Review of HVDC control in weak AC grids

Electric Power Systems Research 162 (2018) 194–206

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Review of HVDC control in weak AC grids

T

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Javad Khazaei , Peter Idowu, Arash Asrari, A.B. Shafaye, Lakshan Piyasinghe Department of Electrical Engineering at Penn State Harrisburg, Middletown, Pennsylvania, United States

A R T I C LE I N FO

A B S T R A C T

Keywords: Short Circuit Ratio Power synchronization control Vector control High Voltage Direct Current Weak AC grids

Interconnection of High Voltage Direct Current (HVDC) transmission systems to a weak AC grid has been a challenge in recent years. The main target of this paper is to provide a comprehensive review of the “converter control” approaches for: (1) the Line Commutated Converter (LCC)-based HVDC and (2) the forced commutated converter-based HVDC systems in weak AC grids. The control architecture for each HVDC technology (forced commutated and line commutated) is included. The stability limitations associated with HVDC systems, including LCC-HVDC, Voltage Source Converter (VSC)-based HVDC, and the Current Source Converter (CSC)based HVDC, are elaborated. Moreover, the most recent control approaches for possible integration of LCCHVDC and VSC-HVDC to very weak AC grids are introduced. Finally, the reliability modeling for each HVDC technology in weak AC grid integration is included for corrective and preventive reliability analysis.

1. Introduction 1.1. Problem formulation High Voltage Direct Current (HVDC) transmission is the best option to deliver generated power to long distances. The best application would be offshore wind farms where the wind turbines are installed far away from the shore to take advantage of high wind energy potential. The transmitted DC power is then converted to AC onshore station in order to interconnect to the main AC grid [1–4]. It is worth mentioning that HVDC lines connected to AC grids through long transmission lines are usually weak with low Short Circuit Ratio (SCR) and low effective DC inertia constant. Furthermore, with the advent of renewable energy resources, wind power has become one of the most suitable sources for power generation. However, areas with sufficient wind resources are geographically far from the consumers where the power grid is relatively weak (low SCR). The lower the SCR, the weaker the AC grid, which generates many problems such as voltage drop, voltage flicker, harmonic distortion, and frequency deviation [5–9]. Also, when an HVDC system is connected to a weak AC grid, oscillations and interactions may be experienced. Depending on the type of HVDC, these interactions will differ. The interactions and instabilities in this case are due to:

• Interactions between HVDC controllers and AC system [6], • Failure in synchronization of HVDC converters with the AC system [7],

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Corresponding author. E-mail address: [email protected] (J. Khazaei).

https://doi.org/10.1016/j.epsr.2018.05.022 Received 6 February 2018; Received in revised form 9 May 2018; Accepted 22 May 2018 0378-7796/ © 2018 Elsevier B.V. All rights reserved.

• Resonances between the inverter DC side capacitor and the AC system components [9], • Commutation failures in the HVDC converter, etc. [10]. Several studies have focused on analyzing and troubleshooting the above problems related to interconnection of the HVDC systems and weak AC grids, which will be reviewed in this paper. 1.2. Literature review There are two types of HVDC systems:

• Line Commutated Converter HVDC (LCC-HVDC) [11], • Forced commutated converter-based HVDC [12]. The LCC-HVDC technology is the best option associated with high power capacities around 10,000 MW for a bipole configuration [13]. Forced commutated converter-based HVDC is the second type of HVDC transmission which is normally applied for medium power levels up to 1000 MW [13,14]. However, since the advent of Modular Multi-level Converters (MMCs), high power application of VSCs has become a reality [15]. For power transmission lines, the following two different types of converters have been established so far: (1) LCCs, which are Current Source Converters (CSCs) using Thyristor switches, and (2) Voltage Source Converters (VSCs), which use IGBT switches [14]. Other combinations and power electronic switches such as forced commutated converter-based CSCs are possible, but are not common at the

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[34,38],

moment for power transmission applications [16,17]. Compared to the forced commutated HVDC, higher power and voltage can be offered by LCC-HVDC which can increase the capacity of the entire system and decrease the total loss [18,19]. Depending on the type of the HVDC converter, the instabilities due to the weak AC grid connection will differ. The main focus of this article is to review: (1) the interactions caused by different types of HVDC converters and (2) the most recent approaches to overcome the dynamic instability of the HVDC transmission systems in weak AC grid connections. The LCC-HVDC is a widespread technology around the world, but the reactive power absorption of LCC-HVDC is always a problem when interconnection to weak AC systems is required [20–23]. Therefore, the LCC-HVDC requires reactive power support from the AC grid in order to commutate reliably; thus, when connected to weak AC grids, it cannot operate stably and reliably. A reactive power compensation method is proposed in [20] which maximizes shunt capacitor size in AC systems so that the number of shunt capacitors is minimized. A small signal model of a multi-infeed HVDC transmission system containing LCCs and VSCs is developed in [21], where the converters are included in the Effective Short Circuit Ratio (ESCR) calculations. It was shown that with commonly used control strategies for LCCs and VSCs, the predicted maximum power transfer can only be achieved by reducing the controller gains. Another study analyzed the effect of low ESCR and the effective DC inertia constant on the stability of the interconnection of DFIG-based wind farms with LCC-HVDC [22]. Some studies suggested the application of the Flexible AC Transmission System (FACTS) when LCC-HVDC is connected to a weak AC grid to support the reactive power of the LCC-HVDC [24–27]. For example, a shunt FACTS has been implemented for the Baltic Cable HVDC link between Germany and Sweden to improve the power transfer level [26]. Due to the fact that the main cause of failure in LCC-HVDC connection to a weak AC grid is the commutation failure, Burr et al. [28] has tested different technologies for improving the commutation failure for LCC-HVDC systems. A commutation index has been defined and tested for various compensation structures. In another case, a dynamic reactive compensation algorithm was presented in [29] to calculate the amount of reactive power needed to be compensated when LCC-HVDC is connected to a weak AC grid. Nevertheless, a compensation device by FACTS is still necessary to compensate for the calculated amount of reactive power. An analysis approach was introduced in [22] to study the frequency dynamics for interconnection of the Doubly Fed Induction Generator (DFIG)-based wind farm, with an LCC-HVDC for very weak AC systems; but a solution has not been provided. A methodology was proposed in [30] for stabilization of LCCs connected to weak AC grids using a selfgenerated signal from a local oscillator for the converter's main inner control loop. However, this method has a major drawback; it is more challenging to suppress over-currents during network disturbances. Because FACTS are expensive and they require high maintenance, Li et al. [31] suggested a new reactive power balance strategy near the converter bridges which provides an additional commutation voltage and suppresses the harmonic currents near the harmonic source. This filtering method has enabled the reliable commutation of LCC-HVDC in weak AC grid connections. VSC-based HVDC (VSC-HVDC) is the most commonly used approach in medium and long length DC transmission systems due to its flexibility, reliability, and independent active and reactive power control capability [17,32,33]. The vector control of VSC-HVDC enables the independent control of the active and reactive power while it limits the converter current in fault conditions. The main sources of these dynamic instabilities for VSC-HVDC have been reported as:

• Interactions of outer control loops in VSC [34], • Impact of the constant power load on VSC dynamics when connected to a weak AC grid [35,39,38].

A few papers have focused on modeling and analyzing the effect of different VSC-HVDC control loops in weak AC grid interconnections [40–44]. For example, Wang et al. [41] investigated the impact of VSCHVDC AC voltage controller gain on the stability of a VSC-HVDC system interconnected to a weak AC grid. As an another example, in [43], a small signal model was derived for a VSC-HVDC system connected to a weak AC grid and the Nyquist stability analysis was carried out to investigate the effect of the distributed parameter DC cable and π-section DC cable. Detailed investigation of PLL parameters on instability of VSC-HVDC has been reported in [35,45–48]. It was shown that PLL gains affect the maximum power transfer capability and theoretical power transfer limit can be achieved if the PLL gains are small. Impact of the PLL parameters on stability of VSC-HVDC in weak AC grid connections has also been investigated in [35,46]. A modified PLL approach named as Impedance-Conditioned (IC) PLL has been introduced in [47] in order to synchronize a VSC-HVDC to weak AC grids. The proposed method can successfully remove the barriers of traditional PLLs, but only works when the VSC-HVDC is controlling the alternating voltage. There has been a significant improvement in control of VSCHVDC in the weak AC grid connection as explained in [49,50]. For example, Egea-Alvarez et al. [49] investigated the capability curve analysis of a VSC-HVDC connected to a weak AC grid, but did not provide a solution. The possibility of the offshore wind farm integration to a weak AC grid using VSC-HVDC has been investigated in [50], but the designed controller needs to be switched to the classical vector control when faults happen which is not optimized. Similar to [50], a frequency control based approach is introduced in [51] to control a VSC-HVDC system in weak AC grid connections. This design method requires switching to the classical vector control during a fault, which makes the design very complicated. A power compensation control scheme was also introduced in [52] to address the shortcoming of VSCHVDC in weak AC grid connections. The proposed method modified the outer-loop control of the VSC in order to compensate for the required power transfer. As this method modifies the outer-loop, it operates properly only if the converter is controlling the active power. An advanced vector control method was introduced in [53] in order to overcome the barriers of VSC-HVDC, especially when connected to a very weak AC grid. The designed controller can robustly handle the interactions between the active power and voltage control. However, the design requires a gain scheduling technique, whose tuning adds to the complexity of the design. Virtual inertia is another technique that can be used especially in the case of VSC-HVDC connected to offshore wind farms [54–57]. As high level of wind energy penetration makes the main grid inertia-less, a virtual inertia can be supplemented to the system using HVDC control. For instance in [55], a coordinated control strategy is proposed which applies the electrical energy stored in DC capacitors of HVDC converters and the kinetic energy of wind turbine rotors to emulate the inertia of synchronous generators in weak AC grids. This method, however, is only limited to the offshore wind farm integration of VSCHVDC. Some other researchers have explored synchronizing the HVDC system to the main grid without a PLL and called it synchronverter [58–63]. The idea was firstly introduced in [58,59] where an inverter control method was proposed to mimic the behavior of a synchronous generator. Compared to the dynamic model of a synchronous generator, the mechanical power exchanged with the prime mover in synchronous machine is replaced with the power exchanged with the DC bus in synchronverter. Among existing literature on synchronverters, only [60] considered a weak AC grid integration, which was a pure simulation based research and therefore, detailed analysis and validation is

• Inner current controller loop interacts with the system and generates low-frequency resonances [34], • Dynamics of Phase-Locked Loop (PLL) can result in instabilities [35–37], • Resonances between the line inductance and the DC-bus voltage 195

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yet to be carried out. The power synchronization control is another alternative for the VSC-HVDC when the AC grid is very weak [8,9,64,50,65]. The idea comes from the ability of synchronous generators to maintain synchronism using transient power transfer. As this power transfer is determined by a current which involves the interconnection network, a power synchronization loop is used to control the converter angle. This idea is different than synchronverters, where dynamic model of synchronous machines are used. Power synchronization control directly controls the converter output voltage angle using a power synchronization loop and the converter output voltage magnitude is controlled using a proportional integral (PI) controller. This controller is specifically designed for weak AC grid control where the vector control fails to synchronize the converter to the grid. For example, Zhang et al. [8] investigated integration of two very weak AC grids using a VSC-HVDC system that was enhanced with power synchronization. It also studied the stability issues regarding the reactive power controller and voltage controller of the HVDC converters. Another case study was considered in [50] where an offshore wind farm was integrated into a weak AC grid using a VSC-HVDC enhanced with the power synchronization control. The main drawback of power synchronization control was under the fault conditions, where a backup PLL was needed to synchronize the converter after the fault [8,9]. Forced commutated converter-based CSCs provide an additional short-circuit protection and flexibility in grid integration because of the boost nature and more reliability compared to VSCs [17,66–68]. However, CSCs need an extra diode to be added in series with each IGBT in order to increase the reverse voltage withstanding capability which doubles the switching losses. Additionally, as a choke is used instead of the DC link, the power losses in the DC choke is normally 2 to 4% which is higher than 0.5% in the DC link. Such barriers have restricted the widespread application of CSCs in HVDC transmissions and there is no HVDC transmission system with forced commutated CSCs. However, with the development of reverse blocking IGBTs and the integrated gate commutated thyristor (IGCT), these obstacles have been resolved and thus future applications of CSCs in HVDC transmission is expected to become more common. The interconnection of current source converters with weak AC grids was investigated in [17]. An active compensation technique was used to introduce additional degrees of freedom which finally would stabilize the HVDC dynamics in weak AC grids.

Fig. 1. A typical topology for a HVDC system connected to weak AC grid [69].

solution for weak AC grid integration of LCC-HVDC systems is reviewed. Section 4 introduces force commutated converters and two control algorithms for weak AC grid integration of VSC-HVDC systems. Section 5 discusses the normal operation of CSC-HVDC systems and introduces a solution for weak AC grid integration of CSC-HVDC. Furthermore, remarks of the paper are summarized in Section 6. Finally, Section 7 concludes the review. 2. Weak AC grid philosophy The AC grid is called weak if it has high impedance relative to the DC power, or it provides very low inertia relative to the DC power. As the impedance is increased, undesirable effects such as voltage deviations are more likely to be observed and resonant frequencies will be lower. The weakness of an AC system is normally defined by the SCR which is in proportion with the AC system impedance. When an AC system is connected to an HVDC system, the SCR definition is modified to reflect the HVDC rating. Short Circuit Power (SCP) or Short Circuit Capacity (SCC) is used in this case to represent the strength of the AC system connected to an HVDC transmission line [69]. Referring to Fig. 1, the AC system SCR value, SCRac in megavolt-amperes (MVA) at the Point of Common Coupling (PCC) is defined as [6,8,69]:

SCR ac =

2 VPCC Zac

(1)

where VPCC is the AC voltage at the PCC and Zac is the AC system impedance. For the AC system connected to the HVDC transmission with rated DC power of Pdc in megawatts (MW), the SCC definition will be [8,70]:

1.3. Concentration of this paper Considering the fact that the weak AC grid connection has recently appeared to be a challenge for HVDC systems, and due to the new improvements in HVDC applications, the key contribution of this research is “to summarize all the recent efforts in weak AC grid integrations of HVDC system”. As an HVDC control in the weak AC grid interconnection highly depends on the type of the HVDC converter and the control topology, this paper outlines the possible control techniques for the forced commutated and the line commutated HVDC systems. Furthermore, the instabilities and interactions related to each control topology is studied in detail. In addition, a solution for each converter topology is proposed and discussed in detail. To the authors’ best knowledge, this is the first research that highlights the weak AC grid integration challenges for different HVDC converter types and summarizes the solutions for each HVDC converter topology. In the following, more detailed investigation of weak AC grids will be presented. In addition, advanced control algorithms for interconnection of various HVDC transmission links to the weak AC grids will be discussed. A reliability study has also been considered in this paper to model all the components of HVDC systems in weak AC grid integration. These reliability models are valid for VSC-HVDC, LCC-HVDC and CSC-HVDC systems. The rest of the paper is organized as follows; Section 2 introduces the concept of weak AC grids and short circuit ratio. The LCCHVDC system under normal condition is explained in Section 3 and a

SCC =

SCR ac Pdc

(2)

If the resistance of the AC system is neglected and the AC system impedance (Zac) is represented as jωL, further simplifications can be achieved. Here, the main assumptions are [8]: 1. The PCC voltage is the same as the nominal AC voltage (Vbase), 2. The rated DC power is the same as the rated AC power (Pdc = Pbase). Under these two assumptions, the base impedance of the AC system can V2

be defined as Zbase = PPCC ; therefore, the SCC definition for an AC dc system linked to an HVDC transmission can be defined as:

SCC =

V2 SCR ac Z 1 = PCC = base = Pdc ωLPdc ωL Zp.u

(3)

As a result, the SCC definition is inversely proportional to the p.u impedance. The minimum value of SCC with rated DC power transmission level must be considered in analyzing the limiting operating conditions. The lower the SCC value, the weaker the system, and the greater the interactions between DC and AC systems. To classify the AC/DC system 196

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components such as: converters, harmonic filters, shunt capacitors, DC reactors and DC cables. The converter achieves conversion of energy from DC to AC or AC to DC, configured typically as two 6-pulse bridges connected in series on the DC side and the switching is performed by the converter control. The rectifier transfers power from AC side to DC side. On the other hand, the inverter transfers power from DC side to AC side. Detailed information about the conversion principles are broadly studied in [72]. Harmonics generated by the conversion process on the DC and AC sides are filtered out using filters. Both DC and AC filters are implemented to filter out different harmonic orders on the respective sides. Due to the fact that the LCC-HVDC-based system consumes reactive power up to 60% of the transferred active power, shunt capacitors are installed at the AC bus in order to support the reactive power [72]. These capacitors can contribute to harmonic alleviation, as well. The DC reactor is in charge of smoothing out the DC current and reducing the harmonic voltages in the DC line. Moreover, in case of short circuit faults, the DC reactor limits the crest currents. However, reactors might create challenges in the process of starting motors if their rating is less than the inrush currents of the associated downstream motors. So, they should be designed with the consideration of several factors.

interconnections, different SCC levels are defined [3,6,70,71]:

• Strong system: The AC/DC system with SCC values greater than 3, • Weak system: The AC/DC system with SCC values between 2 and 3, • Very weak system: The AC/DC system with SCC values less than 2. Very low SCC value will impose voltage stability and power transfer limitations in AC/DC interconnections. In this case, the power transfer capability of HVDC system will be limited. Referring to the power transfer equation between the two voltage sources linked with series impedance of jωL:

P=

V1 V2 sin θ ≈ SCC sin θ ωL

(4)

where V1 and V2 are voltage magnitudes at two buses and θ is the angle difference between two voltage sources, also known as load angle. Eq. (4) is valid because in normal operating conditions V1 and V2 are 1 p.u. It is also noted that in a very weak AC grid with SCC value of 1, the power transfer is limited to 1 p.u maximum. In the very low SCC condition, the HVDC converter operation is in the unstable region of AC voltage/DC power curve, and therefore, the operation of AC/DC system is possible if the AC voltage is controlled at sufficiently fast speed. Traditional approaches suggested the application of synchronous compensators to strengthen the AC system, or by stabilizing the AC voltage with static voltage compensators [3,36,39]. However, in modern power system applications, the desired fast voltage control is anticipated by the HVDC converters. Detailed information about various HVDC control approaches and improvements toward HVDC control in weak AC grid connections are provided in the rest of this paper.

3.1. LCC-HVDC normal control A typical LCC-HVDC control structure is composed of a DC current or power controller at the rectifier station and extinction angle controller at the inverter station. A hierarchical structure of LCC-HVDC control is composed of a power controller as the outer loop on top of the DC current controller at the rectifier station. Additional control functions are usually introduced for specific modes of operation [1,18–20,72]. During normal operation, PI controllers are deployed for rectifier and inverter stations to regulate the DC current and the inverter extinction angle, respectively. A marginal current control at the inverter station may be implemented to achieve a new operating point during the AC voltage dips. The inverter can also be supplemented with the DC voltage controller. However, one should consider that these three control modes at the inverter station cannot operate together (i.e., only one mode can be operated at the time). The Voltage-Dependent Current Order Limit (VDCOL) reduces the DC current during AC under-voltage faults in order to protect the valves against AC grid faults [1,18,19]. The block diagram of an LCC-HVDC control is illustrated in Fig. 3. Compared to the VSC-HVDC, the LCC-HVDC systems suffer from a slow power control, a slow fault recovery speed, and an uncoordinated inverter station control. Moreover, if the LCC-HVDC is connected to weak AC grids, the DC voltage control at the inverter station and DC current control at the rectifier station are highly recommended for stable operations. In the next sections, detailed information about problems associated with LCC-HVDC systems in weak AC grid connections are addressed.

3. LCC-HVDC system Fig. 2 shows a schematic diagram of an LCC-HVDC system. In an LCC-HVDC system, the commutation is done by the AC system voltage. At very weak AC conditions, the LCC-HVDC will have major difficulties because of unreliable commutation associated with faults or operating point changes. This difficulty has forced the HVDC planners to increase the reactive power compensation with increase in DC power levels for LCC-HVDC systems in weak AC grid connections. However, for bulk power systems, the LCC-HVDC is still known as the most reliable, efficient and practical option especially at high power transfer levels [20,21,31]. There are many applications in which LCC-HVDC plays an important role such as: submarine and underground applications, asynchronous link between AC systems, and overhead lines for bulk power transmission in long distances [1,3]. Because of high technical capability, economic advantage, and low operating losses, the LCC-HVDC is the best option for enhancing and enlarging power system interconnections. There are several configurations for the LCC-HVDC such as back-toback, mono-polar, bipolar or multi-terminal which are beyond the scope of this research and detailed information about each interconnection can be found in [1,3,72]. The LCC-HVDC system shown in Fig. 3 is composed of many

3.2. Converter control in LCC-HVDC connected to weak AC grid Several studies have focused on the improvement of the LCC-HVDC stability while connected to weak AC grids, among which the

Fig. 2. A basic topology of LCC-HVDC systems [20]. 197

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Fig. 3. General control block for LCC-HVDC system [19].

[31] which enables the LCC-HVDC systems to operate in very weak AC grid conditions. This topology is illustrated in Fig. 4. A new transformer is also proposed for the LCCs. The primary side of the transformer is Y grounded and the secondary side is prolonged Δ. Fully Tuned (FT) branches are included between the prolonged winding and the Δ winding. The impedance coordination between the new converter transformer and related fully tuned branches performs the inductive filtering approach which not only can solve the harmonic current problems, but also will improve the operation of LCC-HVDC in weak AC grid connections. Simplified Representation: The converter generates high amount of harmonics due to the switching topology. Based on the new configuration, high harmonics first flow into the prolonged winding of the transformer at the secondary side. Then, the Δ winding at the secondary side will induct the harmonics and make them balanced. Therefore, the harmonic currents will not flow into the primary windings. As a result, harmonic losses will not spread throughout the system. The rated capacity of the transformer can also be reduced significantly as the

application of FACTS is the most famous one. For example, a shunt FACTS was installed at the 400 kV terminal of the Baltic Cable LCCHVDC link between Germany and Sweden in order to enhance the power transfer limit [26]. Another example is the Southern China Power grid where a Static Compensator (STATCOM) was installed in a 500 kV substation in order to control the AC voltage [73]. The problem with these solutions is that FACTS add a huge amount of cost to the converter stations in HVDC systems. Moreover, the operating efficiency of the converter station will be reduced by adding additional FACTS. As a result, the best solution would be designing a new controller algorithm in order to improve the reliability and operation of the LCCHVDC without adding new devices to the system. A recently proposed approach is to use inductive filters which provide additional commutation voltage for the LCC-HVDC and mitigates the unwanted harmonic currents at the converter bridge. Inductive filtering was primarily introduced in [31], and its application to LCC-HVDC was studied based on the characteristic parameters of the converter transformer. Also, a Q-compensation method was proposed in

Fig. 4. LCC system enhanced with Q-compensation algorithm connected to weak AC grid [31]. 198

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Fig. 5. Forced commutated based HVDC, (a) monopolar VSC-HVDC and CSC-HVDC, (b) bipolar VSC-HVDC and CSC-HVDC [1].

Fig. 6. Voltage source converter control of HVDC [14].

integrations [67], or static synchronous compensators [68]. Compared to the VSCs, CSC offers an additional short circuit protection due to the directly controlled DC voltage current. Furthermore, as VSC is a buck converter, its DC link should be at least twice the AC voltage in order to avoid over modulation. However, CSC is a boost inverter which is more flexible in grid integration. The DC side element of the CSC is a DC choke which is more reliable than electrolytic DClink capacitors in VSCs. One disadvantage of the CSC over VSC is that power losses in the DC choke are between 2% and 3%, but losses in the DC link are around 0.5%.

harmonic content in the grid is reduced significantly. The transformer can also provide reactive power for the converter which will greatly improve the stability of the entire system especially when connected to very weak AC grids. This compensation method is called Q-compensation [31]. The main idea is that the proposed secondary winding will have a current component in the primary windings which leads the primary winding current and leaves the HVDC system with no need to take a large amount of reactive power from the AC grid. Although this method can greatly improve the performance of the LCC-HVDC system in weak AC grid connections, it adds a new component with a new configuration which for the high voltage level application will add an additional cost.

4.1. Normal control of VSC-HVDC Vector control is the most commonly used approach in controlling the VSC-HVDC systems. A basic control structure of the VSC-HVDC has been illustrated in Fig. 6. As is demonstrated, the controller has two levels; a lower level control or inner current controller, and an upper level control or the outer loop. The current controller regulates the dq components of the current through the coupling filter. The control structure uses PI controllers to regulate the converter current flowing into the grid filter. If the grid filter is considered as purely inductive with inductance L (ignoring the filter's resistance, R), dynamics of the inner current loop can be expressed as [1,14]:

4. Forced commutated converter HVDC Forced commutated converter-based HVDC systems use converters based on GTOs or in the recent industrial cases IGBTs. A typical topology of VSC/CSC-based forced commutated HVDC systems is illustrated in Fig. 5 [1,3,24,25]. Compared to the LCC-HVDC, which needs compensation for voltage or reactive power support, the forced commutated HVDC has abundant features. VSC-HVDC provides independent control of the active/reactive power, the ability to supply passive loads, and possibility of connection to weak AC grids. Moreover, the VSC-HVDC can operate without external commutation voltage and has a small footprint due to the small harmonic filter size. Unlike LCC-HVDC, forced commutated converters based on CSCs share similar features with VSCs such as: an independent active/reactive power control, the ability to connect to weak AC grids, short circuit protection, and a relatively small footprint. By applying a reverse blocking IGBTs (RB-IGBTs), or Integrated Gate Commutated Thyristors (IGCTs), the CSC will be supplemented with a semiconductor device with the reverse voltage blocking capability. This topology has been successfully applied to photo-voltaic applications [66], wind farm

( + i Lω − (K

vd* = ud − iq Lω − Kp +

Ki s

vq* = uq

Ki s

d

p

+

) (i * − i ) ) (i * − i ) d

d

q

q

(5)

where ud and uq are feed-forward terms which are derived by filtering the PCC dq voltage through a low pass filter ( 1 ). The controller gains τs + 1 (kp and ki) are tuned using the internal mode current control (Kp = Lcα, 1 Ki = Rcα), where α = τ is the desired closed loop bandwidth and normally is selected 5 to 10 times slower than the converter switching frequency. More information relevant to the inner current controller design can be found in [14]. 199

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k3(p), and k4(p) are derived.

The outer loop, on the other hand, generates the references for the inner current controller (id*, iq*). The d-axis loop mainly controls the active power or the DC voltage and the q-axis controls the reactive power or the AC voltage magnitude at the PCC. A classical controller for outer loop would be a PI controller. The design considerations for the outer loop controllers can be found in [14]. Dynamic equations for a VSC-HVDC outer loop with active power and voltage magnitude control are expressed as:

id* = Kpp +

(

Kip

(

Kiv s

iq* = Kpv +

s

4.3. Power synchronization control (PSC) of VSC-HVDC in weak AC grids Power synchronization is a recently proposed approach for synchronizing the converters with the grid without PLL [8,9,64,50,65]. This control is similar to the power-angle control where the phase angle and the voltage magnitude are directly applied to control the active and reactive power. The major advantage of the PSC over the power-angle control is that there is no resonant peak at the grid frequency and thus the converter current is enhanced with an over-current limitation technique. It was shown in [9] that the power-angle control transfer function has a pair of complex poles which causes resonances at the grid frequency. Therefore, the voltage control law in power synchronization control introduces a high-pass filter to damp out the resonant poles as:

) (P* − P) ) (|V |* − |V |)

(6)

A Phase-Locked Loop (PLL) is also used to synchronize the converter with the grid. The PLL is based on the q-axis voltage feedback by a PI controller to obtain the angular velocity and an extra integrator to obtain the PCC voltage angle [1,14].

c Vref = V0 −

4.2. Vector control of VSC-HVDC in weak AC grids

HHP (s )

(8)

The high-pass current control (HHP(s)) behaves as an “active resistor” and provides damping to the various resonances in the system, however, does not consume power. The parameters of the high-pass filter are chosen based on the trade-off between the damping effect and the phase margin [9]. Using the PSC, the active power output from the VSC is directly controlled by the power-synchronization loop and the reactive power (or alternating voltage) is controlled by adjusting the magnitude of the voltage [8,9,64]. Consequently, the inner current control loop is removed from the controller design. The PSC has also been shown as a superior alternative for the vector control of VSCHVDC systems in connection to weak AC grids [8,9,64,50,65]. Unlike the PLL that synchronizes the converter with the PCC, the PSC directly synchronizes the converter with the grid through a power control loop. Therefore, VSC-HVDC is able to transfer 1 p.u in a very weak AC system (SCR is 1). The key structure of the PSC is illustrated in Fig. 8. The idea behind the PSC comes from the analogy of synchronous machines, which is the power angle relationship [8]. In the PSC, synchronization takes place by controlling the active power through the converter and using the output as the reference angle for the VSC PWM unit. Referring to Fig. 8, the difference between the reference active power of the converter and K the measured power is sent to an integral controller ( p ), the output of s which presents the synchronization angle (θ). Dynamic equations of the PSC are [8,9,65]:

When the voltage source converter is connected to a weak AC grid using vector control, dynamics of PLL play an important role in the instability of the converter. Depending on the outer loop, the control design may vary. It has been shown in [53] that the outer loop will fail to stabilize the converter connected to the weak AC grid. A new upper level control has been suggested in [53] in order to enhance the stability of the VSC with classic outer loop connected to a weak AC grid which is shown in Fig. 7. The proposed method adds four decoupling gains between the power and voltage errors (if the VSC is controlling the power and voltage) before being processed by the PI. The main objective is to suppress the interactions between the active power and the voltage controller using four decoupling gains. A parameter-varying control scheme using a gain scheduling technique is used for decoupling gains and PI controllers. Dynamics of the controller can be expressed as:

id* = PIp (k1 (p) ep + k3 (p) eu ) iq* = PIu (k2 (p) ep + k 4 (p) eu )

kv s c i s  + α v

(7)

where k1(p), k2(p), k3(p), and k4(p) are the decoupling gains, ep is the power error, eu is the voltage error, and PIp, PIu are proportional integral controllers for the outer loop. Due to the nonlinear nature of the plant dynamics, multiple local controllers are designed for a specific operating point to cover the active power transmission from −1.03 p.u to 0.89 p.u. To tune the coupling gains, the H-infinity fixed structure control design can be implemented; refer to [74] for more information. A brief tuning procedure is included here; at any given operating point, an H-infinity fixed-structure control tuning is implemented. Several operating points are randomly selected and controller gains are tuned using non-smooth optimization by means of Clarke sub-differential of the H-infinity objective. The tuning procedure is then repeated for all the possible operating points until the scheduled gains k1(p), k2(p),

θ (s ) =

Kp s

(P * (s ) − P (s )),

ωtPSC = ω*t − Δθ .

(9)

The backup PLL is used in case of a fault to synchronize the converter with the grid. In this case, a current limitation algorithm is applied to send commands to a selector which decides between the normal operation (PSC) or fault (vector control). The current limitation algorithm also generates the dq reference frame voltages for the pulse generation module [8,9,64]. A reactive power control is designed to control the reactive power generated by the converter. The voltage control loop is also included as an inner loop for the reactive power control in order to control the voltage magnitude. 5. CSC-HVDC application Generally, in HVDC applications, CSC regulates the voltage/power/ current through current loops. The vector control is the most appropriate type of control in forced commutated converters as it provides the capability to control the converter current and independent active/ reactive power control. Current source converters-based forced commutated switches are also known as pulse width modulated current source converters (PWM-CSC). A typical structure of the vector control

Fig. 7. Advanced vector control algorithm for weak AC grid connection [53]. 200

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Fig. 8. VSC-HVDC enhanced with power synchronization control connected to very weak AC grid [8].

Fig. 9. A basic topology of CSC-HVDC system [67].

5.1. Vector control of CSC-HVDC in weak AC grids

of PWM-CSC for an HVDC application has been illustrated in Fig. 9. However, in offshore wind farm applications, a wind farm supervisory control (WFSC) scheme will be supplemented to the outer-loops for both grid side and wind farm side converters. Details of PWM CSC control in offshore wind farm applications can be found in [67]. The inverter side is usually in charge of controlling the dc current (similar to active power) and reactive power through PI controllers. The rectifier side, on the other hand, is in charge of controlling the dq component of the AC current. It should be mentioned that, m and α are the modulation index and the delay angle, respectively. The decoupling blocks include the feed-forward compensation and the decoupling inductance terms which eventually will be added to the current refer* , Iqs * ) to generate the converter reference currents in the dq ences (Ids reference frame (Id*c , Iq*c ). Dynamics of the system can be represented as:

* − ωs Cvqc Id*c = Ids * + ωs Cvdc Iq*c = Ids

When a CSC is connected to a weak AC grid, the main objective is to synchronize the converter with the grid. Under very weak AC grid conditions, the vector controlled CSC suffers from instability because of PLL gains, which cannot synchronize the converter to the grid. An active compensation technique has been introduced in [17] for a CSC in order to control the converter in a very weak AC grid (with the SCR ratio of 1) to transfer 1 p.u active power. As the active compensation design is independent of the CSC vector control, parameter tuning is not needed. Fig. 10 shows the vector controlled CSC enhanced with an active compensator. As is illustrated, the controller has two main levels; an inner current control and a voltage control. The terms Yd and Yq are the active compensation inputs for the weak AC grid integration. The active compensation inputs will damp out the resonance peak resulting from the combination of the capacitive filter (C) and the equivalent grid inductance (L). Extra outer loops are added to the CSC controller for the sake of active and reactive power control. As mentioned earlier, one advantage of the CSC over the LCC-based HVDC is the ability to independently control the active and reactive power. Therefore, the active current component (Id) is selected to control the active power and the reactive current component (Iq) is selected to control the reactive power [17]. The active compensation technique will add additional degrees of freedom to improve the system's dynamic response in weak AC grid connections [17]. Two compensation signals yd(s) and yq(s) will be added to the reference active and reactive current components (Idref , Iqref ) which can be represented as:

(10)

where C is the AC side filter's capacitor, ωs is the nominal frequency of the system, and vdc, vqc can be expressed as:

vdc = − ωs Li qs + vdpcc vqc = ωs Li ds

(11)

where vdpcc is the d-axis PCC voltage, and ids, iqs are the dq axis PCC currents. Furthermore, the DC current control, the reactive power control, and the AC current controllers are simply proportional integral k controllers (kp + si ). The space vector modulation based pulse width modulation (SVM-PWM) unit then generates the pulses for the converters. Detailed information regarding the control can be found in [67].

yd (s ) = kd

2ζd ωd s s 2 + 2ζd ωd s + ωd2 ωq

yq (s ) = kq s + ω Vqc − kf q

201

ω − kf ωf s + ωf

ωf s + ωf

Vdc

Vdc (12)

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Fig. 10. Active compensation design for CSC connected to very weak ac grid [17].

Due to the fact that the PLL has a major impact on destabilizing the converter connected to the weak AC grid, the compensators are designed in order to mitigate the adverse PLL impact. The PLL output ω, and the control variable of the PLL Vqc will be used as inputs for the compensator. A band-pass filter is used for the PLL output frequency which has ξd damping ratio and ωd cut-off frequency. A low pass filter is also used after the PLL control variable Vqc which has a cut-off frequency of ωq and a gain of kq. Also, d component of the PCC, Vdc , passing through a low-pass filter with a cut-off frequency of ωf and a gain of kf will be supplemented to the compensation signals yd(s) and yq(s). ωf Adding the second component (− kf s + ω Vdc ) to the compensators will

FOR =

provide more damping and disturbance rejection capability in case of sudden load changes. In [17], it has been proved that these components will add sufficient damping in very weak AC grid connections which allows the CSC to control the system without any trouble. Moreover, under steady state conditions, these two components are zero which will not affect the system stability. The first step in designing the compensators is to design the lowpass filter for the PLL control variable Vqc considering the SCR of the system. It has been illustrated that decreasing the cut-off frequency of the low-pass filter (ωq) will increase the damping performance. Plus, increasing the kq will enhance the damping performance as well. Next step is to add a band-pass filter to the PLL's output. Such band-pass filter will be tuned to move the dominant poles to the more damped locations in the left hand side of the s-plane. Although increasing kd will improve the damping performance, it will move the poles to the right hand side if it is too high. Therefore, special care should be taken into account while selecting the cut-off frequency and damping ratios.

MTTF =

1 λ

(15)

MTTR =

1 μ

(16)

MTBF = m + r =

1 f

(17)

Capacity outage probability table, which is a simple array of out of service capacity levels and the associated probability of existence, is then used to study the reliability and find the reliability indices of the system. The readers are encouraged to refer to [75,76] for more information on capacity outage probability table. The HVDC schemes consist of a rectifier station at the sending end, an inverter station at the receiving end and transmission lines between them. For the forced commutated converters (VSCs and CSCs) in weak AC grids, single bridge (monopole) system is considered as shown in Fig. 5(a). However, for the LCC-HVDC system in weak AC grids (Q-compensation method), a multi-bridge (monopole) system is considered, as shown in Fig. 4. The entire HVDC system for each configuration can be divided into three main subsystems; the rectifier/inverter subsystem, the transmission line and pole equipment subsystem, and the AC filters subsystems. These subsystems can then be analyzed independently and finally combined for the reliability of the complete HVDC link in each configuration. In the following, the modeling procedure for each subsystem is provided.

6. Reliability study This section briefly introduces the reliability modeling of the considered HVDC schemes for weak AC grids for corrective and preventive maintenance. To analyze the reliability of an HVDC system, first the concept of availability and unavailability of a unit must be defined. Consider a two-state model shown in Fig. 11, which is applicable to a base load generation unit. Such a unit is either operating or forced out of service, where λ is the expected failure rate and μ is the expected repair time. The concept of availability (A) and unavailability or unit Forced Outage Rate (FOR) are defined as [75,76]:

f μ m m = = = λ+μ m+r T λ

(14)

where m is the Mean Time to Failure (MTTF), r is the Mean Time to Repair (MTTR), f is the cycle frequency, m + r is the Mean Time between Failures (MTBF), and T is the cycle time. The indices MTTF, MTTR and MTBF are defined as [75,76]:

f

A=

f λ r r = = = λ+μ m+r T μ

6.1. Rectifier/inverter bridge The bridge is the heart of the converter stations and includes power electronics switches (valves), damping, protection, and control equipment. The structure of the bridge for the VSCs and CSCs for each converter station in weak AC grids includes a single-bridge in monopole configuration. Therefore, the simplified bridge model in terms of capacity states for reliability analysis can be shown by the state space diagram illustrated in Fig. 12. For the forced commutated converters, λe is the equivalent failure rate and μe is the equivalent repair rate. The probability of state A (fullμγ capacity) is and the probability of state B (zero-capacity) is

(13)

λb (μ + γ ) + μγ

λb (μ + γ ) , λb (μ + γ ) + μγ

where λe = λb and μe =

μγ μ+γ

[75]. In the above definitions,

λb is the bridge failure rate, λ is the valve failure rate, μ is the valve repair rate, and γ is the valve installation rate. For the Q-compensation algorithm in LCC-HVDC, which was shown in Fig. 4, a multi-bridge structure can be modeled as Fig. 12(b). The probability indices (full capacity (PA), half-capacity (PB), and zero

Fig. 11. A two-state model for a base load generation unit [75]. 202

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Fig. 12. Equivalent models for single-bridge and multi-bridges; (a) bridges in forced commutated converters in weak ac grids (VSCs and CSCs), (b) bridges in LCCHVDC (Q-compensation scheme).

Fig. 13. Equivalent models for a converter station for single-bridge station (VSC-HVDC and CSC-HVDC); (a) detailed model, (b) simplified model.

Fig. 14. Equivalent models for a converter station for multi-bridge stations (LCC-HVDC with Q-compensation); (a) detailed model, (b) simplified model.

operate as a series system and a combined failure rate (λa) and repair rate (μa) can be considered for these elements. The equivalent models of a converter station for a single-bridge (forced commutated converters in weak ac grids) and its equivalent state space model are depicted in Fig. 13. The equivalent model of a converter station with a multi-bridge configuration (LCC-HVDC with Q-compensation) and its equivalent state space model for reliability analysis is illustrated in Fig. 14. In this figure, λc = λa + λb, and λc1 = 2λc2 = 2(λa + λb) = 2λc. Other parameters and more information about the modeling procedure can be found in [75–78].

capacity (PC)) for the equivalent two bridges can then be evaluated. More information about multi-bridge modeling and capacity outage probability calculations can be found in [77]. 6.2. Converter stations Each converter station consists of a bridge (in case of back to back VSC-HVDC and CSC-HVDC) or multi-bridge (in case of LCC-HVDC with Q compensation), converter transformers, and circuit breakers. The new elements can be combined with the bridge models described in the previous subsection. Each bridge is associated with its own transformer, circuit breaker, and terminal equipment. Therefore, these components 203

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Fig. 15. Equivalent models for (a) AC filters, (b) transmission lines.

6.3. Transmission lines and filters

•

It is assumed that at each converter station, there exists a filter with the equivalent failure and repair rates of λf, μf, respectively. Therefore, for an HVDC system, two filter banks are considered (one for each converter station) and the reliability model for the combined filter banks can be represented by Fig. 15(a). Similarly, the model for the transmission lines can be derived except the fact that the system can still be operational when one of more lines of a multi-line system are out of service. For a bipole transmission link, the reliability model can be illustrated as Fig. 15(b) [76]. The indices used for transmission line model should represent the composite reliability indices of the transmission line and its associated pole equipment which are connected in series. It is noted that these models are valid for both forced commutated converters and line commutated converters in weak ac grids. The combined model can then be derived for each HVDC technology based on the simplified models represented in Figs. 12–15. The combined model for the forced commutated converter based HVDC (CSCHVDC and VSC-HVDC) systems is included in [75], Chapter 11, and the combined model for the LCC-HVDC with Q-compensation algorithm is similar to the model presented in [77], and therefore are skipped in this part. These combined models can then be used for reliability analysis of various HVDC technologies in weak AC grids, which is considered for the future work of this research.

•

8. Conclusion This paper reviews different converter schemes for HVDC systems connected to weak AC grids. The SCR which is a general indicator of an AC system's strength is used as an index to compare multiple converter schemes in weak AC grid interconnection of HVDC systems. An overview of LCC-HVDC and forced commutated converter-based HVDC systems are provided and the control approach in normal condition is discussed. Stability limitations of FCC-HVDC systems are studied and reactive power compensation algorithm is introduced as a potential solution for interconnection of LCC-HVDC systems to weak ac grids. For the forced commutated converter based HVDC systems, VSCs and CSCs are considered and normal operating principles for these two types of converters are discussed. Advanced vector control and power synchronization control are studied as two possible approaches in controlling the VSC-HVDC systems in weak AC grid integrations. Stability issues and limitations of these two controllers are also discussed in detail. For the CSC-based systems, active compensation technique is studied which provides stability and synchronization capability in weak AC grid interconnections. Finally, reliability modeling of various HVDC schemes for weak AC grid integration has been studied. Future study will focus on the analysis of different controllers using capability curves and/or impedance analysis approaches for interconnection of HVDC systems to weak AC grids.

7. Remarks This section summarizes the key points from the previous sections:

• SCR is a general index to measure the weakness of AC grids. • When an HVDC system is connected to an AC grid, the performance of the system will deteriorate if the AC system is weak. • Commutation failure is the main cause of instability in LCC-HVDC

•

Nevertheless, a back-up PLL is required in case of faults to synchronize the converter with the AC grid after faults occur. CSC-HVDC is another type of HVDC system which has recently been implemented and applied to many applications in power systems. Same as the VSC-HVDC, the CSC-HVDC lacks synchronization when connected to weak AC grids. An active compensation approach has been introduced recently to provide decoupling terms on the outer control loops of CSC-HVDC which enables interconnection of CSCHVDC to very weak AC grids. As the PLL input signal degrades the converter synchronization in weak AC grids, a recent work by Cigre group [79] suggested to acquire the input PLL signal at a stiffer AC grid bus. To this end, Phasor Measurement Units (PMUs) can be implemented on strong AC bus in order to transmit the data to the weak AC grid. This idea has been validated in weak AC grid integration of wind power plants, but its application to VSC-HVDC transmission lines is yet to be studied.

integration to weak AC grids. A reactive power compensation is a primary approach to resolve this issue. The FACTS can be used to provide reactive power compensations and a fast voltage control for LCC-HVDC connected to weak AC grids. However, a recently proposed approach named Q-compensation of LCC-HVDC coupling transformers provides abundant merits at lower cost for LCC-HVDC converters connected to weak AC grids. The VSC-HVDC lacks synchronization to the main AC grid when the AC grid is weak. The PLL is the major cause of instability in the weak AC grid integration of VSC-HVDC. Advanced vector control provides four decoupling gains to the vector control of VSC-HVDC that enables integration of VSC-HVDC with very weak AC grids. Power synchronization control is another alternative for VSC-HVDC integration with weak AC grids which removes the PLL from the control loop and synchronizes the converter using a power loop.

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