The demand for clean, renewable energy is changing the face of the power industry. For example, to get power from off-shore wind farms, rather than converting wind-generated electricity to high-voltage alternating current (HVAC), high-voltage direct current (HVDC) is a better fit. HVDC is the best option for underground and underwater transmission because the capacitance per unit of ac cable makes it impractical for lengths beyond about 100 km. In addition, direct current (dc) can transmit large amounts of power over long distances, with lower capital costs and lower losses than alternating current (ac). (In electric power transmission engineering, high voltage is usually considered any voltage over approximately 35 kV.)

HVAC transmission methods arose in the early 1900s because Thomas Edison's dc configuration worked well at low voltages but less well over long distances due to internal resistance (IR) loss. Another downside was that dc required the use of expensive voltage converters rather than simple transformers to get down to end-use voltages. In addition, associated technology, such as dc breakers for multi-terminal dc grids, had fallen behind other developments. (An HVDC grid is called “multi-terminal” when the dc system connects to more than two nodes on the ac network.) In fact, researchers are still trying to design a breaker able to force dc current to zero to avoid dangerous arcing during switching operations.

HVDC became more economical and therefore more attractive in the late 1960s with the development of new technologies which included high-power rectifiers such as mercury arc valves, and, since the mid-1970s, high-power thyristors.

Lack of technology, however, has not stopped Europe from using HVDC. In fact, one of the first commercial HVDC lines was a 98-km-long submarine cable with ground return between the island of Gotland and the Swedish mainland. It was built in 1954.

Conventional HVDC configurations now fall under the categories of long-distance transmission via overhead lines >1,000 km long; submarine cable — e.g. undersea cable — > 100 km long; or what is called back-to-back transmission. A back-to-back dc facility connects two adjacent ac grids without a dc transmission line. The converters are in the same station. This configuration serves multiple purposes, such as trading power between asynchronous networks, stabilization of different layers of a grid, and control of power interchange.

Although the power flow in a single dc link is relatively simple to control, it can be a conceptual challenge to coordinate a complex, multi-terminal dc grid.

Fortunately, PSS/E (power system simulation software for engineers) from Siemens Power Technologies International in the U.S. and in Germany lets users simulate both steady state and dynamic multi-terminal dc installations. The software uses the latest numerical algorithms to efficiently solve both large and small networks.

PSS/E models can simulate long-distance overhead dc line transmission and back-to-back facilities to analyze power flow control, improve system dynamic performance, and relieve congestion. With these models, planners can investigate the impact on steady state and dynamic performance of the systems when an HVDC link is added.

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Users can also compare ac and dc alternatives for connections of off-shore wind farms to the on-shore grid. Further, users can design and test special HVDC controls and protective schemes to subsidize future converter specifications. And planners can develop PSS/E models that simulate special HVDC attributes.

### Simulating steady-state HVDC

Before considering the HVDC case, consider the analysis of a conventional ac system. Load-flow calculations in an ac grid involve determining branch power flows and node voltages. The network is represented by a set of algebraic equations and inequalities. The equations are algebraic because they represent the model of a system in steady state (no time variation involved) and nonlinear because of the trigonometric functions of the node voltage angles. The nonlinearity means the solution to the equations is numerical, rather than analytical. Several iterative solution methods are used by PSS/E such as Newton-Raphson and Gauss-Seidel and their variations.

In the case of HVDC, PSS/E software simulates a link with special models consisting of a coordinated rectifier-inverter pair, dubbed a converter. A converter basically changes ac to dc or vice versa. In terms of analysis, each pair places a coordinated set of special boundary conditions on the ac buses where the link connects. All two-terminal dc lines consist of what are called line commutated converters (LCC). The converter stations may include a commutation capacitor, which suppresses the harmonics generated in the conversion process and reduces the requirement for harmonic filters on the ac grid.

The commutation capacitor affects the dc line model and its solution. PSS/E represents each terminal as a series of linear and nonlinear constraint equations that get solved by non-iterative methods. This supplies the ac iterative steps with dc boundary conditions, represented by megawatt (MW) and megavolt-ampere-reactive (MVAr) loads.

First consider the non-capacitor commutated two-terminal dc line. It is modeled as a series of linear and nonlinear equations that are symmetric between the rectifier and inverter. The rectifier and inverter are coupled by a transmission line equation, but the control equations for each converter are decoupled; that is, they have no effect on the other equations. The state of each circuit can be obtained by solving these equations in the appropriate sequence. This solution process is non-iterative and reliably provides dc boundary conditions for every ac iteration.

Now consider the capacitor-commutated dc line. It consists of the transmission line and at least one capacitor-commutated converter. The constraints for the capacitor-commutated converter are a system of linear equations. When both rectifier and inverter are capacitor-commutated, each converter's system of equations may be coupled or decoupled to the other depending on the control mode. PSS/E derives the converter state by solving these equations simultaneously using an iterative technique.

Power-flow-solution logic adjusts both the phase control angle (the leading or lagging angular difference between voltage and current) and transformer tap position to adjust dc voltage and current. In normal conditions, the dc lines, when controlling dc voltage and current, are operated according to the converter attributes when the rectifier ac voltage is sufficient for the phase angle control of current. Suppose the ac voltage at the rectifier output is below normal. Then the software stops controlling the dc voltage and the inverter is adjusted to maintain the dc current at a value which is the desired current reduced by the current margin. The line may be instructed to hold either a desired dc current or a desired dc power.

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For a non-capacitor commutated converter, the power control is maintained as long as the dc voltage at the inverter exceeds a specified threshold value. This control continuously prevents the line from seeking a combination of low dc voltage and high dc current. The combination produces commutation difficulties in the inverter as well as an excessive ac reactive power requirement at both converters.

If the inverter dc voltage falls below the threshold value when the line is specified to be in power-control mode, the line current is set to be a level determined by the desired power divided by the dc voltage schedule. (The voltage schedule is a target voltage to be maintained within a tolerance band during a specified period.) This makes the actual dc received power fall in proportion to the dc voltage.

In the case of a capacitor-commutated converter, the software controls power by calculating the amount of dc current needed to get a certain amount of dc power control, assuming the right dc voltage. The voltage threshold plays no role in power control in this case.

For the voltage source converter (VSC)-based HVDC, PSS/E has a generic model with no manufacturer-specific controls; it is independent of the conventional two-terminal dc line model. It represents dc resistive losses and converter switching losses. For this model, the transformers are external and the power-flow boundary conditions are defined by parameters and converter operating limits.

PSS/E can simulate multi-terminal conventional HVDC systems with monopole and bipole configurations. A monopole HVDC configuration uses a single high-voltage transmission line and the earth, sea, or a metallic conductor as a return. A bipolar system uses two terminals, usually with grounding electrodes at the terminals; or alternatively with a continuous metallic conductor strung on the same overhead line. Users must select a single voltage-controlling inverter on each pole. Models for VSC-based dc multi-terminal grids are not available yet, but Siemens PTI plans on developing them as technologies from the predominant manufacturers emerge. Monopoles are equivalent to a single circuit, whereas bipoles are equivalent to a double circuit and offer redundancy in the event of a pole outage.

### Simulating dynamic HVDC

Because dc transmission behavior is dominated by its controls, these controls must be modeled. The control bandwidth is far greater than that of the PSS/E simulation in general, so it is usually not practical to represent the detailed dynamics of controls.

Each converter bridge is controlled by a local feedback loop of critical parameters (that is, voltage, current, firing angle) consistent with the firing-delay accuracy requirements of the rectification-inversion process. These local loops work independently to maintain bridge current or voltage at desired values. These values are provided by an outer control loop that works in a supervisory role and coordinates the action of the several converter bridges and the ac power system.

The modeling of dc transmission accounts for three distinct actions the controls can take: normal regulation of dc converter operation; temporarily overriding dc converter setpoints to handle disturbances of ac system voltages during faults; and modulation of the dc power setpoint by a supplementary control device which varies the net power interchange.

There are dc transmission models for different current and voltage setpoints and delay angle limits. During feasibility studies, designers don't yet know the particular control attributes of the HVDC. So they can start with the generic dc transmission model of PSS/E.

### The state of HVDC today

Presently, there are a number of large (greater than 800 MW) off-shore wind farms connecting to mainland Europe over distances greater than 100 km where sea depths are approximately 40 m. Given the distance offshore, the submarine cable connections to the mainland grid require HVDC, combined with the compact design benefits of voltage sourced converter (VSC)-based HVDC technology. The offshore, floating, self-lifting platforms are designed to accommodate all the requisite electrical equipment for the HVDC converters.

China has constructed a number of high-power dc energy highways, superimposed on the ac grid, to efficiently (that is, minimize losses) transmit electric power from huge hydro power plants in Central China to load centers located as far away as 2,000 to 3,000 km. These ultra-high-voltage (UHV) HVDC systems at 800 kV require state-of-the-art line-commutated converter technology. The world's first 5 GW ±800 kV 1,418 km HVDC system entered service in 2009, which helps save around 33 million tons of CO_{2} when compared with local power generation. In China, a total of 35 “bulk power” HVDC projects are planned for 2010 to 2020, with a combined transmission capacity of 217 GW. A great number of these projects are for power transmission from hydro power plants situated in the middle of the country to distant load centers.

The application of multi-terminal offshore HVDC is in the planning phase to develop backbone transmission off the coast of the Mid-Atlantic states in the U.S. The ambitious project aims to connect 6,000 MW of offshore wind — multiple wind farms, all in relatively shallow water — via an HVDC transmission backbone (driven by the distances offshore along with the associated benefits of HVDC). In addition, the HVDC project will provide grid congestion relief to the existing land-based transmission system.