmenau University of Technology

2 2. Gas Turbine System Description According to the Brayton cycle, an ideal gas turbine system consists of both isentropic and isobar processes thermodynamically. Thus heavy-duty gas turbine consists of combustion chambers, a multi stages axial flow compressor connected to a multi stages expansion turbine which drives an electric generator for electrical power supply. Also the inlet air flow rate is maintained by guide vanes (VIGV) in the compressor entrance. Temperature of the gases entering the turbine cannot exceed the limit imposed by the high temperature resistance of the materials. Nevertheless, if this temperature decreases too much, the plant (both gas turbine and HRSG) efficiency would become unacceptably low. Therefore turbine firing temperature ( ) must be kept under a higher limit (technical) and over a lower limit (economical), as close as possible to the optimum economical point [16]. According to the thermodynamic explanations it is presented by [22] as below: (1) W T f (W a,w f,t a,x) =T f D.K+T W a 1+ (X1) a comp Here X is: defined X=[CPR W a ] 1 In the SPEED TRONIC MARK IV, quantities T f and w a are not measured directly, because of some technical considerations. Thus T f is maintained by means of T x and CPD thermodynamically. Thus T x can be expressed by relation (2) [22]: (2) T x Turbine,T f,x = 1 (1 1 X ) Turbine T f Parameters T x and CPD which indirectly explain combustion quality are system main outputs. In other hand, T x and CPD are correspondent to T f and W a respectively. Parameters W a and CPD, vary with ambient air temperature T a, shaft speed and IGV variations by considering constant site pressure. Also exhaust gas flow rate W x can be assumed equal to the W a eliminating fuel rate W f against the W a in the combustor (see [2, 14]). Therefore, W a can be expressed as followings: W a =q(t a,p a )u( c ) sin ( IGV 0 ) (3) sin ( max 0 ) Where: q(t a,p a ) = P a T a0 P a0 T a (4) u( c ) =1+A 0 c +A c +A 2 c (5) c = c 1 (6) In relation 3, the air flow ( W a ) equation includes the ambient factor, q(t a,p a ), which represents the effects of the ambient temperature (T a in K) and the atmospheric pressure (P a ), where T a0 = 288 K and P a0 = 1 atm. The airflow depends on the shaft speed () through the temperature-corrected speed ( c ) by following relations: c = T a0 T a (7) The air flow speed factor (u) with parameters A 0, A l and A 2 approximates the effects of the temperaturecorrected speed ( c ). The air flow speed factor and temperature-corrected speed are both dimensionless quantities that are similar to Mach numbers. They relate, respectively, the speed of the air and the speed of the compressor blades to the speed of sound. The VIGVs can be represented with the sine. The parameter max is the maximum angle the IGVs can attain and 0 is a parameter dependent on the IGV geometry. Considering W a and W f as system main inputs exhaust temperature is expressed using these equations as below (14): T x =T a + A 3 P a P a0 +A 4W f W a (8) where A 3 and A 4 are constant values that are related to turbine design characteristics. Consequently, by replacement equation 3 in 8 and doing some simplifications F is defined as nonlinear s which express T x respectively by means of independent variables: T x =F(T a,igv,,w f ) (9) Turbine output torque is not appreciably affected by guide vane action and can be estimated to within 0.05 per unit accuracy by [10, 16]: T out = 1.16 (W f1.33) (10) Output electrical power (P e ) is the plant extreme. Generally, the output mechanical power is evaluated in both isolated and nonisolated modes. In isolated mode it is a of shaft speed and fuel flow rate. Inversely in nonisolated mode power is a of fuel flow only (network frequency is constant). But if in this mode the DROOP coefficient be considered, the power will be affected via network frequency too. Thus in a general form [10, 16]: P e =f(,w f ) (11) Instead using fuel flow command and mechanical power, it is possible to relate them with FSR (fuel stroke reference) and electrical power output respectively [14, 20]. The ambient air temperature fluctuations should be considered for power calculations because of its direct affects on gas turbine performance. By using fuel command, the dynamic of stop-ratio and control valves is taken into account with combustion system. In addition, the electrical generator and rotor dynamics are considered with the power system. Figure 1 illustrates the gas turbine cycle overview schematically.

3 Fig. 1: Gas Turbine Cycle 3. Artificial Neural Network An artificial neuron is a computational model inspired in the natural neurons. Natural neurons receive signals through synapses located on the dendrites or membrane of the neuron. When the signals received are strong enough (surpass a certain threshold), the neuron is activated and emits a signal though the axon. This signal might be sent to another synapse, and might activate other neurons [32]. From the viewpoint of the engineer, it is important to define how a network should behave, without having to specify completely all of its parameters, which are to be found in a learning process. Artificial neural networks are used in many cases as a black box [32]. The complexity of real neurons is highly abstracted when modeling artificial neurons. These basically consist of inputs, which are multiplied by weights, and then computed by a mathematical which determines the activation of the neuron. Another computes the output of the artificial neuron. ANNs combine artificial neurons in order to process information. The higher a weight of an artificial neuron is, the stronger the input which is multiplied by it will be. Weights can also be negative, so we can say that the signal is inhibited by the negative weight. Depending on the weights, the computation of the neuron will be different. By adjusting the weights of an artificial neuron we can obtain the output we want for specific inputs. But when we have an ANN of hundreds or thousands of neurons, it would be quite complicated to find by hand all the necessary weights. But we can find algorithms which can adjust the weights of the ANN in order to obtain the desired output from the network. This process of adjusting the weights is called learning or training. The backpropagation algorithm is used in layered feedforward ANNs. This means that the artificial neurons are organized in layers, and send their signals forward, and then the errors are propagated backwards. The network receives inputs by neurons in the input layer, and the output of the network is given by the neurons on an output layer. There may be one or more intermediate hidden layers. The backpropagation algorithm uses supervised learning, which means that we provide the algorithm with examples of the inputs and outputs we want the network to compute, and then the error (difference between actual and expected results) is calculated. The idea of the backpropagation algorithm is to reduce this error, until the ANN learns the training data. The training begins with random weights, and the goal is to adjust them so that the error will be minimal [25]. The first step to formulate the problem is identification of proper inputs and outputs sets. According to relations that are explained in previous section air temperature (T a ), speed (), fuel stroke reference (FSR) and inlet guide vane position (IGV) as input signals and electrical output power and Exhaust temperature of gas turbine as output signals are considered. 4. Simulation Results and Network Performances Neural Network toolbox in MATLAB R2009a is used for simulation and training process. Delayed feed forward network is chosen for implementing ANN. The three layers are input layer, hidden layer and output layer respectively. Some hidden layers are taken and number of neurons is varied from 4 to 20 in each layer in order to arrive at final architecture. After enough experimentation and simulation one hidden layer is selected. The hidden layer contains four neurons in related to four inputs and output layer contains two neurons in related to two outputs. For dynamic response for each input three delays are considered. The neural network architecture is displayed in figure 2.

4 TABLE I: Neural Network Parameters Epochs 1000 Training TRAINL M Fig. 2: Neural network architecture Before simulation for better neural network performance, all input and output signals are normalized and then they are used in neural network training procedure. Eighty percent of data is used for training, ten percent of input is used for validating and ten percent of data is used for testing network. All Input and output data are gathered from logging system and operational documents from Montazer- Ghaem Power Plant. Simulations run for more than twenty times and results are compared for best performance and minimum error. All architectures were trained for 1000 epochs. The training s and parameters are given in table- 1. Learning curve for training, validating and testing data is showed in figure 3. Fig. 3: Learning Curve Figures 4 and 5 are simulation results that are compared with NARX method that authors are published in references [23] and [24]. For better comparison, relative error between artificial neural network outputs and NARX model outputs are displayed in figures 6 and 7 and table 2. Adaption learning Hidden layer transfer LEARNGD A TANSIG Max fails 30 Input layer transfer Output layer transfer Performan ce TANSIG PURELIN MSE Mu Time Inf Mu-max Goal Results and Discussion ANN techniques are applied to the single shaft heavy duty gas turbine paralleled to a HRSG. Thus the effect of some fuel and guide Vanes swings on system outputs can be observed. These swings are often existed by boiler temperature or levels control purposes or network power and frequency fluctuations or part load mode selecting for operating gas turbine. Data sampling is done from FSNL (full speeds no load) to full load (86.17 MW base load) conditions with sampling interval 1.0 sec. During data collecting, the HRSG is loading and consequently the related steam turbine is paralleled to the network. Due to the starting HRSG and loading the gas turbine, the control module was manually and the guide vane was controlled by operator. Gas turbine behaviors are extremely depends on ambient condition Thus it is mentioned that site ambient temperature oscillations were 28 to 32 C. Recorded signals are air temperature (T a ), speed (), FSR and IGV as input signals to estimate P e and T exhaust as output signals. Experiments showed that the ambient temperature is a crucial parameter. Thus the model can be valid in the identified data limit. Moreover, a comparison is presented for ANN, NARX models and experimental measurements in 4 and 5 (a, b and c) for output power and exhaust temperature. Based on simulation results and table 2 it is shows that the ANN model can describe the system behaviors more adequate than NARX model for each output. TABLE II: Error of System Identification Identification Method Mean Squared Error Output Power Exhaust Temperature ANN NARX

5 a- Full Load a- Full Load a- Full Loading a- Min Loading b- Min Load b- b- Min Min Loading c- Loading Fig. 4: Output Power Estimations c- Loading Fig. 5: Exhaust Temperature Estimations Fig. 6: Output Power Error Fig. 7:Exhaust Temperature Error

6 6. Conclusions In this paper, electrical output power and exhaust temperature of heavy-duty single shaft gas turbine are identified from full speed no load to full load, which is mounted in Montazer Ghaem Power Plant. The investigated gas turbine is a General Electric frame nine, MS9001E series. Outputs are estimated by ANN identification methods and results are compared with NARX models. The validity studies show the ANN model can estimate the turbine characteristics well. In addition, by experimental results the ANN model is found more accurate than conventional nonlinear models. 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