Advances in Electrical Engineering

Volume 2015, Article ID 685943, 15 pages

http://dx.doi.org/10.1155/2015/685943

## Effect of DC Link Control Strategies on Multiterminal AC-DC Power Flow

Department of Electrical Engineering, Delhi Technological University, Delhi 110042, India

Received 20 September 2014; Accepted 18 March 2015

Academic Editor: George E. Tsekouras

Copyright © 2015 Shagufta Khan and Suman Bhowmick. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

For power-flow solution of power systems incorporating multiterminal DC (MTDC) network(s), five quantities are required to be solved per converter. On the other hand, only three independent equations comprising two basic converter equations and one DC network equation exist per converter. Thus, for solution, two additional equations are required. These two equations are derived from the control specifications adopted for the DC links. Depending on the application, several combinations of valid control specifications are possible. Each combination of a set of valid control specifications is known as a control strategy. The number of control strategies increases with an increase in the number of the DC terminals or converters. It is observed that the power-flow convergence of integrated AC-MTDC power systems is strongly affected by the control strategy adopted for the DC links. This work investigates the mechanism by which different control strategies affect the power-flow convergence pattern of AC-MTDC power systems. To solve the DC variables in the Newton-Raphson (NR) power-flow model, sequential method is considered in this paper. Numerous case studies carried out on a three-terminal DC network incorporated in the IEEE-300 bus test system validate this.

#### 1. Introduction

Multiterminal DC (MTDC) systems have been proven to be more versatile on account of their ability to fully exploit the economic and technical advantages of HVDC technology. Since the success of the first MTDC system “Sardinia-Corsica-Italy Scheme” in 1991, the application of MTDC systems has shown a steady increase. Further, with the rapid progress of renewable energy sources and offshore wind farms, MTDC applications are increasing. MTDC transmits bulk power from several generating stations to several load centres. It is more flexible and economical, being capable of connecting more than two asynchronous AC systems [1–4].

Now, for planning, operation, and control of power systems incorporated with MTDC links, power-flow solution of such systems is required. Power-flow solution of integrated AC-MTDC systems requires five quantities to be solved per converter. These include the DC voltage, the DC current, the control angle, the converter transformer tap ratio, and the converter power factor. On the other hand, only three independent equations comprising two basic converter equations and one DC network equation exist per converter. Thus, for solution, two additional equations are usually required. These two equations are derived from the control specifications adopted for the DC links. Thus, mathematically, the control specifications are used to bridge the gap between the number of independent equations and the number of unknown quantities. Control specifications usually include specified values of converter transformer tap ratio, converter control angle, DC voltage, DC current, or DC power. Depending on the application, several combinations of valid control specifications are possible. Each combination of a set of valid control specifications is known as a control strategy. The number of possible control strategies increases drastically with increase in the number of the DC terminals or converters. Out of a myriad of combinations, only some control strategies are practically adopted in practice.

To carry out power flow in AC-MTDC systems, two different algorithms have generally been reported in the literature. These are known as the unified and the sequential method, respectively. Some excellent research works on the unified and the sequential power-flow method are presented in [5–19]. Unlike the unified method, the sequential method is easier to implement and poses lesser computational burden due to the smaller size of the Jacobian matrix. Consequently, in this work, only the sequential AC-DC power-flow algorithm has been considered.

In the sequential AC-DC power-flow algorithm, the AC and DC systems are solved separately in each iteration and are coupled by injecting an equivalent amount of real and reactive power at the terminal AC buses. It is observed that each different control strategy affects the sequential power-flow convergence in a uniquely different manner. For standard control strategies, that is, constant DC voltage or current or power, the convergence rate can be improved by solving the DC and AC systems independently. On the other hand, for nonstandard ones like constant tap ratios and constant terminal voltage, the convergence may suffer. The mechanism by which this occurs has not been very clear and has not been exclusively addressed in the literature. This motivated the authors to investigate how different control strategies affect the power-flow convergence. The work is validated by numerous case studies carried out on a three-terminal DC network incorporated in the IEEE 300-bus test system. Although a large number of control strategies are possible with the three-terminal DC network, however, due to a lack of space, only results corresponding to nine different control strategies are reported here.

This paper is arranged as follows: in Section 2, the mathematical modelling of the AC-MTDC system is presented. Section 3 details a few of the control strategies possible for a three-terminal DC network. In Section 4, the AC-MTDC power-flow equations are presented, with the DC link powers acting as an equivalent load on the converter AC buses. Section 5 details the case studies carried out with a three-terminal DC network incorporated in the IEEE 300-bus test system. The conclusions are presented in Section 6.

#### 2. AC-MTDC System Modelling

Figure 1 shows a typical AC power system incorporating a three-terminal DC network. The DC network contains two HVDC links. The first link is connected in the branch “” between any two system buses “” and “” of the network while the second one is connected in the branch “” between system buses “” and “.” The three converters representing one rectifier and two inverters are connected to the AC system at buses “,” “,” and “,” respectively, through their respective converter transformers. The effect of the DC links is accounted for as equivalent amount of real and reactive power injections , , , , , and at the converters’ AC terminal buses “,” “,” and “,” respectively. Although these power injections are not shown in Figure 1, they are included in the analysis by appropriate modifications of the power-flow equations as detailed later in Section 4.