Concept of Reactive Power Balance

    Just like active power balance, the reactive power in a power system must also be balanced at every moment.

       In a power system, frequency and active power form a unity of opposites. When the active load balances with the active power output, the frequency is normal, reaching the rated value of 50Hz. When the active load exceeds the active power output, the frequency drops; conversely, when the active power output exceeds the active load, the frequency rises. Similarly, voltage and reactive power form a unity of opposites. When the reactive load balances with the reactive power output, the voltage is normal, reaching the rated value. When the reactive load exceeds the reactive power output, the voltage drops; conversely, when the reactive power output exceeds the reactive load, the voltage rises.

      However, it should be noted that the relationship between voltage and reactive power is much more complex than that between frequency and active power. Generally, there are the following points:

      ① In a parallel-operated power system, the frequency at any point is the same, but this is not the case for voltage and reactive power.

      When reactive power is balanced, the voltage of the entire power system as a whole will be normal and can reach the rated value. Even so, this refers to the overall situation; in reality, the voltage at some nodes may not be qualified. If reactive power is not in a balanced state, the situation becomes more complex. When reactive power output exceeds reactive load, the voltage generally tends to be higher, but there may also be individual places where it is lower, and vice versa.

      ② The reactive power required by the system is far greater than the reactive power output that generators can provide. This is because modern ultra-high voltage power grids, including transformers at various levels and overhead lines, consume a large amount of reactive power when transmitting electrical energy, which is called "reactive power loss." Generally speaking, these reactive power losses are roughly the same magnitude as the reactive load in the entire grid. Let's take a 50MVA 110kV transformer as an example to understand the reactive power loss during transformer operation.

      The transformer parameters are: Ue =110kV, Se=50MVA, Uk%=17%. The calculation formula for reactive power loss when the transformer transmits electrical energy is:

    Q = SeUk%(I/Ie)2

    Where I--the load current of the transformer;

　　 Ie--the rated current of the transformer, which is related to the reactive power loss of the transformer, the load rate of the transformer, the rated capacity of the transformer, and the short-circuit impedance.

      If this transformer operates at full load, its reactive power loss is: Q=50MVA×17%=8.5Mvar

      At this time, the reactive power loss of the transformer is quite large, and the capacity of the shunt capacitor bank installed on its low-voltage side may even be insufficient to compensate for the reactive power loss of the transformer at full load.

      ③ Reactive power is not suitable for long-distance transmission. When the transmitted power and transmission distance reach a certain limit, the transmission of power becomes impossible. This is because transformers and lines at ultra-high voltage levels have relatively large reactance, and their reactive power loss Q = I2X is correspondingly large, so the transmitted reactive power is all lost in the transformers and lines. In addition, when transmitting a large amount of reactive power, the line voltage loss is also quite large, which can also result in the inability to transmit.

      Reasonable local reactive power compensation plays a very important role in adjusting system voltage and reducing line losses.

      Suppose there is a 110kV line using LG-300 type conductor (conductor resistance 0.095W/km) with a total length of 20km, transmitting active power of 30MW and reactive power of 40Mvar. Below, we calculate the line power loss and the reactive power that should be compensated when the power factor cosf = 0.6 and 0.9, respectively. This problem only calculates the power loss of the conductor resistance, without considering other factors.

       1) At cosf = 0.6, active power P = 30MW, reactive power Q = 40Mvar, apparent power S = 50MVA, current I = S/U = 50MVA/(110kV×31/2) = 263A, power loss P = I2•R = 2632×0.095×20×3 = 394kW.

       2) At cosf=0.9, active power P=30MW, apparent power S=33.333MVA, reactive power Q= 14.528Mvar, I=S/U=33.333MVA/(110kV×31/2) =175A, power loss P = I2•R = 1752×0.095×20×3 = 175kW. The reactive power to be compensated = 40-14.528 = 25.472Mvar.

       The active power loss difference before and after compensation is 219kW. From the calculation results, it can be seen that after compensating reactive power of 25.472Mvar, the line loss can be reduced by 219kWh per hour.

       The importance of reactive power compensation to the power system is increasingly recognized. Reasonable switching and use of reactive power compensation equipment plays a very important role in adjusting grid voltage, improving power supply quality, suppressing harmonic interference, and ensuring the safe operation of the power grid.