Towards HVDC interoperability - assessing existence of equilibrium with reference to converter terminal behaviour

Abstract

A key challenge to enable the interoperability of a Multi-Vendor-Multi-Terminal (MVMT) HVDC network is to assess the stability without requiring open sharing of the vendor Intellectual Property (IP) relating to control functions. An analytical criterion is therefore proposed as a first step of this assessment. The criterion is indexed by the margin against loss-ofequilibrium for a MVMT-HVDC network with terminal behaviour of connected converters. Based on a classical control architecture, a static analytical model is established, including relevant parameters within the DC network, its topology and operation. By linearizing the system at 0 Hz, the principle of assessing the singularity of the matrix of extended conductance is proposed and proved with the theorem of implicit function and principle of analytic continuation. Two types of scaler index are proposed and then normalized to indicate the margin against loss-of-equilibrium. The effectiveness of the indices is verified and analysed with simulations in the environments of both Matlab/Simulink and RTDS with pseudo-steady-state and detailed Electro-Magnetic Transient (EMT) modelling, respectively. This approach attempts to represent one MVMT control scheme to support practical specification, testing and demonstration of the first multi-vendor multi-terminal HVDC control system outside of China.

Towards HVDC Interoperability - On Dominance of Nodal Impedance

“…(a) Current Perturbation (b) Voltage Perturbation Fig. 1 Input perturbation and output response at ith terminal When a perturbation vector of terminal voltage 𝑉 𝑝 (𝑠) ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ , is applied to the grid (and assuming there is no structural change in the system), the response of nodal current flowing into all positive nodes of DC terminals contributed by the rest of the system, 𝐼 𝑟 (𝑠) ⃑⃑⃑⃑⃑⃑⃑⃑⃑ , shall comply with Kirchhoff's current law again with nodal current analysis [14] as 𝑌 𝑒𝑥 (𝑠)𝑉 𝑝 (𝑠) ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ = 𝐼 𝑟 (𝑠) ⃑⃑⃑⃑⃑⃑⃑⃑⃑ (7) Vice versa, when a perturbation vector of nodal current injection 𝐼 𝑝 (𝑠) ⃑⃑⃑⃑⃑⃑⃑⃑⃑ , is applied to the same grid, the response of (converter) terminal voltage, 𝑉 𝑟 (𝑠) ⃑⃑⃑⃑⃑⃑⃑⃑⃑⃑ , shall again comply with (9) as long as the grid is linearizable around an equilibrium guranteed by appropriate control strategy over DC power flow [2].…”

“…Once an equilibrium is secured within a pre-defined domain of operating point [2], a stable HVDC grid should ideally settle at the equilibrium after a small disturbance. Such stability can be assessed by checking if all accumulative quantities, e.g.…”

“…Given an HVDC grid is linearized at an equilibrium [2][6], the small-signal dynamics can be characterized by a linear circuit in Laplace (s) domain. Therein, a nodal current perturbation 𝑖 𝑝𝑗 (𝑠) is exclusively injected to an n -terminal HVDC grid at j th terminal, which is demonstrated in Fig.…”

“…It is impossible to make the nodal impedance positive real when a converter is under digital control across all operating scenario, especially under the DC Constant Power Load (CPL) or voltage dependent control [2]. Among them, CPL mode will make an HVDC converter unstable on its own by introducing negative resistance starting from 0 Hz [2].…”

“…the HVDC system and would not expect to interpose themselves in the detailed controllers of a convertor affecting and related to the internal design of equipment as specific to each vendor. Thus, it is desirable for a universally available approach to multi-terminal control that characterizes and where appropriate then specifies the measurable performances with reference to the terminal behavior of every disconnected converter [2]-within the DC network operated by the TSO, echoing similar philosophies of operation which have operated upon the AC system for several decades. Unlike the AC system which is dominated by classical physical concepts of synchronized power generation and consumption across network characteristics, in relation to an inherently coupled power frequency a DC system is control dominated by the characteristics of the convertor system responses to the resultant voltages across the DC system under operation.…”