The Efficacy of Generator Protection under Sudden Loss of Excitation using Offset-type MHO-relay

Abstract

A synchronous generator is forced to asynchronous operation under sudden loss of excitation (LOE). Operation under LOE has many undesirable effects, for example, thermal injury of the faulted machine, poor voltage profile in its neighbourhood, pulsations in voltage and power etc. These effects are more pronounced for a salient pole hydrogenerator compared to a cylindrical pole turbo generator. For these reasons, sustained operation under LOE cannot be permitted for a long time and the faulted machine is to be switched off. The general practice is to use an off-set type mho-relay with an appropriate time delay to distinguish LOE from recoverable swings. In this paper, the performance variables under sudden field failure for a non-salient pole generator and its impedance looking from the terminals have been computed by specially constructed programs based on numerical methods. Taking the example of a 210 MW turbo generator set of Bharat Heavy Electricals Ltd., it has been established that the offset type mho-relay protection is adequate under all possible conditions of asynchronous operation following an LOE. A comparison has been made between the field directly short-circuited and the same closed through a properly chosen value of discharge resistance. It has been found that the use of discharge resistance is beneficial, but the relay operates even in its absence.

Appendix

Algorithm for numerical solution of Eq. 8 using Newton–Raphson method is given below:

Step-1:

${\text{Read}}\,\,\text{P}_{\rm ref} ,\text{V},\text{X}_{\rm d} ,\text{X}_{\rm d}^{\prime } ,\text{X}_{\rm d}^{{{\prime \prime }}} ,\text{X}_{\rm q} ,\text{X}_{\rm q}^{{{\prime \prime }}} ,\text{T}_{\rm d}^{'} ,\text{T}_{\rm d}^{{{\prime \prime }}} ,\text{T}_{\rm q}^{{{\prime \prime }}} ,\text{f},\text{r}_{\rm f} ,\text{r}_{\rm d} ,\text{X}_{\rm e} ,\text{R}_{\rm u}$

Step-2:

$\text{X}_{\rm de} \leftarrow \text{X}_{\rm d} + \text{X}_{\rm e} ;\text{X}_{\rm qe} \leftarrow \text{X}_{\rm q} + \text{X}_{\rm e} ;\text{X}_{\rm de}^{\prime } \leftarrow \text{X}_{\rm d}^{\prime } + \text{X}_{\rm e} ;\text{X}_{\rm de}^{{{\prime \prime }}} \leftarrow \text{X}_{\rm d}^{{{\prime \prime }}} + \text{X}_{\rm e} ;\text{X}_{\rm qe}^{{{\prime \prime }}} \leftarrow \text{X}_{\rm q}^{{{\prime \prime }}} + \text{X}_{\rm e}$

Step-3:

$\text{T}_{\rm do}^{\prime } \leftarrow \text{T}_{\rm d}^{\prime } \text{X}_{\rm d} /\text{X}_{\rm d}^{\prime } ;\text{T}_{\rm do}^{\prime \prime } \leftarrow \text{T}_{\rm d}^{\prime \prime } \text{X}_{\rm d}^{\prime } /\text{X}_{\rm d}^{\prime \prime } ;\text{T}_{\rm qo}^{\prime \prime } \leftarrow \text{T}_{\rm q}^{\prime \prime } \text{X}_{\rm q}^{\prime } /\text{X}_{\rm q}^{\prime \prime } ;\text{T}_{\rm dom}^{\prime } \leftarrow \text{T}_{\rm do}^{\prime } \text{r}_{\rm f} /(\text{r}_{\rm f} + \text{r}_{\rm d} )$

Step-4:

$\text{T}_{\rm d}^{\prime } \leftarrow \text{T}_{\rm dom}^{\prime } \text{X}_{\rm de}^{\prime } /\text{X}_{\rm de} ;\text{T}_{\rm d}^{\prime \prime } \leftarrow \text{T}_{\rm do}^{\prime \prime } \text{X}_{\rm de}^{\prime \prime } /\text{X}_{\rm de}^{\prime } ;\text{T}_{\rm q}^{\prime \prime } \leftarrow \text{T}_{\rm qo}^{\prime \prime } \text{X}_{\rm qe}^{\prime \prime } /\text{X}_{\rm qe}$

Step-5:

$\text{k}_{\rm 1} \leftarrow \text{V}^{2} \text{T}_{\rm d}^{\prime } (1/\text{X}_{\rm de}^{\prime } - 1/\text{X}_{\rm de} )/2;\text{k}_{2} \leftarrow \text{V}^{2} \text{T}_{\rm d}^{\prime \prime } (1/\text{X}_{\rm de}^{\prime \prime } - 1/\text{X}_{\rm de}^{\prime } )/2;\text{k}_{3} \leftarrow \text{V}^{2} \text{T}_{\rm q}^{\prime \prime } (1/\text{X}_{\rm qe}^{\prime \prime } - 1/\text{X}_{\rm qe} )/2$

Step-6:

${\text{Initialize}}\,{\text{slip}},{\text{convergence}}\,{\text{constant}},\,{\text{maximum}}\,{\text{number}}\,{\text{of}}\,{\text{iteration}}:\text{s},\varepsilon ,\text{n}_{\hbox{max} }$

Step-7:

$\text{f} \leftarrow - \text{P}_{\rm ref} + \text{s}/\text{R}_{\rm u} + \text{s}(1 - \text{s})\left[ {\frac{{\text{k}_{1} }}{{1 + (\text{sT}_{\rm d}^{\prime } )^{2} }} + \frac{{\text{k}_{2} }}{{1 + (\text{sT}_{\rm d}^{\prime \prime } )^{2} }} + \frac{{\text{k}_{3} }}{{1 + (\text{sT}_{\rm q}^{\prime \prime } )^{2} }}} \right]$

Step-8:

$\text{f}^{\prime } \leftarrow 1/\text{R}_{\rm u} + \left[ {\frac{{\text{k}_{1} \{ 1 - 2 \text{s} - (\text{sT}_{\rm d}^{\prime } )^{2} \} }}{{\{ 1 + (\text{sT}_{\rm d}^{\prime } )^{2} \}^{2} }} + \frac{{\text{k}_{2} \{ 1 - 2 \text{s} - (\text{sT}_{\rm d}^{\prime \prime } )^{2} \} }}{{\{ 1 + (\text{sT}_{\rm d}^{\prime \prime } )^{2} \}^{2} }} + \frac{{\text{k}_{3} \{ 1 - 2 \text{s} - (\text{sT}_{\rm q}^{\prime \prime } )^{2} \} }}{{\{ 1 + (\text{sT}_{\rm q}^{\prime \prime } )^{2} \}^{2} }}} \right]$

Step-9:

s_new ← s − f/f^′

Step-10:

$\text{If}\left| {\text{s}_{\rm new} - \text{s}} \right|\, < \,\varepsilon \,{\text{then}}\,{\text{goto}}\,{\text{step}}\,14$

Step-11:

${\text{count}} \leftarrow {\text{count}} + 1$

Step-12:

${\text{If}}\,{\text{count}} > \text{n}_{\hbox{max} } \,\,{\text{then}}\,{\text{goto}}\,{\text{step}}\,19$

Step-13:

$\text{s} \leftarrow \text{s}_{\rm new} :\,{\text{goto}}\,{\text{step}}\,7$

Step-14:

s ← s_new

Step-15:

$\text{P}_{\rm as} = \text{s}(1 - \text{s})\left[ {\frac{{\text{k}_{1} }}{{1 + (\text{sT}_{\rm d}^{\prime } )^{2} }} + \frac{{\text{k}_{2} }}{{1 + (\text{sT}_{\rm d}^{\prime \prime } )^{2} }} + \frac{{\text{k}_{3} }}{{1 + (\text{sT}_{\rm q}^{\prime \prime } )^{2} }}} \right]$

Step-16:

$\text{Q}_{\rm as} = \text{s}\left[ {\frac{{\text{k}_{1} \text{sT}_{\rm d}^{\prime } }}{{1 + (\text{sT}_{\rm d}^{\prime } )^{2} }} + \frac{{\text{k}_{2} \text{sT}_{d}^{\prime \prime } }}{{1 + (\text{sT}_{\rm d}^{\prime \prime } )^{2} }} + \frac{{\text{k}_{3} \text{sT}_{\rm q}^{\prime \prime } }}{{1 + (\text{sT}_{\rm q}^{\prime \prime } )^{2} }}} \right]$

Step-17:

S_as ← (P ²_as  + Q ²_as )^1/2; I_as = S_as/V

Step-18:

${\text{print}}\,\text{s},\text{P}_{\rm as} ,\text{Q}_{\rm as} ,\text{S}_{\rm as} ,\text{I}_{\rm as} :{\text{goto}}\,{\text{step}}\,20$

Step-19:

${\text{No}}\,{\text{convergence\,in}}\,'\text{n}_{\hbox{max} }'\,{\text{number}}\,{\text{of}}\,{\text{iterations}}.\,{\text{Try}}\,{\text{again}}\,{\text{changing}}\,{\text{initial}}\,{\text{value}}.$

Step-20:

${\text{stop:end}}$