Genetic Algorithm and HVDC Based Mixed AC/DC/AC Optimal Power Flow Incorporating FACTS Devices

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

Abstract—In this paper, we presents an efficient and reliable evolutionary-based approach to solve mixed AC/DC/AC Optimal Power Flow (OPF) in electrical network by the application of the Genetic algorithm (GA’s) methods, in the presence of FACTS devices in the modern electrical power networks. Our main goal is to minimize the objective function necessary for a best balance, between the energy production and its consumption in the mixed AC/DC/AC electrical networks, under normal operation. The function characterizing this balance is presented in the form of a nonlinear function, taking into account the necessary constraints of equality and of inequality. The objective function is a minimization of the cost function of the power generation and active power losses while preserving the powers of the generators, the voltages magnitudes, the capacitors of the shunts condensers, the inductances of the series reactors and the ratios of the transformers within acceptable limits. The incorporation of FACTS devices (STATCOM), the introduction of the HVDC system or a DC link and the GA method will be the main object of this study for the OPF of the mixed AC/DC/AC modern network. GA’s method have been examined and tested on the standard IEEE 14-bus test system with different objectives that reflect active power losses minimization and active power generation cost minimization. The results of used method have been compared and validated with those reported in the recent literature. The results are promising and show the effectiveness and robustness of proposed approach methods.

Index Terms— Optimization; Newton-Raphson Method (NRM); Power Flow (PF); High Voltage Direct Current (HVDC); Voltage Source Converter (VSC); DC-link; FACTS; STATCOM; AC-OPF; DC-OPF; Mixed AC/DC/AC OPF; GA Method.

I. INTRODUCTION

The OPF problem has been one of the most widely studied subjects in the power system community. He was first discussed since its introduction by Carpentier in 1962 [1]-[6]. As the OPF is a very large, non-linear mathematical programming problem, it has taken decades to develop efficient algorithms for its solution. Many different mathematical techniques have been employed for its solution.

OPF is an important tool for power system operators, both, in planning and operating stages. The main task is to adjust some control variables (e.g. active power generation from power plants, generator terminal voltage, reactive power

compensation and on-load tap changers of transformers) in a power system, so that the best operating point can be achieved. The word ‘best’, here, means that the operating point can minimize or maximize certain objective function (e.g. active power loss in the target system or the social welfare from the target system) while satisfying certain constraints (e.g. bus voltage magnitude limits and generator generation limits) [7].

The construction of both generation facilities and new transmission lines have been delayed, during the last two decades, due a certain number of new policies on the energy production and consumption, the environment protection and the deregulation market of power utilities.

Therefore, the OPF problem is a large-scale highly constrained nonlinear non-convex optimization problem [4]. To solve it, a number of conventional optimization techniques such as nonlinear programming (NLP) [8], quadratic programming (QP) [3], linear programming (LP) [9], sequential quadratic Programming [10], and interior point methods [11] have been applied. All of these mathematical methods are fundamentally based on the convexity of objective function to find the global minimum. However, the OPF problem has the characteristics of high nonlinearity and non convexivity. Therefore, conventional methods based on mathematical technique cannot give a guarantee to find the global optimum. In addition, the performance of these traditional approaches also depends on the starting points and is likely to converge to local minimum or even diverge. Recently, many attempts to overcome the limitations of the mathematical programming approaches have been investigated such as Genetic Algorithm (GA), Evolutionary Programming (EP), and Evolution Strategies (ES). Their applications to global optimization problems become attractive because they have better global search abilities over conventional optimization algorithms. The proposed GA based OPF were evaluated on an IEEE 14-bus system and the obtained results were compared and validated with those reported in the recent literature. An enhanced GA with adaptive crossover and mutation based on the fitness statistics of population was applied to minimize the active power loss in the transmission network and active power generation cost minimization [4].

Transmission networks of modern power systems have been causing problems because of growing demand and restrictions on building new lines. One of the consequences of such a system is the threat of losing stability following a disturbance. In order to expand or enhance the power transfer

F Boukhenoufa1, N. Mezhoud2, A. Bahri3

1_{Electronics and Industrial Electrical Laboratory, Jijel University 18000, Algeria} 2_{Department of Electrical Engineering, University of August 20}th_{, 1955, Skikda 21000, Algeria}

32_{Department of science & technology, University of Ghardaia, 47000, Algeria}

Genetic Algorithm and HVDC Based Mixed

AC/DC/AC Optimal Power Flow Incorporating

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capability of existing transmission network the concepts of FACTS (Flexible AC transmission system) is developed by the Electric Power Research Institute (EPRI) in the late 1980s. The main objective of FACTS devices is to replace the existing slow acting mechanical controls required to react to the changing system conditions by rather fast acting electronic controls. FACTS means alternating current transmissions systems incorporating power electronic based and other static controllers to enhance controllability and increase power transfer capability [12]. FACTS devices are found to be every effective in a transmission network for better utilization of its existing facilities without sacrificing the desired stability margin. There are various forms of FACTS devices, some of which are connected in series with a line and the others are connected in shunt or a combination of series and shunt [12].

Better utilization of existing power system capacities by installing FACTS devices has become imperative. The application of FACTS in the electric power system, such as static VAr compensator (SVC), static compensator (STATCOM), thyristor-controlled series capacitor (TCSC), solid-state series controller (SSSC), thyristor switched series Capacitor (TSSC), thyristor controlled series reactor (TCSR), thyristor-switched series reactor (TSSR), thyristor controlled phase angle regulators (TCPAR), unified power flow controllers (UPFC) among others, is intended for the control of power flow, improvement of stability, voltage profile management, power factor correction, loss minimization, and reduced cost of production. The OPF becomes even more complex when FACTS devices are taken into consideration as control variables [6], [12].

Since its existence, the power system was produced, transported and distributed in AC [13]. But, in the last few years, the incorporation of subsets of transmission HVDC in AC transmission networks brought a significant change in the transport of the electric power [13]-[18].²² The technical and economic factors were modified and must obey to the decision and the selection criteria for a good mixed farm. The HVDC transmission lines are much more preferable than the AC ones because they are more economic and more reliable, in particular applications such as :

 Connection between two systems with different

frequencies.

 Interconnection between two very distant blocks,

where transport by AC transmission lines becomes almost to be impossible.

The basic of the power flow in a mixed AC-DC system has the same interest as that of the AC three phase systems. This will enable us to know, constantly, in any point, the energy state of the mixed AC-DC system, for a much better exploitation.

The knowledge of the bus voltages of the network is very significant because they make it possible to calculate exactly the power flow between the buses. The resolution of the load flow problem in a mixed AC-DC system is different than that known in the AC systems. We must, then, introduce new parameters and make some modifications in the basic methods to simplify the complexity of the problem [13].

HVDC transmission lines constitute a key application of the power electronics technology to electric power networks. The economics of bulk power transmission by underground means is increasingly moving in favour of direct current technology. The HVDC links have the ability to exert instantaneous power control in neighbouring AC systems.

Great research efforts have been directed towards realising HVDC models for stability studies and power flows [19].

However, HVDC models for OPF studies have received limited attention and are, so far, underdeveloped. De Martinis et al. have developed an HVDC model but the solution algorithm is a sequential gradient restoration algorithm [20]. Lu et al. have, also, developed an HVDC model, which was incorporated in a sequential quadratics programming techniques [18]. These methods suffer from using a ‘soft’ solution method, i.e. Newton’s method is more robust. To avoid this problem, the above authors propose a simultaneous solution, in which the DC equations are combined with the AC equations in a single frame-of-reference for a unified iterative solution using GA method.

Equations for the two-terminal HVDC link are developed and implemented in an mixed AC-DC OPF using GA method. The basic model of the HVDC link is based on the formulation given in [19], [21].

Genetic algorithm is an optimization technique inspired by the theory of evolution. In a simple genetic algorithm, individuals are simplified to a chromosome that codes for the variables of the problem. The strength of an individual is the objective function that must be optimized. A population of candidates evolves by genetic operators: mutation, crossover and selection. The characteristics of good candidates have more chances to be inherited, because good candidates live longer. So the average strength of the population rises through the generations. Finally, the population stabilizes, because no better individual can be found. At that stage, the algorithm has converged, and most of the individuals in the population are mostly identical, and represent a sub-optimal solution to the problem [22]. Moreover, they always produce high quality solutions, and therefore, they are excellent methods for searching optimal solution in a complex problem. Additionally, GAs are practical algorithm and easy to be implemented in the power system analysis [23]-[25].

II. PROBLEMFORMULATION

The OPF problem consists of obtaining the optimal settings for control variables in an electric power system so that certain operational goals can be achieved. These are

represented by a predefined objective functionf, subject to a

set of constraints. The operating state of a power system provided by an OPF is one that guarantees affordability, reliability, security, and dependability. Generally, the OPF problem can be expressed as [2]-[6], [26]-[29]:

)

,

(

x

u

f

Min

(1)

Subject to

0

)

,

(

x

u



h

(2)

0

)

,

(

x

u



g

(3)

Where

x

is the vector of state variables,

u

is a vector of

control variables, f(x,u) is the objective function to be

optimised,

h

(

x

,

u

)

represents the power flow equations, and

) , (xu

g consists of state variable limits and functional

operating constraints.

(3)

is a feasible solution point where the objective function is minimised within a neighbourhood. The global minimum is a local minimum with the lowest value in the complete feasible region.

A. Objective Function

In this paper, the objective functions of OPF are

minimization of fuel cost for all generators

f

₁ and active

power losses minimization

f

₂ which can be formulated as:









ng

i k gk k gk k

c

P

b

P

a

f

1 2

1

min

(4)

 

 





nl

k nl

j kj jk

P

f

1 1

2

min

(

)

(5)

WhereP_gk,

n

_gand

n

_l are the active power output generated

by the ith_{generator, the total number of generators and total}

number of branches. _a_k,_b_k and _c_k are the cost coefficients

of unit k.

B. Equality Constraints

The equality constraints

h

(

x

,

u

)

are the sets of nonlinear

power flow equations that govern the power system, i.e.:

0 )

,

(  _dk  _gk 

k V P P

P  (6)

0 )

,

(  _dk  _gk 

k V Q Q

Q



(7)

WhereP_k, Q_k, P_dk, Q_dk are the active and reactive power

injections at bus k, the active and reactive power loads at bus

k, respectively. P_gk and Q_gk are the scheduled active and

reactive power generations at bus k, respectively.

V

and



are the nodal voltage magnitudes and angles.

C. Inequality Constraints

The inequality constraints

g

(

x

,

u

)

are the set of

constraints that represent the system operational and security limits like the bounds on the following:

 Generators active and reactive power outputs:

max min

gk gk

gk

P



where

k



1

,...,

n

_g (8)

max min

gk gk

gk

Q



where

k



1

,...,

n

_g (9)

 Voltage magnitudes and angles at each bus:

max min

k k

k

V



where

k



1

,...,

n

_b (10)

max min

k k

k





where

k



1

,...,

n

_b (11)

 Transformer tap settings:

max min

k k

k

T



where

k



1

,...,

n

_T (12)

 Reactive power injections due to STATCOM:

max min

k STAT k

STAT k

STAT

Q









 where k1,...,nSVC (13)

Where T, n_T, n_b, nSTAT and QSTAT are the transformer tap

settings, total number of transformers, total number of buses, total number of STATCOM and reactive power injected by STATCOM.

III. MODELLING OFSTATICCOMPENSATOR:STATCOM

The STATCOM is a member of the FACTS family that is connected in shunt with AC power systems [30]. The STATCOM has played an important role in the power industry since the 1980s. The STATCOM consists of one VSC and its associated shunt-connected transformer. It is the static counterpart of the rotating synchronous condenser but it generates or absorbs reactive power at a faster rate because no moving parts are involved. In principle, it performs the same voltage regulation function as the SVC (static Var compensator) but in a more robust manner because, unlike the SVC, its operation is not impaired by the presence of low voltages [31].

A schematic representation of the STATCOM and its equivalent circuit are shown in Fig. 1a and Fig. 1b, respectively.

[image:3.595.306.547.333.413.2]

(a) (b)

Fig. 1 Static compensator (STATCOM) system; (a) schematic representation; (b) equivalent circuit

The STATCOM will be represented by a synchronous voltage source with maximum and minimum voltage magnitude limits. The synchronous voltage source represents the fundamental Fourier series component of the switched voltage waveform at the AC converter terminal of the STATCOM [31].

The bus at which the STATCOM is connected is represented as a PVS bus, which may change to a PQ bus in the event of limits being violated. In such a case, the generated or absorbed reactive power would correspond to the violated limits. Unlike the SVC, the STATCOM is represented as a voltage source for the full range of operation, enabling a more robust voltage support mechanism. The STATCOM equivalent circuit shown in Fig. 1b is used to derive the mathematical model of the controller for inclusion in power flow algorithms.

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converter operation is associated with internal losses caused by non-ideal power semiconductor devices and passive components. Without any proper control, the capacitor voltage will be discharged to compensate for these losses. The capacitor voltage is regulated by introducing a small phase shift between the converter voltage and the AC power systems [30].

The power flow equations for the STATCOM are derived below from first principles and assuming the following voltage source representation [31]:



vR vR



vR

V

j

E



cos





sin



(14)

Based on the shunt connection shown in Fig. 1b, the following may be written:



* *



* * k vR vR vR vR vR

vR V I V Y V V

S    (15)

After performing some complex operations, the following active and reactive power equations are obtained for the converter and bus k, respectively:











_vR _vR _k _vR _vR _k



k vR vR vR

vR V G V V G B

P  2  cos   sin  ₍₁₆₎











vR vR k vR vR k



k vR vR vR

vR V B V V G B

Q  2  sin   cos  ₍₁₇₎











vR k vR vR k vR



vR k vR k

k V G VV G B

P  2  cos   sin  ₍₁₈₎











vR k vR vR k vR



vR k vR k

k V B VV G B

Q  2  sin







 cos







₍₁₉₎

Using these power equations, the linearised STATCOM model is given by equation (20), where the voltage

magnitude

V

_vR and phase angle



_vR are taken to be the state

variables:                                                                                                                  vR vR vR k k k vR vR vR vR k k k vR vR vR vR vR k k k vR vR vR vR k k k k k k vR vR vR k k k k k k vR vR k k V V V V V V Q Q V V Q Q V V P P V V P P V V Q Q V V Q Q V V P P V V P P Q P Q P vR vR vR vR vR vR           (20)

IV. MODELLING OFHVDC-VSC

The HVDC-VSC comprises two VSC’s: One operating as a rectifier and the other as an inverter. The two converters are connected either back-to-back or joined together by a DC transmission, depending on the application. Its main function is to transmit constant DC power from the rectifier to the inverter station, with high controllability. A schematic representation of the HVDC-VSC is shown in Fig. 2.

[image:4.595.47.255.454.561.2]

One VSC controls DC voltage and the other acts on the active power transmission through the DC link. Assuming lossless converters, the active power flow entering the DC system must equal the active power reaching the AC system at the inverter end minus the transmission losses in the DC cable. During normal operation, both converters have independent reactive power control [20] - [21].

Fig. 2 HVDC-VSC transmission [19], [21]

The converter stations perform the AC/DC/AC conversion process, and consist of valve bridges and LTC (load tap changer) transformers. The thyristors switch each phase of the AC three phase systems at the appropriate point of the voltage cycle to produce a direct current. The basic equations describing the two-terminal HVDC are summarised as follows [13], [19], [21], [32]-[33].

d k ck k k k k

dk naV X nI

V

  2 cos 3

3 _  (21) d m cm m m m m

dm n aV X n I

V  _

 3 cos 2 3 _  (22) d dk dk V I

P  _and P_dmV_dmI_d ₍₂₃₎

d k k k

dk K naVI

S



2 3

 and SdmK3_2nmamVmId (24)

2 2

dk dk dk S P

Q   and Qdm Sdm2 Pdm2 (25)

Where the factorKis given by [19] as :























  



                cos cos 4 2 sin sin 2 2 2 cos 2

cos 2 2

K (26)

dk

V and

V

_dm are the DC voltage magnitudes at the terminals

of the rectifier and the inverter, respectively.

n

_k and

n

_m are

the numbers of series connected bridges in the rectifier and

inverter, respectively.



_k is the ignition angle for rectifier

operation, and



_m is the extinction angle for inverter

operation. X_Ck and X_Cm are the commutation reactance in

the rectifier and inverter, respectively. V_k and Vm are the

effective line to line voltage magnitudes at the AC terminals

of the rectifier and inverter, respectively.

I

_d is the direct

current.

In equation (26),



can be either



_k or



_m . If the

commutation overlap is not taken into account, the

parameters



andkwould be taken as:





0

and k1

[19]. The transfer of current from one phase to another requires a finite time which is called commutation time or overlap time. The result of this is a short circuit for a short duration between the two commuting thyristors leading to a temporary voltage reduction. This effect does not explicitly appear in the set of equations presented above, but for the rectifier is given as :

d k Ck d X n I

V _3

 ₍₂₇₎

(5)

d DC dm

dk

V

R

I

V





₍₂₈₎

Where

R

_DC is the DC resistance.

The HVDC-VSC system is suitably represented by two shunt-connected voltage sources linked together by an active power constraint equation. Each voltage source is connected to the AC system by means of its transformer reactance.

V. GENETICALGORITHMMETHOD

Genetic Algorithm (GA) is a search heuristic that mimics the process of natural evolution, was first proposed by Holland in the early 1970s and put into practical applications in the late 1980s [33]. In power systems GA’s have been recently applied for optimization of generation expansion planning, optimal power flow, economic dispatch, unit commitment and reactive power planning [34]-[35].

GA is a search algorithm based on the mechanics of natural selection and natural genetics. GA is different from other optimization methods in the following features, which make GA a robust algorithm to adaptively search the global optimal point of certain class of engineering problems. The advantages of GA over other traditional optimization techniques can be summarized as follows:

GA searches from a population of points, not a single point. The population can move over hills and across valleys. GA can therefore discover a globally optimal point, because the computation for each individual in the population is independent of others. GA has inherent parallel computation ability.

GA uses payoff (fitness or objective functions) information directly for the search direction, not derivatives or other auxiliary knowledge. GA therefore can deal with non-smooth, non-continuous and non differentiable functions that are the real-life optimization problems. OPF in FACTS is one of such problems. This property also relieves GA of the approximate assumptions for a lot of practical optimization problems, which are quite often required in traditional optimization methods.

GA uses probabilistic transition rules to select generations, not deterministic rules. They can search a complicated and uncertain area to find the global optimum. GA is more flexible and robust than the conventional methods.

GA’s are a family of computational models inspired by evolution. These algorithms encode a potential solution to a specific problem on a simple chromosome-like data structure and apply recombination and mutation operators to these structures so as to preserve critical information. An implementation of a GA begins with a population of (usually random) chromosomes.

One then evaluates these structures and allocates reproductive opportunities in such a way that those chromosomes which represent a better solution to the target problem are given more chances to reproduce than those chromosomes which are poorer solutions. This is called survival for the fittest. The goodness of a solution is typically defined with respect to the current population. They operate on string structures (chromosomes), typically a concatenated list of binary digits representing a coding of the control parameters (phenotype) of a given problem. Chromosomes themselves are composed of genes. The real value of a control parameter, encoded in a gene, is called an allele. GA’s

is an attractive alternative to other optimization methods because of their robustness. There are three major differences between GA’s and conventional optimization algorithms. First, GAs operates on the encoded string of the problem parameters rather than the actual parameters of the problem. Each string can be thought of as a chromosome that completely describes one candidate solution to the problem. Second, GAs uses a population of points rather than a single point in their search. This allows the GA to explore several areas of the search space simultaneously, reducing the probability of finding local optima. Third, Gas do not require any prior knowledge, space limitations, or special properties of the function to be optimized, such as smoothness, convexity, unimodality, or existence of derivatives [24].

They only require the evaluation of the so-called fitness function (FF) to assign a quality value to every solution produced. The genetic algorithm can be viewed as two stage process. It starts with the current population. Selection is applied to the current population to create an intermediate population. Then recombination and mutation are applied to the intermediate population to create the next population. The process of going from the current population to the next population constitutes one generation in the execution construction of the intermediate population is complete and recombination can occur. This can be viewed as creating the next population from the intermediate population. Crossover is applied to randomly paired strings with a probability. A pair of strings is picked with probability for recombination. These strings form two new strings that are inserted into the next population. After recombination, mutation operator is applied. For each bit in the population, is mutated with some low probability. Typically the mutation rate is applied with less than 1 % probability. In some cases mutation is interpreted as randomly generating a new bit in which case, only 50 % of the time will the mutation actually change the bit value. After the process of selection, recombination and mutation, the next population can be evaluated. The process of evaluation, selection, recombination and mutation forms one generation in the execution of a genetic algorithm. Assuming an initial random population produced and evaluated, genetic evolution takes place by means of three basic genetic operators [24].

VI. SIMULATION& RESULTS

The IEEE 14-bus test system is used in this paper. In the modified IEEE 14-bus system there are 14 buses, out of which 5 are generator buses. Bus 1 is the slack bus, 2, 3, 6 and 8 are taken as PV generator buses and the rest are PQ load buses. The network has 20 branches, 17 of them are transmission lines and 3 are tap changing transformers as shown in Fig. 3.

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[image:6.595.55.299.51.241.2]

Fig. 3 Modified 14-bus system

In this section, the modified IEEE 14-bus system has been used to test the effectiveness of the proposed method. There are three cases to be discussed. Case A is the normal operation case which no HVDC and FACTS devices installed.

In case B, one STATCOM is installed at bus 9.In case C, two

STATCOM are installed at buses 9 and 10. The results are

shown on next section.

A. Interpretation of PF Results

[image:6.595.330.522.55.292.2]

The AC power flow results obtained by the MATLAB programming applied to the 14-bus network without STATCOM and HVDC are shown in Fig. 4a and Fig. 5a. The AC power flow results obtained by the NR method applied to the 14-bus network with an STATCOM-1 are presented in Fig. 4b and Fig. 5b. The AC power flow results obtained by the NR method applied to the 14-bus network with STATCOM-2 and two STATCOM are shown in Fig. 6 and Fig. 7. Within seven iterations, the total active power losses in the AC network without HVDC and STATCOM are found to be 12.30 [MW]. The total active power losses in the AC network with STATCOM-1, STATCOM-2 and the two STATCOM’s are 12.88 [MW], 12.89 [MW] and 13.13 [MW], respectively.

1 2 3 4 5 -50 0 50 100 150 200 250 P [ M W ] & Q [ M V A r] Bus Number Actives and reactive powers generations in each bus

Active generations Reactive generations

123456789 10 11 12 13 14 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 2 V [ pu ] & A ng le s [D eg ] Bus Number Nodales voltages magnitudes and phasees angles in each bus

Magnitudes Voltages Angles Voltages

(a)

1 2 3 4 5

-50 0 50 100 150 200 250 P [ M W ] & Q [ M V A r] Bus Number Actives and reactive powers generations with an STATCOM installed at bus 14

1 2 3 4 5 6 7 8 9 10 11 12 13 14 -14 -12 -10 -8 -6 -4 -2 0 2 V [ p u ] & A n g le s [ D e g ] Bus Number

Nodales voltages magnitudes and phasees angles with STATCOM installed at bus 14

Voltages Magnitudes Voltages Angles

[image:6.595.337.523.336.552.2]

(b)

Fig. 4 Variations of active and reactive power generations, magnitude and

angle voltages in each bus; (a)

without HVDC and STATCOM, (b) with STATCOM-1

0 2 4 6 8 10 12 14 16 18 20 -200 -150 -100 -50 0 50 100 150 200 P [ M W ] & Q [ M V A r] Branches Active and reactive power flows, Active and reactive power losses in each branch

+ Active Powers - Active Powers + Réactive Powers - Réactive Powers Active losses Réactive losses

(a)

0 2 4 6 8 10 12 14 16 18 -200 -150 -100 -50 0 50 100 150 200 P [ M W ] & Q [ M V A r] Branches

Active and reactive power flows, Active and reactive power losses with an STATCOM installed at bus 14

(b)

Fig. 5 Positive and negative transfer of active and reactive power flow, active

and reactive power losses in each branch; (a) without

HVDC and STATCOM, (b) with STATCOM-1

1 2 3 4 5 -50 0 50 100 150 200 250 P [ M W ] & Q [ M V A r] Bus Number Actives and reactive powers generations with an STATCOM installed at bus 14

123456789 10 11 12 13 14 -14 -12 -10 -8 -6 -4 -2 0 2 V [ pu ] & A ng le s [D eg ] Bus Number Nodales voltages magnitudes and phasees angles with STATCOM installed at bus 14

(a)

1 2 3 4 5

-50 0 50 100 150 200 250 P [ M W ] & Q [ M V A r] Bus Number

Actives and reactive powers generations with two STATCOM installed at buses 9 and 14

1 2 3 4 5 6 7 8 9 10 11 12 13 14 -14 -12 -10 -8 -6 -4 -2 0 2 V [ p u ] & A n g le s [ D e g ] Bus Number

Nodales voltages magnitudes and phasees angles with two STATCOM installed at buses 9 and 14 Active generations

Reactive generations

(b)

Fig. 6 Variations of active and reactive power generations, magnitude and

angle voltages in each bus; (a)

[image:6.595.80.262.521.738.2]

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0 2 4 6 8 10 12 14 16 18 -200

-150 -100 -50 0 50 100 150 200

P

[

M

W

]

&

Q

[

M

V

A

r]

Branches

Active and reactive power flows, Active and reactive power losses with an STATCOM installed at bus 14

(a)

0 2 4 6 8 10 12 14 16 18 -200

-150 -100 -50 0 50 100 150 200

P

[

M

W

]

&

Q

[

M

V

A

r]

Branches

Active and reactive power flows, Active and reactive power losses in each branch with two STATCOM installed at buses 9 and 14 + Active Powers - Active Powers + Réactive Powers - Réactive Powers Active losses Réactive losses

[image:7.595.80.263.59.302.2]

(b)

Fig. 7 Positive and negative transfer of active and reactive power flow, active

and reactive power losses in each branch; (a)

STATCOM-2 and (b) with two STATCOM

The STATCOM’s absorbs an amount of reactive power of 28.18 [MVAr] and 02.00 [MVAr] into bus 9 and 14, respectively, and keeps the nodal voltage magnitude at 1 [pu].

The solution values of the HVDC link are given as follows :

Case 1 : PF with HVDC-1

The active power flow level across the HVDC is 58.67 [MW]. The active power losses in the AC network and HVDC-1 are 13.64 [MW] and 0.56 [MW], respectively.

Case 2 : PF with HVDC-2

The active power flow level across the HVDC is 59.72 [MW]. The active power losses in the AC network and HVDC-2 are 12.75 [MW] and 0.53 [MW], respectively.

Case 3 : PF with HVDC-1 and HVDC-2

The active powers flow level across the two HVDC are 58.67 [MW] and 45.22 [MW], respectively. The active power losses in the AC network and the two HVDC are 13.64 [MW], 0.56 [MW], 45.22 [MW], respectively.

The active and reactive powers generations, voltage magnitudes and angles in each bus, positive and negative transfer of active and reactive power flows, active and reactive power losses in each branch are shown in Fig. 8 and Fig. 9. The DC Link control parameters are given in table 1.

1 2 3 4 5 -100

-50 0 50 100 150 200 250

P

[

M

W

]

&

Q

[

M

V

A

r]

Bus Number Actives and reactive powers generations with HVDC in each bus

123 45678 9 10 11 12 13 14 -18

-16 -14 -12 -10 -8 -6 -4 -2 0 2

V

[

pu

]

&

A

ng

le

s

[D

eg

]

Bus Number Nodales voltages magnitudes and phasees angles with HVDC in each bus

(a)

1 2 3 4 5 -50

0 50 100 150 200 250

P

[

M

W

]

&

Q

[

M

V

A

r]

Bus Number Actives and reactive powers generations with HVDC in each bus

123456 789 10 11 12 13 14 -18

-16 -14 -12 -10 -8 -6 -4 -2 0 2

V

[

pu

]

&

A

ng

le

s

[D

eg

]

Bus Number Nodales voltages magnitudes and phasees angles with HVDC in each bus

[image:7.595.336.516.61.295.2]

(b)

Fig. 8 Variations of active and reactive power generations, voltage magnitudes and angles in each bus with an HVDC link;

(a) with HVDC-1 and (b) with HVDC-2

From Fig. 5a, Fig. 5b, Fig. 7a and Fig. 7b, with regard to, the parts positive and negative of the flow of powers in the branches, we can notice that the algebraic sum gives the power losses due to transport, for each branch. The total power losses are obtained by the summation of the losses of the entire branches.

The comparisons of active and reactive powers generations for all cases are reported in the Fig. 10.

0 2 4 6 8 10 12 14 16 18 20 -200

-150 -100 -50 0 50 100 150 200

P

[

M

W

]

&

Q

[

M

V

A

r]

Branches

Active and reactive power flows, Active and reactive power losses in each branch with HVDC

(a)

0 2 4 6 8 10 12 14 16 18 20 -200

-150 -100 -50 0 50 100 150 200

P

[

M

W

]

&

Q

[

M

V

A

r]

Branches

Active and reactive power flows, Active and reactive power losses in each branch with HVDC

[image:7.595.339.512.449.689.2]

(b)

Fig. 9 Positive and negative transfer of active and reactive power flows,

active and reactive power losses in each branch with an HVDC link; (a)

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TABLEI

DC LINK CONTROL PARAMETERS FOR THE14-BUS SYSTEM

DC Limits Initial

condition PF solutions

Variables Min

Max

HVDC-1 HVDC-2 2-HVDC

Vdk[pu] 0.95 1.1 1.0 1.000 0.9210

ak[Deg] - 15 20 0.0 - 4.358 -10.019

Vdm[pu] 0.95 1.1 1.0 1.017 1.0189

am[Deg] - 15 25 0.0 - 10.303 - 8.7576

Pdk[MW] 9.089 3.749

Pdm[MW] 6.650 7.579

Qdk[MVAr] 18.338 43.64

Qdm[MVAr] 41.487 45.09

Id[pu] 0.237 0.226

Active power losses [MW] 13.64 12.75

B. Interpretation of OPF Results

The mixed AC/DCAC OPF results with the GA method without and including HVDC’s are given as follows :

Case 1 : OPF without HVDC

The active power losses in the AC network are 3.921 [MW] and the active power generation cost for this test network is 637.78 [$/h].

Case 2 : OPF with HVDC-1

The active power losses in the AC network are 3.24 [MW] and the active power generation cost for this test network is 637.52 [$/h].

Case 3 : OPF with HVDC-2

The active power losses in the AC network are 3.38 MW] and the active power generation cost for this test network is 638.39 [$/h].

Case 4 : OPF with HVDC-1 and HVDC-2

[image:8.595.317.547.460.574.2]

The active power losses in the AC network with two HVDC are 3.15 [MW]. The active power generation cost for this test network is 637.85 [$/h].

Fig. 11 presents optimal solutions and best compromise solution obtained from test system with two competitive objectives: active power losses and generation cost.

Fig. 12 shows the convergence characteristics of the GA method without and with HVDC’s for the best solutions. It can be seen from Fig. 12 that the value of the objective function settles at the minimum point after about 60 iterations for the case without HVDC and 100 iterations for the case with two HVDC.

1 2 3 4 5 0

10 20 30 40 50 60 70 80 90

P

[

M

W

]

Bus Number Actives Powers Generations

W/o HVDC W/ HVDC1 W/ HVDC2 W/ 2 HVDC

1 2 3 4 5 0

5 10 15 20 25 30 35

Q

[

p

u

]

Bus Number Reactives Powers Generations

Fig. 11 Variations of active and reactive powers generations; (a) active power generations and (b) reactive power generations

0 50 100 150 200 250 300

636 638 640 642 644 646 648 650 652 654

O

b

je

c

ti

v

e

F

u

n

c

ti

o

n

[

p

u

]

Iterations/Gererations Convergence Characteristic of GA method for 14-bus System W/o & W/ HVDC

[image:8.595.71.255.564.684.2]

Fig. 12 Convergence characteristics of the PSO method for 14-bus system

Control variables for the best compromise solutions and complete mixed AC/DC/AC OPF solution are given in table 2. The optimal solutions of IEEE 14-bus test system using GA algorithm are compared with certain methods given in [19].

TABLEII

SUMMARY OFOPFAND OPTIMAL SETTING OF CONTROL VARIABLES OF

14-BUS SYSTEM

OPF solution w/o and with HVDC

Without HVDC With HVDC-1 With HVDC-2 With two

HVDC

[MW] V [pu] [MW] V [pu] [MW] V [pu] [MW] V [pu]

1 88.934 1.0600 88.213 1.0600 87.4017 1.0600 87.581 1.0600

2 80.000 1.0450 80.00 1.0450 80.000 1.0450 80.00 1.0450

3 50.000 1.0300 50.000 1.0200 50.000 1.0200 50.00 1.0300

4 - 1.0205 - 1.0239 - 1.0127 - 1.0242

5 - 1.0227 - 1.0261 - 1.0247 - 1.0263

6 10.000 1.0700 10.000 1.0700 10.000 1.0710 10.00 1.0700

7 - 1.0303 1.0319 - 1.0233 - 1.0322

8 34.000 1.1000 34.051 1.1100 35.000 1.1000 34.592 1.1100

9 - 1.0495 - 1.0515 - 1.0447 - 1.0522

10 - 1.0457 - 1.0474 - 1.0418 - 1.0480

11 - 1.0542 - 1.0551 - 1.0424 - 1.0555

12 - 1.0570 - 1.0571 - 1.0566 - 1.0572

13 - 1.0539 - 1.0542 - 1.0533 - 1.0544

14 - 1.0509 - 1.0522 - 1.0479 - 1.0526

Losses

[MW] 3.91 3.24 3.38 3.15

Cost [$/h] 637.78 637.52 638.39 637.85

Pg [MW] 262.93 262.26 263.11 262.282

Qg [MW] 76.02 49.51 73.21 50.17

QSTAT-1

[MVAr] 0.2 11.01 -0.24 12.31

QSTAT-2

[MVAr] 0.114 3.832 -0.121 6.7534

For the modified system, 17 control variables (5 generator outputs, 5 generator voltages and 5 transformer taps and two STATCOM) were optimized. The comparisons of the magnitudes voltages for the power flow and optimal power flow without and with STATCOM and HVDC-VSC obtained by the MATLAB programming applied to the 14-bus network are reported in the Fig. 13.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 0

0.2 0.4 0.6 0.8 1 1.2 1.4

V

[

pu

]

Buses Comparisons of the Magnitudes Voltages

NRPF w/o STATCOM & HVDC NRPF W/ STATCOM1 NRPF W/ STATCOM2 NRPF W/ 2 STATCOM NRPF W/ HVDC1 NRPF W/ HVDC2 NRPF W/ 2 HVDC GAOPF W/o HVDC GAOPF W/ HVDC1 GAOPF W/ HVDC2 GAOPF W/ 2 HVDC

1.1

0.9

Fig. 13 Comparison of the voltages magnitudes

VII. CONCLUSION

In this paper, a new GA approach to solve the mixed AC/DC/AC OPF control problem with shunt FACTS devices is proposed, where the STATCOM is used as power flow controllers. STATCOM can provide the necessary functional flexibility for mixed AC/DC/AC OPF control. This approach allows the combined application of phase angle control with controlled shunt reactive power compensation. The total generation fuel cost and the total power losses are used as the objective function and the operation and security limits are considered. Simulation studies are carried out in a modified IEEE 14-bus system to show the effectiveness of the GA method.

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slowly if the numbers of variables systems augmented. The execution CPU time was found rapidly increase with the size of power system increasing and the convergence is slowing.

The simulation results on the 14-bus system have been presented for illustration purpose. The obtained proposed approach results have been compared and validated with those reported in the recent literature [19]. The proposed approach algorithm has reliably and accurately converged to the global optimum solution in each case and is capable to produce better results compared with other methods [13], [19] & [27].

The numerical example has shown that the HVDC link model and the GA method incorporating shunt FACTS devices (STATCOM) work very well to solve the mixed AC/DC/AC OPF problems. The results are promising and show the effectiveness and robustness of the proposed approach.

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Equations in Optimal Power Flow Methods Using Sequential Quadratic Programming Techniques", IEEE Transactions on Power Systems, pp. 1005-1011, Vol. 3, No. 3, August 1988.

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[13] Mohamed Laouer, Ahmed Allali, Kaddour Hachemi, Hamid Bouzeboudja and Abdelkader Chaker,"Study of the Load Flow in

the AC/DC Electrical Supply Networks", High Efficiency Maximum Power Point Tracking Control in Photovoltaic-Grid Connected Plants, Faculty of Electrical Engineering and Informatics, Technical University of Košice, Slovak Republic, ISSN 1335-8243, 2007.

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[26] M. A. Abido, "Optimal Power Flow Using Particle Swarm Optimization", Electrical Power and Energy System, USA, Elsevier Science Ltd, 0142-0615/02/$ ©, 2002.

[27] C. Kumar and Ch. Padmanabha Raju, "Constrained Optimal Power Flow using Particle Swarm Optimization", International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, Volume 2, Issue 2, February 2012).

[28] M. Balasubba Reddy, Y. P. Obuleshé and S. Sivanaga Raju, "Particle Swarm Optimization Based Optimal Power Flow for Volt-VAr", ARPN Journal of Engineering and Applied Sciences, ISSN 1819-6608 Vol. 7, No. 1, January 2012.

[29] K. S. Pandya and S.K. Joshi, "A Survey of Optimal Power Flow Methods", Journal of Theoretical and Applied Information Technology, Pakistan, Vol. Xx, N°: YY, 2008.

[30] Mahmoud Ebadian Reza Abdoli, "Evaluation of Voltage Stability in a Microgrid with STATCOM", International Journal of Advanced Research in Computer Science and Software Engineering (IJARCSSE), ISSN: 2277 128X, pp. 696-701, Vol. 4, No. 10, October 2014.

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Photos

[32] A. Panosyan and B. R. Oswald, "Modified Newton-Raphson Load Flow Analysis for Integrated AC/DC Power Systems", Institute of the Electric Power Systems", 39th International Conference

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1-86043-365-0, INSPEC, Bristol, UK, 6-8. Sep. 2004.

[33] Y. K. Fun, D. Niebur, CO. Nwankpu, H. Kwatny and R. Fischl, "Multiple Power Flow Solutions of Small Integrated AC/DC Power Systems", ISCAS 2000, IEEE International Symposium on Circuits and Systems, May 28-31, 2000, Geneva, Switzerland, 0-7803-5482-6/99/$10.00 ©, IEEE 2000.

[34] Inadyuti Dutt, Soumya Paul and Dr. S. N. Chaudhuri, "Implementation of Network Security Using Genetic Algorithm", International Journal of Advanced Research in Computer Science and Software Engineering (IJARCSSE), ISSN: 2277 128X, pp. 234-241, Vol. 3, No. 2, February 2013.

[35] H. C. Leung and T. S. Chung, "Optimal Power Flow with a Versatile FACTS Controller by Genetic Algorithm Approach", IEEE Power Engineering Review, pp. 2806-2811, 200. 0-7803-5935-6/00/$10.00 © 2000 IEEE.

Farouk Boukhenoufa was born in Tahir Jijel, Algeria in 1980. He received the Diploma of Applied University Studies in Electrical Engineering (Industrial control) from University of August 20th, 1955, Skikda, Algeria, in 2001, the Engineer Degree in Electrical Engineering (Electrical Networks) from the University of August 20th, 1955, Skikda, Algeria, in 2004, MSc degree in Electrical Engineering (Modeling & Simulation of Electrical Power Networks) from the same University in 2008. His areas of interest are: MagnetoHydroDynamic Study & Modelling of Cooled Transformers.

F. Boukhenoufa, Department of Electrical Engineering, University of Jijel, 18000, Algeria. Email: [email protected], Phone: + (213) 6 70 37 59 17

Nabil Mezhoudwas born in El-Milia, Jijel, Algeria in 1977. He received the Diploma of Applied University Studies in Electrical Engineering (Industrial control)from University of August 20th_,

1955, Skikda, Algeria, in 2001, the engineer degree in Electrical Engineering (Electrical Networks) from University ofAugust 20th_{, 1955, Skikda, Algeria, in}

2004, MSc degree in Electrical Engineering (Modeling & Simulation of Electrical Power Networks) from University of August 20th_{, 1955,}

Skikda, in 2009 and PhD in Electrical Engineering (Modeling & Simulation of Electrical Power Networks) from the same University in 2017. He is published several research papers in conferences, Journals &Reviews. Currently, He is working is a Lecturers Professor &Member of LES Laboratory and Scientific Committee of the Electrical Engineering Department at the University of August 20th_{, 1955, Skikda,}

Algeria. His areas of interest are: FACTS Modeling and Simulation in Electrical Power Systems, Application of Intelligent and Metaheuristic Techniques to solution of the Optimal Power Flow (OPF) Problem, AC/DC OPF and Muli-Objective OPF with Considering of FACTS Devices,Power System Stability & Control, High Voltage Direct Current (HVDC) Modeling, Simulation and Application in Electrical Power Systems.

N. Mezhoud, Department of Electrical Engineering, University of August

20th_{, 1955, Skikda 21000, Algeria. Email:}_{[email protected]}_{, Phone: +}

(213) 5 51 26 72 29.

BAHRI Ahmed was born in Bouhatem, Mila, Algeria in 1980. He received the Diploma of Applied University Studies in Electrical Engineering (Industrial control)from University of August 20th, 1955, Skikda, Algeria, in 2001, the Engineer degree in Electrical Engineering (Electrical Networks) from University of August 20th, 1955, Skikda, Algeria, in 2004, MSc degree

in Electrical Engineering (Modeling & Simulation of Electrical Power Networks)from University of August 20th, 1955, Skikda, in 2009. He is published several research papers in conferences, Journals & Reviews.Educational Officer, Faculty of Science and Technology, University of Ghardaïa, Responsible for renewable energies, Currently, His areas of interest are: work on the optimization of the electrical energy produced by multi-source systems (photovoltaic system connected with a wind system or other renewable system) subsequently injected into the electricity grid, Power System Stability & Control.

A. BAHRI, Department of science and technology, University of Ghardaia