DESIGN OF A HVDC-BASED CONTROLLER FOR LOAD CHANGE COMPENSATION AND STABILIZATION OF INTER-AREA OSCILLATIONS

As an interconnected power system via a High-Voltage Direct Current (HVDC) link is subjected to a rapid load change with the frequency of inter-area oscillation mode, system frequency and tie line power may be severely disturbed and oscillate. To compensate for the rapid load change and stabilize both frequency and tie line power oscillations due to the inter-area mode, the dynamic power flow control via a HVDC link can be exploited. To implement this concept, a new design method of HVDC-based controller is proposed. To grasp a physical characteristic of the inter-area oscillation frequency, the technique of overlapping decompositions is employed to achieve the subsystem embedded with the inter-area mode. Consequently, the second-order lead/lag controller of HVDC link can be designed in this subsystem. To acquire the desired overshoot of frequency oscillations, the parameters of the controller are automatically optimized by the Tabu Search (TS) algorithm. The effectiveness of the designed controller is investigated in a three-area longitudinal interconnected power system which represents the interconnection between the south of Thailand and Malaysia power systems.


INTRODUCTION
At present, a significant growth of electric energy demand, in combination with financial and regulatory constraints, has forced power utilities to operate systems near stability limits.Thus, a great reliance is being placed on the use of special control aids to enhance system security, facilitate economic design, and provide greater flexibility of system operation.Under this circumstance, a High-Voltage Direct Current (HVDC) link offers major advantages in meeting these requirements 1,2 , e.g., a long distance overhead bulk power transmission, an enhancement of damping in AC power system, a back-to-back asynchronous interconnection etc.Even in Thailand, the Electricity Generating Authority of Thailand (EGAT) has already implemented the I. Ngamroo Design of HVDC-based Controller 300 MW, 300 kV, 100 km HVDC Interconnection project to receive additional 300 MW from the Malaysian power system.In addition, a HVDC link can be applied as an energy transfer device from one power system to compensate for rapid load changes in other systems.Subject to large loads with sudden change such as a magnetic levitation transporter, a testing plant for nuclear fusion or even an ordinary scale factory like a steel manufacturer etc., the frequency of AC power system and the power flow in a tie line may be considerably perturbed from the normal operating values.This may lead to severe problems of frequency and tie line power oscillations due to an insufficient compensation of load change.The deviations of frequency and tie line power oscillations that exceed the normal limit, directly interrupt the operation of power system.Moreover, if the frequency of changing load is in the vicinity of the inter-area oscillation mode, system frequency and tie line power oscillations may experience a serious stability problem due to an inadequate system damping 3 .Under this situation, the conventional frequency control, i.e. a governor, may no longer be able to compensate for rapid load change due to its slow response.In addition, since the governor has no any stabilizing effects on the inter-area oscillation mode, the alleviation of frequency and tie line power oscillations can not be expected 4 .
To overcome this crux, this paper takes the advantage of the fast control offered by a HVDC link not only to compensate for the fast load change but also to stabilize the frequency and tie line power oscillations due to the inter-area mode.To implement this concept, a new design method of HVDC-based controller is presented.In the proposed design, the technique of overlapping decompositions 5 is used to obtain the subsystem where the physical characteristic of inter-area oscillation mode is embedded.As a result, a HVDC-based controller can be designed to serve two purposes in this subsystem.In this study, a HVDC-based controller is practically in form of a second-order conventional lead/lag compensator.The control parameters are automatically optimized by the tabu search (TS) algorithm 6 .The effectiveness of the designed controller is evaluated in a three-area longitudinal interconnected power system which representing the interconnected power systems between Thailand and Malaysia.
The organizations of this paper are as follows.Section 2 describes the problem statement.Next, the design methodology is presented in section 3. Subsequently, the TS algorithm is given in section 4. The experimental results are discussed in section 5. Finally, the main outcome from this study is summarized.The three-area interconnected power system with longitudinal configuration is shown in Fig. 1.This study system emulates the interconnected power systems between Thailand and Malaysia.Area 1 represents the greater Bangkok power system network including the northern and northeastern parts of Thailand.The south of Thailand denoted by the area 2 is connected to the Malaysian power system (area 3) via a HVDC link.In a real situation, an area 2 is connected to an area 1 via a weak and long tie line.In addition, large loads with rapid change, which are considered as system disturbances, frequently occur in area 2. However, a power generation in area 2 is not enough to compensate for changing loads.Thus, the bulk power transfer from an area 1 is required during the peak load period.Nevertheless, the power transfer in a tie line 1-2 is inevitably constrained by thermal and stability limits.Power transmission from other sources is significant required.Due to insufficient load compensation, a severe frequency oscillation becomes a serious stability problem in area 2. Especially, if the frequency of the changing load is in the vicinity of the inter-area mode between areas 1 and 2, this may drastically cause both frequency and tie line power oscillations.

PROBLEM STATEMENT
On the other hand, an area 3 has sufficiently the frequency control capability.During the occurrence of load disturbances, a HVDC link is used as the energy transfer device from area 3 to area 2. The tie line power flow control of HVDC link via the area interconnections can be applied to compensate for the fast load change as well as stabilize the frequency and tie line power oscillations due to the inter-area mode.Therefore, a HVDC-based controller is designed to solve this problem.The linearized model of a three-area interconnected power system 3 around the normal operating condition for design of HVDC-based controller is shown in Fig. 2. The HVDC link is represented by the active power controller with a time constant T DC = 0.05 sec 7 .Since the response of HVDC link is much faster than that of governor, the dynamics of governors are ignored in this model.For simplicity, the linearized state equation with neglecting T DC can be expressed as

DESIGN OF HVDC-BASED CONTROLLER
where ∆f 1 , ∆f 2 , ∆f 3 are frequency deviations in areas 1, 2 and 3, respectively.∆P T12 is a tie line power deviation.∆P DC is a power flow controlled by a HVDC link.∆u DC is a control signal from a HVDC-based controller.System parameters are given in part 5.
In order to extract the subsystem where the inter-area oscillation mode between areas 1 and 2 is preserved, from the system S, the technique of overlapping decompositions 5 is applied.First, the state variables of S, are classified into three groups, i.e., χ 1 = [∆f 1 ], χ 2 = [∆P r12 ] and χ 3 = [∆f 2 , ∆f 3 ] r .Therefore, the system S can be expressed in compact form as where The sub-matrices A ij and B il , (i, j = 1, 2, 3) have appropriate dimensions identical to the corresponding state and input vectors.According to the process of overlapping decompositions, the system S can be expanded as The system S in (3) can be decomposed into two interconnected overlapping subsystems, The state variable x 2 , i.e. the tie line power deviation between areas 1 and 2 (∆P T12 ), is repeatedly included in both subsystems, which implies "Overlapping Decompositions". ( For system stabilization, consider two interconnected subsystems S1 and S2 .The terms in the right hand sides of ( 4) and ( 5) can be separated into the decoupled subsystems (as indicated in the parenthesis in ( 4) and ( 5)) and the interconnection subsystems.As mentioned in a reference 5, if each decoupled subsystem can be stabilized by its own input, the asymptotic stability of the interconnected overlapping subsystems S1 and S2 and are maintained, moreover the asymptotic stability of the original system S is also guaranteed.Consequently, the interactions with the interconnection subsystems in ( 4) and ( 5) are regarded as perturbations and are neglected during control design.As a result, the decoupled subsystems of S1 and S2 and can be expressed as In ( 6) and ( 7) there is a control input ∆P DC appearing only in the subsystem SD2 .Here, the decoupled subsystem SD2 is employed to design a HVDC-based controller.Note that the eigenvalues corresponding to the inter-area oscillation mode between areas 1 and 2 in (7) are almost identical to that of (1).This exhibits the merit of overlapping decompositions that the physical characteristic of the original system is still preserved in the decoupled subsystem.
In this study, the structure of HVDC-based controller is in form of a second-order lead/lag compensator as depicted in Fig. 3.There are five parameters for the designed controller consisting of time constants T 1 , T 2 , T 3 , T 4 and a stabilization gain K.The control purpose of the designed controller is to damp the peak value of frequency oscillation in area 2 after the load disturbance.
Therefore, ∆f 2 is selected as the input signal of the controller.To achieve this purpose, TS is employed for parameters optimization.The objective function (F) used here is based on the design specification that requires the maximum overshoot of ∆f 2 against the step load to be.
M p, design .Therefore, the optimization problem can be formulated as follows.
where P i is the actual value of the i-th parameter, P i,max and P i,min are the maximum and minimum value of the i-th parameter.B i is the decimal integer value of binary string of the i-th parameter.
In this paper, 10 bits are used to represent each parameter.
On the other hand, the actual value of each parameter can be obtained by (9) for objective function evaluation.
where M p,actual is the actual maximum overshoot of ∆f 2 against the step load for each trial solution.K max and K min are maximum and minimum stabilization gains which are set to 50 and 0.1, respectively.T i,max and T i,min are maximum and minimum time constants which are set to 5 and 0.01, respectively.

TABU SEARCH ALGORITHM
As a promising tool, TS is an iterative improvement procedure, which can start from any feasible initial solution and attempt to find a better solution.TS is a heuristic method that is based on a local search method with the ability to escape from being trapped in local optima 6 .Following, the basic components of TS are briefly described.Subsequently, the procedure of TS is presented.

TS Components
Encoding and Decoding Scheme : The concatenated encoding method is employed as shown in Fig. 4.Each parameter is encoded in a binary string normalized over its range.This encoding method stacks each normalized string in series with each other to construct the string individual.
The same number of n bits is used to represent each parameter string.As the only control parameter of TS 6 , the size of TL, or so-called the tabu length, is dependent to the application.However, observing the quality of the solution can identify the appropriate size of the tabu length.If the size of the tabu length is too small, the cycling of solution occurs in the search process.On the other hand, if the size is too large, the search process is too restricted and may deteriorate the quality of the solution.In this paper, the tabu length is set to ( 0.7 Termination criterion : This criterion is set to allow the search process to stop and return the best solution.In this paper, TS will stop if the maximum allowable number of iteration is reached.

TS Procedure
To apply TS for parameter optimization, the initial feasible solution is generated arbitrarily.A trial solution is created and examined if TL does not restrict it.The best solution is updated during the search process until the termination criterion is satisfied.The following notations are defined for the TS procedure: In this paper, NS is set up to 95% of the total number of bits used ( 0.95 where N is a number of searched parameter.

Tabu List Restriction :
As an adaptive memory, a tabu list (TL) is used to control the search process to avoid being trapped in local optima.Systematically, TL keeps attributes (bit positions) that created the best solution of past iterations for a certain period so that they are fixed and cannot be used to create new solution candidates.As the iteration proceeds, TL stores a new attribute as a fixed attribute and releases the oldest one as shown in Fig. 6.The TS procedure can be described as follows: 1. Read the constraints of searched parameters, the initial feasible solution, and the design specification.
2. Specify the length of TL, k max , and the size of NS.
3. Initialize iteration counter k to zero and empty TL.
4.8.If m is less than NS, m = m + 1 and go to 4.2.
4.9.If there is no feasible solution, set X o k +1 = X b .Otherwise, set X o k +1 = X cb k , and update TL.
5. If k < k max , then k = k + 1, and go to 4.
6. TS is terminated and X b is the best solution found.

EXPERIMENTAL RESULTS
Based on the proposed method, a HVDC-based controller is designed in a three-area interconnected system.System data are given in table 1.The design specification M p,design is set to 25% of that of no controller installed.For TS, the size of TL is set to 35 and the maximum allowable number of iterations is 100.First, the subsystem ( 7) is extracted from the original system (1) by using overlapping decompositions.Table 2 compares eigenvalues of ( 1) and (7).In (1), only λ 2,3 are complex eigenvalues.Therefore, they correspond to the inter-area oscillation mode between areas 1 and 2. After the process of overlapping decompositions, the damping ratios (ς) and the oscillation frequencies (f) of the inter-area mode in both systems have rarely changed.This clarifies that the physical characteristics of the inter-area mode are still preserved in (7).After applying the TS algorithm, a HVDC-based controller can be expressed as (10) The effect of HVDC-based controller installed in ( 7) is illustrated in Fig. 7, in comparison with the case of no controller installed.Subject to a 0.01 [pu.MW] step load, the maximum overshoot of area 1 frequency deviation is satisfactorily reduced from 0.04 [Hz] to 0.011 [Hz], that is about 25% of the original value.
Next, the coordinated control of HVDC-based controller and conventional governors is investigated in the power system model including governor 3 as depicted in Fig. 8.All parameters are given in table 1.Note that, the dynamic characteristic of HVDC link representing by the time constant  1) and The Subsystem (7).
T DC is also taken into consideration in the simulation study.The effectiveness of designed controller is evaluated under several load disturbances and various system operating conditions as follows.

Case 1. Step load change
It is assumed that a step load, e.g.large steel mill and arc-furnace factories 8 , increase of 0.01 [pu.MW] occurs in an area 2 at t = 1.0 [sec].Figures 9-12 illustrates the control effects of the designed controller.First, consider the control area 2 in Fig. 10, the overshoot of frequency deviation in area 2 is rapidly suppressed from that in case of no controller.Subsequently, the steady-state error is slowly eliminated by governors.This implies the coordinated control effects of both devices.In addition, as depicted in Fig. 9, the frequency deviation in area 1 is also improved.The frequency in area 3 shown in Fig. 11, however, is inevitably deviated from the operating frequency about 0.007 [Hz] in case of with designed controller.This is due to the rapid transferred energy from area 3 to area 2 by a HVDC link.In practice, this small deviation of frequency is acceptable.In addition, the tie line power deviation (∆P T12 ) between areas 1  This signifies that the necessary MW capacity of HVDC-based controller is much less than the size of step load.

Case 2. Sinusoidal load change at the frequency of inter-area oscillation mode
It is assumed that the sinusoidal load change is installed in an area 2. The frequency oscillation of this load is equal to that of the inter-area oscillation mode between areas 1 and 2. Accordingly, this load change is represented by ∆P 1,2 (ωt) = 0.01 sin (2π ft) where the frequency of the inter-area oscillation mode (f) is 0.283 Hz (see Table 2).Figures 13-15 show the frequency deviations of areas 1, 2 and 3, respectively.In case of no controller, the sinusoidal load change causes the severe oscillations at the frequency of inter-area mode.
After the controller is operated, the frequency oscillations are suppressed significantly.The tie line 1-2 power deviation depicted in Fig. 16, is also stabilized effectively.Furthermore, the maximum power output of HVDC-based controller (Fig. 17) is about 0.0025 pu.MW which is much less than the magnitude of sinusoidal load change.

Case 3. Combined sinusoidal load changes
The changing load assumed here consists of three different components in the frequency domain, one of which has a frequency of the inter-area mode as follows.

Case 4. 30% increase in system parameters
It is assumed that not only the sinusoidal load change in case 3 is applied to the area 2, but also the parameters of a three-area interconnected system are increased by 30% .Figures 23-27 clearly show the effectiveness of HVDC-based controller.Without controller, the frequency deviations in areas 1 and 2, and the tie line 1-2 power deviation severely oscillate and diverge.The interconnected areas 1 and 2 lose their stability.On the other hand, the frequency and tie line power deviations are perfectly stabilized after the controller is operated.This implies the robustness of the designed controller against system parameter variations.

Case 5. Negative damping due to a severe fault
Here, it is assumed that the severe fault such as a short circuit etc. occurred in the area 2. This fault causes the area 2 to be unstable.As a result, the damping coefficient D 2 becomes negative.In this study, the same sinusoidal load change in case 3 is applied to the area 2 while These case studies explicitly confirm that the proposed HVDC-based controller is very effective in load change compensation as well as suppressing inter-area oscillations against any load disturbances.Additionally, the designed controller is considerably robust to various system operating conditions, parameter variations and several load disturbances.

CONCLUSIONS
In this paper, the new design method of HVDC-based controller for load change compensation and stabilization of inter-area oscillation is presented.The proposed design utilizes the technique of overlapping decompositions to acquire the subsystem where the inter-area oscillation mode is preserved.Subsequently, the tabu search is employed for optimizing parameters of the controller in this subsystem.Since, the design specification is selected based on the required overshoot of frequency oscillation, this is not only suitable for a real problem but also simple for any designer.Furthermore, the controller has a structure of second-order lead/lag compensator, this makes it easy to implement in the practical power system.Simulation studies clearly confirm both load change compensation and damping effects of the designed controller against several load disturbances.Moreover, a HVDC-based controller can be effectively coordinated with the conventional governors.From the simulation results, the high robustness of the designed controller against system parameter variations, operating conditions, several load disturbances has been clarified.

Figure 1 :
Figure 1 : A HVDC System in a Three-area Longitudinal Interconnected Power System.

Figure 2 :
Figure 2 : A Linearized AC-DC Interconnected Power System Model without Governors.

Figure 5 :
Figure 5 : Concept of Trial Solution Generation.

Figure 8 :
Figure 8 : Linearized System Model of Area i Including Governor.
Figures 18-22 express the stabilizing effects of HVDC-based controller.Without controller, the frequency oscillation in area 2 and the power oscillation in a tie line 1-2 drastically fluctuate.After applying a HVDC-based controller, they are significantly alleviated.
D 2 is set to -0.16 [pu.MW/Hz].The effectiveness of HVDC-based controller is demonstrated in Figs.28-32.Without controller, the oscillations of frequency deviations in areas 1 and 2, and tie line 1-2 power deviation severely fluctuate and finally diverge.After applying the proposed controller, frequency and tie line power oscillations are significantly damped.A stability of the interconnected areas is effectively maintained.

Table 2 :
Eigenvalues of The Original System (