Method of transient-free transformer energization and black start using inverter based resources

A system for energizing a transformer with inverter-based resources (IBRs), the system comprising:

• a processor;
• and
• a machine-readable medium in operable communication with the processor and an inverter of the transformer and having instructions stored thereon that, when executed by the processor, perform the following steps:
• regulating a current of the inverter of the transformer to zero via a switching-cycle-based direct current (DC) feedback loop with an input current of zero;
• generating an estimate of a remanent flux in the transformer using samples of the current of the inverter, a DC voltage of the inverter, and an inverter switching function;
• determining an initial voltage phase angle of the inverter based on the estimated remanent flux in the transformer;
• and
• starting the inverter with the initial voltage phase angle of the inverter,
• wherein the estimate of the remanent flux in the transformer is generated using Equation 5 as follows:
• Φ
• r
• =
• T
• s
• N
• 1
• ·
• i
• 1
• (
• n
• +
• 1
• )
• ⁢
• v
• t
• ⁢
• 1
• (
• n
• )
• -
• i
• 1
• (
• n
• )
• ⁢
• v
• t
• ⁢
• 1
• (
• n
• +
• 1
• )
• i
• 1
• (
• n
• )
• -
• i
• 1
• (
• n
• +
• 1
• )
• ,
• (
• 5
• )
• where Φr is the estimate of the remanent flux in the transformer, Ts is a time period, N1 is a number of turns of a first winding of the transformer, i1(n) is a current in the first winding of the transformer in a first sampling, i1(n+1) is the current in the first winding of the transformer in a second sampling, vt1(n) is a voltage of the inverter in the first sampling, and vt1(n+1) is the voltage of the inverter in the second sampling.