OLTC derivatives - Modelling Distributed Energy Resources in Energy Service Networks - page 182

The second derivatives are obtained by taking (E.1)-(E.4) and deriving them
according to the following terms:
⎡
⎣

⎤
⎦

θ k θ k θ m θ k τ θ k | V k | θ k | V m | θ k | t |

θ m θ k θ m θ m τ θ m | V k | θ m | V m | θ m | t |

τθ k τθ m τ 2 τ | V k | τ | V m | τ | t |

(E.5)

2

| V k | θ k | V k | θ m | V k | τ | V k | | V k || V m || V k || t |

2

|

V m |

|

V m |

|

V m |

|

V m || V k |

|

V m |

|

V m ||

|

θ k θ m τ t

2

| t | θ k | t | θ m | t | τ | t || V k | | t || V m | | t |