Voltage Compensation in Wind Power System using STATCOM Controlled by Soft Computing Techniques

ABSTRACT


INTRODUCTION
Considering that the total global wind power production at the end of 2015 was 432883 MW (data provided by the official website of Global Wind Energy Council), wind is definitely one of the key renewable power sources which are transforming the power sector. The suitability of DFIG for grid-connected wind power generation has been illustrated by enumerating its benefits including superior voltage control and compensation of reactive power, supply of good quality controllable power at low wind speeds, decoupled control of real and reactive power and extraction of maximum power and its ability to ride throughvoltage dips and faults [1], [2]. Fluctuations in voltage, harmonics, inadequate reactive power support and poor power factor are some common issues which occur in grid-linked wind energy systems, leading to unsatisfactory performance of devices, unwanted tripping of protection elements and damage to sensitive apparatus. Voltage dip due to low wind speeds, disturbances in the grid, faults and unexpected load variations is one of the most serious issues occurring in grid-connected wind power systems [3]. When faults or disturbances occur in the system, the rotor of the DFIG is short-circuited and the rotor side converter is blocked so that the rotor does not get damaged due to overcurrents. Although the wind farm supplies reduced power in case of faults, it remains in service. However, if severe voltage dips occur in a weak power system (with a low short-circuit ratio and often subjected to low voltage conditions) connected to DFIG-based wind farm, the DFIG grid side converter which has a low rating is unable to provide the required voltage and reactive power support. Consequently, the system may be subjected to voltage instability. In such cases, it 668 becomes compulsory to disconnect the wind turbines and later connect them again after the clearance of the fault. This makes the system highly unreliable. The international grid codes are very strict when it comes to low-voltage ride through and make it compulsory to ensure that the wind farms do not become unstable and get disconnected even when the voltage dips to a very low value. This voltage instability issue can be resolved by employing flexible AC transmission system (FACTS) compensators like static synchronous compensators (STATCOM), which provide transient and steady-state voltage support at the point of common coupling (PCC) by means of dynamic reactive power injection. In spite of the huge expenses involved, the STATCOM is preferred over some other FACTS devices due to its superior performance and flexibility. The reactive power support offered by the STATCOM at lower voltages is greater than that offered by SVC. Also, the response of SVC is slow compared to STATCOM due to firing delays associated with SVC. Research attempts have been directed towards the real time utilization of STATCOM to maintain voltage stability in a weak power system connected to DFIG-based wind farm [4], [5]. The role of FACTS devices in enhancing the stability of gridconnected wind power systems has been enumerated in detail [6]. Fuzzy logic and ANFIS-based control for the STATCOM in a grid-connected PMSG-based wind power system was proposed [7]. AnLuo,et al suggested a fuzzy-PI independent control technique for STATCOM in distribution networks [8]. Fuzzy logic may be memory-intensive and may lead to software overload, particularly in less complicated applications, owing to the use of many localized parameters. Particle swarm optimization (PSO) is acomputationally efficient swarm intelligence based optimization technique which involves cognitive and social interactions and has often demonstrated fast response and improved performance compared to fuzzy controllers. Previously, research work has been done in the field of PSO-controlled STATCOM and in the area of DFIGbased wind farms separately. However, this is a novel attempt to integrate PSO-controlled STATCOM in DFIG-based grid-connected wind power systems. Chien-Hung Liu, et al proposed a flexible controller for STATCOM using PSO, using integral absolute error (IAE) as the evaluation criterion [9]. However, although minimization problems employing IAE as the objective function produce a low overshoot response, they suffer from the drawback of excessively long settling times. Therefore, in this work, a different evaluation criterion was used in the PSO program used to control the STATCOM.
In this work, STATCOM wasemployed for providing voltage compensation at the PCC in a DFIGbased grid-connected wind power system in five test cases, namely, step change (drop) in wind speed simultaneously accompanied by a dip in grid voltage, single line to ground (SLG), line to line (LL), double line to ground (DLG) faults and sudden load increment. The STATCOM was controlled using three soft computing techniques, namely, fuzzy logic (research method 1), PSO (research method 2) and a combination of both fuzzy logic and PSO (research method 3). In the third methodology, both fuzzy logic and PSO were used to tune the PI controller gains in the STATCOM voltage supervisor. This methodology, called fuzzy PSO-PI technique, is a novel STATCOM control technique. Also, it has been used in wind power for the first time. A performance comparison was done among the three artificial intelligence based techniques used to control the STATCOM in terms of the amount of voltage compensation offered at the PCC in all the five test cases. The uniqueness of this research endeavour is also highlighted in two novel test cases which have been considered here, namely, occurrence of step change (drop) in wind speed and grid voltage dip at the same instant and abrupt variation in load by more than a thousand times.

MATHEMATICAL MODELLING OF WIND TURBINE AND DFIG
The net mechanical power obtained from a wind turbine P extracted is given by Equation (1): In Equation (1), , R, V wind and denote the air density, turbine blade radius, wind velocity and power coefficient of wind turbine respectively.
It is seen that: In Equation (2), is the tip speed ratio of the wind turbine which is given by: (2), the value of power coefficient is the maximum and the maximum value is equal to (16/27) = 0.59. This validates the Betz" principle which states that a maximum of 59.3% of the total kinetic energy possessed by wind is converted into mechanical energy [10]. The schematic representation of a wind energy conversion system employing DFIG is shown in Figure 1. A variable frequency ac/dc/ac converter (VFC), which is supposed to control only 25% to 30% of the total power, links the rotor of the DFIG with the grid. The capacitor in the DC link between the Rotor-Side Converter (RSC) and the Grid-Side Converter (GSC) stores energy and reduces ripple in the DC link. The RSC reliably supervises the real and reactive power, speed, torque and power factor at the stator side. Supervision of the voltage of the DC link and provision of regulated reactive power support is done by the GSC.
The DFIG Equations in the dq reference frame for the stator voltages E sd (d-axis) and E s q (q-axis) and the rotor voltages E rd (d-axis) and E rq (q-axis) are stated in Equations (3)-(6) as follows [11]: In Equations (3)-(6), I sd , I sq , I rd , I rq , R s, R r , λ sd , λ sq , λ rd , λ rq , ω and ω r represent d-axis stator current, qaxis stator current, d-axis rotor current, q-axis rotor current, per-phase stator resistance, per-phase rotor resistance, d-axis stator flux linkage, q-axis stator flux linkage, d-axis rotor flux linkage, q-axis rotor flux linkage, rotation speed of dq reference frame and electrical angular speed of the rotor respectively.The Equation relating the mechanical rotation speed of the DFIG ω mech and electrical angular speed ω r is given by ( ) The expression for the electromagnetic torque developed T developed is given in Equation (7): The relationship between the mechanical rotation speed of the DFIG ω mech , developed electromagnetic torque T developed and the mechanical torque applied T ex is stated in Equation (8): (8) In Equation (8), J is the combined polar moment of inertia of the DFIG and prime mover with reference to the shaft of the machine.

STATCOM AND ITS CONTROL SYSTEM
In the STATCOM equivalent circuit in Figure 2, the converter losses are accounted for by R dc, V dc is the voltage across DC capacitor C dc , R s and L s denote the resistance and inductance of the coupling transformer respectively, V and Ө stand for the magnitude and phase angle of STATCOM RMS voltage respectively, u is the modulation ratio and the phase shift is β and the STATCOM currents in dq reference frame are I d and I q [12]. In the dq reference frame, the state Equation of the STATCOM is given by Equation (9): In Equation (9), ( ) and ( ) In the overall block schematic representation of the STATCOM control system is shown in Figure 3, the phase locked loop provides the angle φ for the computation of d-axis and q-axis components of voltages and currents in the STATCOM control system. The AC voltage controller and DC voltage controller generate the reference currents Ref_I Q and Ref_I D respectively. The current regulator operates on the error between the reference and actual q-axis (reactive) currents [13]. The frequency regulator acts on the difference between the standard grid frequency and the DFIG frequency and provided ΔRef_I Q , which is added to Ref_I Q generated by the voltage regulator to get the final value of reference reactive current Ref_I Q (f).

RESEARCH METHOD 1: STATCOM CONTROLLED BY FUZZY LOGIC
The STATCOM performance was enhanced by including fuzzy logic controllers in the voltage, current and frequency regulator blocks of the STATCOM control system. Mamdani fuzzy inference technique was used and the fuzzy outputs were defuzzified using Centre of Area (COA) defuzzification. In the voltage and current regulators, fuzzy logic was used to tune the proportional and integral gain constants of PI controllers; hence this control methodology was termed fuzzy-PI technique. In the STATCOM current and voltage supervisors, the increments in the PI controller gains obtained from fuzzy logic controller, ΔK PR (fuzzy) and ΔK IN (fuzzy), were summed up with the original gain constants of the existing PI controllers, K PR (PI) and K IN (PI), to get the final tuned PI controller gains, K PR (tuned) and K IN (tuned), as shown in Equations (10) and (11): The schematic diagram of the STATCOM voltage regulator supervised using fuzzy-PI technique is shown in Figure 4. In the fuzzy-PI regulated STATCOM voltage supervisor, the difference between the reference voltage (Ref_Voltage) and the measured (actual) value of voltage (Meas_Voltage), which is represented by v err , and the first derivative of this deviation dv err /dt were fed as inputs to the fuzzy system. The fuzzy controller provided the required changes in controller gains, ΔK PR (fuzzy) and ΔK IN (fuzzy). The new PI controller with modified proportional and integral gain constants, K PR (tuned) and K IN (tuned), was used to control the STATCOM voltage supervisor. The reference reactive current Ref_I Q was provided by the STATCOM voltage regulator. The slope of the STATCOM V-I characteristics when it operates in voltage regulation mode is called droop. In the fuzzy-PI regulated STATCOM current supervisor, the difference between the reference reactive current (Ref_I Q ) and the measured (actual) value of reactive current (Meas_I Q ), which is represented by i err , and the first derivative of this deviation di err /dt were fed as inputs to the fuzzy system. The fuzzy controller provided the required changes in controller gains, ΔK PR (fuzzy) and ΔK IN (fuzzy). The new PI controller with modified proportional and integral gain constants, K PR (tuned) and K IN (tuned), was used to control the STATCOM current supervisor. The angular shift between the AC bus voltage and the voltage of the converter, alpha, was provided by the STATCOM current regulator.
The rules applied to obtain ΔK PR (fuzzy) and ΔK IN (fuzzy) in the fuzzy systems in both the voltage and current supervisors are presented in Table 1 and Table 2 respectively. In the membership functions and rule tables, nvb, nb, z, pb and pvb stand for "negative very big", "negative big", "zero", "positive big" and "positive very big" respectively. If error and its first derivative are of greater magnitudes, ΔK PR is also greater. By making ΔK IN  The difference between the grid (reference) frequency and the frequency of the DFIG, f err , and its first derivative, df err /dt, were provided as inputs to the STATCOM frequency regulator. The change in STATCOM reference reactive current, ΔRef_I Q , was provided as output by the fuzzy supervised frequency regulator. This change in STATCOM reference reactive current, ΔRef_I Q , was added to Ref_I Q provided by the voltage regulator to obtain the final value of the STATCOM reference reactive current.
The rules applied to obtain ΔRef_I Q in the fuzzy system in the frequency controller are displayed in Table 3. Large magnitudes of fast rising frequency deviation demand a greater amount of STATCOM capacitive current since the electrical output of the alternators falls below the mechanical input supplied to them. In such situations, the transient stability of the line improves when the STATCOM supplies a greater magnitude of capacitive current since more power is transferred to the receiving end. It was therefore inferred that the STATCOM current must be positive large (mode of operation must be capacitive) when f err and df err /dt are positive large [15].

RESEARCH METHOD 2: STATCOM CONTROLLED BY PSO
PSO was harnessed to adjust the PI controller gains in the STATCOM voltage supervisor, therefore this control methodology was termed PSO-PI technique. The optimized PI controller gains provided by the PSO program, K PR (opt) and K IN (opt), were used in the PSO-PI controlled STATCOM voltage supervisor, as shown in Figure 5. As stated earlier, the voltage regulator provides the STATCOM reference reactive current Ref_I Q as its output, and the slope of the STATCOM V-I characteristics (in voltage control mode) is referred to as droop.All the steps in the flowchart for PSO for STATCOM control shown in Figure 6. Step 1: Initial conditions: In the PSO algorithm for STATCOM control, the gains of the PI controller K PR and K IN were the positions or searching points. The increments in controller gains ΔK PR and ΔK IN were the velocities. The specified ranges for K PR and K IN were chosen to be [0 1.5] and [0 1] respectively. The initial values of ΔK PR and ΔK IN were randomly chosen within the interval [- 1 1]. Pbest (personal best) was the present position for each particle and gbest (global best) was the position of the particle with the best calculated value of evaluation function out of all available pbests.

Figure 6. Flowchart for PSO for STATCOM supervision
Step 2: Attainment of evaluation function value for each agent: Some of the performance criteria commonly utilized for tuning PI controllers are integral absolute error (IAE), integral of squared error (ISE) and integral of time weighted squared error (ITSE). They have their own disadvantages. IAE and ISE can lead to a long settling time although they minimize the overshoot. In spite of the fact that ITSE overcomes the long settling time problem, it involves very complicated and lengthy analytical calculations. In this work, a different evaluation criterion was used. The objective functionObj (K), whose value was to be minimized in this case, is stated in Equation (12): In Equation (12), K= [K PR K IN ], error_ssstands for the error at steady-state, settling_t and rise_tstand for the settling time and rise time respectively, and the peak overshoot is denoted byover_sh. If the weighting factor m exceeds 0.7, the error at steady state and peak overshoot are decreased, and if it is below 0.7, the settling time and rise time are reduced [16]. Therefore, the preferred range for mis [0. 8 1.5], in this program, m was taken to be 1.2. The performance criterion was evaluated for each agent. If a new searching point provided a better evaluated value of objective function, it replaced the current pbest. The best out of all available new pbests replaced the current gbest if it satisfied the design criterion in a better way compared to the present gbest.
Step 3: Updating positions and velocities: The controller gains and their increments were altered using the Equations (13), (14) and (15) In Equations (13), (14) and (15), denotes the position of the particle t at iteration j, stands for the location of particle t at iteration j+1, = is the velocity (increment in controller gain for t th particle ΔK t ) of particle t at iteration j+1, ind_cnstand scl_cnstdenote the constants which account for individual and social behavior respectively, iteration_maxis the pre-specified maximum number of iterations, denote the maximum and minimum inertia weights respectively, j is the number of the present iteration and rdm_1 and rdm_2 are random number sequences within the range [0 1].
Step 4: Check on exit condition: The exit condition was fulfilled if the current iteration count became equal to the maximum number of iterations, which was specified to be 24 in this case.The parameters used in the PSO program for the STATCOM are summarized in Table 4.

RESEARCH METHOD 3: STATCOM CONTROLLED BY FUZZY LOGIC AND PSO
In the fourth methodology, the proportional and integral PI gains of the STATCOM voltage supervisor weretuned using both fuzzy logic and PSO (combination of fuzzy-PI and PSO-PI techniques), hence this technique was called fuzzy PSO-PI technique. The schematic diagram of the STATCOM voltage regulator supervised using fuzzy PSO-PI technique is shown in Figure 7. K PR (PSO) and K IN (PSO) obtained from the PSO program described in section 5were added to ΔK PR (fuzzy) and ΔK IN (fuzzy) obtained from the fuzzy controller described in section 4, to get the final optimized tuned PI gains K PR (final) and K IN (final). As described in section 4, the current regulator was supervised using the fuzzy-PI technique and the frequency regulator was controlled using fuzzy logic.

TEST SYSTEM TOPOLOGY
The test system, whose single linediagram can be seen in Figure 8, was simulated using SimPowerSystems, which is a component of MATLAB/SIMULINK and its parameters are specified in Table  5. The three loads in the test system named Load1, Load2 and Load3 are a 355 MW resistive load, a 450 MW resistive load and a 550 KW, 100 KVAR R-L load respectively. The voltage compensation provided by the 48-pulse GTO based STATCOM at the PCC (bus named "BUS_PCC") is validated in five test cases. In test case one, the speed of the wind was set to drop suddenly at time t=0.1 seconds from 22 m/s to 3 m/s. This was accompanied by a dip in the voltage of the grid to 0.1 pu, which was however brought back to its normal value of 1 pu at time t=0.14 seconds. In test cases two, three and four, the voltage dip was observed at the bus labeled "BUS_PCC" as a consequence of SLG, LL and DLG faults respectively at time t=0.1 seconds for two cycles at the terminals of the bus labelled "BUS_FAULT". The fifth and last test case dealt with an abrupt rise in load at the bus named BUS_PCC. Prior to the load change, the total resistive load at BUS_PCC was 500 KW. By gating an extra 500 MW resistive load at time t=0.1 seconds at BUS_PCC, the resultant resistive load at BUS_PCC became (500 KW + 500 MW), which implied an increment in load at BUS_PCC by a little more than a thousand times. The additional 500 MW load was switched off after two cycles. The speed of the wind was maintained at 15 m/s in all the cases except the first one. The total simulation time was 0.2 seconds in all the test cases. For all the five test cases, the test system was simulated four times, first without the STATCOM, second with fuzzy controlled STATCOM, third with PSO controlled STATCOM, and fourth, with fuzzy PSO controlled STATCOM. Using all the three control techniques separately in the five testcases, the positive sequence voltage was observed at the bus named "BUS_PCC", which was the point of common coupling (PCC).

RESULTS AND ANALYSIS
The voltage magnitudes at BUS_PCC for all the test cases using STATCOM controlled by all the three artificial intelligence based techniques are listed in Table 6.
Three important points can be derived from the results tabulated in Table 6: a. Improvement in the positive sequence voltage at BUS_PCC (common coupling point) is observed in all the test cases, using STATCOM controlled by all the three techniques, namely, fuzzy logic, PSO and fuzzy-PSO. Therefore, in such situations, owing to the dynamic voltage support provided by the

Simultaneous Occurrence of Step Change (Drop) in Wind Speed and Dip in the Grid Voltage
When the wind speed dropped as a step from 22 m/s to 3 m/s and the grid voltage dipped to 0.1 pu simultaneously, the positive sequence voltage at BUS_PCC, which had fallen to 0.68 pu in the absence of STATCOM ( Figure 9) improved to 0.92 pu, 0.95 pu and 0.94 pu in the presence of fuzzy, PSO ( Figure 10) and fuzzy PSO controlled STATCOM respectively. Therefore, we see that the STATCOM controlled using PSO provided the highest voltage compensation out of the three methods. It can also be observed from Figure  11 that the fuzzy PSO controlled STATCOM offered a comparatively smoother voltage response, with fewer oscillations.

Single Line to Ground Fault
It can be seen in figures 12-14 that the positive sequence voltage at BUS_PCC which had dipped to 0.75 pu as a consequence of SLG fault at BUS_FAULT, improved to 0.98 pu when fuzzy controlled STATCOM was connected, 0.995 pu when PSO controlled STATCOM was connected and 0.99 pu when fuzzy PSO controlled STATCOM was connected. Thus, in this case, the PSO controlled STATCOM provided slightly more improvement in voltage compared to STATCOM controlled by the other techniques, as seen in Figure 14.

Line To Line Fault
As a result of LL fault at BUS_FAULT, the positive sequence voltage at BUS_PCC, which had dropped to 0.55 pu in the absence of STATCOM (Figure 15), improved to 0.78 pu, 0.79 pu and 0.8 pu in the presence of fuzzy, PSO and fuzzy PSO ( Figure 16) controlled STATCOM respectively. Therefore, it was observed that the fuzzy-PSO controlled STATCOM offered the highest voltage improvement out of all the three techniques, as seen in Figure 17. It is also clear from Figure 17 that the fuzzy-PSO controlled STATCOM offered a comparatively more stable voltage response with reduced magnitude and frequency of oscillations.

Double Line to Ground Fault
Due to DLG fault at BUS_FAULT, the positive sequence voltage at BUS_PCC, which had sagged to 0.4 pu when STATCOM was not present (Figure 18), rose to 0.575 pu, 0.586 pu and 0.591 pu when STATCOM controlled by fuzzy, PSO and fuzzy PSO techniques (Figure 19) respectively, was incorporated in the system. The voltage magnitude improved to the maximum extent and the response became comparatively smoother when fuzzy-PSO controlled STATCOM was employed (seen in Figure 20).

Sudden Increment in Load by More Than Thousand Times
Corresponding to a sudden increment in load by more than a thousand times as described in section 7, the voltage at BUS_PCC, which had decreased to 0.69 pu in the absence of STATCOM (Figure 21), increases to 0.89 pu when fuzzy controlled STATCOM was connected, and increased to 0.897 pu, when fuzzy-PSO controlled STATCOM was incorporated (can be seen in Figure 22).

CONCLUSION
The STATCOM controlled by the three soft computing techniques, namely, fuzzy logic, PSO and a combination of both was able to provide voltage compensation at the PCC in all the test cases.It was observed that the PSO controlled STATCOM offered the highest voltage improvement in the first two cases, step change (drop) in wind speed simultaneously accompanied by grid voltage dip and SLG fault. In cases of LL fault, DLG fault and sudden rise in load, the STATCOM controlled by fuzzy-PSO technique provided the maximum voltage compensation. Additionally, in all the test cases, it was noted that the voltage response at the PCC provided by the STATCOM controlled by fuzzy-PSO technique was relatively smoother, with few oscillations.Thus, under such circumstances, with the help of the STATCOM, voltage instability due to severe voltage sags is prevented, hence the need for disconnecting the wind turbines due to voltage drops does not arise, and therefore, grid codes (related to low voltage ride-through) are satisfied.In future, the latest variants of PSO and recent hydrid artificial intelligence based techniques may be used to control the STATCOM which provides voltage compensation.