Frequency Stabilization of Two Area Power System Interconnected by AC/DC Links using Jaya Algorithm

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ISSN: 2005-4238 IJAST 548

Frequency Stabilization of Two Area Power System Interconnected by AC/DC Links using Jaya Algorithm

Hussein Abubakr^1,^*, Mahmoud M. Hussein¹, Tarek Hassan Mohamed¹

1Department of Electrical Engineering, Faculty of Energy Engineering, Aswan University, Aswan 81528, Egypt.

[email protected], [email protected], [email protected]

Abstract

This paper presents an application of Jaya based load frequency controller for optimization with the parallel AC/DC of a two area interconnected power system. When an interconnected AC power system undergoes a rapid and large change in loads, system frequency may become oscillatory. A DC link and the existing AC tie line are connected in parallel to stabilize oscillations in frequency. The selection of the optimum controller should not only work in stabilizing the power system for regulation the frequency but also diminish the oscillations in power of the tie line. In common, proportional plus integral (PI) controllers have utilized for load frequency control (LFC) but it unable to eliminate the struggle between the dynamic and static accuracy. This dispute can be resolved by using the principles of Jaya with parallel AC/DC links. For this reason, the parameters of PI-controller have on-line tuned by Jaya algorithm in the presence of the Parallel AC/DC link. The proposed system has examined in case of 20% step load perturbation and the integration of hybrid plug-in electric vehicles (EVs). Simulation results affirmed that the system performance using the proposed design has significantly enhanced as compared to AC/AC and AC/DC links without Jaya. In addition, the suggested system is more vigorous and robust under distinctive operating modes.

Keywords: load frequency control, Jaya algorithm, AC-DC tie lines, electric vehicles (EVs), and Interconnected power system.

1. Introduction

The interconnected power system encounters a major dare in the operation and design of the power system. The problem of LFC has acquired much significance due to the complexity and size of advanced interconnected power systems. Regulating the output power of the plants that needed to be controlled is the main objective of LFC, so that the tie line power and system frequency is kept inside endorsed limits [1–3].

Controlling of power systems is becoming increasingly more complex due to high interconnectivity. In an interconnected network, a disturba nce in a single-line leads to effects on the adjacent systems change in tie-line power and frequency, causing a serious LFC issue [4, 5].

Recently, researchers have proposed several methods to adjust the control parameters using a simulation rather than just the control region being studied and to damp the frequency fluctuation [6-11]. On the other hand, R. Rao has introduced a new technique called Jaya technique [12]. It has many advantages such as a parameter less, therefore, unlike other optimization techniques, and there is no need to tune its own parameters during the computations.

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Recently, the high-voltage DC transmission system

has uncommon advancement within the power system due to its execution and economy over the other options. One of the major applications of HVDC is the operation of a parallel DC link with an AC link for two controlled areas. The system dynamic performance can enhanced with a greater margin of stability under small system disturbances [13, 14].

Many facilities such as buildings and electric vehicles have emerged because of rising the electric power sources demand that can expand the chances for quick variances in loads. In any case, there are upward trends to install the flexible loads such as HPs and EVs in isolated grids [15]. EVs have installed in residential areas for frequency control within the smart grid system [16, 17].

Contributions of this work can be concluded as follows: It is the first time to use the integration of hybrid electric vehicles EVs that controlled by robust controller design called coefficient diagram method (CDM) as described in [17] with a parallel AC/DC links beside using Jaya optimization approach to regulate and maintain the power in tie- lines and system frequency.

2. Statement of the Problem

A single-line diagram and a model of the block diagram for two area power system under examination are shown in figures 1 and 2 respectively. The state variable equation to achieve the minimum proposed persistent model was described in [18].

𝑋 = 𝐴𝑥 + 𝐵𝑢 + Г𝑑 (1)

𝑦 = 𝐶𝑥 (2)

𝑥 = [𝑥_1, 𝑥₂]^𝑇 (3)

𝑢 = [∆𝑃𝑐₁, ∆𝑃𝑐₂]^𝑇 (4)

𝑑 = [∆𝑃𝑑₁, ∆𝑃𝑑₂]^𝑇 (5)

where A is the system matrix, B is the input dispersion matrix, C is the disorder distribution matrix, Г is the distribution matrix output control, u is the control vector, x is the state vector, d is the load disturbance vector.

The DC link comprises of an inverter at side of area 1, a rectifier at side of area 2 through a DC transmission line. Area 2 was supposed to have provided PAC over AC line only to area 1. The demand increases in area 1 and oscillation will occur in frequency due to installation of abrupt loads in area 1. Accordingly, the governor in area 1 has not sufficient frequency control abilities and unable of stabilizing the oscillations in frequency. On the other hand, area 2 has sufficient frequency regulation capability to compensate for area 1. In this manner, area 2 has a D C link introduced in parallel with AC tie line to supply more power to area 1. In expansion, area 2 provide stability of frequency oscillations to area 1 over a DC link.

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Figure 1. Single line diagram of a two-area interconnected power system with parallel AC-DC tie line and EVs unit.

Figure 2. The block diagram model of a two area interconnected non- reheated turbine power system with parallel AC–DC tie line using adaptive

Jaya technique.

3. Dynamic modelling of two-area systems with AC–DC tie lines

Figure 3 shows the exchange work of the DC link. The flow of the tie line from area-1 to area-2 in case of a small load disturbance is given by:

∆𝑃_{𝑡𝑖𝑒 𝐴𝐶} = ^{2𝜋 𝑇}¹²

𝑠 (∆𝐹₁− ∆𝐹₂) (6)

∆𝑃_{𝑡𝑖𝑒 𝐷𝐶} = ^𝐾^𝑑𝑐

1+𝑆𝑇_𝑑𝑐 (∆𝐹₁) (7)

∆𝑃_{𝑡𝑖𝑒 12} = ∆𝑃_{𝑡𝑖𝑒 𝐴𝐶} + ∆𝑃_𝑡𝑖𝑒

𝐷𝐶 (8)

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Where ΔPtieAC: deviation of the AC power in tie line. 2πT12: the coefficient of tie-line power for area 1 and 2. ΔF1, ΔF1: frequency deviation in area 1 and 2 respectively. For minor changes in DC tie-line flow, where ΔPtie12: deviation of the power between area 1 and 2. ΔPtieDC: deviation of the DC power in tie line. Kdc: converter and rectifier gain constant. Tdc: converter and rectifier Time constant. The area control error (ACE) for the two areas is given by:

𝐴𝐶𝐸₁ = 𝑏₁ ∆𝐹₁+ (∆𝑃_{𝑡𝑖𝑒 𝐴𝐶} + ∆𝑃_{𝑡𝑖𝑒 𝐷𝐶}) (9) 𝐴𝐶𝐸₂ = 𝑏₂ ∆𝐹₂+ 𝑎₁₂ (∆𝑃_{𝑡𝑖𝑒 𝐴𝐶} + ∆𝑃_{𝑡𝑖𝑒 𝐷𝐶}) (10) where b1, b2 = Frequency biased parameter. a12 = Area size ratio.

Power system

∆

Figure 3. Transfer function model of the DC link.

The electric vehicles (EVs) are modeled as a first-order lag systems [17, 19] as shown in figure 4.

∆

0 P.u

Rated value

Charging/Discharging power

- +

Control delay LFC signal

Figure 4. Electric vehicles (EVs) model.

4. Jaya Optimization Concepts

Jaya is presented by Rao in [12]. It requires a few parameters unlike other heuristic algorithms and it works only in one phase called „teacher phase‟. It only needs mutual control parameters such as (population size {n}, number of design variables {m} and maximum number of generations {i}) to achieve optimal performance.

The candidate solution of Jaya algorithm for a particular issue can be obtained by moving the algorithm towards the optimal solution and staying far from the worst solution. The steps of the proposed Jaya algorithm can be outlined in the following flowchart as shown in figure 5.

To understand the proposed algorithm, consider the following terminology variables:

f(x) = main function to be optimized.

J = {1, 2, …., m} && K = {1, 2, …., n}.

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At i^thiteration, if the best candidate gives an optimal value of f(x) in population, this means that it is closest to the candidate solutions. On the other hand, the worst value of f(x) got in population for the worst candidate; this means that it is farthest from desired optimal solution of all the candidate solutions. Now any j^th variable whose value at k^thiteration is Xj,k,i will be modified according to the following equation:

𝑋′_{𝑗 ,𝑘,𝑖} = 𝑋_{𝑗 ,𝑘 ,𝑖} + 𝑟_{1,𝑘 ,𝑖} ( 𝑋_{𝑗 ,𝑏𝑒𝑠𝑡 ,𝑖} − (|𝑋_{𝑗 ,𝑘 ,𝑖}|) ) – 𝑟_2,𝑘,𝑖 ( 𝑋𝑗 ,𝑤𝑜𝑟𝑠𝑡 ,𝑖 − (|𝑋_{𝑗 ,𝑘,𝑖}|)) (11) where Xj,best,i is the best value of Xj,k,i , Xj,worst,i is the worst value of Xj,k,i, X‟j,k,i is the modified value of Xj,k,i, and {r1,k,i & r2,k,i} are the random numbers between [0,1].

Finally, X‟j,k,i will be accepted as the desired optimal solution when it gives the best function value. All accepted optimal values will revenue for the next iteration and continue to complete the maximum allowable iterations.

Figure 5. Flow chart of Jaya algorithm [12].

5. Jaya based frequency control with AC/DC parallel tie-lines

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Figure 6 illustrates the simplified model of the proposed micro-grid for any area.

This model will be utilized to drive the desired objective function. The objective is to get the optimum values of the proposed controller parameters that reduces the performance index using ISE criterion.

𝐽 = 𝑋₀^𝑡 _𝑐² 𝑑𝑡 (12)

𝑋_𝑐 = ∆𝑃_𝑡𝑖𝑒

∆𝑓_𝑖 (13)

𝐽 = (∆𝑃₀^𝑡 _{𝑡𝑖𝑒 ,𝑖})²+ (𝛽∆𝑓_𝑖)²𝑑𝑡 (14)

Figure 6. Simplified block diagram of the model of interconnected power system controlled by proposed Jaya controller for any area -i.

6. Results and Discussions

In this paper, a two-area interconnected system with the non-reheat thermal turbine is used to evaluate the effects of the DC link when parallel to the AC link.

System nominal data and Jaya selection parameters are given in the appendix A. In order to validate the proposed PI controller and dynamic response of interconnected two-area micro grid, system with (Jaya + AC/ DC links) was tested into two scenarios:

6.1. First: Performance evaluation under load disturbances.

The system has examined for a 20% step changes in load for areas 1 and 2. The corresponding deviation in frequency ΔF and tie-line power ΔPtie are plotted concerning time. For ease of comparison, ΔF and ΔPtie responses are displayed along with those obtained using the adaptive proportional plus integral controller based on the ISE criterion in figure 7. It is noticed that the transient performance has been significantly enhanced with rapid settling time and over/undershoot for the proposed controller with the application of (Jaya + AC/DC links) as compared to conventional PI-controller with AC- AC and AC-DC links. Figure 8 describes the output gain control signal obtained from the optimizer.

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0 5 10 15 20 25 30 35 40 45 50

-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02

Time in sec

F1 (hz)

AC-AC link AC-DC link AC-DC link +Jaya

(a) Frequency oscillation in area-1 for first scenario.

0 5 10 15 20 25 30 35 40 45 50

-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02

Time in sec

F2 (hz)

AC-AC links AC-DC links AC-DC links+Jaya

(b) Frequency oscillation in area-2 for first scenario.

0 5 10 15 20 25 30 35 40 45 50

-0.02 -0.015 -0.01 -0.005 0 0.005 0.01

Time in sec

P tie (pu)

AC-AC links AC-DC links AC-DC links +Jaya

(c) Power change in tie-line for first scenario.

Figure 7. System Dynamic response in case of 20% load changes.

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0 5 10 15 20 25 30 35 40 45 50

0 0.1 0.2 0.3 0.4 0.5

Time in sec

Optimizer control signal

Figure 8. Jaya output control signal.

6.2 Second: Performance evaluation under plug-in/out of electric vehicles (EVs).

The system has examined in multiple operating conditions, the nominal parameters for two areas assumed as described in the first scenario (nominal case). The system has tested in the presence of electric vehicles (EVs). In addition, EVs are supposed to plug-in and plug-out the system under the suggested multiple operating conditions shown in appendix A.

Figure 9 describes the system response with the proposed PI-controller based Jaya linked with AC-DC links. The conventional PI-controller in case of AC-AC and AC-DC links gives more oscillations in both tie-line power and frequency responses for area 1 and area 2 as compared to the proposed adaptive controller (Jaya algorithm + AC/DC links) which means that the system has been enhanced and can provide a desirable performance response with the suggested control scheme. Figure 10 shows that the power of EVs has been greatly discharged by the proposed control scheme that those of the compared system with other ones.

Finally, simulation results show that (AC/DC links + Jaya) provide better performance and efficiency in damping system oscillations than AC-AC and AC-DC links in terms of frequency deviation and total tie-line power besides using controllable loads like EVs.

0 10 20 30 40 50 60 70 80 90 100

-0.03 -0.02 -0.01 0 0.01 0.02 0.03

Time in sec

F1 (hz)

(a) Frequency oscillation in area-1 for Last scenario.

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0 10 20 30 40 50 60 70 80 90 100

-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04

Time in sec

F2 (hz)

(b) Frequency oscillation in area-2 for Last scenario.

0 10 20 30 40 50 60 70 80 90 100

-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04

Time in sec

F2 (hz)

(c) Power change in tie line for Last scenario.

0 10 20 30 40 50 60 70 80 90 100

-0.015 -0.01 -0.005 0 0.005 0.01 0.015

Time in sec

P tie (pu)

Figure 9. System Dynamic response in presence of electric vehicles with a 20% load changes.

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0 10 20 30 40 50 60 70 80 90 100

-0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01

Time in sec

PEV (pu)

Figure 10. Discharging power in EVs.

7. Conclusion

This paper presents an optimal design using adaptive Jaya controller based LFC for proportional plus integral (PI-controller) for a two area interconnected non- reheated turbine power system with parallel AC/DC links. The proposed controller has been designed to diminish the sudden variations in system frequency and power in tie line due to fluctuations in load.

The proposed system has examined in case of 20% step load perturbation and with integration of the electric vehicles (EVs). Simulation results detect that the designed controller (Jaya + AC/DC links) is not obliged only to suppress the oscillations in frequency and tie-line power but is also able to guarantee the stability of the overall system and improving both the steady state and transient responses as compared to AC-AC links and AC-DC links without Jaya.

For further study, the proposed HVDC control design will be expanded to stabilize the oscillations in frequency with the integration of renewable energy sources such as PVs and wind energy sources in multi-area interconnected power systems. In addition, study the system in the presence of the other controlled loads such as heat pumps (HPs) integrated with electric vehicles (EVs).

Appendix

A.1. Two area interconnected power system with AC/AC tie line Parameters:

Description Symbol Area-1 Area-2 Unit

Inertia Constant M 0.1667 0.2017 [p.u MW.s/Hz]

Damping Coefficient D 0.015 0.016 [p.u.MW/Hz]

Turbine Time Constant Tt 0.4 0.44 [sec]

Governor Time Constant Tg 0.08 0.06 [sec]

Regulation Ratio R 3 2.73 [Hz/p.u.MW]

Bias Coefficient β 0.3483 0.3827 [p.u MW/Hz]

Power Coefficient of Synchronizing (parallel AC-AC lines)

T12AC 0.20 0.20 [MW/rad]

A.2. Data selection of Jaya algorithm.

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Number of design variable = 2.

Number of generation = 30.

Population size = 10.

A.3. Data for EV units.

Power rating of EVs = 2.38 MW TEV = 0.28 sec; KEV =1.

EVs Plug in at 0s, 40s, and 80s.

EVs Plug out at 30s, 70s each for 10s.

A.4. Data for DC link.

Kdc = 1.0; T12dc = 0.05 MW/rad.

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