Optimal Genetic-sliding Mode Control of VSC-HVDC Transmission Systems

Available online at www.sciencedirect.com

ScienceDirect Energy Procedia 74 (2015) 1048 – 1060

International Conference on Technologies and Materials for Renewable Energy, Environment and Sustainability, TMREES15

Optimal genetic-sliding mode control of VSC-HVDC transmission systems M. Ahmeda,b , M. A. Ebrahimc , H. S. Ramadand,a , M. Becherifd,∗ a Zagazig

University, Faculty of Engineering, Electrical Power and Machines Dept., 44519 Zagazig, Egypt GmbH - Robotics Innovation Center, Robert-Hooke-Str. 1, 28359 Bremen, Germany c Benha University, Faculty of Engineering at Shoubra, Electrical Engineering Dept., 108 Shoubra St., Cairo, Egypt d UTBM, FCLab FR CNRS 3539, FEMTO-ST UMR CNRS 6174, 90010 Belfort Cedex, France b DFKI

Abstract This paper deals with the design of a hybrid optimal Genetic-Sliding Mode Control (GA-SMC) approach for VSCHVDC transmission systems for improving the system’s dynamic stability over a wide range of operating conditions considering different parameter variations and disturbances. For this purpose, a comprehensive state of the art of the VSC-HVDC stabilization dilemma is discussed. The nonlinear VSC-HVDC model is developed. The problem of designing a nonlinear feedback control scheme via two control strategies is addressed seeking a better performance. For ensuring robustness and chattering free behavior, the conventional SMC (C-SMC) scheme is realized using a boundary layer hyperbolic tangent function for the sliding surface. Then, the Genetic Algorithm (GA) is employed for determining the optimal gains for such SMC methodology forming a modified nonlinear GA-SMC control in order to conveniently stabilize the system end enhance its performance. The simulation results verify the enhanced performance of the VSC-HVDC transmission system controlled by SMC alone compared to the proposed optimal GA-SMC control. The comparative dynamic behavior analysis for both SMC and GA-SMC control schemes are presented. © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license c 2015 The Authors. Published by Elsevier Ltd.  (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD). Peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD)

Keywords: Dynamic Behavior, Genetic Algorithm, Optimal Control, Robustness, Sliding Mode Control, VSC-HVDC Systems

1. Introduction Voltage Source Converter High Voltage Direct Current (VSC-HVDC) transmission systems, as a part of electrical power grids, have complex and nonlinear natures which may either/both negatively influence the system’s stability and its performance or/and restrict the transmission line capacity [1]. Such complex nonlinear electrical networks present great challenges because of the uncertain parameters, unmodeled dynamics, and unknown disturbances. The power transmission problem has become one of the key issues ∗ Corresponding

author. Tel.: +33 (0) 3 84 58 33 46; fax: +33 (0) 3 84 58 36 36. Email addresses: [email protected] (M. Ahmed), [email protected] (M. Becherif)

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4 .0/). Peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD) doi:10.1016/j.egypro.2015.07.743

M. Ahmed et al. / Energy Procedia 74 (2015) 1048 – 1060

for restricting the development of offshore/isolated-onshore wind farms using VSC-HVDC technologies for long-distance transmission and guaranteeing adequate system dynamic performance and network power quality [2]. Therefore, ongoing research is focused on the nonlinear control and stabilization of such systems to remedy the expected stability and poor performance problems [3-15]. In [16], Cole et al. (2008) have proposed a generic VSC-HVDC model for voltage and angle stability studies considering the trade-off between respect of detail, modeling effort, simulation speed, and data requirements. Zhang et al. (2009) [17] have verified that power-synchronization control is particularly applicable to VSC-HVDC systems connected to weak AC systems via two different design approaches: Internal Model Control (IMC) and H∞ control. As presented by Pandey et al. (2009) [18], a novel self-tuning discrete-time controllers based on multi-rate sampling design HVDC link has been formulated for a two terminal to adaptively cope with the deterministic disturbances acting on the system. However, the proposed controller was rather difficult particularly with the inclusion of the observer dynamics. Ramadan et al. [8-15] have developed different controllers based on Sliding Mode Control (SMC), Lyapunov Control (LC), Asymptotic Output Tracking (AOT) with the aim of the nonlinear control and stabilization of VSC-HVDC transmission systems and the enhancement of their dynamic performance. In addition, a comprehensive robustness evaluation has been performed for the various proposed controllers against parameter uncertainties and disturbances. Ayari et al. (2013) have proposed an optimal PI controller design for the VSC-HVDC transmission system in order to enhance its stability through governing the DC link voltage and controlling the reactive power of Generator-Load VSCHVDC system [19]. Wu et al. (2014) have discussed the key technologies of VSC-HVDC converters particularly for offshore wind including converter topology and the related control strategies [2]. Nayak et al. (2012) have investigated the design of a robust and nonlinear control strategy in a power system interconnected with a VSC-HVDC system via H∞ control to deal with system nonlinearities [20]. Tang and Lu (2014) have presented a modified direct voltage control to enhance the control dynamics in the receiving AC system and to mitigate voltage fluctuations by overcoming the effect of inverter nonlinearities through feed-forward controllers [21]. Das and Mahanta (2014) have addressed an optimal control strategy for nonlinear uncertain systems based on the second order SMC to guarantee chattering mitigation and robustness against parameters uncertainties and disturbances [22]. Merida et al. (2014) has developed two different nonlinear controllers based on quasi-continuous SMC for reaching the maximize aerodynamic power generation and reducing the mechanics loads over the wind turbine considering the nonlinear Behavior, unmodeled dynamics, and unknown disturbances [22]. Sambariya and Prasad (2014) have presented the design of conventional power system stabilizer (CPSS) via the Bat Algorithm (BA) to optimize its gain and pole-zero parameter [23]. Keumarsi et al. (2014) have proposed a hybrid approach based on both Particle Swarm Optimization algorithm (PSO), and Takagi–Sugeno (TS) fuzzy for optimal location of Power System Stabilizers (PSSs) in multi-machine systems with the aim of reducing low-frequency oscillations and improving the system’s dynamic stability over a wide range of operating conditions [24]. To get rid of the difficulties during abnormal operating conditions particularly under parametric uncertainties, disturbances and faults, the use of advanced control techniques such as robust, adaptive, optimal, and Artificial Intelligence (AI)–based methods of control design to improve power systems transient stability has been of the most promising automatic control application areas [3-5]. Modern nonlinear adaptive controllers based on AI algorithms such as Artificial Neural Networks (ANN), Fuzzy Logic (FL) and adaptive neuro-fuzzy approaches have been proposed for nonlinear control design particularly for tuning the controllers’ parameters alongside with the robust ones based on LC, SMC, and Passivity-based Control (PbC) methods with fixed gains [24]. The application of these methods enables system stabilization despite the existed parameter uncertainties and nonlinearities. In addition, different optimization techniques such as PSO, Genetic Algorithms (GA), Differential Evolution (DE), and Simulated Annealing (SA) have been proposed for optimally tuning such parameters to attain enhanced system dynamic Behavior [22-23]. Robust/Adaptive control, on-line design approaches that can deal with uncertainties, are rarely optimal in the sense of formal performance function minimization [8–15]. Moreover, the knowledge of system dynamics is mainly required for offline optimal control design. It is favorable to merge the features of both control designs to establish either an optimal adaptive or an optimal robust controllers. However for reaching sufficient solutions, still the major drawback of optimal

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control techniques is the necessity of system precised mathematical model. Otherwise, the optimal controller should be robust to overcome degraded dynamic behavior and instability in the presence of uncertainty and disturbance [22]. To the best knowledge of the authors, the optimal-robust control problem of VSC-HVDC transmission system under parameter uncertainties and disturbances has been rarely discussed [13,25]. The VSC-HVDC control schemes in the literature are generally neither on-line nor robust/adaptive and optimal control solutions at the same time. Thus, the main contribution of this paper is to verify the dynamic performance of the GA-SMC as an optimal control solution for these DC transmission systems to meet the inherent uncertain parameters, unmodeled dynamics, and unknown disturbances. The GA-SMC is designed by adding the optimality features to the robust C-SMC. The GA-SMC capability towards providing a stabilized performance over a wide range of operating conditions and perturbations is discussed. Nomenclature C1 , Cc , C2 DC shunt capacitors [μF]

CPSS

f1 , f2 ic1 , ic2 iL1d , iL2d iL1q , iL2q

CSC d-q FL FLC

Conventional Power System Stabilizer Current Source Converter Direct & Quadrature rotating frame Feedback Linearization Fuzzy Logic Control

GA HVAC HVDC

Genetic Algorithms High Voltage Alternating Current High Voltage Direct Current

IGBT IMC

Isolated Gate Bipolar Transistor Internal Model Control

LC LTC

Lyapunov Control Load Tap Changing Transformer

ANN

Artificial Neural Networks

PSO RE

Particle Swarm Optimization Renewable Energy

SMC VSC

Sliding Mode Control Voltage Source Converter

VSS WE

Variable Structure System Wind Energy

Frequency of both AC networks DC current in the HVDC line [A] Direct axis component of current for both sides Quadrature axis component of current for both sides Lc1 , Lc2 DC cable inductance [mH] P1 , P2 Active Power to be controlled for both sides [MW] PL1 , PL2 Rated active Power supplied by generators of both sides [MVars] Q1 , Q2 Reactive Power for both sides [MVars] QL1 , QL2 Reactive Power at generator terminals for both sides [MVars] RC1 , RC2 DC cable resistance [Ω] RL1 , RL2 Equivalent resistance of AC generator & transmission line for both sides [Ω] uc1 , ucc , DC shunt voltage on the DC line [kV] uc2 v1dw , v2dw Direct component control signals of both sides v1qw , v2qw Quadrature component control signals of both sides VDC DC Voltage XL1 , XL2 Equivalent reactance of AC generator & transmission line for both sides [Ω] AI Artificial Intelligence AOT Asymptotic Output Tracking

2. System Under Study Due to environmental, technical and economical reasons, the installation of HVDC lines is favored in order to maximize the electric power transmission efficiency through transient stability enhancement, power angle oscillations mitigation and power-synchronization control. Thus, recent significant development in HVDC transmission systems is witnessed for both Current Source Converters (CSC) and Voltage Source Converters (VSC) technologies. The main drawbacks that may limit the application of such DC transmission

M. Ahmed et al. / Energy Procedia 74 (2015) 1048 – 1060

are the system reactive power absorption, the possible harmonic existence, besides value or the thyristor on/off. The HVDC technology are mainly used for [8,15,26,27]: (i) connecting asynchronous systems with different operational frequencies; (ii) reducing active power losses for the same power transmission capacity; (iii) transmitting high energy, particularly in undersea transmission applications. The capacitance becomes higher for longer AC cables that limits the maximum possible transmission distance; (iv) controlling all DC parameters and neighbouring AC parameters with sufficient accuracy and speed of response; and (v) limiting short circuit currents. HVDC transmission systems do not contribute to short circuit current to the AC system.

Fig. 1: Continuous-time VSC-HVDC model.

In the context of the rapid advancement in the power electronic devices, the VSC-HVDC technology is now emerging as a robust and economical alternative for future transmission grid expansion owing to its Insulated Gate Bipolar Transistor (IGBT) which can immediately switch on/off. This innovative know-how is commercially known as HVDC LightT M by ABB and HVDC PlusT M by Siemens [28-33]. VSC-HVDC transmission technology offers competitive benefits to power systems such as: (i) flexible and Independent control of active and reactive power exchange; (ii) avoidance of commutation failure problems; (iii) avoidance the requested communication between two interconnected stations [8,28-33]. In addition, The VSCHVDC system can be properly controlled not only to improve the overall system dynamics and enable its smart operation but also to provide the adequate security and efficiency for the transmission grid especially in the challenging technical issues associated with integration of Renewable Energy (RE) sources. VSC-HVDC links connect mostly asynchronous AC networks, therefore, including converters at each AC side. The schematic representation and the continuous–time equivalent model of the VSC-HVDC transmission system under study are depicted in Fig. 1 and Fig. 2 respectively. The system’s main components are: Load Tap Changing (LTC) transformers, VSC-HVDC converter stations to perform the AC/DC/AC conversion process, AC and DC filters, DC current filtering reactance and DC transmission cable. The VSCs are coupled with AC generation stations via equivalent impedances RL1 + jXL1 and RL2 + jXL2 . Both shunt DC capacitors C1 and C2 , used across the VSCs’ DC sides, limit the impulse current impacts and attenuate the DC side harmonics. For a significant steady state analysis of such DC systems, the following assumptions are considered for the model simplification: (i) strong AC networks than can be modeled as AC voltage sources delivering balanced sinusoidal voltage with constant amplitude and frequency; (ii) the voltage and current harmonics produced by the converters are totally filtered out; (iii) the converter transformers’ resistance and magnetizing impedance are negligible; (iv) lossless converter with neglected dynamics (ideal valves with no arc voltage drop; (v) no DC voltage and current ripples. GG VSC-HVDC transmission system controller design is mainly based on its mathematical model. However, its actual physical system may be influenced by external or internal uncertainties. Among these uncertainties, frequency disadjustments besides the resistance and inductance variations in both DC and AC sides are studied [8]. In Fig. 2, reactive powers (Q1 and Q2 ) on both VSCs’ AC sides should maintain at zero values with the goal of attaining the desired unity power factor. The active power and the DC voltage (P1 and UC2 ) are to be governed to their rated values (200 MW and 300kV) respectively. Indeed, the DC link power losses and voltage drop alongside with the possible bidirectional active power flow control are considered [8]. Considering the systems parameters and operating

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Fig. 2: Continuous-time VSC-HVDC model.

conditions in [8], the 9th order state space representation of the VSC-HVDC transmission system has been deduced in the form: x˙ = A x + g(x) u + R z,

y = h(x, u) x

(1)

where, x, u, z and y refer to state variables, control signals, Park transformation dq components of the AC source and the output signals, respectively.   x = iL1d , iL1q , uc1 , uc1 , ucc , ic2 , uc2 , iL2d , iL2q , (2)   z = vL1d , vL1q , vL2d , vL2q , (3)   u = v1dw , v1qw , v2dw , v2qw , (4) y = [P1 , Q1 , Uc2 , Q2 ] .

(5)

Assuming a balanced three phase networks, synchronized rotation d-q reference frame, and parametric uncertainties existence, the A, g(x), R and h(x, u) matrices are [8]: ⎡ −RL1 ⎢⎢⎢ LL1 ⎢⎢⎢ ⎢⎢⎢−w1 ⎢⎢⎢ ⎢⎢⎢ 0 ⎢⎢⎢ ⎢⎢⎢ 0 ⎢⎢⎢ ⎢ A = ⎢⎢⎢⎢⎢ 0 ⎢⎢⎢ ⎢⎢⎢⎢ 0 ⎢⎢⎢ ⎢⎢⎢ 0 ⎢⎢⎢ ⎢⎢⎢ 0 ⎢⎢⎣ 0 ⎡ 1 ⎢⎢⎢ LL1 ⎢⎢⎢ ⎢0 R = ⎢⎢⎢⎢⎢ 0 ⎢⎢⎢ ⎣ 0

w1

0

−RL1 LL1

0

0

0

0

1 Lc1

0

0

0

0

0

0

0

0

0

0

0

0

−1 C1 −Rc1 Lc1 1 Cc

0

0

0

0

−1 Lc1

0

0

0

−1 Cc −Rc2 Lc2 1 C2

0

0

−1 Lc2

0

0

0

0

0

0

0

1 Lc2

0

0

0

0

0

0

0

0

0

0

−RL2 LL2

0

0

0

0

0

0

−w2

··· ···

···

0 0 0

···

···

0

0 1 LL1

−1 LL2

⎤ 0 ⎥⎥ ⎥⎥⎥ 0 ⎥⎥⎥⎥ ⎥⎥ 0 ⎥⎥⎥⎥⎥ ⎥⎥ 0 ⎥⎥⎥⎥⎥ ⎥⎥ 0 ⎥⎥⎥⎥ ⎥⎥⎥ 0 ⎥⎥⎥⎥ ⎥⎥ 0 ⎥⎥⎥⎥⎥ ⎥⎥ w2 ⎥⎥⎥⎥⎥ ⎥ −RL2 ⎦ LL2

⎡ −1 ⎤ ⎢⎢⎢ 2LL1 x3 0 ⎥⎥ ⎥⎥ ⎢⎢⎢⎢ 0 0 ⎥⎥⎥⎥ ⎥⎥⎥ , and g(x) = ⎢⎢⎢⎢⎢ ⎢⎢⎢ 0 0 ⎥⎥⎥ ⎢⎢⎣ ⎥ −1 ⎦ 0 LL2 4×9

⎡ ⎢⎢⎢v1d ⎢⎢⎢v , h(x, u) = ⎢⎢⎢⎢ 1q ⎢⎢⎣ 0 0

v1q −v1d ··· ···

0 ··· 0 ··· 0 v2d 0 v2q

0

···

0

···

−3 4C2 x8 −3 4C2 x9

1 2LL2 x7

⎤ 0 ⎥⎥ ⎥ 0 ⎥⎥⎥⎥ ⎥ v2q ⎥⎥⎥⎥⎦ −v2d 4×9

9×9

−1 2LL1 x3

3 4C1 x1 3 4C1 x2

···

0

···

0

0

0

⎤ 0 ⎥⎥ ⎥⎥⎥ 0 ⎥⎥⎥⎥ ⎥⎥ 0 ⎥⎥⎥⎥⎥ ⎥⎦ 1 2LL2 x7 4×9

Following the deduction of the VSC-HVDC state space representation, the chattering-free C-SMC feedback control signals should be derived for each converter so that the actual output trajectories (P1 , Q1 , UC2 , Q2 ) tracks their corresponding desired references (P1re f = 200 MW, Q1re f = 0, UC2re f = 300 kV, Q2re f = 0) despite the presence of parameter uncertainties. For this purpose, the SMC approach based on Variable Structure Systems (VSSs) has been considered a suitable candidate for the nonlinear control and stabilization

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of such VSC-HVDC transmission system. [8-15]. For VSS control, the feedback control law decision rule should be conveniently chosen. The decision rule, or the switching function, has some measure of the current system behavior as its input and produces instantaneously a particular feedback controller as an output. Therefore, a combination of subsystems where each of them has its own fixed control structure and is valid for a certain region of system Behavior is illustrated. VSSs are designed to drive and then constrain the system state to lie within a neighborhood of the switching function [34]. The main advantages of CSMC are that the system dynamic behavior can be tailored by properly selecting the switching function in addition to its robustness and chattering-free dynamic behavior [34]. The output signals’ derivatives are assumed null. The system stability is guaranteed in the sense of the Lyapunov stability theorem. A hyperbolic tangent function is used for the sliding surface to avoid chattering problems. Positive tuning gains ensure the system stability however dynamic performance behavior with shorter settling time, lower overshoot and acceptable steady-state error are preferred [8]. Indeed, efficient controllers are those capable of controlling the active and reactive power (P1 and Q1 ) and governing the DC voltage and reactive power (Uc2 and Q2 ) to their rated reference values considering bi-directional power flow. Unity power factors at both HVDCs AC sides are unity be properly controlling reaching zero reactive powers at both converters’ AC sides. With the application of the C-SMC as previously discussed in [8], the nonlinear control signals are deduced as:     v1d 2˙3y1 − α1 + v1q 2˙3y2 − α2

 , (6) u1 = −1 2 2 2LL1 x3 v1d + v1q     v1q 2˙3y1 − α1 + v1d 2˙3y2 − α2

 , (7) u2 = −1 2 2 2LL1 x3 v1d + v1q     1 ˙ 3 − C12 x6 − 4C3 2 iL2q 2˙3y4 − α3 2LL2 x7 v2d y



 , (8) u3 = −3 x8 v2d + x9 v2q x7 8LL2 C2     1 ˙ 3 − C12 x6 − 4C3 2 iL2q 2˙3y4 − α3 2LL2 x7 v2d y



 u4 = (9) −3 x8 v2d + x9 v2q x7 8LL2 C2 where,



−RL1 x1 + w1 x2 + α1 = v1d LL1 −RL1 x1 + w1 x2 + α2 = v1q LL1 −RL2 α2 = v2q x8 + w2 x9 + LL2

1 z1 + v1q −w1 x1 + LL1

1 z1 + v1d −w1 x1 + LL1

1 z3 + v2d −w2 x8 + LL2

−RL1 x2 + LL1 −RL1 x2 + LL1 −RL2 x2 + LL2

1 z2 LL1

1 z2 LL1

1 z4 LL2

(10) (11) (12)

Although the chattering-free and adequate dynamic performance of the C-SMC besides the robustness against disturbances and parameter uncertainties, the lake of robustness with respect to AC side inductance variations is still a disadvantage [8]. Therefore, the GA-SMC is checked as an alternative method to improve the system performance and treat the susceptibility of the C-SMC in presence of AC inductance variations. Using the genetic algorithm, the system parameters in sliding mode variable structure control are optimized in order to improve system performance [8,35]. Besides the complicacy of the GA-based optimization techniques, it may fall in a local minima solution. Alternatively, PSO algorithm, developed by Kennedy and Eberhart in 1995, is an evolutionary algorithm, which is inspired by the mechanism of biological swarm social behavior such as fish schooling and bird flocking. It differs from other evolutionary techniques in the adoption of velocity of individuals, and it can search more randomly than genetic algorithm, unlikely to fall into the local optimum and has faster convergence speed. Due to its simple principles and low computational complexity, it has been widely applied in such areas as electromagnetic optimization, optimal circuit design, and data clustering [35].

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3. Genetic Algorithms Optimization The problem addressed in this paper is the optimization of an objective function f : Rn → R over a domain of interest that possibly includes lower and upper bounds on the problem variables. The derivatives of f are assumed neither symbolically nor numerically available. Hence, this problem belongs to the derivativefree optimization class. In this class of problems, the derivative information is unavailable, unreliable, or impractical to obtain, for instance when f is expensive to evaluate or somewhat noisy, which renders most methods based on finite differences of little or no use [36]. Derivative-free optimization is an area of long history and current rapid growth, fueled by a growing number of applications that range from science and engineering design to facility location problems [37]. Extensively used algorithms of this class are direct local search, simulated annealing, particle swarm, and genetic algorithms. Start

Create Initial Population Cr

Termination Criterion Satisfied?

Yes

Designate Result

No

End

Evaluate Fitne Fitness of Each ach Indi Individual in Population

Next Individ Individual

Yes

Next Gen

ividual? last Individual?

Select Genetic Operation eraation Probabilistically Pr

Pm

No PN c

Select One Individ Individual Based on Fitness

Select Two wo o Indi Individuals ividuals n Fitness Based on

Select ect One Ind Individual Based on Fitness

Perform Reprod Reproduction Copy into New Population

Next In Individual divid dual

Perfor m Mut tation Perform Mutation Insert Mutant into New Population

Perform P m Crossover Crossover Insert Two O Offspringg into New Population

Next In Individual ndivid dual

Fig. 3: The Basic Genetic Algorithm: flowchart.

GA are a type of stochastic global search algorithms that rely on critical non-deterministic algorithmic steps. Some of these algorithms occasionally allow intermediate moves to lesser quality points than the solution currently at hand. The literature on stochastic algorithms is very extensive, especially on the applications side, since their implementation is rather straightforward compared to deterministic algorithms. GA, an evolutionary algorithms introduced by Holland [1], resemble natural selection and reproduction processes governed by rules that assure the survival of the fittest in large populations. Individuals (points) are associated with identity genes that define a fitness measure (objective function value). A set of individuals form a population, which adapts and mutates following probabilistic rules that utilize the fitness function. In GA, for instance, each iteration considers a set of evaluated points and generates new points through multiple randomization processes. GA require first a definition of a search interval and a selection of an ini-

M. Ahmed et al. / Energy Procedia 74 (2015) 1048 – 1060

tial population, randomly chosen inside the search interval, then finally, an iterative application of the three main steps; reproduction, crossover, and mutation, until convergence (stabilization of the fitness function) is obtained. The algorithms provide a way to search a large space of possible solutions in a near-optimal way, using four Bio-Darwinian methods: 1. Natural Selection: find the members of the population with the best fitness, 2. Reproduction: Select the chromosomes from current generation (population) to be parents to the next generation. A chromosome is selected (reproduced) based on its fitness (value of objective function); chromosomes with lowest fitness values, in maximization case, are discarded and chromosomes with higher fitness values, i.e. fittest, are kept for the next generation, i.e. they survive. 3. Crossover: to produce a variety in the next generation, some members (chromosomes) are paired randomly. Each paired string exchanges a randomly chosen portion of its bits with its mate. This produces new chromosomes that maintain many of the characteristics of their parents (population of chromosomes just before crossover). 4. Mutation: after crossover, each member of the population (chromosome) will alter some of its bits, i.e. if a bit is 0 it is changed to 1 and vice-versa. Usually, the number of bits altered is very low, typically an average of 1 in 1000 bits. The mutation step prevents the algorithm from loosing some potentially useful information, that is, reproduction and crossover might not lead to the chromosome that optimizes the fitness function whereas the mutation does. The MATLAB implementation for the GA follow the steps presented in Fig. 3. 4. Optimization Framework This section describes the components of the simulation framework that seamlessly integrates simulation tools from different vendors in addition to the developed tools. This way, the individual parts or components no longer need to be designed apart from each other. Furthermore, integrated simulation facilitates developing the design and test of the optimization problem and system. It can be used also for parameter optimization of the different components of the system. With simulation, real reference experiments can be later conducted to enhance the verification of the virtual models using real reference experiments. The framework can accomplish detailed analysis of precise system behaviors. A typical construction and operation of the framework is shown in Fig. 4. The detailed algorithm of GA is presented next by first defining the fitness function f (x). In the VSCHVDC, it is requested to optimize eight controller parameters (four gains for each side or a couple of gains for each control signal). The GA problem dimensions are set to eight. The population size is fixed to 100 which is sufficient for this problem with a large number of variables to prevent failures due to bias by the highest fitness individuals as suggested by Liepins and Hilliard [4]. To speed up the optimization process, all the initial population is set to 150, which was obtained with the final tuning of the CSMC controller. After some preliminary tests, the value of 150 is attained for the desired number of generations. This value is a good compromise between the overall simulation time and the obtained performance. The stall generations limit is set to 100 that force finishing the optimization process for no change in the best fitness value. With the aforementioned options, the GA optimization is run on the model. The optimization process terminated due to stall generation limit as shown in Fig. 5(d) which plots the percentage of stopping criteria satisfied. The fitness value did not improve any further after generation 75 as shown in Fig. 5(a) where the best and mean score of the population at every generation are demonstrated. The range (the minimum, maximum, and mean) of fitness function values in each generation is depicted in Fig. 5(c) from which the best fitness value for a population is the smallest fitness value for any individual in the population. Fig. 5(b) illustrates the average distance between individuals at each generation. the plot indicates that individuals have a reasonable high diversity due to the large average distance till generation 40 which enables the algorithm to search a larger region of the problem space. The individuals for the controller parameters giving the best fitness value are provided to the system model to further investigate the system performance with them.

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System Parameters & Settings

scripts for optimization, simulation & process management

Model parameters

Simulink simulation model

export simulation

Optimized controller Parameters

Optimization settings

results

Optimization variables Simulation results Genetic Algorithm Optimization

MATLAB Backend

Fig. 4: The simulation framework for controller and system parameter optimization with evolutionary GA module.

5. Simulation Results To investigate reference trajectory tracking of the nonlinear VSC-HVDC system equipped with the proposed controllers, the references of outputs and states (P1 , Q1 , UC2 and Q2 ) supposing the power delivered to station 2 are (200 MW, 0 MVAR, 300 kV, 0 MVAR) respectively [8]. Fig. 6(a) depicts that the active power of the sending side VSC’s AC terminal P1 is perfectly controlled to its 200 MW, 240 MW and 160 MW rated values (i.e., the value to be tracked). After each step, no active power overshoot reveals. Setting time of about 60 ms is required for tracking the new active power reference. From Fig. 6(b), the reactive power Q1 successfully tracks its zero reference value. Therefore, unity power factor is attained for the sending side for both controllers use (C-SMC and GA-SMC). Obviously, the GA-SMC controller provides better performance with smaller overshoots and setting time of about 40 ms. Fig. 6(c), confirms that the DC voltage on the receiving DC terminal of the GG VSC-HVDC is perfectly governed to its rated 300 kV using GA-SMC nonlinear controller with less settling time compared to CSMC. Fig. 6(d) illustrates that the proposed GA-SMC controller’s capability to control the reactive power at the receiving VSC’s AC terminal (Q2 ) to its set-point value of zero is less than C-SMC controller because of the resulting steady state error. Therefore, both active and reactive powers of the first converter (P1 and Q1 ) besides the DC voltage (UC2 ) are perfectly controlled using the proposed GA-SMC controllers. Unity power factor is realized at sending converters’ AC side through zero reactive power tracking. However, the GA fails to properly choose the optimal gain(s) that yields a perfect tracking for Q2 towards its zero reference. This lack of success comes from the fall of the GA into local minima solution. 6. Conclusion The design of optimal robust controllers for nonlinear VSC-HVDC transmission systems present great challenge because of the inherent system parameters uncertainties, unmodeled dynamics and perturbations. After developing the VSC-HVDC system mathematical model, C-SMC can be directly expressed based on

M. Ahmed et al. / Energy Procedia 74 (2015) 1048 – 1060

Fig. 5: The genetic algorithm optimization process performance and results for the eight controller parameters. In (a), the fitness value is almost constant after generation 75. Plot (b) shows that individuals have a reasonable high diversity till generation 40 after which the the average distance between individuals become noticeably low. From the score values in (c), it is noticed again that the algorithm has a slight improvement in performance after generation 75. As shown in (d), the process is terminated because of the stall generation limit.

error functions. Positive gains for the Lyapunov energy function are selected to guarantee both robustness and the tracking performance of the proposed SMC approach. To ensure significant smooth transitions and chattering-free dynamic behavior during the unexpected abnormal situations, C-SMC scheme is realized using a boundary layer hyperbolic tangent function for the sliding surface. The robust nonlinear SMC is designed to govern the DC link voltage and to bi-directionally control the active and reactive powers on both AC sides of VSCHVDC system independently, flexibly and rapidly. The robustness of the C-SMC controller and its dynamic behavior are assessed in presence of parameter uncertainties and penetrations. For conclusion, GA approach is applied to optimally select the SMC positive gains to maximize the dynamic performance improvement and to minimize the steady state error within smaller response time. Simulation results illustrate the capabilities of both robust SMC and optimal GA-SMC approaches for providing system adequate dynamic performance and stability. The main conclusion is that the superiority of the application of C-SMC over the GA-SMC is demonstrated owing to its simpler implementation and the better dynamic behavior. Therefore, the dynamic responses may be further improved by proposing alternative optimization methods such as PSO for tuning the C-SMC parameters to avoid local minima results revealed via GA algorithms. In the forthcoming work, the covariance matrix adaptation method which adapts the resulting search distribution to the contours of the objective function by updating the covariance matrix deterministically using information from evaluated points will be applied to the GA to hopefully reach better performance and to ensure the optimal controller robustness against all types of uncertainties and faults even those for which the C-SMC is susceptible.

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Fig. 6: Simulation results for the controlled VSC-HVDC transmission system. Time response results of: active power P1 (a), reactive power Q1 (b), DC line voltage VC2 (c), and reactive power Q2 (d).

M. Ahmed et al. / Energy Procedia 74 (2015) 1048 – 1060

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