Since the voltage source converter based high voltage direct current (VSC-HVDC) systems owns the features of nonlinearity, strong coupling and multivariable, the classical proportional integral (PI) control is hard to obtain content control effect. Hence, a new perturbation observer based fractional-order PID (PoFoPID) control strategy is designed in this paper for (VSC-HVDC) systems with offshore wind integration, which can efficiently boost the robustness and control performance of entire system. Particularly, it employs a fractional-order PID (FoPID) framework for the sake of compensating the perturbation estimate, which dramatically boost the dynamical responds of the closed-loop system, and the cooperative beetle antennae search (CBAS) algorithm is adopted to quickly and efficiently search its best control parameters. Besides, CBAS algorithm is able to efficiently escape a local optimum because of a suitable trade-off between global exploration and local exploitation can be realized. At last, comprehensive case studies are carried out, namely, active and reactive power tracking, 5-cycle line-line-line-ground (LLLG) fault, and offshore wind farm integration. Simulation results validate superiorities and effectiveness of PoFoPID control in comparison of that of PID control and feedback linearization sliding-mode control (FLSMC), respectively.

Over the past few decades, excessive utilization of natural resources causes rapid fossil fuels depletion and serious environmental degradation [

Basically, VSC-HVDC is a novel type of HVDC based on voltage source converter (VSC) and controllable turn-off device with pulse width modulation technique. By contrast with conventional current source converter based HVDC (CSC-HVDC), its main technical advantages are as follows: (1) Insulated gate bipolar transistor (IGBT) based fully-controlled power electronic devices can self-shut off its current and can work in passive inverter mode without the need for an external system to provide commutation voltage, the receiving end system can be a weak AC system or passive network [

Proper control design for VSC-HVDC is of great importance for its operation. Traditional vector control (VC) combined with PI/PID mechanism is popularly adopted owing to its high dependability [

With the view of enhancing the dynamic performance and robustness of VSC-HVDC systems, based on VSC-HVDC state space equation, constant power controller and constant voltage controller are developed by using

However, the structures of nonlinear control schemes for VSC-HVDC systems are usually complex, which hinders its applications in practice. In order to realize a more realistic control design of VSC-HVDC systems, this paper is designed to adopt perturbation observer based fractional-order PID (PoFoPID) control [

Motivated by the above discussions, the finds/outcomes of this paper can be concluded as follows:

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The structure of this paper basically contains as following: Firstly, the modelling of VSC-HVDC systems can be shown in Section 2; Then, primary mechanism of CBAS algorithm is presented in Section 3; Section 4 offers detailed design of PoFoPID control strategies for VSC-HVDC systems; Section 5 undertakes three case studies to validate its effectiveness. At last, Section 6 concludes the whole paper.

A common VSC-HVDC system with two VSCs is given in

where

The dynamic equation of inverter can be represented as [

where

The rectifier and the inverter are connected by a DC cable, yields

where

Not that AC grid voltage

Lastly, power flows of AC grid can be described as [

BAS algorithm is a novel biology-based meta-heuristic algorithm, which is mainly based on special food detecting and searching behaviour of long-horn beetles characterized by extremely long antennae in nature [

In BAS algorithm, at the

where

Besides, for more accurately replicating actual searching behaviour of beetle’s antennae, right-hand and left-hand searching behaviours are adopted, as follows:

where

b)

where

Particularly, the updating rule of parameters which directly influences searching behaviour, e.g., antennae length

BAS algorithm only adopts a single beetle to seek a potentially better solution, which is prone to be sunk at a local optimum. To overcome such drawbacks, CBAS algorithm employs a cooperative group with multiple beetles to find potential better solutions, as demonstrated in

where subscript

Like other meta-heuristic algorithms, it is significant to achieve a stable and desirable optimization of a suitable trade-off between local exploitation and global exploration. As an example, if CBAS algorithm attaches more attention to local exploitation, it will easily result in a low-quality local optimum; otherwise, it will result in a low optimization efficiency to seek a better solution. In order to realize optimal search, weights in

where

Note that global exploration weight

Furthermore, parameters of BAS method, e.g.,

where

Details for PoFoPID control can be referred to authors’ previous work [

Let system output

where

and

The determinant of matrix

Suppose overall the nonlinearities are uncharted, make a definition of the perturbations

where constant control gain

Then system (16) is able to rewritten as

Define

where observer gains

Define

where observer gains

The PoFoPID control for VSC-HVDC systems (16) can then be described by [

where optimal control parameters

Choose system output

where

and

The determinant of matrix

Suppose entire the nonlinearities are uncharted, make a definition of the perturbations

where the constant control gain

Then system (25) is able to overwritten as

Define

where observer gains

where observer gains

The PoFoPID control for VSC-HVDC systems (25) can then be described by

where optimal control parameters

where the weights _{max}=100.

In addition, the Oustaloup approximation [

where 2

In

Lastly, the entire controller structure of PoFoPID can be depicted in

For the sake of assessing the control performance of PoFoPID, two typical controllers, i.e., PID control [_{max} is set to be 100. ^{R} CoreTMi5 CPU at 3.4 GHz and 16 GB of RAM.

Method | Rectifier control | Inverter control | ||||||
---|---|---|---|---|---|---|---|---|

Algorithm | Fitness function (p.u.) | Convergence time (Hour) | Iteration number of convergence | ||||||
---|---|---|---|---|---|---|---|---|---|

Max. | Min. | Mean | Max. | Min. | Mean | Max. | Min. | Mean | |

2.67 | |||||||||

A series of step changes of active and reactive power are implemented at _{1} of PID is 36.10% and 33.71% during the second and third step variation, while PoFoPID can realize smooth active and reactive power tracking. Meanwhile, the convergence time of _{1} of PID, FLSMC, and PoFoPID are 0.16s, 0.10s, and 0.08s during the second step variation, respectively [

A 5-cycle LLLG fault occurs at AC bus 1 at when _{dc1} of PID, FLSMC, and PoFoPID are 0.46 s, 0.39 s, and 0.26 s, respectively. Moreover,

Offshore wind farm has a more strong and constant wind speed than the onshore wind farm, which are the promising development trend in coming decades. In particular, AC side of offshore wind farm integration is as same as a weak power, which voltage _{s1} is a time-varying function. Hence, this case simulates a voltage fluctuation _{s1} = 1 + 0.15 sin (0.2_{d1} and _{q1} of PoFoPID is 32.56% and 57.58% of that of PID, respectively.

The integral absolute error (IAE) indices describe the error accumulation of the controlled variable relative to its reference value during time

Furthermore, the overall control costs

Method | Case | |||
---|---|---|---|---|

Active and reactive power tracking | ||||

PID | ||||

FLSMC | ||||

PoFoPID | ||||

Method | Case | |||

5-cycle LLLG fault | Offshore wind farm integration | |||

PID | ||||

FLSMC | ||||

PoFoPID |

In this paper, a new PoFoPID controller is designed for VSC-HVDC systems, which with the purpose of enhancing the robustness and control performance of the system. The major novelties/contributions can be concluded as follows:

(1) PoFoPID control is able to dramatically boost dynamical responses of VSC-HVDC systems integrated with offshore wind farm, which owns great robustness against various uncertainties owing to real-time compensation of perturbation;

(2) Compared to original BAS algorithm, CBAS algorithm can remarkably improve optimization efficiency via a cooperative group of multiple beetles instead of a single beetle. Besides, it can also acquire a high-quality optimum through a dynamic and suitable balance mechanism between local exploitation and global exploration. CBAS algorithm is utilized to optimally tune PoFoPID controller parameters, such that the overall tracking error can be minimized under various operating conditions;

(3) Simulation results validate that PoFoPID controller can achieve the highest tracking speed and lowest tracking error, along with the lowest entire control costs compared with that of other two controllers. Especially, in active and reactive power tracking, the convergence time of _{2} of PID, FLSMC, and PoFoPID are 0.048 s, 0.16 s, and 0.13 s during the second step variation, respectively; the maximum overshoot of active power and reactive power of PoFoPID is 62.63% and 54.53% of that of PID, respectively. In 5-cycle LLLG fault, the recovery time of DC voltage V_{dc1} of PoFoPID is 56.52% and 84.78% of that of PID and FLSMC, respectively; the maximum overshoot of control input _{d1} and _{q1} of PoFoPID is 32.56% and 57.58% of that of PID, respectively. And in offshore wind farm integration, the convergence time of _{1} of PID, FLSMC, and PoFoPID are 0.03 s, 0.13 s, and 0.09 s, respectively; the maximum overshoot of control input _{d1} and _{q1} of PoFoPID is 32.56% and 57.58% of that of PID, respectively. Moreover, PoFoPID can obtain the smallest IAE indices and overall control costs in all cases, which has the highest efficiency and feasibility. Particularly, the

Future study will undertake a dSpace based hardware-in-loop (HIL) experiment for PoFoPID control of VSC-HVDC system, which aims to validate the implementation feasibility of the proposed approach. Besides, it can employ PoFoPID control for multiterminal VSC-HVDC systems via CBAS with offshore wind integration in future researches.

_{1}

equivalent resistance

_{1}

equivalent inductance

_{1}

DC bus capacitor

_{dc1}

DC voltages of rectifier

_{L}

DC cable current

_{0}

equivalent DC cable resistance

_{rd},

_{rq}

d-q axis inputs voltage of rectifier

_{sd1},

_{sq1}

d-q components of AC grid voltages

_{id},

_{iq}

d-q axis inputs voltage of inverter

_{sd2},

_{sq2}

d-q components of AC grid voltages

_{dim}

location dimensions

current best solution until the (

dynamic weights of global exploration

dynamic weights of local exploitation

maximum iteration number

alternating current

high voltage direct current

voltage source converter based high voltage direct current

fuzzy logic control

proportional integral

fractional-order PID

conventional current source converter based HVDC

insulated gate bipolar transistor

static synchronous compensator

interactive teaching-learning optimizer

modular multilevel converter based HVDC

perturbation observer based fractional-order PID

cooperative beetle antennae search

sliding-mode perturbation observer

feedback linearization sliding-mode control

_{infinite}controller for transient stability enhancement of Vsc-Hvdc transmission systems