In the selection, matching, maintenance, and upgrade of excitation equipment for small hydropower plants, power station users often encounter the problem of calculating rectifier transformer parameters. Many electrical design manuals provide design formulas for rectifier transformers, but these formulas apply to standard application conditions, which differ from the actual operating environment of small hydropower plants. Transformers designed based on these formulas may not be practical. At the same time, there is a lack of professional technicians at the grassroots level of small hydropower plants, and users often find the selection and calculation of rectifier transformers very difficult. Therefore, it is necessary to provide a simple calculation method for grassroots users. 1.1 Selection of Rectification Method: Currently, low-voltage units basically adopt self-excited static thyristor excitation. The rectification methods generally include three-phase full-wave semi-controlled rectification and three-phase half-wave rectification. Full-wave rectification transformers have higher efficiency (95%) and better waveform. Half-wave rectification uses fewer silicon elements, but DC current flows through the secondary winding of the transformer, resulting in lower efficiency (74%) and greater waveform distortion. It is used in rectifier circuits smaller than 10kW, although some earlier designed larger units also used half-wave rectification. The calculation formulas for transformers of the two rectification methods differ. 1.2 Type of Rectifier Transformer: Epoxy dry-type transformers are used. Capacity is generally within 10-100kVA, nominal primary voltage (grid end) 400V, secondary voltage (valve end) within 100V, and current within 100-300A. Due to the relatively small capacity, it is housed in the same distribution panel as the rectifier. The rectifier transformer is self-cooled; heat dissipation is relatively good when no sealing plate is installed on the panel side. 1.3 Insulation Class and Heat Dissipation Method: The insulation class of dry-type epoxy transformers used in small hydropower projects is generally Class B, with a maximum insulation system temperature resistance of 130℃. Therefore, it is normal for the transformer's surface temperature to be hot to the touch when operating at full load. If the transformer is effectively forced into air cooling, its output power can be increased by 10% to 30%. Conversely, if the transformer operates in a sealed distribution box with poor heat dissipation, its current capacity must be reduced by 10% or more. 1.4 Impedance Voltage: In the generator excitation system, factors such as rectifier tube breakdown or DC circuit short circuit may occur. Therefore, the short-circuit impedance voltage of the rectifier transformer must be higher than that of ordinary transformers to limit excessive short-circuit current. The parameters of the short-circuit impedance voltage are designed by the transformer manufacturer and will not be discussed here. However, users must specify that it is a thyristor rectifier transformer when ordering from the manufacturer. Connection Group: The connection group of the rectifier transformer must match the phase requirements of the thyristor rectification control. For new designs, the following principles can be considered. Generally, the D,y11 method is adopted, that is, the grid side (primary) uses a delta connection and the valve side (secondary) uses a y connection. In this connection, the secondary phase voltage lags behind the primary phase voltage by 30° in phase. The D,y11 connection method is suitable for both three-phase half-wave and full-wave rectification. If the existing rectifier transformer connection group is Y,d11, it can also be used, but it cannot be used for three-phase half-wave rectification. As for the Y,y connection group, its use is not recommended. We know that the third harmonic voltage generated by three-phase controlled rectification is very high, reaching more than 50% of the fundamental value. The D-connection of the transformer can cancel out the third harmonic flux, minimizing its impact. However, if a Y,Y connection is used, the magnetic flux of the third harmonic generated by the rectifier circuit has no closed loop and cannot be canceled. Excessive third harmonics will cause excessive waveform distortion, affecting the normal operation of the transformer, generator, and other instruments and electrical equipment. When a power station submits order data to the manufacturer, it should clearly specify the transformer connection group and the primary and secondary voltages (and must specify whether it is phase or line voltage). Regarding the selection of the primary line voltage U1, the rated line voltage at the generator terminal of a small unit is 400V. However, small hydropower stations are generally located at the far end of the power grid, with long lines and high impedance from substations. This results in excessively high grid voltage at the end, especially during peak power generation periods in the high-water season, when the grid voltage (generator terminal) often reaches over 460V. If the primary voltage is still designed based on 400V at this time, the transformer will experience overvoltage, increasing losses and causing excessive heat generation. The iron loss of a rectifier transformer is related to the fourth power of its voltage multiple. For example, a rectifier transformer designed for 400V will have its iron loss increase to (480V)^4 = 2.07 times when operating at 1.2 times (480V). These losses are ultimately converted into heat within the transformer, causing a significant increase in temperature. Even worse, when the power supply voltage becomes excessively high, the magnetic flux density of the transformer core will enter the saturation region, causing a surge in primary current and potentially burning out the coil. Due to cost considerations, some rectifier transformers are designed and manufactured with a higher core magnetic flux density (Bm) while maintaining a primary winding voltage of 400V. Therefore, transformer burnout in areas with excessively high grid voltage is not uncommon. To address this, the primary winding voltage should be appropriately increased so that the transformer can handle a +20% increase in grid voltage. Generally, transformers have a 5% voltage overload capacity, so we can use an empirical formula to select the rated line voltage value of the primary winding: U1 = 0.95U1(MAX), where U1(MAX) is the highest grid voltage (converted to the generator terminal). If the calculated result is less than 400V, then select 400V. After increasing the primary voltage, the secondary voltage should also be increased by the same ratio to keep the transformation ratio constant, so as to maintain the same proportional increase and decrease in excitation voltage and generator terminal voltage, because the higher the generator voltage, the greater the required excitation power. Increasing the primary voltage is equivalent to increasing the number of turns per volt, both of which are aimed at reducing the magnetic flux density of the transformer core, preventing it from entering the saturation section of the magnetic flux density curve. The benefits also include reducing the transformer's no-load current and iron losses. Of course, there are some negative effects as increasing the number of winding turns increases the transformer's internal resistance and slightly increases current loss (copper loss), but this does not significantly affect the normal operation of the transformer. When calculating the voltage adjustment factor n, U1 = 440V can be used for simplicity, which can meet the requirements of most power grid conditions (400V-470V). The calculation of the secondary voltage U2 involves considering factors such as the excitation system's maximum excitation voltage, maximum excitation current, thyristor conduction angle, harmonic distortion, and the rectifier circuit's power factor. According to relevant specifications, the excitation circuit should provide 1.6 to 1.8 times the rated excitation voltage, meaning the transformer's secondary voltage needs to be 1.6 to 1.8 times its rated value. However, in reality, very few small hydropower units in my country operate as isolated power grids; the vast majority are connected to large power grids for electricity sales. They lack the need and capacity to provide strong excitation power to the grid—it should be noted that the capacity of large power grids is enormous, and the impact of a single small hydropower unit on it is negligible. If the secondary voltage is selected by increasing it by 1.6 to 1.8 times, the rectified voltage will be relatively high. During excitation, the thyristor rectifier system will be in a deeply controlled state for extended periods, resulting in a smaller thyristor conduction angle, increased waveform distortion, a worse power factor, and a larger short-circuit current during faults. All of these factors are detrimental to the operation of the transformer and generating unit. Furthermore, for the same transformer power capacity, a higher voltage inevitably leads to a lower current, a smaller conductor cross-sectional area in the coil windings, and increased current losses. Based on our experience, selecting a maximum rectified voltage of 1.3 times the rated excitation voltage is more appropriate. This not only addresses the disadvantages of excessively high voltage but also retains a certain rectified power margin, adapting to changing operating conditions. The formulas for calculating phase voltage U2 are: Three-phase full-wave rectification U2 = 1.3 * 1.06 (nUE + 2.5) Three-phase half-wave rectification U2 = 1.3 * 1.06 (nUE + 1.7) Explanation of each term in the above formula: UE—Rated excitation voltage of the generator (V); Coefficient 1.3—As mentioned above, it is the margin value of the excitation voltage; Coefficient 1.06—The compensation value for voltage drop caused by the leakage reactance of the transformer internal resistance when the current is at full load. Here, a simple fixed value is used to replace the complex calculation, and the error is not too large; n—voltage adjustment coefficient, see the previous section; coefficient 2.34 (or 1.17)—the ratio of the output DC voltage to the input AC phase voltage when all three-phase full-wave (or half-wave) rectifier elements are fully conducting, i.e., UE /U2＝2.34 (or UE / U2＝1.17); number 2.5 (or 1.7)—the sum of voltage drops in the excitation circuit, including the forward voltage drop of the rectifier elements (1.5V or 0.75V), and the voltage drop of the feeder wires and carbon brush collector rings (1.0V). Transformation ratio K=U2 / U1. For simplified calculations, the first and second terms of the above result can be combined, resulting in U2 = 0.71 UE (full wave) or U2 = 1.4 UE (half wave). The current calculations for the three-phase full-wave rectifier are: primary current I2 = 0.816 KIE, secondary phase current I1 = ; primary current I2 = 0.472 KIE, secondary phase current I2 = . Here, the value of I1 does not yet consider the transformer efficiency. Power Calculation: Excitation Power: PE = UEIE (W) Transformer Secondary Power: Full-wave rectification P2 = 3U2I2 = 3(0.59nUE + 1.47) * 0.816IE = 1.45nPE + 3.60IE (W) Half-wave rectification P2 = 3U2I2 = 3(1.18nUE + 2.0) * 0.577IE = 2.04nPE + 3.46IE (W) Transformer Capacity Calculation: Full-wave rectification S1 = P2 / (0.8 * 97%) = 1.29 P2 = 1.29 (1.45nPE + 3.60IE) = 1.87nPE + 4.64IE (VA) Half-wave rectification S1 = P2 / (0.8 * 97%) = 1.29 P2 = 1.29 (2.04nPE) +3.46IE) = 2.63 n PE + 4.46 IE (VA) Where 0.8 is the rated power factor of the transformer, and 97% is the primary efficiency of the transformer. For simplified calculation, the first and second terms of the above result can be combined, resulting in S1 = 2.2 PE (full-wave) or S1 = 3 PE (half-wave). In actual ordering, we sometimes find that some manufacturers use less material in transformer manufacturing to reduce costs, resulting in higher operating temperature rise of the transformer. In this case, to be on the safe side, it is best to increase the transformer capacity by 10%. At this time, the voltage value of the transformer remains unchanged, but the primary and secondary currents must be increased proportionally. Example calculation: A small hydropower station needs to order an excitation rectifier transformer. The generator parameters are: generator power 400kW, rated voltage 400V, generator excitation voltage UE = 49.4V, excitation current. Operating conditions: the excitation device is a thyristor three-phase full-wave semi-controlled rectifier, the unit is connected to the main power grid, and the maximum grid voltage (at the generator end) is 460V. The solution steps are as follows: 1) Connect group D; 2) Excitation power PE = UEIE = 49.4 × 153 = 7558.2 (W); 3) Primary line voltage U1 = 460 × 0.95 = 437 (V), take the voltage adjustment coefficient; 4) Secondary phase voltage U2 = 0.59nUE + 1.07 = 0.59 × 1.1 × 49.4 + 1.07 = 33.13V, optional; 5) Transformer ratio; 6) Secondary current I2 = 0.816 IE = 0.816 × 153 = 124.85 (A), optional; 7) Primary current I1 = 0.816 KIE = 0.816 × 153 × 0.0773 = 9.65 (A), optional; 8) Power capacity S1 = 1.87nPE + 4.64 IE = 1.87 × 1.1 × 7558.2 + 4.64 × = 16257 (VA), Optional. Finally, fill in the order list: Three-phase dry-type rectifier transformer order data: Transformer capacity: 17 kVA; Connection group: D, voltage ratio 440 V (line) / 34 V (phase); Current (primary current can be omitted); Power factor: 0.80; Duty cycle: Long-term continuous operation. According to the calculation results in this article, the transformer's load rate is 0.77 under rated operating conditions, which is in an economical operating state. The control angle of the rectifier thyristor is approximately 65° when the rated excitation current is output. We wrote a calculation program using MS Excel (spreadsheet) software. During calculation, only three parameters need to be input: excitation voltage UE, current IE, and maximum grid voltage U1 (MAX). The program will automatically calculate all the data for the rectifier transformer and provide the order list. This program can be downloaded via a link from the website of Shenzhen Puwei Electric Co., Ltd. (szpwr.com), or the website can perform the calculations on your behalf. The simplified calculation method uses the same generator parameters as before: excitation voltage UE = 49.4V, excitation current, and excitation power: P = 40.3 × 161.4 = 7558.24 (W). Taking the primary line voltage, the secondary phase voltage U2 = 1.4UE = 1.4 × 49.4 = 69.2 V, and the selectable transformer capacity S1 = 3 × 7558 = 22674 (VA). Taking the secondary phase voltage U2 = 0.71UE = 0.71 × 49.4 = 35.1 (V), and the selectable transformer capacity S1 = 2.2 × 7558.2 = 1662 (VA). Comparing the results with the previous section, it can be seen that the error of the simplified calculation method is not large and it can be applied. When the excitation voltage UE is large, the U2 value of the simplified method will be slightly larger, but it will not affect the actual operation.