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Power uprates pose a threat to electrical generators due to possible parasite effects that can develop potential failure sources with catastrophic consequences in most cases. In that sense, it is important to pay close attention to overheating, which results from excessive system losses and cooling system inefficiency. The end region of a stator is the most sensitive part to overheating. The calculation of magnetic fields, the evaluation of eddy-current losses and the determination of loss-derived temperature increases, are challenging problems requiring the use of simulation methods. The most usual methodology is the finite element method, or linear regression. In order to address this methodology, a calculation method was developed to determine temperature increases in the last stator package. The mathematical model developed was based on an artificial intelligence technique, more specifically neural networks. The model was successfully applied to estimate temperatures associated to 108% power and used to extrapolate temperature values for a power uprate to 113.48%. This last scenario was also useful to test extrapolation accuracy. The method is applied to determine core-end temperature when power is uprated to 117.78%. At that point, the temperature value will be compared to with the values obtained using finite elements method and multivariate regression.

In the power generation industry, there is a question with no consistent answer over time: should we invest in new generation assets and increase installed power? Or on the contrary, should we improve existing installations to increase their performance and therefore their power output as well?

In economic scenarios such as the current one, in which power demand is stagnated and the expansion policies of most Western Europe utilities are a thing of the past, the question answered is the second one, relating to increased performance and power output of existing generation assets. By choosing the second option, investment is minimized and production unit costs optimized because, although actual production expenditure remains stable, energy generation increases.

For all these reasons, many authors develop solutions based on power uprates or comprehensive performance enhancements [

After determining end-core temperature as a limiting parameter [

Currently, there are two types of techniques to estimate end-core temperature: the finite element method (FEM) [

Using the abovementioned neural network requires a training process based on actual machine conditions and data, which means that it is necessary to have information on known operating states. Once the network simulates end-core temperatures with a minimum error under known conditions, it is time to extrapolate temperature values under power uprate conditions. In this case, there are available data for generator and end-core temperatures for an initial rated generator power of up to 108.57%. These data will be used to train the network and extrapolate end-core temperature values for power levels of up to 113.48%. Once this power is reached, the accuracy of the first extrapolation value will be checked. If extrapolation is accurate, the network will be rendered adequate and data will be gathered for a 113.48% power level which, together with available 108.57% power values, will be used to train the network and extrapolate data for a power level of 117.78%, which is what the licensee actually wants. The extrapolated value will be compared to the results obtained using the abovementioned two methods so as to analyze numerical values, calculation capabilities and method advantages.

The problem described will be analyzed in an energy production plant with the aim of determining the expected electrical generator core-end temperature for a power uprate.

The model is developed to estimate, simulate or extrapolate the core-end temperature in a liquid and gas cooled 4-pole [

After defining the problem and determining the equipment (generator) on which power uprate simulations and forecasts will be carried out, it is time to establish the physical model so that target parameters can be known, calculated and extrapolated.

Inside the generator there are several physical phenomena: electrical, magnetic, thermal and fluid-mechanical. The phenomenon favoring energy creation inside the generator is the rotation of the magnetic field, which is in turn caused by the electrical phenomenon of rotor turning and subjected to intensity. In this case study, turning speed is considered to be constant. A secondary phenomenon is stator electricity, characterized mostly by phase (3) intensity and terminal voltage. These two phenomena are responsible, together with grid conditions (reactive power), for heat and thermal generation due to parasite processes and losses.

Inside the water-and hydrogen-cooled generator there are two heat sinks: one for water and the other for hydrogen. The variables regulating the hydrogen heat sink are hydrogen purity and pressure as they impact the thermal coefficient of the gas, the thermal difference of hydrogen inside the coolers and also hydrogen temperature at the cooler outlet. In the case of coil water, the key variables are coil water flow rate and water temperature in generator inlet and outlet.

These variables, which can be seen in

The critical part in this type of generators is the core-end, which is exposed to magnetic flux and significant eddy current-induced losses in the tooth tips of the first magnetic plate packs. In this location the cooling effect of the hydrogen and water is not fully developed so the temperature is always higher than any other location. Output variables will be the core-end tooth tip.

For the purposes of this study, an artificial neural network has been selected as the best method because it is a general tool [

Once the conceptual model, tool and calculation process input and output variables have been determined, it is time to present the model scheme in which calculation stages, acceptance criteria values and admissible error rates will be developed.

The process starts by measuring the value of variables in

Description | Units |
---|---|

Gross generator power | MW |

Reactive generator power | MVAR |

Generator phase A current | A |

Generator phase B current | A |

Generator phase C current | A |

Generator field voltage | V |

Generator field current | A |

H_{2} generator purity | % |

H_{2} generator pressure | KG/CM^{2} |

Hydrogen temperature, cooler 1 inlet | ˚C |

Hydrogen temperature, cooler 1 oulet | ˚C |

Hydrogen temperature, cooler 2 inlet | ˚C |

Hydrogen temperature, cooler 2 oulet | ˚C |

Water temperature, stator inlet coils | ˚C |

Water temperature, stator outlet coils | ˚C |

Description | Units |
---|---|

Temperature between slots 70 & 71 (tooth tip) TC80 | ˚C |

Temperature between slots 69 & 70 (tooth tip) TC82 | ˚C |

Temperature between slots 68 & 69 (tooth tip) TC84 | ˚C |

Temperature between slots 67 & 68 (tooth tip) TC86 | ˚C |

Temperature between slots 64 & 65 (tooth tip) TC89 | ˚C |

Temperature between slots 63 & 62 (tooth tip) TC93 | ˚C |

for final extrapolation.

As previously mentioned, the power uprate value targeted by the licensee is 117.78%, for an apparent power of 1277 MVA and a power factor of 0.95. For end-core temperature value extrapolation, a network entry data sheet needs to be put together, similar to

In parallel, the values of

Given extrapolation criticality and the stochastic nature of neural networks, this final step will be described in further detail. The neural network will be tested using known data (108.57% and 113.48%). When the point in which the calculated error of end-core temperature values is lower than 0.1˚C, temperature values are calculated in the same point for a power level of 117.78%. In this case, the input variables included in

The method based on artificial neural networks provides a solution of acceptable quality with very little effort.

Description | Value | Units |
---|---|---|

Gross generator power | 1150 | MW |

Reactive generator power | −378 | MVAR |

Generator phase A current | 34940 | A |

Generator phase B current | 34940 | A |

Generator phase C current | 34940 | A |

Generator field voltage | 424 | V |

Generator field current | 5831 | A |

H_{2} generator purity | 98 | % |

H_{2} generator pressure | 5.27 | KG/CM^{2} |

Hydrogen temperature, cooler 1 inlet | 52 | ˚C |

Hydrogen temperature, cooler 1 oulet | 38 | ˚C |

Hydrogen temperature, cooler 2 inlet | 43 | ˚C |

Hydrogen temperature, cooler 2 oulet | 38 | ˚C |

Water temperature, stator inlet coils | 27.5 | ˚C |

Water temperature, stator outlet coils | 45 | ˚C |

A multilayer neural network (Feedforward) has a feature that was mentioned before: it is a universal approximator. The neural network is conditioned by the input layer, the output layer, as well as the transfer functions that together with the synaptic weights and biases, make up network parameters.

Focusing on the problem under analysis, a multilayer Feedforward network will be adopted. The neural network will have three layers: input, output and hidden. The first layer (input) will have as many neurons as variables in

・ The number of hidden neurons should be in the range between the size of the input layer and the size of the output layer. So the range will be between 15 and 6.

・ The number of hidden neurons should be 2/3 of the input layer size, plus the size of the output layer. In this particular case they are 16.

・ The number of hidden neurons should be less than twice the input layer size, so the number should be less than 12.

Obviously only the second condition is not coherent with the first and third, therefore, it will be neglected. So finally 12 neurons will be implemented in the hidden layer (see

Once the architecture to be used in a particular problem has been defined, it is necessary to adjust the neural network weight through the training process. The training process is composed of three sub-processes: learning, validation and test. The learning algorithm includes a problem of inference associated to free network parameters and related neuron connections.

The learning process of a Feedforward neural network is ought to be supervised because network parameters, known as weights and biases, are estimates based on a set of training patterns (including input and output patterns). In order to estimate network parameters, a backpropagation algorithm is used as generalization of the delta rule proposed by Widrow-Hoff [

This error estimates how the neural network can be adapted to the problem under analysis. Process results include not only error evolution during the learning phase, but also error distribution throughout the different phases as well as fitting between network-simulated values and real values. These results are specifically addressed in the following section.

This section will address network errors, both in the training and validation phases. The analysis will be more thorough than a mere evaluation of

The first analyzed figure (

In order to support the previous analysis, a linear regression between the data obtained by the trained neural network and the data actually measured (

・ R values or correlation coefficient are near 1; this means that neural network temperature output values match real values. It is also worth mentioning that data dispersion near the line is very small or null.

・ Line slope values are 1 in all cases, meaning that simulated values and measured values have a 1:1 equivalence. The result obtained is very close to reality, with an average error value of zero.

・ The simulation is slightly biased (value lower than 0.1), but it is considered residual and therefore negligible. The former analysis concludes that simulated values are realistic, with a high degree of accuracy.

In the previous section, the neural network was dimensioned and trained, and errors and results were analyzed in scenarios in which the temperature value provided by the trained neural network was taken as real.

According to the scheme in

In parallel and considering that this operational condition is feasible for the plant, real temperature measurements are taken at the selected points (

Measured points are compared to extrapolated (simulated) data by means of four graphs or techniques:

correlation, histogram, error-active power correlation and temperature versus time plot for extrapolated (simulated) and measured cases.

An analysis of linear correlation between extrapolated (simulated) and measured temperature data leads to the conclusion that the simulation is good when the adjustment value obtained is 0.94092 (

A histogram analysis (

According to

An analysis of active power and error correlation (

Finally and for information purposes,

In summary, it was verified that during the training phase, error is lower than 0.1˚C whereas in the extrapolation

phase for values at a power level 113.85%, error is under 5%. Thus, it is concluded that the neural network simulates well the thermal status of the generator and its core-end. The data and analyses provided in previous paragraphs support the credibility and robustness of the method, which is ultimately aimed at determining core- end temperature in advance, for a 117.78% power level in relation to initial generator rated power.

This is a clear, extreme case of extrapolation, which as opposed to a 113.85% power level (in relation to initial rated power), will render values that cannot be checked. That is precisely the motive for this work: obtaining an estimate to make decisions on the viability of a power uprate. In this case other simulated values are available. For this additional simulation, the finite element method (FEM) and regression method have been used.

As established in the introduction and the sequence of

In order to be coherent with previous analyses, correlations between real measures and neural network results during the training, validation and testing phases are shown in

Once the network is trained and due to the stochastic nature of neural networks, the training-simulation process should be repeated at least 30 times. In other words, it is important to train the network before applying the entry values of variables included in

Comparison with the values of other evaluation methods is shown in

The values of

Considering all these information and findings, it is possible to assert that the required power increase is viable without the need to modify any auxiliary generator parameter.

End core temperature | Method |
---|---|

87.48˚C | Neural network (average) |

81.3˚C | Finite elements |

127˚C | Multivariate regression |

This study leads to many conclusions. Firstly, the neural network used is found to be not only a good simulator of the core-end temperature value in an electrical generator, but also a valid option to predict and determine the expected power uprate core end temperatures. This concept can be broadened by using the network to determine core-end temperatures for non-tested conditions, hence considering this a forecasting model.

After looking at the three models used (

This tool allows a sensitivity study to determine the effect of each of the 15 input variables on the final result, hence favoring the establishment of cooling strategies if needed and anticipating unexpected scenarios and the best way to respond to them. This model is a very useful generator simulator, improving decision-making pro- cesses and training strategies for power plant operators.

Finally some remarks about the performance of the simulated electrical generator should be highlighted. The simulated electrical generator has an apparent power of 1120 MVA, and is working at a point of 0.98 power factor. In situations in which the grid has a capacitive behavior, the operator must reduce active power to avoid unwanted situations or cross the URAL curve (limit). This power reduction constitutes an economic impact. The proposed power uprate, in addition to setting the thermal behavior of the magnetic core, and new URAL curve based on that, leads to optimize the operation of the generator and the benefits of its exploitation. The other important point is that no plant modifications are required for the power uprate because none auxiliary system is limiting.