Optimal Regulation of Phase-Shifting Transformers in .... Basic. Appl. Sci. Res., 2(9)8659... · networks is active power distribution control and phase shifting transformer is a

J. Basic. Appl. Sci. Res., 2(9)8659-8669, 2012

© 2012, TextRoad Publication

ISSN 2090-4304 Journal of Basic and Applied

Scientific Research www.textroad.com

*Corresponding author: Majid Bavafa. Department of Electrical Engineering, Islamic Azad university, Natanz Branch, Natanz, Iran. Tel.: +98-912_543 104 E-mail address: [email protected]

Optimal Regulation of Phase-Shifting Transformers in Connected Power Network of Countries: Iran, Iraq, Turkey and Syria Using

Monte Carlo Simulation Method

Reza Ebrahimi Abyaneh1, Majid Bavafa2 , Javad Olamaei1 , Hamid Lesani1

1Islamic Azad University, South Tehran Branch, Faculty of Advanced Studies. 2Department of Electrical Engineering, Natanz Branch, Islamic Azad university, Natanz,Iran.

ABSTRACT

Nowadays there have been huge changes in power systems; and power transmission networks have extremely developed, resulting changes in their performance. Recently, an important issue in power networks is active power distribution control and phase shifting transformer is a sample of active power distribution controllers. In power systems to achieve the best performance of phase shifting transformers there should be coordination among equipments. A main goal is maximization of power transmission capability among different areas and countries without restriction of network safety and reliability. In this paper effects of some parameters of phase shifting transformers on net transmission capacity are considered, using Monte Carlo simulation method in a connected power network among four countries: Iran, Iraq, Turkey and Syria. These parameters include transformers placement and their regulating method. KEYWORD: Phase-Shifting Transformers,Total Transmissions Capacity, Transmission Reliability, Net

Transmission Capacity, Power Shifting, Monte Carlo Simulation, Searching Space

1. INTRODUCTION

Recently European Network of Transmission System Operators for Electricity (ENTSOE) has presented the procedure for calculation of transmission capacity among countries. The maximum power which can be transmitted, without disturbance in scale of network reliability, between countries A and B is called Total Transmission Capacity (TTC). Of course conditions of power system performance cannot be predicted accurately. Because information this organization owns, about consumers, markets and measurements done in past, are mostly unreliable and unwarrantable. So a safety margin is introduced called Transmission Reliability Margin (TRM) which usually has a constant value and can vary with structural or seasonal changes. The transmission capacity which can be delivered to market is named as Net Transmission Capacity (NTC) [1,2].

(1)NTC TTC TRM So NTC should be utilized as optimization criterion, but the amount of NTC is dependent on TRM and it’s a problem. For instance Transmission System Operator (TSO) in a country can assign TRM to be 300 megawatts while TSO in other country define it 500 megawatts, so it’s more proper to choose TTC as optimization criterion. In order to increase the exchanged power between to areas, generation in a country should be reduced while in other country is increased. Variation in the level of generation is called power shifting(PS). This shifting continues to reduce or increase unless the restriction of network safety is violated. The maximum

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Abyaneh et al., 2012

increase and maximum decrease in generation of the area are called MAXPS and

MAXPS respectively [3,

4]. Graphic presentation of transmission capacities are shown in figure 1[5].

Figure 1Transmission capacities related to ETSO

2. CALCULATION BASED ON SIMULATION TTC parameter is usually obtained from load distribution calculations (using linear technique

method). Suppose that calculations for power imports from Iran to Iraq is defined, first PS is used. For instance the level of total generation in Iran is increased by a specific amount (for example 100 megawatts) and decreased equally in Iraq. Hence an extra power distribution happens between two countries. In studying power imports and power exports PS is assumed negative and positive respectively. So in power exports study signs are different. Depends on the way it is distributed on the generators of an area, PS can be obtained in different ways[6]. A prevalent way is to assign a portion or fraction of PS to each generator in the area (proportional to the generator power). In special case even just some of the generators are utilized to assess PS.

After PS assessment, active power load distribution in each junction is calculated and compared with old conditions. In each line power sensitivity is obtained as below [7, 8]:

(2)LL

PSPS

SLis supposed to be constant for all PS’s. Hence power of each line can be considered as a function of PS:

,0 (3)L L LP P S PS Line power should not exceed its nominal value:

,: (4)L L rL P P

By two equations above, maximum acceptable PS ( MAXPS and

MAXPS ) depends on whether calculation is for exports or imports can be achieved. It’s the linear approximation principle and is shown in figure 2 for three power exchange axles with the same nominal powers [9, 10]. For positive PS upper bound of line 2 is the highest bound and for negative PS the highest restriction is the upper bound of line 3.

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Figure 2 Graphic presentation of linear technique method in load distribution

3. MONTE CARLO PRINCIPLE

Basically Monte Carlo’s techniques are developed for numerical calculation of integrals. Its principles are easily understood, considering Random Monte Carlo Method. Suppose we want to calculate Integral I [11, 12]:

( ) (5)b

a

I g x dx

which variable x and function g(x) belong to these intervals: 0 ( ) , (6)g x c a x b

As it is shown in fig 3 rectangular Ω is defined as:

, , 0 (7)x y a x b y c

(X, Y) is a random vector which is uniformly distributed on Ω [13]. Consider this Probability Density Function (PDF) function:

1 ( , )( )( , ) (8)

0X Y

if x yc b af x y

otherw ise

Figure 3Random Monte Carlo Method

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The purpose is estimation of integral I using the approximation of the area under the g(x) curve. Suppose we consider N independent points (X,Y) if HN expresses the number of incidences for

points in region S the probability P can be approximated as P̂ :

ˆ (9)HNPN

Hence estimator θ to estimate I is calculated as below:

( ) (10)HNI c b aN

It can be proved that standard deviation of the estimator is obtained by the equation11.

1122 (11)N I C B A I

Hence if the number of samples increases, the estimator converges to I. the most important feature of Monte Carlo Methods is capability of extracting reliable information from limited number of data.

4. MONTE CARLO SIMULATION

In many applications, the output parameter of each process is utilized as a function in several input parameters. Sometimes equations controlling this process are totally unknown. Sometimes even there is simulation model but the analytical equation representing input-output relation is missed. In this case we can use multi-simulations to extract information. In Monte Carlo Simulation (MCS), input parameters distributions are sampled several times. These distributions can have every shape or can be independent or depends on a specific degree. Hence the accuracy of PDF output can grow with an increase in number of samples. This fact is mathematically compatible with Monte Carlo integral. For output variable X the number of output samples less than given X’ is counted as incidence and expresses a relative number in the interval [0, 1]. If this case happens for several values of X’, their incidence relative number is an approximation for cumulative distribution function (CDF) of output variable X. So it will converge to CDF or PDF (based on the usage) with increase in numbers of samples [14, 15]. 4.1 Search Space Considering the fact that each (Phase-Shifting Transformers)PST changes the power distribution in the whole system; the parameter TTC is different for each combination of PST regulations. If only one PST is installed, TTC can be calculated for every possible regulation and the optimal state is easily obtained. If we consider all possible states, computation time increases exceedingly. In general, dimensions of search domain, including all possible values of inputs are defined as [16, 17]:

1

max min (12)d

i ii

SV

Where d is the number of input variables or in other words the dimensions of the problem. Furthermore imin and imax are the minimum and maximum of the i th variable respectively. Assuredly in problems with more dimensions, it’d be practically impossible to consider all possible states one by one [18]. In addition to the problem with high number of dimensions, and the fact that TTC is obtained by simulation and can’t be achieved through an analytical model; Monte Carlo Simulation method (MCS) seems to be a proper technique in this field. The goal is to determinate and optimize TTC as the function of PST regulation. So, different PST regulations are assumed to be distributed continuously between the maximum and minimum. In this case search field will be conjunct and continuous as it is shown for 2 dimensions sample in figure 4. The simulation output is histogram of TTC which will converge to PDF with increasing of samples. The best and the worst value of TTC and other valuable data can be derived from this histogram [19].

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Figure 4Search space for 2 variables in MCS

4.2. Preparing Simulation The model network used for TTC calculations is Iran, Iraq and neighbouring countries network during 2010. Briefinformation is represented in table 1.

Table 1 network data as a model for simulation WORK ELEMENT NUMBER

BUSSES 1272 GENERATORS 289

LOADS 980 LINES 2689

TRANSFORMERS 640

For load distribution calculations Power System Simulator for Engineering (PSS/E) is utilized. Because of multiple required computations just some of automation systems can be used. Using Python Script automate rules are provided [20]. The major part of Python program is utilizing some numbers of generators to sample for distribution of random PST regulation as input. In each sample random regulation is applied to PSTs and load distribution is computation is done. Since next regulations are independent, the network outputs and results can be completely different from the past results and it may cause divergence in AC load distribution. Hence primarily DC load distribution is applied to the system as a preparation for the next step: AC load distribution. In the next stage calculation related to TTC is done, using linear technique presented in past section. This calculation is considered as a separate part in PSS/E. Finally results are written down in a text file in order to be processed in MATLAB. Codes of this program can be seen in algorithm 1.

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Algorithm1 MCS codes for parameter TTC as a function of PST

4.3 Relation between TTC and PSTs of Iran Region To explain the effect of PST on TTC, we calculate the entering TTC of Iran from Turkey and Iraq,

for different PST regulations in region 1 of Iran. Other PSTs in region are regulated on 0 °. In figure5 results are represented; assuming other PSTs regulations vary between - °30 to +30°. As mentioned before input capacities are considered negative.

Specifically, TTC is a piecewise-linear function. Each linear piece is defined by random pairs and restricting elements. Restricting element is a line having an overload in the beginning, and happens when the desired output occurs.

(a) Turkey to Iran

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(b) Iraq to Iran

Figure5 Entering TTC to Iran from Turkey (a) and Iraq (b)

Restricting line and output line is shown with “lim” and “con” respectively.

In fig 5 (a) we can see that a huge part of negative regulations are related to the power passing through region 1 of border areas in Iran and Turkey which makes them restricting elements. High positive regulations steer the power to connection lines in region 2 of border areas in Iran and Turkey. The optimal point which belongs to the highest entering TTC occurs in negative balanced regulation around -11°.

As it is shown in fig 5 (b) entering TTC from Iraq is not affected much by PSTs in region 1 of Iran (in large scale regulations). However extreme negative regulation turns the connection regions 1 in Iran and Turkey to restricting element. Similar process happens for entering TTC from Turkey. Extreme positive regulation likewise steer the power through connection regions 2 in Iran and Turkey.

4.4 Monte Carlo Simulation for TTC with all PSTs MCS method is applied to the network mentioned in section 4.2 and numbers of different samples

are used. For each sample, TTC from Syria and Turkey entering to Iran and Iraq is calculated. All connection lines are monitored and no extra outputs is considered in order to simplify random analysis.

Calculation run time for complete MCS (50000 samples) was about 8 hour and 12 minutes using a 3.2 GHz Intel p4 computer. The results of simulation are shown in fig 6 histograms. As usual entering TTCs are negative.

Considering these figures below, the main features of MCS are defined as below: Increment in the number of samples makes the result histograms a more accurate estimation of PDF

as output parameter (for TTC specially). X axle is cut in 0 megawatt to represent the best region; but in reality histograms in region with

positive TTC have a long tail. It means for some combinations of PST regulations, no power can enter Iran; due to overload problems. This problem can be solved just by power imports to Turkey or Syria which can result in positive quantities for entering TTC.

Fig 7 shows passing power distribution from connection points in worst sample state (worst state of entering TTC). It is in relation with PST regulations in 2nd row of table 2. In connection line of region 1 in Iraq and region 4 in Iran there has been overload.

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Considering the weak coordination of PSTs in region 1 and 2 in Iraq, an internal power distribution loop is created (regions 1 Iraq, 4 Iran, 3 Iran, 2 Iraq and again 1 Iraq). It causes extreme power accumulation and its related problems. Even it can be observed that passing power from Turkey border is not distributed equally that can express improper utilization of PSTs (specially, in the case of PSTs in region 1 in Iran). In fact a power distribution loop is inducted from north to south through Turkey. In addition unbalanced load occurs in border of Iraq and Syria.

Fig 8 shows power distribution in the best case sample (best state of entering TTC). It is in relation with PST regulations in 1st row of table 2. Power distribution in Iran – Turkey and Iraq – Syria is spread more equally; and no power distribution loop is created in borders of Iran – Iraq. Hence in this case PST is utilized more properly.

Table 2PST regulations (degree) for best and worst cases IRN1 TUR2 IRQ1 IRQ2 IRQ3 SUR2

BEST -21.81 -10.92 -13.01 8.02 23.98 -4.73 WORST 15.56 6.49 24.04 24.43 23.85 -10.40

Fig 6Histograms of entering TTC to Iran and Iraq from Turkey and Syria; Data is obtained by MCS method with different number of samples

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Figure7border power distribution (megawatt) for worst case sample (worst entering TTC)

Fig 8 shows power distribution in the best case sample (best state of entering TTC). It is in relation with PST regulations in 1st row of table 4.4.1. Power distribution in Iran – Turkey and Iraq – Syria is spread more equally; and no power distribution loop is created in borders of Iran – Iraq. Hence in this case PST is utilized more properly.

Figure 8 border power distribution (megawatt) for best case sample (best entering TTC)

5. CONCLUSION

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Main purpose in this paper was maximization of Total Transmission Capacity (TTC) which shows the reachable transmission Capacity. Search space is a multi-dimension function relating TTC to different PST regulations which in special case of Iran-Iraq is a 6-dimension function. Monte Carlo Simulation (MCS) can be applied as a research tool in the search space. In this case PST regulations due to their continuous nature cover all the search space and assumed to have uniform distribution. The more samples we have the more accurate results are; but more time is required. Then application of (MCS) in calculation of TTC in Iran – Iraq network was presented (in best and worst scenarios). More observation in these scenarios showed poor coordination among PSTs, cause internal power distribution loops and extreme overloads. On the other hand proper coordination among PSTs prevents these distribution loops and equal load devotion in connection points in borders can adjust the sample network.

REFERENCES

[1] J. Verboomen, F. J. C. M. Spaan, P. H. Schavemaker, and W. L. Kling, 2008. Method for calculating maximum total transfer capacity by optimising phase shiftingtransformer settings," in CIGRE Session 2008 - C1-111, Paris, France, 7 pages.

[2] J. Verboomen, G. Papaefthymiou, W. L. Kling, and L. van der Sluis, 2008. Use of phase shifting transformers for minimising congestion risk, in Probabilistic Methods applied to Power Systems (PMAPS), Rinc_on, Puerto Rico, 6 pages.

[3] P. Bresesti et al., 2004. Application of Phase Shifting Transformers for asecure and efficient operation of the interconnection corridors, in IEEEPower Engineering Society General Meeting, pp. 1192–1197.

[4] J. Bladow and A. Montoya,1991. Experiences with Parallel EHV ShiftingTransformers, IEEE Transactions on Power Delivery, vol. 6, no. 3, pp. 1096–1100.

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[8] IEEE Power Engineering Society,2009.IEEE Guide for the Application, Specification, and Testing of Phase-Shifting Transformers.

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[12] J. Verboomen, D. Van Hertem, P.H. Schavemaker, F.J.C.M. Spaan, J.-M. Delince´ ,W.L. Kling, R. Belmans,2007. Monte Carlo simulation techniques for optimisationof phase shifter settings, Eur. Trans. Electr. Power 17 (3) 285–296.

[13] W. M. Spears, K. A. D. Jong, T. B¨ack, D. B. Fogel, and H. de Garis, 1993. “Anoverview of evolutionary computation,” in Proceedings of the EuropeanConference on Machine Learning (ECML 93), P. B. Brazdil, Ed., vol.667. Vienna, Austria: Springer Verlag, pp. 442–459.

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[14] C. J. G. Spoorenberg, B. F. van Hulst, and H. F. Reijnders, 2003. Specificaspects of design and testing of a phase shifting transformer, in XIIIthInternational Symposium on High Voltage Engineering.

[15] J. Verboomen, D. Van Hertem, P. H. Schavemaker, W. L. Kling, and R. Belmans,2005. Phase Shifting Transformers: Principles and Applications,”in Future Power Systems Conference, Amsterdam.

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[17] J. Bladow and A. Montoya,1991. Experiences with Parallel EHV Shifting Transformers, IEEE Transactions on Power Delivery, vol. 6, no. 3, pp. 1096–1100.

[18] A. Kramer and J. Ruff,1998. “Transformers for Phase Angle Regulation Considering the Selection of On-Load Tap-Changers,” IEEE Transactions on Power Delivery, vol. 13, no. 2, pp. 518–525.

[19] A. Marianakis, M. Glavic, and T. van Cutsem, 2007. Control of phase shifting transformers by multiple transmission system operators," in Proc. of IEEE PowerTech.

[20] http://www.python.org.

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Optimal Regulation of Phase-Shifting Transformers in .... Basic. Appl. Sci. Res., 2(9)8659... · networks is active power distribution control and phase shifting transformer is a