Dynamic performance improvement of isolated power system using intelligently controlled SMES

Isolated power system comprising of wind, diesel and energy storage presents an effective economical approach for supplying power. Advanced and intelligent control techniques are required to improve the power dispatch between storage devices and wind-diesel system especially during disturbances. This paper focuses on development of one step ahead adaptively controlled superconducting magnetic energy storage (SMES) for smoothing the power ﬂuctuations of a standalone wind-diesel power system. Two sets of gate turn off (GTO) converters are utilized for obtaining a four quadrant operation of SMES system. System is represented by a third order autoregressive discrete time model. For estimating the system parameters online, recursive least square algorithm is used. System is considered as a two input two output system, where real and reactive powers demanded by SMES are the control signals issued by the controller. To restrict the energy trade within limits, constraints are imposed on the SMES current. Discrete time model of SMES is used for con-verting SMES current constraints into the energy level predictions and a separate model is then used for imposing the constraints. Scheme is tested for two disturbances and in both the cases, SMES current constraints are never violated while reducing the frequency and voltage deviations signiﬁcantly.


INTRODUCTION
Due to the limited availability of fossil fuels, environmental concerns and rapid increase in energy demand, more attention is focused on harnessing the power from non conventional energy sources like wind power [1][2][3]. Wind energy conversion system is one of the most mature renewable energy technology and can be operated both in isolated or grid connected mode. In standalone mode of operation, if integrated with the diesel generator set for supplying power to a remote location reduces the operation cost of the diesel engine [4]. However, due to low inertia any disturbance in wind speed will pose a significant threat to power quality, especially in case of high wind penetration power system. To mitigate the power quality issues, energy storage systems are often used in synchronicity with the wind-diesel system to maintain an instant balance between generation and demand [5]. Integration of energy storage system enhances the robustness of the system,  [3,6,7]. Energy storage devices with fast response time, high ramp rates and high cyclic efficiency are well suited for mitigating the power fluctuations that are generated due to stochastic nature of wind power. In this context, energy storage devices like battery energy storage system, super capacitor energy storage (SCES) and superconducting magnetic energy storage (SMES) are the favourable option [2]. Super capacitors have lower energy density and cell voltage, on the other hand batteries have short service life in terms of number of charge and discharge cycles. The service period of battery is also influenced by the depth of discharge, where as in case of SMES service life period is independent of depth of discharge and thus has large number of cycles of charge and discharge [8]. Power exchange between SMES and power system is very fast as compared to BESS, as energy conversion is not required [1]. Since the 1970's SMES has been used in power system for transient and dynamic stability, enhanced power quality and automatic generation control [9][10][11].
Efficiency of above 90%, even after considering the losses makes it suitable for isolated system operation.
Potency of the SMES unit to handle the uncertainties is determined by the control strategy that has been used to handle both real and reactive power flow in a power system comprising of intermittent power sources like wind [12].
Performance of fixed gain controllers worsens due to nonlinearities and uncertainties occurring in the system. Moreover, they are not capable to handle the constraints which are integral part of any realistic system [13]. Power system being a nonlinear time varying multiple inputs / outputs system has many closed loops. So, for modelling a particular system idealized assumptions and simplifications are considered, as a result the models that is obtained do not adequately capture the physical system. From a control design point of view, a control system is to be designed to maintain satisfactory system performance under various uncertainties. Fixed gain controllers require accurate system modelling, i.e system is based on apriori information and may fail while handling a disturbance /uncertainty of higher magnitude [14,15]. For a fixed gain controller, accurate system modelling is required to reduce the system performance error. So, there exists a direct trade off of performance with uncertainty. Therefore, for a high level of uncertainty fixed gain controller fails to maintain acceptable system performance [6,16]. They do not consider the change in dynamics and structure. On the other hand adaptive controller does not depend on the system modelling excessively and improves itself for any dynamic or adverse condition. Adaptive controller is a fixed structure controller with self tuning feature that adjusts the system parameters automatically while dealing with the parametric uncertainty. It deals with finding algorithms for parameter adjustment which ensure global stability and convergence.
In [17], a multilevel control scheme based on the decoupled current control strategy has been used for SMES unit. Fast controllability of SMES is achieved, improving both dynamic and transient behaviour of the system, though no thoughts were given to limits of SMES unit.
In [18], SMES model based on set membership affine projection algorithm (SMAPA) was proposed. It has been shown that fluctuations in the wind farm's output can be smoothened easily by using an SMAPA based adaptive control SMES unit without enormous effort to fine tune the controller parameters. Nonetheless, there were no restrictions on SMES current.
In [19], an SMES unit based on the robust tube based model predictive control strategy unit has been used for transient stability enhancement where, scheme has been utilized for dealing with uncertainties and disturbances. Control command sent to storage devices dynamically coordinate the SMES active and reactive powers, However, SMES current constraints are totally ignored.
In [20], a non-linear neural adaptive predictive control scheme has been developed for modulating the SMES active power, where limits on SMES current level are not considered. Though limits on SMES converter rating has been considered but the system has been tested for disturbances of smaller magnitudes (1%) only.
Again in [21] adaptively controlled SMES unit has been used for damping tie power oscillations where thyristor based technology has been used which has the flaw of absorbing network's reactive power while interchanging the active power. Moreover, constraints are not included in the controller formulation.
From the literature it is clear that though SMES has been used for solving the power system problems like load frequency control, transient stability enhancement and smoothing fluctuations in wind farms [17][18][19][20][21]. But in all the studies, constraints on the SMES maximum and minimum energy level/SMES coil current have not been accounted for in the problem formulation. However any practical storage system has a certain maximum/ minimum limit to exchange energy. Therefore, all the schemes discussed are just academic studies and may fail to perform satisfactorily when implemented practically.
It is also a well-established fact that adaptive controllers are far more superior compared to the conventional controllers owing to the fact that adaptive controller is capable of updating its parameters whenever a system is subjected to any disturbance.
Thus keeping in view the above facts, a one step ahead adaptive predictive control scheme based SMES unit is proposed for a standalone wind-diesel power system to take care of any uncertainties that are occurring in the system. In such scheme, future behaviour of the state variables are estimated linearly at time t+∆t depending on the system state variables at time 't' and previous dynamical behaviour of the system itself [22]. One step ahead prediction is used with adaptive feature, using an on-line identification technique for parameter estimation [23,24]. The scheme is suitable for a non linear and time varying system and automatically updates itself, in case system is exposed to some uncertainties.
The main contributions of this paper are: (i) Both frequency and voltage fluctuations are reduced significantly by a single controller under step load change of 10% and continuous wind perturbation, (ii) Adaptive predictive controller-based control strategy is an effective technique which specifically takes into account the system constraints explicitly in the controller formulation. Restrictions on SMES energy/current level are considered in this paper, (iii) Control scheme is optimal, which delivers effective control commands to fully utilize the SMES system and hence is economical, (iv) Proposed scheme ensures that system constraints are never violated even in case of uncertainties of higher magnitudes (10%), ensuring safe operation and hence long life of SMES unit, (v) Proposed scheme is capable of handling multiple inputmultiple output system. A two input-two output system is considered in this paper where both voltage and frequency deviations are controlled by a single controller, (vi) Continuous control of SMES is achieved and is demonstrated through results.

System identifier
Wind-diesel-SMES system Multi input multi output Self-tuning regulator In this paper, both frequency and voltage deviations are used as regulated variables by the self tuning regulator, which controls the SMES unit by generating an appropriate control signal without affecting the performance of the controllers that are already in the system like automatic voltage regulator (AVR) and speed governor. To avoid damage to SMES power conversion system (PCS), prediction feature is used for applying limits on energy level of SMES device so that power transfer between SMES unit and wind-diesel system is restricted depending on the constraints. The system identification and computation of control signal is carried out using S-function coding which is appended with a separate model for imposing constraints on SMES energy level. Performance of the adaptive predictive controlled SMES for power quality (simultaneous real and reactive power) enhancement of a stand-alone wind diesel system is examined under two types of disturbances. This paper has been organized as follows. Problem formulation is described in section 2, where controller formulation and control law is presented. In section 3, recursive least square algorithm is presented in detail for parameter estimation. In section 4, modelling about the SMES unit and its control is presented. Section 5 presents the incorporation of constraints on SMES energy. In section 6 simulation results are discussed and finally conclusion is drawn in section 7.

Controller formulation
Purpose of the adaptive controller is to automatically adjust the parameters of the controller on-line, for satisfactory performance, when the system is prone to uncertainties. General structure of the self tuning regulator for the online estimation of the system parameters is shown in Figure 1. Plant is identified by a model of a pre-assigned model order. Parameters of the model are computed by identifier at each sam-pling instant, which are used by regulator for generating the control signal. Since the system considered is a third order model system and thus can be described by an autoregressive discrete time model as expressed as [15,25].
Since the system under study is a two input two output system, equation (1) can be written as follows: Where Y(k) is an output vector representing the deviation variables, U(k) is a control vector at kth sampling instant, n is the model order. A 1 , A 2 , B 1 and B 2 are the model parameter matrices which are to be identified on line and are shown in matrix form as.

Control objective
Primary objective of the control is to minimize frequency and voltage deviations. For regulator setup to take care of disturbances occurring in the system, a cost function is defined as follows.
where q 1 , q 2 and r 1 , r 2 are the elements of the weighting output matrix [Q] and weighting control signal matrix [R] respectively. Values of r 1 and r 2 are selected by analysing their effect on performance of the system. System performance is measured in terms of the performance index which is based on the summation of integral square of frequency deviation and voltage deviations at generator buses and load bus. Performance index is expressed as follows.
In this paper [Q] is taken as a unit matrix which makes the calculation easier. Matrix [R] which results in minimization of integral square error as per Equation (4) comes out to be a diagonal matrix with elements r 1 = 0.7 and r 2 = 2.7. W 1 , W 2, W 3 and W 4 are the weights corresponding to the various variables as shown in (4). For formulation of optimal control law, expression for Y(k+1) is required which is obtained by writing Equation (2) for the (k+1)th sampling instant in terms of y 1 and y 2 as.ŷ Minimizing Equation (3) with respect to U(k) will give the optimal control law, so setting both Expanding Equations (7) and (8) by substituting y 1 (k+1) and y 2 (k+1) and rearranging the terms leads to a compact form of matrix equation expressed as: Equation (9) in a general form can be written as Equation (10) which is the control law for achieving an optimal control [23].
TITO Plant

Multiple input multiple output against multiple input single output identification
For an n-step ahead identification, multi input multi output approach is preferred as shown in Figure 2(a), but for traditional one step ahead identification, multiple MISO (multi input single output) identification approach is preferred. In view of this, a two MISO approach is used. Therefore, TITO system shown in Figure 2(a) is split in to two MISO system as shown in Figure 2(b) [26].
By setting the parameter matrix B 1 equal to unity matrix for saving identification time, (2) can be written in a component form as Equations (11) and (12).
Above equations in the compact form can be written as: Generally recursive least square algorithm is used for estimating the model parameters (θ i ) based on the input and output data [27]. Application of RLS to our two MISO system will result in following equations: Since the considered case is a two-two input single output system so writing the above equation as: By substituting Equation (15) in Equations (16) and (17), (18) and (19) are obtained respectively, which gives the estimated values of the system parameters.
where Z 1 (k) and Z 2 (k) are derived from actual measurements as shown in Figure 2(c). At each sampling instant, based on the previous estimated parameters and new measurements, system outputẐ (k) is predicted. Prediction error is calculate by comparing the predicted and measured values of Z(k) which along with the complete history of measurements is stored in error covariance matrix G(k−1). Weighted sum of last identified parameter that iŝ(k − 1) and error, are used to calculate modified set of system parameters. Information of the new measurements is stored in error covariance matrix G(k) for further use. Optimal control vector is computed based on the latest parameter estimate. The complete scheme of self tuning regulator is carried out in the following three steps at each sampling instant.

Modelling of SMES unit
SMES unit is installed at load bus (bus 4) of the wind-diesel system, two synchronous generators with AVR and governor are installed at bus 1 and 2. Equivalent induction machine for harnessing wind power is at bus 3 as shown in Figure 3. SMES is modelled as a controllable current source that can inject/absorb both real and reactive power with the system. By using two sets of GTO based converters, four quadrant operation of SMES capable of exchanging both real and reactive power with the wind-diesel system is developed as shown in Figure 4(a). Firing angles α 1 and α 2 for the two sets of converters are calculated as per equations [28,29].   Figure 4(b) are determined as: Area I use Equations (20) and (23) with lower side complex sign. Area II use Equations (20) and (22) with upper side complex sign. Area III use Equations (20) and (23) with upper side complex sign. Area IV use Equations (21) and (23) with upper side complex sign. Figure 4(c) depicts modelling of the SMES unit. Energy constraint strategy block is explained in Section 5. Firing angle are calculated as per equation (20)(21)(22)(23) and based on the firing angles, real and reactive power transfer between the system considered and SMES is given by the following set of equations.
Negative sign in Equations (26) and (27) represents that active and reactive powers are being injected by SMES unit into the system. To integrate the SMES unit model with the network model of the wind-diesel system, active and reactive powers injected by the SMES are to be translated into direct and quadrature current components in synchronously rotating reference frame using Equation (28).
I DSMES and I QSMES are the direct and quadrature current components in synchronously rotating reference frame. V D and V Q are the direct and quadrature axis voltage components in synchronously rotating reference frame at load bus.

Application of the developed control scheme on SMES unit
The control law and identification algorithm derived in Sections 2.2 and 3.1 respectively are implemented in this section. Since the SMES unit considered is a two input two output system, the implementation of the proposed scheme is depicted in Figure 4(d) where y 1 and y 2 are the regulated variables as defined in Equations (29) and (30) and u 1 and u 2 are the active power (P d ) and reactive power (Q d ) commands issued by the regulator to SMES unit.
where y 1 is a function of change in SMES current and frequency deviation and y 2 is the voltage deviation at the load bus terminal of wind-diesel system.
where f o is the rated frequency of the system. In order to ensure continuous control, second term in Equation (29) is included so that the SMES current can return to its nominal value after handling a disturbance. In the steady state both frequency and SMES current deviations are equal to zero. Value of k c should be selected carefully, if value of k c is large, it will reduce the effectiveness of SMES in reducing the frequency deviations on the other hand very small value of k c will not bring the SMES coil current back to its initial value.

Description of various blocks involved in simulation algorithm
For implementing the control law derived in Equation (9) for a wind-diesel-SMES system, model parameters matrices A 1 , A 2 , B 1 and B 2 should be known, a priori. Values of model parameters are not known in advances and moreover, they vary with the operating conditions. So, parameter identification technique is used at each sampling instant, for estimating these matrices online. Identifier block represents the RLS algorithm which is used for estimating the system parameters has been discussed in Section 3.1.  regulator block to generate the optimal power commands for the SMES unit. Regulator block generates the optimal control signals as per the Equations (1) to (9) derived in Section 2. Details pertaining to SMES modelling have been given in Section 4 and wind-diesel system under study is taken from [30].

CONSTRAINTS ON SMES ENERGY LEVEL
Power command which is the control variable for an SMES device should never exceed the rating of converter. To keep the energy exchange between SMES unit and wind-diesel system within prescribed limits determined by the power conversion system, constraints are imposed on the energy transfer.
For continuous control, limit should be imposed on minimum stored energy level of SMES [31]. The SMES current/energy should always remain well within the upper/lower values, for obtaining profitable operation and continuous control. In this article, limits for the SMES coil current are chosen as 410 and 300 A, respectively, this corresponds to a maximum (E SMESmax ) and minimum (E SMESmin ) stored energy of 22.189 and 11.88 kJ respectively. Current constraints of SMES coil are converted into energy level constraints and energy level predictions are achieved using the discrete-time model as shown in Figure 5, where T is the SMES unit time constant, ZOH is the zero order hold, E 0 SMES and E SMES are the steady state and actual energy levels of the SMES unit respectively. The constraints on energy/current are imposed online as discussed below.
It is well established in literature that SMES reference and actual active power are related through a first order transfer function [11,32]. In Figure 5, presence of ZOH is obvious because we are implementing the discrete time (computer) control. Beauty with the discrete time system shown in Figure 5 is that energy level remains always within the constraints provided we ensure it does not violate the constraints at the sampling instants. For this purpose we have developed the following procedure.
Energy stored by SMES at (k+1) sampling instant can be related to power command at kth sampling instant using the following discrete time system [32]. pulse transfer function of Figure 5 is written as: In Equation Equation (31) Power command at kth sampling instant should be applied in such a manner that minimum and maximum limits of energy are not exceeded and are given by Equations (34) and (35).

SIMULATION STUDIES
Initially the system under study is assumed to be in steady state. Wind-diesel power system is first subjected to load disturbance and then continuous wind perturbation separately. Because of these disturbances, system frequency and voltage will obviously deviate from their steady state values. The incorporation of proposed adaptively controlled SMES unit will enhance the power quality of the system. Centre of inertia concept is utilized for estimating the system frequency.
The variation of load with respect to time is given by Equation (36). At time t = 0 s both real and reactive load on the system is decreased by 10%, at time t = 10 s load is raised to its rated value and finally at time t = 20 s the load is again decreased by 10%.
Different reduced bus admittance matrices will be obtained according to Equation 36. Load disturbance in the system is shown in Table 1.
In the second scenario, the system is exposed to a wind disturbance of the form shown in Figure 7 where wind speed variation is represented by variation in turbine mechanical torque in p.u.

Discussion on results for load disturbance
Simulation results of the system for a load disturbance of type described in Table 1  (i) Frequency deviation plots of the proposed system is shown in Figure 8 and voltage deviation plots are shown in Figure 9 (a-c). Figure 8 demonstrate an improved frequency response of the system by incorporation of adaptive predictive controller (APC) based SMES device. Considerable reduction in peak frequency deviations is observed from the figure. During the first interval from tine 0 ≤ t < 10 s load is reduced and frequency deviation is positive, Peak frequency deviation is reduced by 28 Table 2. (ii) Voltage deviation plots are shown in Figure 9(a-c). Voltage deviation at synchronous generator bus, induction generator bus and load bus are shown in Figures 9(a), 9(b) and 9(c) respectively. All the figures demonstrate the pragmatic effect of incorporating the SMES device. (iii) Figure 9(a) reveals that synchronous generator voltage returns to its initial steady state value after the disturbance  where as Figure 9(c) shows that the induction generator voltage does not return to its initial steady state values. It is because at synchronous generator bus AVR is installed, where as no AVR is installed at induction generator bus. (iv) Figures 8 and 9 demonstrates that with the proposed scheme not only the peak deviations in frequency and voltage are reduced but oscillatory responses of the system are also damped out quickly.
(v) Figure 10 shows the SMES coil current under load disturbance. During the first interval when load is decreased, SMES is charged and absorbs power from the system which is demonstrated by increase in SMES coil current from its nominal value of 350-410 A. Results show that the SMES device after handling the disturbance returns to its nominal/steady state value and always stays within the restrictions dictated by the constraints. In first interval, SMES current touches its maximum value of 401 A and never exceeds its maximum value ensuring safe and economical operation of device. During the second interval of load disturbance SMES coil discharges and SMES current reduces from its nominal value to 300 amperes. In the third interval SMES coil charges to its maximum value and then returns to its nominal value of 350 A. In all the intervals SMES current returns to its nominal value ensuring continuous control.
However, in case of FPC SMES, current constraints are violated in the first interval representing the unsafe operation of

Discussion on results for wind perturbation
Wind perturbation is the second scenario for which the proposed scheme has been tested on wind-diesel system and a comparison is shown in results between the APC SMES and FPC SMES. The results can be summarized as follows: (i) Figure 11 shows the frequency deviation plot of the system for a continuous wind perturbation of the form shown in Figure 7. Figure demonstrates that with the APC SMES device peak frequency deviation is reduced by 44% against the 36% in case of FPC SMES. (ii) Figure 12(a-c) shows the voltage deviation plots. Voltage deviation at synchronous generator bus, induction generator bus and load bus are shown in Figures 12(a), 12(b) and 12(c) respectively. Figures demonstrates that a significant reduction in voltage deviations are obtained by using the proposed scheme. (iii) SMES coil current is shown in Figure 13. Figure 13 shows that SMES coil current will not returns to its nominal value after handling the disturbance because wind speed is continuously changing. It can be seen from the figure that the SMES coil current is hitting the lower constraint of 300 A at time 3 s and upper constraint of 410 amperes at time 12.8 sec but never exceeds these constraints. This will ensure safe and economical operation of SMES.
However with the FPC SMES, constraints are violated at time 12.8 s, representing unsafe mode of operation of SMES unit. At time equal to 3 s SMES current is not hitting the constraint representing that the SMES unit is underutilized and is thus un economical. All the results discussed above thus demonstrate the phenomenal effect of incorporating the adaptive controller based SMES unit in the wind-diesel power system

CONCLUSION
In this paper, application of one step ahead adaptive control scheme based SMES unit has been presented for mitigating the power quality problems that are caused due to the stochastic nature of wind. A discrete time model of SMES unit has been utilized to generate a suitable power command for the SMES unit. For estimating the system parameters, two-input two-output system is decomposed in to a two two-input singleoutput system. Recursive least square algorithm is utilized for estimating the system parameters and a separate model is then used for imposing constraints on SMES energy/current level. By considering the constraints in the controller formulation, not only a significant reduction in frequency and voltage deviations is witnessed but SMES current/energy limits are always well within limits as dictated by the constraints. The proposed scheme has been tested for disturbances of two different categories viz continuous wind perturbation and step load disturbance of higher magnitude. Under each disturbance, SMES constraints are never violated while keeping the frequency and voltage deviations to minimum. The adaptive controller based SMES unit presented in this paper can be a better choice for other renewable source based power systems.