2.1 Generator Voltage Control

In the advanced country, there is usually no need to install the OLTC on the generator main transformer since the power grid is sufficiently stable. Contrary, in the developing countries, because of severe voltage fluctuation on the grid, an OLTC should be installed on the generator’s main transformer in many cases⁽¹⁰⁾. With the increment of variable energy source such as renewable energy sources, the stability of the grid is getting challenged even in advanced countries also⁽¹¹⁾. The synchronous generator’s automatic voltage regulators (AVR) is much faster than the OLTC, it can provide more robust voltage regulation. In addition, its operation is smooth and does not cause step voltages as in the case of the OLTC transformer. On the other hand, its range of control is limited by the reactive power capability of the machine. For these reasons, generator AVR control could be used for fast, fine voltage regulation and the OLTC control could be used for coarse, secondary control⁽¹²⁾.

Thus, this paper aims to regulate voltage excursion on the unit’s MT and its inherent effect on the generator output voltage of an NPP in Nigeria. Also implementation of artificial neural network (ANN) as a control mechanism for the effective and efficient operation of the MT OLTC tap settings is proposed.

2.2 Connection of NPP to Electric Grid

The key equipment and their characteristics important to the interaction between the electric grid and an NPP proposed in this study are shown by the schematic power system illustrated in fig. 1.

2.3 Limits on Generator Operation

The main generator(MG) must be able to provide reactive power to the power grid as well as absorb reactive power from the power grid in order to maintain the grid voltage within acceptable range.

The typical generator reactive power capability curve is shown in the fig. 2⁽⁶⁾ for a rated generator voltage. The curve shows the three thermal limits under which the generator operates and these are the overexcited limit, the stator heating limit, and the under excited limit ⁽¹³⁾.

The generator megawatt (MW) output is limited bythe turbine capability as shown in the fig. 2. The MT MVA rating should never restrict the generator MW output for any given turbine output.

The generator usually operates with lagging power factor (PF) to supply both active and reactive power to the grid. In a deregulated grid system such as Nigeria, a key decision must be made whether the connected NPP is to operate as a base load or having the capability to perform load following within its transmission system ⁽⁶⁾. The IEEE Std C50.13-2005 states that “Generators shall be thermally capable of continuous operation within the confines of their reactive capability curves over the range of ± 5% in voltage.” Reactive power flow depends on the voltage magnitude difference between generator voltage and system voltage. Therefore reactive power range should be taken into account primarily in the selection of impedance and turns ratio.

3.1 Grid Voltage and Operation Conditions

The key characteristics of the Nigerian grid as related to this research in accordance with the country’s grid code are as follows:

The high-voltage side of the MT is connected to the 330kV of the grid. The transmission company of Nigeria (TCN) i.e. the system operator, shall endeavor to control the different busbar voltages to be within the voltage control ranges specified in the table 1. Under system stress or following system faults, voltages can be expected to deviate beyond the above limits by a further +/-5% ⁽⁷⁾.

The nominal frequency of the system shall be 50 Hz. The national control center will endeavor to control the system frequency within a narrow operating band of +/-0.5% from 50 Hz (49.75–50.25 Hz). But under system stress, the frequency on the power system could often experience variations within the limits of +/-2.5% from 50 Hz (48.75 – 51.25 Hz). Each generating unit must be capable of supplying rated power output (MW) at any point between the limits of 0.85 power factor lagging and 0.95 power factor leading ⁽⁷⁾

3.2 Generator Terminal Voltage Evaluation by Power Transfer Formular

The evaluation of the effect of severe voltage degradation on the MG output voltage of APR1400 when connected to the 330 kV Nigerian grid was performed through two different approaches; the use of power transfer equation according to IEEE Std. C57.116-2014,

load flow analysis using ETAP® software.

Considering a power system represented by fig. 3, the power transfer equation between the transmission system and the NPP generator’s output voltage is given by equation (1)⁽¹³⁾

Making Vg the subject of the equation:

Note: The bar over and are complex numbers.

Where:

Vs = system voltage, kV

$\delta$ = voltage angle (Vs is d degree lag than Vg)

Vg = generator voltage (assumed to be at zero angle for reference) per unit on Vgbase

(MW$\pm$jMvar) = generator output (less unit auxiliary loads) MW and Mvar

MVAT = megavoltampere rating of MT for VTHV tap

(RT+jXT) = resistance and reactance of MT, per unit at the nominal MT turns ratio.

When active power of the generator is constant, the variation in the reactive and apparent power due to changes in power factor (PF) for values between 0.9 leading and 0.85 lagging are as shown in table 2⁽¹⁴⁾. The effect of the voltage degradation of the Nigerian 330 kV grid on the MG output voltage is calculated using the equation (2) above and the calculated values of P and Q for the PF values between 0.90 leading and 0.85 lagging as shown in table 2. This calculation was done with the input data of the daily voltage variations profile of the Nigerian 330 kV electric grid over specific period of time.

The results from the power transfer equation calculation shows that the MG output voltage will go beyond the tolerable ±5% limit of its rated voltage during degraded voltage condition of the grid. This is undesirable for the reactive power generation capability of the MG of the NPP.

The rated terminal voltage of the MG is maintained during voltage fluctuation conditions from the grid through appropriate tap settings of the OLTC installed on the MT.

3.3 Voltage Control Simulation by ETAP Program

The second approach used to evaluate the effect of voltage degradation of the Nigerian 330 kV transmission system on the generator’s output when connected to the NPP shown in fig. 3was modelled in detail using ETAP® 20.0.0. A load flow analysis was performed to assess the capability of the MG of the NPP to operate within the tolerable limit of ±5% of its rated terminal when subjected to the Nigerian grid characteristics and MG operating limit under normal power operation mode and loading conditions. The switchyard voltage was set at 110%, 105%, 100%, 95%, 90%, and 85% of the nominal value (330 kV). This was determined based on the maximum and minimum expected value of grid voltage during transient conditions.

4.1 Architecture of ANN

A multiple-layer perceptron (MLP) ANN consisting of the input layer, multiple hidden layers and an output layer was used in the proposed ANN technique as fig. 4shows ^(9)(15): Keras in Python was used to develop the ANN model for the MT OLTC tap settings prediction. The model has one input layer with three input variables, the activation function for that layer was 'relu'. The input data to the ANN model for the MT OLTC tap settings prediction are the system voltage (Vs), active (P) and reactive (Q) power which are the generator outputs dependent on the power factor of the generator while the generator output voltage is dependent on the system (grid) voltage and this is illustrated as in table 3. The model has six hidden layers, the first 128 neurons, and the second to sixth layers have 256 neurons. The activation function for the hidden layers are 'ReLU' and the kernel optimizer is 'normal'. The output layer has one neuron for the regression output, also the layer has activation function of ‘linear’ and optimizer of ‘Adam’. ^{(16) (17)}.

4.2 Training and Testing processes of the ANN Model

table 3 shows the parameters of the ANN model used for the MT OLTC tap settings prediction. The model was trained with 60% of the input data from load flow analysis results as shown in table 3 and validated with 40% of the training data. A new data set was seeded in the model for the testing purposes. The ANN model was trained with a batch size of 32 and various numbers of epochs with optimal number of 500. Adam optimizer was adopted to minimize the loss of the ANN model. The mean absolute error (MAE) was used to evaluate the model's loss function and accuracy.

5.1 Load flow analysis results

The load flow analysis result for normal power operation shows that during voltage variation of the grid, the MG tried to maintain its terminal rated within the tolerable limit of ±5%. This is usually done by the automatic voltage regulator but, the sufficient reactive power to counteract the condition was not usually met by the AVR.

table 4 shows the summary of the load flow analysis results for all the PF values between 0.90 leading and 0.85 lagging including how the OLTCs on the MT automatically adjusts their turn ratios in order to keep the MG output voltage within the tolerable limit in spite of the voltage excursion from the grid.

The MG rated terminal voltage level are maintained within the tolerable limit of ±5% by appropriate adjustment of the voltage tap settings of the MT.

5.2 ANN training and test results

The essential step in any machine learning model is to evaluate the accuracy of the model. The mean squared error (MSE), mean absolute error (MAE), root mean squared error(RMSE), and R-Squared or coefficient of determination metrics are used to evaluate the performance of the model in regression analysis ⁽¹⁸⁾. Figures 5 through 7 show the performance of ANN model after training. They illustrate the drop decline in MAE and MSE values, and the excellent performance of XGBoost regression, R-Value 1.0000.

The comparison of the value of the MT OLTC tap settings from the IEEE Std. C57.116 power transfer equation and the ANN model OLTC tap settings prediction are then compared to see which of them have closer values to that obtained from the ETAP simulations results (target) as the appropriate tap settings required to mitigate voltage excursion. The result of which is shown in table 5.

The comparison of the MT OLTC tap settings position amongst the different approaches used in the research showed the results from the ETAP simulation curve (red) matches fitly with the ANN model curve (green-superimposed under the red curve) are much closer compared to that from the power transfer equation as shown in fig. 8.

The evaluation metric for the prediction model are as follows: Mean absolute error (MAE): This metric measures the closeness of the predicted values to that of the actual or real values. The best model is obtained with the minimum MAE. The MAE is defined by the equation 3:

Where:

n = samples number

$y_{i}$ = actual output value

$\overline{y_{i}}$= predicted values

Mean squared error (MSE): This metric measures the squared errors average between the predicted values to that of the actual or real values. The best model is obtained with the minimum MSE. The MSE is defined by the equation 4:

Where:

$SE\widetilde y$ = Squared error of the regression line

$SE\widetilde y$ = Squared error of the regression line

The metrics obtained from the ANN model for the MT OLTC tap settings prediction are displayed in the table 6. The performance of the ANN model is measured with the MAE metric value of which implies that the MT OLTC tap settings prediction at any point in time would only be off the target value from ETAP simulation approximately by 9.8611 X 10^-5%