Scholarly article on topic 'Multi-terminal HVDC Modeling in Power Flow Analysis Considering Converter Station Topologies and Losses'

Multi-terminal HVDC Modeling in Power Flow Analysis Considering Converter Station Topologies and Losses Academic research paper on "Electrical engineering, electronic engineering, information engineering"

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{"Multi-Terminal HVDC" / "Converter Station Loss Modelling" / "Load Flow Analysis"}

Abstract of research paper on Electrical engineering, electronic engineering, information engineering, author of scientific article — Guang Zeng, Tobias Hennig, Kurt Rohrig

Abstract In this publication the authors present several aspects of integrating High-Voltage Direct Current (HVDC) transmission into power flow analysis algorithms. In particular, the authors will discuss speed and robustness of two different power flow approaches, the integration of droop-control schemes and the loss modeling of converter stations based on power electronic device characteristics considering different converter topologies.

Academic research paper on topic "Multi-terminal HVDC Modeling in Power Flow Analysis Considering Converter Station Topologies and Losses"


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Energy Procedía 80 (2015) 123 - 130

12th Deep Sea Offshore Wind R&D Conference, EERA DeepWind'2015

Multi-Terminal HVDC Modeling in Power Flow Analysis Considering Converter Station Topologies and Losses

Guang Zenga, Tobias Hennig*a, Kurt Rohriga

aFraunhofer IWES, Division Energy Economy and Grid Operation, Königstor 59, 34119 Kassel, Germany


In this publication the authors present several aspects of integrating High-Voltage Direct Current (HVDC) transmission into power flow analysis algorithms. In particular, the authors will discuss speed and robustness of two different power flow approaches, the integration of droop-control schemes and the loss modeling of converter stations based on power electronic device characteristics considering different converter topologies.

© 2015 The Authors.Publishedby ElsevierLtd. This is an open access article under the CC BY-NC-ND license


Peer-review under responsibility of SINTEF Energi AS

Keywords: Multi-Terminal HVDC; Converter Station Loss Modelling; Load Flow Analysis

1. Introduction

The HVDC technology has been used basically in the form of point-to-point transmission. The integration of renewable energy sources and the connection of several onshore and offshore energy sources and energy customers over several voltage levels lead to a requirement for new transmission solutions [1]. Recently, there has been a lively interest in meshed multi-terminal HVDC grids from the academic institutions, the grid operators and manufacturers [2]. The hybrid AC/DC systems with multi-terminal HVDC have been therefore often discussed and need to be studied furthermore with respect to the total system losses in different management concepts or control modes. The detailed studies on converter station loss modeling and load flow analysis enable the creation of a concrete model to analyze those problems. The VSC-HVDC, which is based on the use of voltage source converter

* Corresponding author. Tel.: +49-561-7294-1720; Fax: +49-561-7294-260. E-mail address:

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license


Peer-review under responsibility of SINTEF Energi AS


(VSC), is a relatively new technology compared with classical HVDC with line-commutated converters (LCC). The IGBT is mainly used in today's VSC applications. As a result, the loss modeling is based on the IGBT device characteristics and considers different converter topologies.


f general function AC alternating current

J Jacobian Matrix DC direct current

P active power IGBT Insulated Gate Bipolar Transistor

Q reactive power q source quantity (load flow model)

V voltage s voltage angle

x state-variables v iteration step

y power mismatches E energy

I current R resistance

2. Power Flow Analysis

2.1. Integration of VSC-HVDC into power flow analysis

In the conventional load flow calculation, the steady-state operation point of a power system is determined by the complex voltages of all nodes in this system, e.g. voltage magnitude and voltage angle in polar coordinates. The nonlinear AC power flow equations can be solved using Newton-Raphson method as given in Eq. (1).

A^ac =-/AC AJAC (1)

The steady-state operation point of voltage source converters in a VSC-HVDC system can be similarly described by the complex voltages of the source nodes (Vq and ¿q), the node between converter transformer and converter as depicted in [3]. Those state variables of the converters could also be integrated in a vector of complex voltages xq of the source nodes. For solving the power flow of a hybrid AC/DC system with multi-terminal HVDC transmission links there are two different approaches in the recent literature: the sequential approach [4] and the parallel approach [5]. For those systems, the DC systems' steady-state operation point should also be determined within the power flow calculation and this problem could be solved analogously by using Newton-Raphson method as given in Eq. (2).

= -J dC AJDC (2)

In the sequential approach, the power flow analysis of the AC system and DC system are undertaken by solving the Eq. (1) and (2) one after another separately, whereas with the parallel approach, the power flow of the entire hybrid AC/DC system is calculated simultaneously as given in Eq. (3) [6].

iAxAC ) Axq Ax



,-4?dc y

To make sure that the power flow with parallel method remains solvable, the Jacobian matrix of the original AC and DC systems should be extended by four sub-matrices [3]: JUL, JUR, JLL and JLR. In the vector of converter

mismatch equations A/Vsc control strategies and targets of the converters are considered. Details of how to build different converters mismatch equations and the four sub-matrices can be also found in [6].

2.2. Case study o/ two different power /low approaches

To validate the two different power flow approaches and to evaluate the robustness and efficiency of convergence of both algorithms, the IEEE 9 bus system is modified with an embedded multi-terminal HVDC grid as shown in Fig. 1.

For a general numerical method, the convergence efficiency is determined by how quickly and with how many iterative steps the result with a certain initial value is found. The robustness of the convergence makes itself declared by how much the convergence efficiency depends on the choice of the starting value. For the evaluation of the two algorithms different starting conditions are used. In the standard power flow calculation the nominal voltages of the nodes are usually set as initial values, because the solution lies close to it according to experience. To compare the two algorithms, a dimensionless quantity /A is defined, which is referred to as the initial value factor. The nominal values of the bus voltage magnitudes are multiplied by /A and taken as initial values for the calculation. In this case study/A varies around one in positive and negative direction with a step size of 0.005. If the solution is not converging anymore, or converges to a wrong solution, the test will be aborted. The total iterations needed for the tests v were recorded and are shown in Fig. 2. As shown there, the sequential algorithm requires more iterations than the parallel algorithm. Generally, the higher the difference between the initial condition and the nominal value is, the more iterations are needed for the calculation in both algorithms. The solutions with both algorithms can converge to the same results within a certain area of initial conditions. The tests for the sequential algorithm has been only carried out with /A in the range of 0.8 to 1.2, because it is already significantly greater than the convergence region of the parallel algorithm, which means that the sequential algorithm is more robust in the iterative calculation. Due to the compactness of the parallel algorithm, the solution converges faster than the sequential approach. However, the Jacobian matrix must be modified for the application of the parallel algorithm as mentioned before. The conclusions of this case study are consistent with the statements from [7]. Due to the fact that the Jacobian matrix already represents the linearization of the system, it can be reused in sensitivity analysis. In static stability analysis sensitivities provide also estimation and valuation on power system stability. This is the reason why for operation purposes the parallel approach is still preferred in order to identify system interactions.

18 ■■ 16 ■ ■ 14 ■■ 12 10 ■■ 8 ■■ 6 ■■ 4 ■■ 2 ■■ 0 ■ — 0,8

parallel sequential

0,84 0,88 0,92 0,96 1 1,04 1,08 1,12 1,16 1,2

Initial value factor fA

Fig. 2. Comparison of two power flow approaches on convergence robustness and efficiency

2.3. Integration of Droop-Control

The different control methods for VSC-HVDC system with respect to the active power behavior on the DC side, which have been introduced in recent years, can be divided into two main groups, the constant DC voltage control (also known as master slave control) and the distributed DC voltage control (also known as droop control) [8] [9]. For the former, only one converter station of the complete DC system is used as so-called slave converter. The active power of this slave converter is controlled in such a way that the power balance of all converter stations can be achieved in this DC system with consideration of losses. The other converters in this system are referred to as master converters. A possible outage of a master converter could result in immediate failure of the entire DC grid. To solve this problem, the distributed DC voltage control could be used. Unlike the master slave control the control task of DC voltages would be distributed over several converters using this scheme. Several converters adapt their active powers set-points simultaneously to regulate the DC voltage according to their droop characteristic. The slope of the droop characteristic is often referred to as DC droop constant, which is the ratio of change in DC voltage to the corresponding change in converter active power. The method of including the DC voltage droop control in the power flow algorithm can be found in [10] and was integrated into the analysis. The effects of a converter outage on the power flows in a hybrid AC/DC system with the two different control strategies are discussed in this section by using the offshore study case of the CIGRE B4 Test System from [1].

Fig. 3. DC network power flow of DCS 3 with master slave control (a) and droop control (b) by outage of a converter

The DCS 3 in the CIGRE Test System is a multi-terminal HVDC system, which is connected with the other AC or DC systems by five AC-DC converter stations and two DC-DC converter stations. The outage of a converter in DCS 3 with both DC voltage control strategies are studied, as shown in Fig. 3. The converter station Cb-A1 was taken as slave converter in the master slave control (see Fig. 3 (a)). When for example the converter station Cb-D1 fails, the other master converters remain on their power set-point and the slave converter Cb-A1 have to transfer additional about 1000 MW active power. This task leads to an increase of active power of the slave converter to a value far over its nominal power, which is technically not permitted. This entire system state is therefore stationary prohibited. In the case of droop control (Fig. 3 (b)) all other AC-DC converters adapt their active power simultaneously according to the droop characteristic. The DCS 3 system could work after the outage of the same converter now. The new system state after a failure is technically allowed and does not lead to shutdown of the entire transmission system. By means of the system operators security analysis the droop control setting have to be defined using operational constraints such as DC voltage limits, deviations from agreed schedules, the ability of the system to withstand an outages and the losses of the system.

3. Converter Loss Model

One important aspect in operating hybrid AC/DC systems is the power loss evaluation of the converter systems. In commercial software for simulation and modelling of power systems the various components of converter losses are usually subdivided into two groups: load losses (conduction losses) and no load losses (switching losses). The load losses are approximately modelled by series resistances on the AC side of the converter and concurrently the no load losses are presented by equivalent shunt resistances on the DC side [11]. This loss implementation is to some degree inaccurate and a more detailed modelling approach is introduced as below.

3.1. Loss model of power semiconductor

Conduction losses. In the conducting state, the power semiconductor (IGBT or diode) exhibits a small on-state voltage of a few volts. The two different power semiconductors share similar characteristics and their on-state voltages depend both non-linearly on current. It is usually approximated as a piecewise-linear function of current with a threshold voltage V0 and the slope resistance R0 of the device. By using this assumption, the average conduction losses of each device can be evaluated with the average and root mean square currents though this device as given in Eq. (4).

^cond = Vo • Im + Ro • C (4)

Switching losses. The turn-on energy Eon and turn-off energy Eoff are referred to as switching energies of IGBTs. They both depend non-linearly on current and can be modelled as a quadratic function of current as in Eq. (5), with the parameters D0T, E0 T and F0T describing this relationship.

Esw, T = Eon + Eoff = (D0,T + E0,T '1C + F0,T '1C ) ' V (5)

The parameters can be evaluated by analysing the relevant characteristic diagrams on the data sheet of the IGBT manufacturer. However the switching energies of devices (IGBTs or diodes) also depend on the DC link voltage of each device VCC at the instant of switching. Therefore the average switching energies should also be fixed with the reference voltage Vref from the routine test. The turn-on process of the diode is very fast and turn-on losses are only a few percent of the turn-off losses. The latter one are modelled analogously to Eq. (5) while the turn-on losses are neglected.

3.2. Loss model of converter topologies

Two-level converter. To evaluate the conduction and the switching losses of the devices within the two-level converter an accurate analytical expression was used that is explained in detail in [12]. It solves the loss equations Eq. (6) and (7) using the converters' duty cycle, the current through each device, the switching frequency and the switching interval.

Three-level (NPC) converter. The three-level neutral point clamped (NPC) converter (diode clamped) has three DC terminals connected to a centre-tapped DC source, which can achieve three different voltage levels. Along with four IGBT valves, two extra clamping diode valves (D5 and D6) are needed. To be able to switch voltages higher than the rated voltage of single device in the HVDC applications, several IGBT modules or diode modules are connected in series in each valve. Due to the unsymmetrical stress of the devices in the three-level converter, the conduction and switching losses of different devices have to be evaluated separately. However, the devices in the upper and in the lower arm of the three-level converter are symmetrical. Even though it is much more complex to derive, an analytical expression can be found for the solution of the device losses in [13] using the same calculation parameters as for the two-level converter topology.

Modular multi-level converter. The modular multilevel converter (MMC) along with the cascaded two level converter (CTLC), which shares similar topology with MMC, allow the devices to be switched at a significantly lower frequency as in the conventional two-level or three-level converters with PWM. The MMC submodule is available in two main forms, half-bridge (HB) and full-bridge (FB). Due to the lower losses, the half-bridge arrangement is more suitable for the offshore HVDC applications, where cable is the dominant solution for the power transmission and no self-healing capability of isolations is designed. In contrast to the former topologies, no accurate analytical expression can be found for the device losses. However, an approximation can be made according to [14]. For the loss modelling at system level, it is not necessary to know the losses in each individual device. Only the total losses of converter are needed for the power flow analysis. In a half-bridge submodule, it is always one and only one semiconductor device (IGBT or diode) in conduction. As a result, the on-state characteristic of the submodules can be modelled as a combination of IGBTs and diodes in respect of the conduction proportions of each device. In general, inverter mode gives rise to IGBT conduction losses while rectifier mode gives rise to diode conduction losses. In the analytical calculation, an appropriate split of characteristics between IGBT and diode is found to be 80% to 20% [14].

3.3. Connection with the Power Flow Analysis

The complete loss model in the power flow calculation is shown in Fig. 4. The converter transformer losses are modeled with the iron loss resistance RFe and the winding resistance RT. The losses of the harmonic filter are modeled with RF similarly. The total losses of one converter station consist thus of the losses of the converter, the losses of transformer and the losses of the harmonic filter. All the quantities needed for the loss calculation are either given by the project or calculated within the power flow algorithm. The second-order high-pass filters are widely used as AC filter in HVDC applications [15]. For the MMC topology AC filter is normally not required [16]. The component parameters of the second-order high-pass filter are calculated according to [17] and [18].

Fig. 4. Loss model of converter station in power flow analysis

3.4. Loss Comparison of Different Topologies within CIGRE B4 Benchmark System

The modified power flow calculation method including converter station loss model was used to solve the power flow of the CIGRE B4 Benchmark system with the system data and the operating point described in [1]. Thereby, a modular expansion planning for developing this system was assumed using different topologies and devices based on the nominal voltage and nominal power of the stations. The assumptions for the converter topology and the dedicated IGBT modules by ABB and Mitsubishi with characteristics taken from the data sheets are given in table 1.

Table 1: Assumptions for converter stations

VSC Topology IGBT module

Cm-A1 3-Level 5SNA 1300K450300

Cb-A1 MMC CM1500HG-66R

Cb-B2 MMC CM1500HG-66R

Cm-B2 3-Level 5SNA 1300K450300

Cb-B1 MMC CM1500HG-66R

Cm-B3 MMC CM1500HG-66R

Cb-D1 3-Level 5SNA 1300K450300

Cm-E1 2-Level 5SNR 10H2500

Cm-F1 3-Level 5SNA 1300K450300

Cm-C1 3-Level 5SNA 1300K450300

Cb-C2 2-Level 5SNR 13H2500

For each converter station the losses are calculated for the reference load flow scenario given in [1]. The results are given in Fig. 5 and are consistent with recent publications. For example the MMC converters provoke less than 1% station losses. However, one remarkable result can be seen for the three-level converter Cm-B2 of the system. Although the loss are expected to be about 1.5% in nominal conditions, since this converter at the particular operating point is only utilized by 17%, the switching losses are dominant which degrades the efficiency of the converter a lot. This result shows the need for accurate loss models for low-load scenarios and also shows the advantage of the MMC in those conditions.

4. Conclusion

The authors discuss the topics using the comprehensible example of the IEEE 9-Bus System and the offshore study case of the CIGRE B4 Benchmark System. The proposed loss model relies on IEC 62751 -1/2 draft standards and also respects converter transformers and filters. Thereby, it has taken two-level, three-level (neutral point clamped) and modular multi-level (including cascaded two-level) converter topologies into account. The link of the complex loss model with the parallel hybrid AC/DC load flow is explained. The integration of a sequential algorithm where AC and DC systems are solved consecutively and a parallel approach is investigated. The robustness of convergence of both algorithms is evaluated using different starting conditions and the speed is analyzed using number of iterations needed. A generic droop control implementation is performed applying and extending the parallel algorithm. Moreover, the outage of one converter station is analyzed applying standard master-slave control and droop-control scheme. The suitability of the loss modeling approach is proven using the CIGRE B4 Benchmark System.

VSC stations Cm-A1 (3-Level)

Cb-A1 (MMC)

Cb-B2 (MMC)

Cm-B2 (3-Level)

Cb-B1 (MMC)

Cm-B3 (MMC)

Cb-D1 (3-Level)

Cm-E1 (2-Level)

Cm-F1 (3-Level)

Cm-C1 (3-Level)

Cb-C2 (2-Level)

Conduction Losses Switching Losses cCuopper Losses fIeron Losses Filter Losses

0,00 0,50 1,00 1,50 2,00 2,50 3,00 3,50

Fig. 5. Losses of converter stations PV of the CIGRE B4 DC Benchmark system at given load flow scenario


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