Interval Type-ii Fuzzy Rule-based Statcom for Voltage Regulation in the Power System

The static synchronous compensator (STATCOM) has recently received much attention owing to its ability to stabilize power systems and mitigate voltage variations. This paper investigates a novel interval type-II fuzzy rule-based PID (proportional-integral-derivative) controller for the STATCOM to mitigate bus voltage variations caused by large changes in load and the intermittent generation of photovoltaic (PV) arrays. The proposed interval type-II fuzzy rule base utilizes the output of the PID controller to tune the signal applied to the STATCOM. The rules involve upper and lower membership functions that ensure the stable responses of the controlled system. The proposed method is implemented using the NEPLAN software package and MATLAB/Simulink with co-simulation. A six-bus system is used to show the effectiveness of the proposed method. Comparative studies show that the proposed method is superior to traditional PID and type-I fuzzy rule-based methods.


Introduction
A static synchronous compensator (STATCOM) is a volt-ampere-reactive (VAR)/voltage regulation device that is used in both electric transmission and distribution networks.The STATCOM utilizes a OPEN ACCESS voltage-or current-source converter and can act as either a source or sink of reactive power in the power system.If the STATCOM is connected to a source of power, it can also provide the real power.
Traditionally, STATCOMs have been used to study the stability problem.Wang and Hsiung presented a STATCOM control scheme to enhance the damping of a grid-connected 80 MW offshore wind farm and 40 MW marine-current farm [1].The damping controller was designed using modal control theory and has been examined under different operating conditions.Wang and Truong presented a damping controller of the STATCOM by using a pole-assignment approach to ensure adequate damping of the dominant modes of the studied power system [2].Beza and Bongiorno presented an adaptive power oscillation damping controller for a STATCOM equipped with an energy storage device [3]; this was achieved using a signal estimation technique based on a modified recursive least-square algorithm, which supported the adaptive estimation of low-frequency electromechanical oscillations from locally-measured signals during power system disturbances.
Recently, STATCOMs have been also used to deal with the voltage problems in the power system.Wang and Crow developed a feedback linearization controller to regulate bus voltages [4].Chen et al. investigated the use of a STATCOM for system voltage control, during peak solar irradiation, in order to increase the PV installation capacity of a distribution feeder and avoid the voltage violation problem [5].Aziz et al. presented a method for VAR planning with a STATCOM for an industrial system that comprised multiple distributed generation units.The impact of the placement of STATCOM on voltage recovery and the rating of the STATCOM were determined through time-domain simulations [6].Xu and Li proposed an adaptive PI control, which can self-adjust the control gains in response to a disturbance such that the desired response is maintained, regardless of any change in the operating conditions [7].
On the other hand, conventional fuzzy rules (also called a type-I (T1) fuzzy logic system) have been used to design controllers and have been found to be effective when the controlled plant is not complex.On the contrary, an interval type-II (IT2) fuzzy logic system outperforms T1 if the system is complex.Zadeh introduced the concept of type-II fuzzy sets, as an extension of type-I fuzzy sets, incorporating an additional dimension that represents uncertainty in degrees of membership [8].Liang and Mendel proposed a simplified method to compute the input and antecedent operations for IT2 fuzzy logic systems [9].They showed that all of the results that are needed to implement an IT2 fuzzy logic system can be obtained using T1 fuzzy logic mathematics [10].Other works have elaborated IT2 fuzzy logic systems, such as [11][12][13][14].A tutorial about IT2 fuzzy logic systems is also available in [15].
Recently, the IT2 fuzzy logic system was applied to solve power system problems.Tripathy and Mishra proposed an IT2 fuzzy logic-based thyristor-controlled series capacitor to improve power system stability.They used the concept of uncertainty bounds for type-reduction to overcome the limitation of the time-consuming iterative method generally used for type reduction [16].Khosravi et al. proposed the application of IT2 fuzzy logic systems to the problem of short-term load forecasting [17].Mikkili and Panda proposed a shunt active filter to improve the power quality of the electrical network by mitigating the harmonics with the help of T1 and IT2 fuzzy logic controllers [18].Jafarzadeh et al., proposed T1 and IT2 Takagi-Sugeno-Kang (TSK) fuzzy systems for both modeling and prediction of solar power [19].Khosravi and Nahavandi used IT2 fuzzy logic systems for day-ahead load forecasting, which introduced an optimal type reduction algorithm to improve the approximation [20].Murthy et al. addressed that the failure rate and the repair rate of any component of a power system for reliability studies are uncertain; therefore, a membership representation using precise and crisp functions seems practically unreasonable [21].
In this work, IT2 fuzzy rules are applied to the STATCOM to mitigate voltage variations caused by large load changes and intermittent photovoltaic power.The proposed IT2 fuzzy rule-based STATCOM is more robust than those described elsewhere [4][5][6][7].The proposed method is implemented by integrating the NEPLAN software package with MATLAB/Simulink.The NEPLAN software package is utilized to perform a dynamic power flow simulation while MATLAB/Simulink is used to design the IT2 fuzzy rule-based controller and STATCOM.
The rest of this paper is organized as follows.Section 2 provides the background of IT2 fuzzy logic systems.Section 3 presents the method based on the IT2 fuzzy rule base for mitigating the voltage variations in the power system.Section 4 summarizes the simulation results of a six-bus distribution system with PV generation.The conclusions are presented in Section 5.

IT2 Fuzzy Sets
A traditional type 1 (T1) fuzzy set Ã in X is defined as a set of ordered pairs, as follows.
where X is the universal set and μÃ(x) is the membership function (MF) of x in Ã. Notably, the MF represents the degree to which x belongs to Ã and the value of MF is normally between zero and unity.A high value of the MF indicates that x is very likely to be in Ã. Figure 1a shows an example of a T1 fuzzy set, Ã.Any number in the x domain corresponds to a membership value.The MF μÃ(x) of a T1 fuzzy set can be chosen either based on the user's experience or using algorithms.
A traditional T1 fuzzy set is certain in the sense that its membership values are crisp.In contrast, the type II fuzzy set is characterized by MFs that are themselves fuzzy.The IT2 fuzzy set is a special case of type II fuzzy sets.Figure 1b shows an example of an IT2 fuzzy set.The membership value of an IT2 fuzzy set lies within an interval.An IT2 fuzzy set is bounded by two type-1 MFs, Ā and  , which are referred to as upper MF (UMF) and lower MF (LMF), respectively.The area between Ā and  is called the footprint of uncertainty (FOU).IT2 fuzzy sets are particularly useful when specifying exact MFs is difficult.

IT2 Fuzzy Rules
Figure 2 shows a schematic diagram of an IT2 fuzzy logic system.The outputs of the inference engine are IT2 fuzzy sets.A type-reducer is needed to convert IT2 fuzzy sets into a T1 fuzzy set before defuzzification is carried out.Where Ãin (i =1, 2, …, M) are IT2 fuzzy sets and Yn=[yn, y n ] is an interval.Assume that the input vector . The IT2 fuzzy reasoning can be implemented using the following steps [22].
(1) Evaluate the membership of x* on each Ãin, (2) Evaluate the firing interval of the nth rule, Fn(x*) (3) Conduct type reduction using Fn(x*) and [yn, The sets {yn} and { y n } are sorted in ascending order.The values of  y and yr in Equations ( 3) and ( 4) can be evaluated using Karnik-Mendel algorithms [23].

Proposed Method
A STATCOM can be operated with either current source or voltage source converters; the latter are the more popular.Essentially, the main function of the STATCOM is to regulate voltages by reactive power control unless an additional energy storage system is connected to the DC bus of the STATCOM.Figure 3 illustrates the model of the STATCOM that is used herein [1,2].The DC voltage st dc V can be transformed to be the d-and q-axis components of the output terminal of the STATCOM as follows [1,2].
where θbus and st dc V denote the phase angle of the controlled AC bus and the DC voltage across the DC capacitance Cm, respectively The variables km and are the modulation index and the phase angle of the STATCOM, respectively.From Figure 3, one can obtain Equations ( 8) and ( 9) as follows [1,2].
where st dc I is the DC current that flows into the positive terminal of st dc V .Rm is the equivalent resistance of the STATCOM.st d i and st q i are the d-and q-axis currents that flow into the terminals of the STATCOM, respectively.

Dynamic Equations of STATCOM
Let V st be the voltage at the STATCOM and Vdbus and Vqbus be the voltages of the dand q-axes at the controlled AC bus, respectively.From the model of the STATCOM, the following dynamic equations are attained.Let the controlled bus voltage magnitude be Vt = 2 bus 2 bus Vq Vd  .
The following dynamic equations can be obtained: where Kc and Tc are parameters of the transfer function between α and .
st dc

ΔV
Vref is a given voltage reference.
where Ks and Ts are parameters of the transfer function between km and Vt The dynamic phenomenon in the power system can be studied using the above dynamic equations, the swing equations of synchronous machines, and network equations.

IT2 Fuzzy Rules for Controllers
This paper proposes an IT2 fuzzy rule-based controller for mitigating the voltage variation, as shown in Figure 4.The term Vref − Vt in Equation ( 11) will be replaced by the output (modified ∆Vt) of the IT2 fuzzy rule base.The proposed IT2 fuzzy rule is expressed as IF x1 is Ã1n and x2 is Ã2n then y is Yn.n = 1, 2, …, 25.where x1 is the output of the PID controller (denoted as Vt') and x2 is the change rate of Vt'.The variable y is the modified ∆Vt, which replaces the term Vref − Vt in Equation (11).
A total of 25 IT2 fuzzy rules are implemented in the proposed method (i.e., N = 25), as shown Table 1.The symbols NB, NS, ZR, PS, PB, IB, IS, KV, DS, DB, represent "Negative Big", "Negative Small", "Zero", "Positive Small", "Positive Big", "Increasing and Big", "Increasing and Small", "Keeping Value", "Decreasing and Small", and "Decreasing and Big", respectively.All UMF and LMF of Ã1n and Ã2n are expressed as trapezoid functions.Possible conditions of x1 and x2 could be NB, NS, ZR, PS or PB and the consequent actions y could be IB, IS, KV, DS or DB, as shown in Table 1.

Co-Simulation between NEPLAN and SIMULINK
Two software packages, namely NEPLAN [24] and MATLAB/Simulink (MathWorks, Natick, MA, USA), are used to implement the proposed method.The NEPLAN software package deals with the dynamic power flow simulation while the IT2 fuzzy rule-based controller and STATCOM are modeled by MATLAB/Simulink, as shown in Figure 5.

Discussions of the Proposed Method
Two comments about the proposed method are discussed as follows: (1) The proposed method utilized 25 IT2 fuzzy rules to implement the STATCOM controllers.In power system problems many facilities require controllers, which may be realized by different types of fuzzy rules, to stabilize the power system.Table 2 summarizes eight fuzzy rule-based controllers with their corresponding problems, number of fuzzy rules, types of fuzzy rules, and hardware [25][26][27][28][29][30][31][32].It can be found that the numbers of fuzzy rules are in the range of 16-60.The state-of-the-art DSP chip or CPU is able to accommodate these numbers of fuzzy rules and provide fast calculation for controlling the kW-or MW-scaled facilities in the power system.
(2) The existing STATCOM works, such as References [4][5][6][7] mentioned in Section 1, have the following limitations and are less robust than the proposed method.(i) The work of Wang and Crow in [4] needs to linearize the nonlinear system before applying the feedback linearization transformation.The state feedback matrix needs to be determined by linear control techniques, such as pole assignment.As described in [4], when an operating point crosses the singular surface of the power system problem, the system matrix becomes ill-conditioned and the trajectory curves are more likely to oscillate dramatically near this point.This may cause unexpected uncontrollability and chaotic behavior in the STATCOM dynamics.(ii) All the control gains in Chen's work [5]

Scenario 2: Increasing and then Decreasing Irradiations
The loads at buses 2 and 3 are 30 MW + j20 MVAR and 10 MW + j3 MVAR, respectively.The irradiation changes linearly.Initially, the MW generation from the PV is 0.063 p.u., as shown in Figure 9.The MW generation starts to decrease at t = 17 s and becomes 0.0363 p.u. at t = 21 s.
Figure 10 shows the controlled voltage at bus 3 obtained using three methods-traditional PID, T1 fuzzy rules, and IT2 fuzzy rules.As shown in Figure 10a, the voltage decreases slightly near t = 18 s and increases back to the nominal value near t = 21 s.The proposed IT2 fuzzy rules yield the best voltage performance, as shown in Figure 10c.

Scenario 3: Varying Irradiations
Buses 2 and 3 have demands of 30 MW + j20 MVAR and 10 MW + j3 MVAR, respectively.The irradiation is 1000 W/m 2 at t = 0 s.The irradiation increases to 1400 W/m 2 at t = 10, and thereafter linearly changes to be 1000, 1400, and 1000 W/m 2 at t = 12, 15 and 18 s, respectively, in the third scenario.The variations of MW generations from PV are shown in Figure 12.

Unscheduled Photovoltaic Outage
In this scenario, an unscheduled PV outage occurs at t = 10 s. Figure 15 reveals that the voltage increases rapidly at t = 10 s.The proposed method attains quickly-damped voltage variations.The dynamic voltage obtained by the T1 fuzzy rules is slowly damped from t = 10 to 12 s and oscillates as t approaches infinity.To reduce the voltage at t = 10 s, the reactive power produced from the STATCOM must be reduced as shown in Figure 16.The proposed IT2 fuzzy rule-based method outperforms both the traditional PID and T1 fuzzy rule-based methods.

Conclusions
An interval type-II (IT2) fuzzy rule-based STATCOM is proposed to mitigate voltage variations in this paper.The voltage error and rate of change of the voltage error are utilized to serve as inputs of the IT2 fuzzy rules; the action parts of IT2 fuzzy rules produce modified voltage errors.IT2 fuzzy rules are more applicable to nonlinear and time-varying systems than traditional T1 fuzzy rules because the upper and lower membership functions are implemented in an IT2 fuzzy set.A six-bus system is used to validate the proposed method.Four scenarios that involve large load changes and variations of MW generation from a PV farm are studied.Simulation results indicate that the proposed method always outperforms the traditional PID and T1 fuzzy rule-based methods.
are fixed and not adaptive to a change of scenarios.(iii) Aziz's work in[6] addressed the application of STATCOM at the planning stage.Aziz tuned the PID parameters by taking the step response of the open-loop plant into consideration.The results were verified in the peak load condition only.(iv) The work of Xu and Li lies in three essential parameters: allowed delayed time of response and ideal ratio of Kp over Ki for both current and voltage control loops, where Kp and Ki denote the parameters of proportional and

Figure 7b .Figure 7 .
Figure 7b.Again, the steady-state voltage is still oscillating.When the proposed IT2 fuzzy rules are used, the rising time and overshoot of the voltage are almost negligible, as shown in Figure 7c.

Figure 8 Figure 8 .
Figure8illustrates the reactive power injection from the STATCOM obtained using the three methods.The variations of voltages, shown in Figure7, are consistent with those of the reactive powers shown in Figure8.

Figures 13
Figures 13 and 14 plot the controlled voltages and MVAR from the STATCOM, respectively.It can be found that the proposed IT2 fuzzy rule-based method always acquire the most stable performance than traditional PID and T1 fuzzy rule-based methods.