Impact of wind power generating system integration on frequency stabilization in multi-area power system with fuzzy logic controller in deregulated environment

Abstract

Among the available options for renewable energy integration in existing power system, wind power is being considered as one of the suited options for future electrical power generation. The major constraint of wind power generating system (WPGS) is that it does not provide inertial support because of power electronic converters between the grid and the WPGS to facilitate frequency stabilization. The proposed control strategy suggests a substantial contribution to system inertia in terms of short-term active power support in a two area restructured power system. The control scheme uses fuzzy logic based design and takes frequency deviation as input to provide quick active power support, which balances the drop in frequency and tie-line power during transient conditions. This paper presents a comprehensive study of the wind power impact with increasing wind power penetration on frequency stabilization in restructured power system scenario. Variation of load conditions are also analyzed in simulation studies for the same power system model with the proposed control scheme. Simulation results advocates the justification of control scheme over other schemes.

Graphical abstract

Keywords

two area power system / automatic generation control / wind power generating system (WPGS) / deregulated environment / fuzzy logic controller (FLC)

1 Introduction

Reduction of fossil fuel-based energy has been among the top priority goals of regulatory agencies around the world. Therefore, there is an urgent need to exploit more sources of renewable energy. Particularly, wind energy is one of the most promising options among renewable sources of energy. For areas with abundance wind power potentials, wind energy is gradually replacing the capacity of the conventional fossil fuel generating units. Wind power generation is highly important and challenging compared to conventional sources of energy since the availability of wind energy source is unpredictable and uncontrollable. Therefore, an efficient integration of large amounts of wind turbines into the existing electrical networks can significantly impact grid stability. It has been noticed that without a suitable control strategy, full integration of wind energy with high penetration would not be possible, particularly in ancillary services such as frequency regulation.

This paper attempts to study and examine the role of wind power generating system (WPGS) for wind power generation in frequency and tie-line power oscillation control with different levels of wind penetration into the system. The fuzzy logic based WPGS control system is developed for the two-area restructured interconnected system. It has been observed that little emphasis has been put to the concept of inertial support by WPGS in order to minimize inter area oscillations in the restructured power system. The concept of releasing the kinetic energy of a WPGS when the frequency of the power system is reduced in order to prevent the reduction of system inertia is presented [1]. The experimental results of a doubly fed induction generator (DFIG)-based wind turbine using converters [2], modeling of variable-speed wind turbine concepts in power system dynamic simulations [3], and impact assessment of high penetration of wind energy to the Irish network [4] are also available in literature. Frequency regulation and inertial support is also discussed in Refs. [5,6]. The proposed work adopts a systematic approach to address this issue of frequency and tie-line oscillations in the modern power system. The steps listed below are followed:

1) Development of mathematical model of two area system in deregulated environment.

2) WPGS modeling with inertial support feature.

3) Intelligent control strategies for frequency regulation.

4) Simulation and analysis of different cases for varying load and wind power penetration with different sets of conventional generators.

2 System modeling

2.1 Mathematical model of two-area power system in deregulated environment

The system examined consists of two control areas, each having two generation companies (GENCOs) and two distribution companies (DISCOs). In this paper, reheat thermal and hydro-based generating units are considered as the conventional generating units. In the first and second case, the control Area 1 is composed of two reheat thermal GENCOs of equal capacity and control Area 2 is composed of two hydro GENCOs of equal capacity, as shown in Fig. 1. In the third case, different combinations of various GENCOs with WPGS are taken into consideration.

The model is considered in continuous operation. System parameters used for study are given in Table 1. In restructured environment, the concept of contract participation factor matrix (CPFM) makes the visualization of contracts. In CPFM, the number of rows indicates the number of GENCOs and the number of columns indicates the DISCOs [7] and sum of all cpfs is unity in a column of matrix.

The frequency regulation depends on the control signal composed of tie-line deviation and weighted frequency deviation. It is called area control error (ACE), as shown in Eq. (1).

(1){\mathrm{ACE}}_i=\Delta P_{\mathrm{tie},i}+{\mathit{\beta }}_i\Delta f_i,

where {\mathit{\beta }}_i is the frequency bias constant, \Delta f_i is the frequency deviation, and \Delta P_{\mathrm{tie},i} is the change in tie-line power for the ith area [8].

In deregulated environment, within a control area, ACE is again distributed among several GENCOs by coefficients termed as ACE participation factors (apfs). The area participation factor matrix (APFM) is illustrated in Eq. (2). Within a control area, the addition of all apfs is equal to 1.

(2)\mathrm{APFM}=\left[\begin{array}{llll}{\mathrm{apf}}_{\mathrm{1}}\hfill & \mathrm{0}\hfill & \mathrm{0}\hfill & \mathrm{0}\hfill \\ \mathrm{0}\hfill & {\mathrm{apf}}_{\mathrm{2}}\hfill & \mathrm{0}\hfill & \mathrm{0}\hfill \\ \mathrm{0}\hfill & \mathrm{0}\hfill & {\mathrm{apf}}_{\mathrm{3}}\hfill & \mathrm{0}\hfill \\ \mathrm{0}\hfill & \mathrm{0}\hfill & \mathrm{0}\hfill & {\mathrm{apf}}_{\mathrm{4}}\hfill \end{array}\right].

The contracted scheduled loads in DISCOs in Area 1 are \Delta P_{\mathrm{Ld}\mathrm{1}\mathrm{}\_\mathrm{cont}} and \Delta P_{\mathrm{Ld2}\_\mathrm{cont}}but in Area 2 they are \Delta P_{\mathrm{Ld}\mathrm{3}\mathrm{}\_\mathrm{cont}} and \Delta P_{\mathrm{Ld}\mathrm{4}\mathrm{}\_\mathrm{cont}}, as shown in the \Delta P_{\mathrm{Ld}\_\mathrm{cont}} matrix. The uncontracted local loads in DISCOs in Area 1 are \Delta P_{\mathrm{Ld}\mathrm{1}\mathrm{}\_\mathrm{uncont}} and \Delta P_{\mathrm{Ld}\mathrm{2}\mathrm{}\_\mathrm{uncont}} but in Area 2 they are \Delta P_{\mathrm{Ld3}\_\mathrm{uncont}} and \Delta P_{\mathrm{Ld}\mathrm{4}\mathrm{}\_\mathrm{uncont}}, as shown in the \Delta P_{\mathrm{Ld}\_\mathrm{uncont}} matrix [9].

\Delta P_{\mathrm{LD}\_\mathrm{cont}}=\left[\begin{array}{l}\Delta P_{\mathrm{Ld}\mathrm{1}\mathrm{}\_\mathrm{}\mathrm{cont}}\hfill \\ \Delta P_{\mathrm{Ld}\mathrm{2}\mathrm{}\_\mathrm{cont}}\hfill \\ \Delta P_{\mathrm{Ld}\mathrm{3}\mathrm{}\_\mathrm{cont}}\hfill \\ \Delta P_{\mathrm{Ld}\mathrm{4}\mathrm{}\_\mathrm{cont}}\hfill \end{array}\right],

\Delta P_{\mathrm{LD}\_\mathrm{uncont}}=\left[\begin{array}{l}\Delta P_{\mathrm{Ld}\mathrm{1}\mathrm{}\_\mathrm{uncont}}\hfill \\ \Delta P_{\mathrm{Ld}\mathrm{2}\mathrm{}\_\mathrm{uncont}}\hfill \\ \Delta P_{\mathrm{Ld}\mathrm{3}\mathrm{}\_\mathrm{uncont}}\hfill \\ \Delta P_{\mathrm{Ld}\mathrm{4}\mathrm{}\_\mathrm{uncont}}\hfill \end{array}\right].

The total demanded load power \Delta P_{\mathrm{LD}} is represented by Eq. (3):

(3)\Delta P_{\mathrm{LD}}=\Delta P_{\mathrm{LD}\_\mathrm{cont}}+\Delta P_{\mathrm{LD}\_\mathrm{uncont}}.

Similarly, the contracted generated powers in Area 1 are , but in Area 2 they are , as given in the \Delta P_{\mathrm{G}\_\mathrm{cont}} matrix. are uncontracted generated powers from Area 1, but are uncontracted generated powers from Area 2, as given in the \Delta P_{\mathrm{G}\_\mathrm{cont}} matrix.

\Delta P_{\mathrm{G}\_\mathrm{cont}}=\left[\begin{array}{l}\Delta P_{\mathrm{g}\mathrm{1}\mathrm{}\_\mathrm{cont}}\hfill \\ \Delta P_{\mathrm{g}\mathrm{2}\mathrm{}\_\mathrm{cont}}\hfill \\ \Delta P_{\mathrm{g}\mathrm{3}\mathrm{}\_\mathrm{cont}}\hfill \\ \Delta P_{\mathrm{g}\mathrm{4}\mathrm{}\_\mathrm{cont}}\hfill \end{array}\right],\Delta P_{\mathrm{G}\_\mathrm{uncont}}=\left[\begin{array}{l}\Delta P_{\mathrm{g}\mathrm{1}\mathrm{}\_\mathrm{uncont}}\hfill \\ \Delta P_{\mathrm{g}\mathrm{2}\mathrm{}\_\mathrm{uncont}}\hfill \\ \Delta P_{\mathrm{g}\mathrm{3}\mathrm{}\_\mathrm{uncont}}\hfill \\ \Delta P_{\mathrm{g}\mathrm{4}\mathrm{}\_\mathrm{uncont}}\hfill \end{array}\right].

Contracted generated power by GENCOs, \Delta P_{\mathrm{G}\_\mathrm{cont}} is calculated by Eq. (4):

(4)\Delta P_{\mathrm{G}\_\mathrm{cont}}=\mathrm{CPFM}\cdot \Delta P_{\mathrm{LD}\_\mathrm{cont}}.

Uncontracted generated power by GENCOs, \Delta P_{\mathrm{G}\_\mathrm{uncont}} is calculated by Eq. (5):

(5)\Delta P_{\mathrm{G}\_\mathrm{uncont}}=\mathrm{APFM}\cdot \Delta P_{\mathrm{LD}\_\mathrm{uncont}}.

Therefore, the total required generation power by each GENCO is visualized in the \Delta P_{\mathrm{G}} matrix, as expressed in Eq. (6):

(6)\Delta P_{\mathrm{G}}=\Delta P_{\mathrm{G}\_\mathrm{cont}}+\Delta P_{\mathrm{G}\_\mathrm{uncont}}.

The scheduled tie-line power flow between Areas i and j can be represented in Eqs. (7) and (8):

(7)\Delta P_{\mathrm{L},\mathrm{A}i\to \mathrm{A}j}={\displaystyle \sum }_{m=\mathrm{1}}^M{\displaystyle \sum }_{n=\mathrm{1}}^N\left({\mathrm{cpf}}_{mn}\times \Delta P_{\mathrm{Ld}\left(n\right)\_\mathrm{cont}}\right)

(8)\Delta P_{\mathrm{tie}ij,\mathrm{sch}}=\Delta P_{\mathrm{L},\mathrm{A}i\to \mathrm{A}j}-\Delta P_{L,\mathrm{A}j\to \mathrm{A}i}.

2.2 Wind turbine model for frequency regulation

In this paper, the model developed is based on a commercial WPGS model [10], and its simplified diagram is demonstrated in Fig. 2. A one-mass model is considered for the mechanical drive of the turbine. The mechanical power developed by the turbine is given in Eq. (9):

(9)P_{\mathrm{M}}={\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\mathit{\rho }\mathrm{\pi }{R}^{\mathrm{2}}{C}_{\mathrm{p}}\left(\lambda ,\mathit{\beta }\right)v^{\mathrm{3}},

where R is the rotor radius, ρis the air density, v is the wind speed, and C_{\mathrm{p}} is the power coefficient of the turbine which depends on the pitch angle β, and the tip-speed ratio \lambda, which is defined by Eq. (10):

(10)\lambda ={\displaystyle \frac{R{\omega }_{\mathrm{e}}}{v}},

where {\omega }_{\mathrm{e}} is the rotor speed of the wind turbine. The power coefficient is a characteristic of the wind turbine, which in this paper, can be approximated by Eq. (11):

(11)C_{\mathrm{p}}\left(\lambda ,\beta \right)={\displaystyle \sum _{i=\mathrm{0}}^{\mathrm{4}}{\displaystyle \sum _{j=\mathrm{0}}^{\mathrm{4}}{\alpha }_{i,j}{\beta }^i{\lambda }^j}}.

Therefore, it can be concluded that to optimize the amount of power captured by the wind turbine, the rotor speed and the pitch angle must be controlled. Thus, a reference speed {\omega }^{*} is generated based on the electric power P_{\mathrm{e}} for maximum power tracking. The reference is generated as following: the speed is kept at 1.2 pu if the electric power is above 75%, but if the power is reduced below 75%, the reference speed is generated using Eq. (12):

(12){\omega }^{*}=-\mathrm{0.67}{P}_{\mathrm{e}}^{\mathrm{2}}+\mathrm{1.42}{P}_{\mathrm{e}}+\mathrm{0.51}.

Then, the generator speed is controlled by a PI controller that has an output of, as given by Eq. (13):

(13)P_{\omega }^{*}=K_{\mathrm{P}}\left({\omega }^{*}-{\omega }_{\mathrm{e}}\right)+K_{\mathrm{I}}{\int }^{}\left({\omega }^{*}-{\omega }_{\mathrm{e}}\right)\mathrm{d}t.

The frequency support to the grid, the so-called inertial control, must be added to the system, as explained in Ref. [11]. Actually this controller adds to the power reference output signal given by Eq. (14):

(14)P_{\mathrm{f}}^{*}=-K_{\mathrm{df}}{\displaystyle \frac{\mathrm{d}\mathrm{\Delta }f}{\mathrm{d}t}}-K_{\mathrm{pf}}\mathrm{\Delta }f,

where K_{\mathrm{df}} and K_{\mathrm{pf}} are constants and chosen as weights to the frequency deviation derivative and frequency deviation respectively. By this inertial control mechanism, there is an extra increment in the system inertia, so it indirectly supports the frequency variation.

Thus, the total active power reference for the wind turbine must be calculates by Eq. (15):

(15)P_{\mathrm{f}\omega }^{*}=P_{\omega }^{*}+P_{\mathrm{f}}^{*}.

3 Control strategies

This paper discusses two different optimized control strategies which are implemented on system under study in order to present the comparative analysis. The first is the integral controller optimized by genetic algorithm (GA) and the second is the optimized fuzzy controlled system. Later, a comparative analysis is done between the two.

3.1 GA optimized controller

In this control strategy, the integral controller selected as a controller is optimized using GA. The controller input is ACE_x, K_ix is inertial gain of controller, and u_x is the output of the controller in control area-x [12,13], as shown in Eq. (16):

(16)u_x=-K_{ix}{\int }^{}\mathrm{A}\mathrm{C}{\mathrm{E}}_x\mathrm{d}t.

GA is an evolutionary algorithm based on natural genetics mechanics, capable of generating optimal solutions [14]. To get optimum results, the integral gain (K_i) is achieved using GA in which the ISE function is used as fitness function, as per Eq. (17):

(17)J_{\mathrm{ISE}}={\displaystyle {\int }_{\mathrm{0}}^T\left(\mathrm{\Delta }\mathrm{A}\mathrm{C}{\mathrm{E}}_{\mathrm{1}}^{\mathrm{2}}+\mathrm{\Delta }\mathrm{A}\mathrm{C}{\mathrm{E}}_{\mathrm{2}}^{\mathrm{2}}\right)\mathrm{d}t,}

where T the is minimum simulation time, when the system is stable. The optimization converges and the values of K_i gain for both controllers obtained are listed in Table 2.

3.2 Fuzzy logic controller (FLC) design

FLC is a successful control technique for uncertain and nonlinear complex systems and widely accepted as an alternative approach for the conventional approach in many engineering applications. In complex and multi-variable power systems, the conventional control strategies may not give satisfactory solutions. FLC modeling consists of three steps of fuzzification, formation of fuzzy control rule base and defuzzification.

This FLC is designed based on multiple input and single output (MISO) type with two inputs and one output. The first input is ACE_i and the other one is derivative from ACE_x ({\mathrm{dACE}}_x/\mathrm{d}t) and u_x is the output control signal, as displayed in Fig. 3. Table 3 presents the view of rules for FLC utilized to the design controller. There are seven triangular membership functions and centroid as defuzzification technique is considered [15].

4 Simulation test cases

Simulations have been conducted in a two area thermal-hydro power system with FLC and integral controller optimized by GA. There are three test cases taken where the first case is with step load disturbance, which is subjected to the thermal-hydro system. The second is with variation of load profile, while the third is to observe the effect of wind penetration on various combinations of conventional plants. Matlab/Simulink is used for the simulation purpose.

4.1 Test Case A: step load

For test cases A and B, all the DISCOs contract power with the GENCOs. Each DISCO demands power from GENCOs as defined by the cpfs in the cpf_matrix and each GENCO participates in automatic generation control as defined by the following apfs: apf₁= 0.5, apf₂= 0.5; apf₃= 0.5, apf₄= 0.5. The contract participation factor matrix (CPFM) is

\mathrm{CPFM}=\left[\begin{array}{llll}\mathrm{0.5}\hfill & \mathrm{0.5}\hfill & \mathrm{0.0}\hfill & \mathrm{0.0}\hfill \\ \mathrm{0.5}\hfill & \mathrm{0.5}\hfill & \mathrm{0.0}\hfill & \mathrm{0.0}\hfill \\ \mathrm{0.0}\hfill & \mathrm{0.0}\hfill & \mathrm{0.5}\hfill & \mathrm{0.5}\hfill \\ \mathrm{0.0}\hfill & \mathrm{0.0}\hfill & \mathrm{0.5}\hfill & \mathrm{0.5}\hfill \end{array}\right],

\mathrm{\Delta }{P}_{\mathrm{LD}\_\mathrm{uncont}}=\left[\begin{array}{l}\mathrm{0.00}\hfill \\ \mathrm{0.00}\hfill \\ \mathrm{0.00}\hfill \\ \mathrm{0.00}\hfill \end{array}\right],\mathrm{\Delta }{P}_{\mathrm{LD}}=\left[\begin{array}{l}\mathrm{0.05}\hfill \\ \mathrm{0.05}\hfill \\ \mathrm{0.05}\hfill \\ \mathrm{0.05}\hfill \end{array}\right].

In simulated test Case A, the demanded load power is within the contract limit. To meet the load demand, the power to be generated is given by

\mathrm{\Delta }{P}_{\mathrm{G}}=\left[\begin{array}{l}\mathrm{0.05}\hfill \\ \mathrm{0.05}\hfill \\ \mathrm{0.05}\hfill \\ \mathrm{0.05}\hfill \end{array}\right].

The peak undershoot and settling time are dynamic parameters to analyze the performance of controllers when it is subjected to step perturbation. Table 4 is a comparison of controllers based on performance parameters with and without frequency support from WPGS. The frequency deviations of both areas and tie-line deviation at step load perturbation as per test Case A are depicted in Fig. 4.

4.2 Test Case B: varing load with different level of penetration

To evaluate the performance of the proposed controller with and without wind power input, variable step load transient responses are obtained. The variable load profile is displayed in Fig. 5. The frequency deviations of both areas and tie-line deviation at variable load as per test Case B are shown in Figs. 6, 7 and 8 for 10%, 15% and 20% wind penetration in Area 1 and Area 2, respectively.

4.3 Test Case C: different combinations of GENCOs

In this paper, four different combinations are taken and each area has two similar generating units. The combinations are thermal-thermal with wind power connected in Area 2 (TT-TTW), thermal-thermal with wind power connected in both areas (TTW-TTW), thermal-hydro with wind power connected in Area 2 (TT-HHW), and thermal-hydro with wind power connected in both areas (TTW-HHW). Further, the impact of wind power penetration in each of the cases is simulated and analyzed. Step disturbance is impressed in all four cases.

4.3.1 Test Case C. 1 (TT-TTW)

In this case, a two area system with thermal-thermal units, wind power is fed in Area 2 only, as per Fig. 9. The simulation results are shown in Fig. 10. It is observed from the deviation in Area 1 that the frequency does not have substantial impact as compared to the deviation in Area 2. Area 2 benefits more from this distributed generation planning than Area 1, due to WPGS frequency support. The tie-line power is zero initially as the load on both areas is balanced, but as wind penetration increases the tie-line starts carrying more and more power.

4.3.2 Test Case C. 2 (TT-HHW)

In this case of thermal-hydro system, the WPGS is integrated in Area 2 only, as per Fig. 11. The effect is quite visible of increasing wind power in Area 2. The fast and smoother stabilization of frequency deviation in both areas as well as tie-line power are visible in the results shown in Fig. 12, perhaps due to the fuzzy controller used in the system.

4.3.3 Test Case C. 3 (TTW-TTW)

In this case, both areas consist of similar units of the same ratings, as per Fig. 13 and loading is also the same. The tie-line does not carry any power as there is no deviation. Since wind energy is fed into both areas, the frequency deviation is substantially supported and helps to improve better power quality. The results are shown in Fig. 14.

4.3.4 Test Case C. 4 (TTW-HHW)

In this case, wind power is penetrated into both areas with equal penetration, as exhibited in Fig. 15. The result is shown in Fig. 16. Not only do the frequency deviations in Area 1 and Area 2 get better profile with more penetration but tie-line power flow is smooth and fast. With wind power, system frequencies keep oscillating for quite a long time which is always undesirable for grid stability.

5 Results and discussion

Frequency deviations of both areas and tie-line deviation at step load perturbation as per test Case A are shown in Fig.4. The results obtained justify the stability and effectiveness of the proposed controller. The comparison of dynamic performances of the proposed FLC with wind support shows better results than GAI with wind support. Different levels of wind penetration are applied for simulation and assumed wind speed is constant. As per simulation results, major dynamic performance parameters i.e. peak undershoot and settling time are better with fuzzy controller as compared to GA optimized integral controller.

The varying load scenario is a practical situation therefore, in test Case B, frequency deviations of both areas and tie-line deviation are obtained for varying load at different wind penetrations. The results again prove the robustness of the proposed controller. Frequency deviations of both areas and tie-line deviation at variable load as per test Case B are shown in Figs. 6, 7 and 8 for 10%, 15% and 20% wind penetration in Area 1 and Area 2 respectively. So, not only in step disturbance, but also in varying load perturbations, the proposed FLC with wind support shows better results for different levels of wind penetration.

In test Case C, different combinations of GENCOs with WPGS frequency support are examined for different wind penetration. In this test case, frequency deviations of both areas and tie-line deviation are shown in Figs. 10, 12, 14, and 16 for all four different cases. In test Case C. 1, it is observed that active power support is given in Area 2 and it is only getting benefitted in managing its load. This observation justifies the distributed generation strategy to have better local support. In test Case C. 2, where areas are equipped with different types of generating units, oscillations are bound to happen when areas are subjected to load disturbance. In test Case C. 3, where areas are equipped with the same types of generating units with individually connected WPGS, frequency deviations in both areas are again effectively mitigated by WPGS when areas are subjected to load disturbance. In test Case C. 4, frequency deviations in both areas get better suppressed by WPGS with more penetration, and tie-line power flow is also smooth and fast. Fuzzy controller in all cases helps to make the transient situation smoother and faster. This ultimately helps to improve grid discipline and stability. Therefore, it is seen that without wind penetration oscillations persisting for a longer time but as soon as the penetration level is increased, the deviation is less and settlement is faster and smoother.

6 Conclusions

This paper analyzed the participation of WPGS in inertial support for reducing frequency and tie-line power oscillations for different set of combination of varying wind power penetration, varying load, and integration with various combinations of conventional sources. For fast frequency response, the WPGS based wind energy system releases the kinetic energy stored in its rotating masses. Simulation studies for step load and varying load perturbations were conducted in a two-area interconnected power system in deregulated environment which demonstrated the contribution of the wind power in inter-area oscillation suppression in terms of frequency deviations in each area and tie-line power. The proposed control scheme with fuzzy logic used frequency deviations to provide fast active power support, which mitigated the oscillation in frequency and tie-line power during transient conditions. Wind power with increased penetration validated the current focus of global strategies including more and more renewable sources, particularly wind, as it provides short-term active power support by increasing inertia of whole system and helps to manage the instant load demand.

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