Rotor angle stability and voltage stability improvement of highly renewable energy penetrated western grid of Bangladesh power system using FACTS device

Abstract

Most of the generations in Bangladesh power system are based on fossil fuels which is 99% of its total generation. Following other countries, Bangladesh is also planning to adopt renewable energy system (RES). It has a plan to incorporate 55 MW wind turbine generator (WT) and 100 MW solar photovoltaic generator (PV) in Western grid of its power system. Though RES is green energy but from stability aspect it needs to be studied as RES has limitations in generating reactive power and maintaining inertia. So, voltage stability and rotor angle stability should be given more attention. However, if any stability problem arises, flexible alternating current transmission system (FACTS) devices can be adopted. With a tuned power oscillation damper, FACTS can reduce the expected rotor angle and voltage stability problem which are associated with RES. This paper examines the stability of the Western grid with the incorporation of hybrid energy of both wind and solar power and shows the positive effect of FACTS devices like thyristor controlled series compensator and static synchronous compensator with respective tuned controller. In present paper, the combination of WT and PV is also examined which shows only incorporation of WT reduces both the steady and dynamic stability more than the only adoption of PV. Inclusion of both WT and PV, reduce the both types of stability more than their individual inclusion. This paper shows that FACTS can improve the stability with individual or both kinds of RES penetration.

Keywords:

• Renewable energy system
• wind turbine generator
• solar photovoltaic generator
• power oscillation damper
• stability
• TCSC
• STATCOM

PUBLIC INTEREST STATEMENT

Bangladesh is running out of fossil fuels day by day or the costs of fuels are ever increasing. Alternative source of energy particularly renewable energy (RE) is the best option to solve the energy issues in future. Bangladesh Power System (BPS) has been planning to insert RE in its power system. To implement primarily it has planned to have 55 MW wind power and 100 MW solar power plant in its western regions. However, RE system has some stability issues, which need to be analyzed from stability perspective. This present work carries out the prospective stability study of BPS when RE will take place of synchronous machines which runs by fossil fuels. Also, the present paper reveals the solution against some stability problems, mainly targeting rotor angle and voltage of the system. So, this paper will enable BPS to foresee the power system stability with RE and can take some measurements if any stability problem arises.

1. Introduction

In last two decades, RES has received a lot of attentions. Overall power generation capacity from RES is 27.3% of worldwide power production. In 2020, yearly global capacity from hydropower is 1170 GW, wind is 778 GW and PV is 760 GW. More than 256 GW of RES was introduced in 2020, most of which from PV by 139 GW. Wind power contributes 93 GW and 20 GW from hydropower. Total of 2839 GW energy is consumed from RES by 2020. More than 34 countries has RES, which is just over 10 GW. Searching for PV and WT is gaining much focus, at least 19 countries have 10 GW of non-hydro RES in 2020. European Union has shown faster growth in using RES, they have 38% RES of overall power generation. Denmark has reached 63%, Uruguay has 43%, United Kingdom has 42%, Ireland has 38% and Germany has 33% RES of its total generation (The Renewables, 2021). In contrast, Bangladesh is still fully dependent on its fossil fuel to generate electricity. It depends 51.97% on gas, 27.25% on HFO, 8.03% on coal, 5.86% on HSD whereas, only 0.59% in PV and .01% in WT (Bangladesh Power Development Board (BPDB)). Sustainable development based on RES is discussed in (Mark Amoah Nyasapoh et al., 2022) and sequestration on climate control is stated in (Bajaj & Thakur, 2022).The role of renewable energy is well analyzed on the country Ghana for a long term development (Al-Shetwi, 2022). Using eight pathways, fully dependency on RES is briefly explained in (JeHolechek et al., 2022) though there are challenges in achieving 100% RES for any power systems (Denholm et al., 2021). Current trends and future prospect of RES in Bangladesh is highlighted in where it shows that by 2035 RES will be leading and by 2050 it will take over everything (2020a). As a part of the future planning, BPS has taken initiative to incorporate RES in its power system. It has a Western grid, where it is going to penetrate WT and PV in two different locations called Bagerhat of Khulna and Sirajganj, respectively. For, Western grid, the penetration level will be at a large scale. Presently, Khulna has HFO-based power plants, which supplies 105 MW of power and Baghabari near Sirajganj area has 125 MW gas based power generation. As both of them are fossil fuel based, it is expected that they will be phased out in near future if RES penetration is implemented.

RES is very popular as it has immense positive aspects for global climates. But penetration of RES to any power system, changes the overall response of stability. It reduces inertia of the system and has limitations in generating reactive power unlike SM. Moreover, these limitations set the constraints in admissible penetration level of RES. In [Edrah et al., 2015-Thapa & Sanjeev Maharjan, 2019], stability problem regarding high level of WT penetration is stated. Negative effect of WT penetration in steady and dynamic state is presented in (Aziz, Dahal, et al., 2010). Small signal stability is analyzed in (Xia et al., 2018), where detrimental effect due to WT is revealed. PV penetration is mechanically untied to any power system. At unity power factor they don’t provide any reactive power to the system. Unlike WT, PV don’t have any inertia also. In [Eftekharnejad, Vittal, Heydt, et al., 2013-Munkhchuluun et al., 2017], voltage and rotor angle stability problem associated with PV incorporation to any system is well discussed. As BPS is going to set up 55 MW of WT and 100 MW of PV into its Western grid at large scale (2020b; Institute for Energy Economics and Financial Analysis, PV magazine, Article: Bangladesh turns to China for help with its Solar development plans), the overall BPS needs to be checked from stability perspective. FACTS devices like TCSC and STATCOM can enable power system to integrate RES at large scale (Saberian et al., 2013). TCSC and STATCOM are adopted to increase the voltage and rotor angle stability of Bangladesh power system is stated in [Barua & Quamruzzaman, 2018b-Barua et al., 2021b]. FACTS plays a vital role in reducing the stability problem oriented with RES when penetrated into any power system. Using TCSC and STATCOM, voltage stability improvement is shown in WT penetrated power system (Honghai et al., 2019). In [Remon et al., 2017-Suresh Kumar et al., 2020], adoption of STATCOM improves the rotor angle stability and voltage stability problem which inherently lies in PV penetration in power system. As TCSC and STATCOM show positive effect in WT and PV separately, so they are expected to exhibit stability enhancing response in combined penetration of WT and PV. Incorporation of FACTS devices may affect the overall dynamic stability of the power system if they are not coordinated. POD with FACTS increases the dynamic-state stability. In [Barua & Quamruzzaman, 2018a-Barua et al., 2021b, Noroozian et al., 2001-Aboul Ela et al., 1996], authors used local or global signal input based POD design with TCSC and STATCOM to increase the dynamic stability of the power system.

To incorporate WT, doubly fed induction generator (DFIG) model is preferred in present work. Both the rotor and stator are connected to grid, so it is called doubly fed system. In (Thomas, 2012), several types of induction generators as discussed beside wound rotor type DFIG. It is capable to work under variable speed, low ratings of electronic devices which is related to slip power and in weak grid it can be manipulated to exchange reactive power. On the other hand, PV is mechanically decoupled source of real power and can hardly generate reactive power within limitations of converter associated with it (Eftekharnejad, Vittal, Thomas Heydt, et al., 2013). It can be P-V type or P-Q type (Tamimi et al., 2013). Our present work treats PV as a source of real power only. Incorporation of both WT and PV assess stability limit differently [Aziz, Sudarshan Dahal, et al., 2010-Tanbhir Hoq et al., 2018]. Voltage stability and rotor angle stability are main focus of this paper. Power system stability means maintaining equilibrium state at normal working condition and achieving acceptable operating point after being lead to any perturbance. Penetration of WT and PV cause reduction of inertia and reactive power from the system as they replace traditional generators, which in return causes potential problem in synchronizing torque and damping torque. Reduction of inertia cause speed deviation much faster when subjected to disturbances and don’t allow much time to stabilizing equipment to adjust themselves to bring back to a new equilibrium position. Lacking of reactive power cause voltage instability in the event of system upsetting. It also reduces synchronizing torque in the system (Prabha, 1994). Stability of any system is determined in three states, they are: steady state, dynamic state and transient state. In [Barua & Quamruzzaman, 2018b-Barua et al., 2021b], authors carried out the stability studies of BPS in all there states. Authors adopted continuation power flow (CPF) technique (Venkataramana et al., 0000), Eigenvalue analysis technique (Prabha, 1994) and time domain analysis to perform their work. Previously no research work was carried out in term of stability having high penetration of RES and adopting FACTS devices to solve the unfavorable issues for BPS. However (Barua et al., 2021a), describes the effect of PV adoption in BPS but no solution is proposed against limitations. Present paper decodes the effect of RES and provides solution in term of FACTS devices. The contributions of the present paper are as follows:

1. Determination of steady-state stability limit of BPS with 55 MW WT penetration at Bagerhat grid of Khulna zone, 100 MW PV penetration at Sirajganj grid separately and jointly.

2. Enhancing the stability limit using TCSC and STATCOM to provide 70% series compensation and 2 p.u shunt compensation respectively.

3. Dynamic modelling of WT and PV to penetrate them into BPS and determination of dynamic stability limit of it.

4. Designing tuned controller for TCSC and STATCOM, to increase the rotor angle stability and voltage stability of the RES penetrated system.

5. Transient stability analysis of the RES penetrated BPS to show the advantageous impact of TCSC and STATCOM.

This paper is organized as: sSection 1 briefly describes the analysis techniques adopted to carry out stability studies. Then, sSection 2 consists of modelling of BPS system and RES. Next sSection 3 depicts the construction of TCSC and STATCOM with its damping controller. Methodology of the present work is provided in sSection 4. Section 5 shows the result and discussion on it. Finally, sSection 6 outlines the overall work.

2. Overview of analysis technique

To determine the steady-state stability limit, Continuation power flow (CPF) technique is adopted. With the CPF technique, critical loading point is diagnosed. Modal analysis technique using Eigenvalue is chosen to carry out the dynamic analysis and to design a damping controller. Time domain analysis reveals the transient stability of the system.

2.1. Continuation power flow analysis

Power system characteristics are highly non-linear. To linearize the equations of power system, Jacobian matrix defines the relation between voltage, angle and reactive power, real power. Conventional power flow analysis is unable to reach the solution point if the determinant of the Jacobian matrix becomes 0. The point at which this phenomenon occurs, can be noted as Saddle node bifurcation (SNB) point and it is well known as critical point. Jacobian Matrix of Newton Raphson power flow becomes singular at this point and the power flow solution near this critical point shows divergence. CPF is a technique which remains well conditioned even at SNB point (Venkataramana et al., 0000). The technique adopts predictor and corrector steps. Its principle is to use locally parameterized continuation technique. From an initial operating point it starts and increased the loads gradually to its maximum point. Active power margin parameter is used to realize the distance from instability point. Either P-V curve or Q-V curve can be taken to check the instability phenomenon. This paper has chosen P-V curve to determine the steady-state stability limit. To get the conception let us consider ith bus among n-number of bus system, now the real and reactive power equation of the ith bus are:

(1) ${\mathrm{P}}_{\mathrm{i}}=\mathrm{\Sigma }\left|{\mathrm{V}}_{\mathrm{i}}\right|\left|{\mathrm{V}}_{\mathrm{k}}\right|({\mathrm{G}}_{\mathrm{ik}}\mathrm{Cos}{\theta }_{\mathrm{ik}}+{\mathrm{B}}_{\mathrm{ik}}\mathrm{Sin}{\theta }_{\mathrm{ik}})$(1)

(2) ${\mathrm{Q}}_{\mathrm{i}}=\mathrm{\Sigma }\left|{\mathrm{V}}_{\mathrm{i}}\right|\left|{\mathrm{V}}_{\mathrm{k}}\right|({\mathrm{G}}_{\mathrm{ik}}\mathrm{Sin}{\theta }_{\mathrm{ik}}-{\mathrm{B}}_{\mathrm{ik}}\mathrm{Cos}{\theta }_{\mathrm{ik}})$(2)

P_i=P_Gi – P_Di; Q_i= Q_{Gi -} Q_Di; Where, G= generation; D= Demand

To represent load changes, a loading parameter λ is injected into demand power P_Di and Q_Di

$\${\mathrm{P}}_{\mathrm{Di}}={\mathrm{P}}_{\mathrm{Dio}}+\mathit{\lambda }\left(\mathrm{P}{\mathrm{\Delta }}_{\mathrm{base}}\right)(3)$

(4) ${\mathrm{Q}}_{\mathrm{Di}}={\mathrm{Q}}_{\mathrm{Dio}}+\mathit{\lambda }(\mathrm{Q}{\mathrm{\Delta }}_{\mathrm{base}}),$(4)

where, P_Dio and Q_Dio are the primary load demands on ith bus whereas, PΔ_base and QΔ_base are chosen to scale λ properly. After Substituting (3),(4) to Equation 1(1) ${\mathrm{P}}_{\mathrm{i}}=\mathrm{\Sigma }\left|{\mathrm{V}}_{\mathrm{i}}\right|\left|{\mathrm{V}}_{\mathrm{k}}\right|({\mathrm{G}}_{\mathrm{ik}}\mathrm{Cos}{\theta }_{\mathrm{ik}}+{\mathrm{B}}_{\mathrm{ik}}\mathrm{Sin}{\theta }_{\mathrm{ik}})$(1) ,Equation 2(2) ${\mathrm{Q}}_{\mathrm{i}}=\mathrm{\Sigma }\left|{\mathrm{V}}_{\mathrm{i}}\right|\left|{\mathrm{V}}_{\mathrm{k}}\right|({\mathrm{G}}_{\mathrm{ik}}\mathrm{Sin}{\theta }_{\mathrm{ik}}-{\mathrm{B}}_{\mathrm{ik}}\mathrm{Cos}{\theta }_{\mathrm{ik}})$(2) , new equilibrium state can be achieved.

F (θ, V, λ) = 0 (5)

Now to get the predictor step, derivatives of (5) is taken.

(6) $\left[\begin{array}{ccc}{\mathrm{F}}_{\theta }& {\mathrm{F}}_{\mathrm{v}}& {\mathrm{F}}_{\lambda }\end{array}\right]\left[\begin{array}{c}{\mathrm{d}}_{\theta }\\ {\mathrm{d}}_{\mathrm{v}}\\ {\mathrm{d}}_{\lambda }\end{array}\right]=0$(6)

To get the solution, (6) can be organized as follows,

(7) $\left[\begin{array}{c}{\mathrm{F}}_{\theta }{\mathrm{F}}_{\mathrm{V}}\mathrm{F}\mathit{\lambda }\\ e_k\end{array}\right]\left[\begin{array}{c}{\mathrm{d}}_{\theta }\\ d_v\\ d_{\lambda }\end{array}\right]=\left[\begin{array}{c}0\\ \pm 1\end{array}\right]$(7)

where, e_k is an appropriate row vector, except kth element is 1, which is sparse in nature. λ is taken as the continuation quantity. By analyzing Equation 19(19) ${\mathrm{X}}_{\mathrm{tcr}}\mathit{\hspace{0.17em}}=\mathit{\hspace{0.17em}}{\mathrm{X}}_{\mathrm{c}}[1\mathit{\hspace{0.17em}}-\mathit{\hspace{0.17em}}\frac{\mathrm{K}{\mathrm{x}}^2(\mathit{\sigma }+\sin \mathit{\sigma })}{(\mathrm{K}{\mathrm{x}}^2-1)\mathit{\pi }}\mathit{\hspace{0.17em}}+\mathit{\hspace{0.17em}}\{\frac{4\mathrm{K}{\mathrm{x}}^2\cos 2(\frac{\mathit{\sigma }}{2})}{\mathrm{p}{(\mathrm{K}{\mathrm{x}}^2-1)}^2}\}\mathit{\hspace{0.17em}}({\mathrm{K}}_{\mathrm{x}}\tan ({\mathrm{K}}_{\mathrm{x}}\frac{\mathit{\sigma }}{2})-\tan (\frac{\mathit{\sigma }}{2})],$(19) , tangent vector can be found and prediction is determined as follows.

(8) ${\left[\begin{array}{c}\mathit{\theta }\\ \mathit{V}\\ \mathit{\lambda }\end{array}\right]}^{\mathrm{P}+1}={\left[\begin{array}{c}\mathit{\theta }\\ \mathit{V}\\ \mathit{\lambda }\end{array}\right]}^{\mathrm{P}}+\mathit{\sigma }\left[\begin{array}{c}{\mathrm{d}}_{\theta }\\ d_V\\ d_{\lambda }\end{array}\right]$(8)

where, P + 1= next prediction solution, σ=step size, selection of step size is crucial.

Now, local parameterization technique is adopted for adjusting predicted solution.

(9) $\left[\begin{array}{c}\mathrm{F}(\mathit{\theta },\mathrm{V},\mathit{\lambda })\\ X_{\mathit{k}-\mathit{\eta }}\end{array}\right]=\left[0\right]$(9)

where, X_k is the state variable and η is the preceding predicted value of the state variable. Newton-Raphson method can be applied to resolve the (9). Equation 1(1) ${\mathrm{P}}_{\mathrm{i}}=\mathrm{\Sigma }\left|{\mathrm{V}}_{\mathrm{i}}\right|\left|{\mathrm{V}}_{\mathrm{k}}\right|({\mathrm{G}}_{\mathrm{ik}}\mathrm{Cos}{\theta }_{\mathrm{ik}}+{\mathrm{B}}_{\mathrm{ik}}\mathrm{Sin}{\theta }_{\mathrm{ik}})$(1) to Equation 19(19) ${\mathrm{X}}_{\mathrm{tcr}}\mathit{\hspace{0.17em}}=\mathit{\hspace{0.17em}}{\mathrm{X}}_{\mathrm{c}}[1\mathit{\hspace{0.17em}}-\mathit{\hspace{0.17em}}\frac{\mathrm{K}{\mathrm{x}}^2(\mathit{\sigma }+\sin \mathit{\sigma })}{(\mathrm{K}{\mathrm{x}}^2-1)\mathit{\pi }}\mathit{\hspace{0.17em}}+\mathit{\hspace{0.17em}}\{\frac{4\mathrm{K}{\mathrm{x}}^2\cos 2(\frac{\mathit{\sigma }}{2})}{\mathrm{p}{(\mathrm{K}{\mathrm{x}}^2-1)}^2}\}\mathit{\hspace{0.17em}}({\mathrm{K}}_{\mathrm{x}}\tan ({\mathrm{K}}_{\mathrm{x}}\frac{\mathit{\sigma }}{2})-\tan (\frac{\mathit{\sigma }}{2})],$(19) are stated in (Barua & Quamruzzaman, 2018b).

2.2. Modal analysis

To determine the voltage stability and rotor angle stability, modal analysis technique is very helpful. It uses Eigenvalues and Eigenvectors of Jacobian matrix. Modes of Eigenvalue can be used to check the stability of the system. Jacobian matrix, which is part of Newton–Raphson method can be represented by

(10) $\left[\begin{array}{c}\mathrm{\Delta P}\\ \mathrm{\Delta Q}\end{array}\right]=\left[\begin{array}{cc}{\mathrm{J}}_{\mathrm{P\theta }}& J_{\mathit{PV}}\\ J_{\mathit{Q\theta }}& J_{\mathit{Q\theta }}\end{array}\right]\left[\begin{array}{c}\mathrm{\Delta \theta }\\ \mathrm{\Delta V}\end{array}\right]$(10)

(Barua & Quamruzzaman, 2018b) where, ΔΡ = change in real power. ΔQ = change in reactive power. Δ = change in transmission angle. ΔV = change in voltage bus.

Eigenvalue of the Jacobian matrix can be real or complex. Eigenvalue with the least damping is called the critical Eigenvalues. If the critical Eigenvalues have negative real part then the system is said stable and more negative real value means the system is more stable. If the critical value has zero real value but some complex value, then the system is oscillatory unstable with no damping. The point is called Hopf Bifurcation (HB) point. The complex critical Eigenvalue with positive real value causes the system to be increasingly oscillatory. Critical Eigenvalue which has real roots of opposite sign, is non-oscillatory unstable system. The point is also called Saddle Node Bifurcation (SNB) point. Each Eigenvalue has right Eigenvectors or left Eigenvectors. Using this Eigenvectors, mode and participation of any variable can be achieved (Prabha, 1994).

Let,

[J] = ѰɅØ (11)

(Barua & Quamruzzaman, 2018b) Where, Ѱ= Right Eigenvector matrix of matrix J.

Ʌ= Diagonal Eigenvalue matrix of matrix J.

Ø= Left Eigenvector matrix of matrix J.

3. System Modelling

3.1. BPS modelling

BPS is composed of Dhaka, Southern, Central, Western and Northern regions. Among them first three regions make Eastern grid and most of the generation is supported by Dhaka region. Northern and Western region form the Western grid. Its generation is always less than its average demand. So it had to depend on Eastern grid. Western grid which is connected to system via two East-West interconnectors. First interconnector is Ghorasal to Ishurdi and second one from Ashuganj to Sirajganj. First interconnector was launched in the year 1982 and second interconnector was installed in 2009. Both the interconnectors were erected across the Jamuna River. Thermal capacity of first interconnector is 315 MVA and second interconnector is 630 MVA. Figure 1 shows the Western grid of BPS [Barua & Quamruzzaman, 2018b-Barua et al., 2021b, Shafiul Alam1 et al., 2015]. It has six generating stations available which are based on fossil fuels. Near Bagerhat, Khulna grid has 165 MVA HFO based power generating plants and Baghabari grid has 195 MVA gas-based power generating plants. Transient model of the synchronous generators are available in NEPLAN (40). To insert the excitation system, IEEE type-1 D.C exciter is used (2006). Turbine and governor used in BPS system is depicted in Figure 2. It is a simple steam turbine where “r” represents speed droop. The signal is then passed through governor, servo and re-heater blocks. Transmission lines are modelled using nominal-Pi model. Overall BPS don’t use any FACTS devices but it has static capacitors in various grids. Loads are considered to be P-Q type. WT has been planned to install in Khulna grid and PV will be installed in Sirajganj grid.

Figure 1. Western grid of BPS.

Figure 2. Turbine and Governor Model.

3.2. DFIG modelling

Mechanical output from wind turbine can be expressed as

(12) ${\mathbf{P}}_{\mathbf{m}}={\mathbf{C}}_{\mathbf{p}}(\mathit{\lambda },\mathit{\beta }).\frac{1}{2}.\mathit{\rho }.\mathbf{A}.{\mathbf{v}}^3\mathbf{,}$(12)

(Thomas, 2012) where, ${\mathrm{P}}_{\mathrm{m}}$is the mechanical output power which relies on air density ($\mathit{\rho }$), wind velocity ($\mathrm{v}$), and blade parameters.

${\mathrm{C}}_{\mathrm{p}}$ has the non-linear relationship between ($\mathit{\lambda },\mathit{\beta }$. Squirrel Cage Induction Generator (SCIG) and DFIG are the popular WT model. DFIG is chosen over SCIG because it can work in sub synchronous and super synchronous speed, separate real and reactive power controllability from rotor side and lower converter ratings (Thomas, 2012).

This paper will use DFIG as WT model as shown in Figure 3(a), where rotor side converter (RSC) and grid side converter (GSC) are used. Stator and rotor flux dynamics of DFIG are faster than the system grid dynamics. Converter at rotor side can also disengage the DFIG from the grid. So, depending on these conditions following can be taken (Vittal et al., 2012),

Figure 3. (a) DFIG based WT; (b) PV.

(13) ${\mathrm{v}}_{\mathrm{ds}}=-{\mathrm{r}}_{\mathrm{s}}{\mathrm{i}}_{\mathrm{ds}}+\left({\mathrm{x}}_{\mathrm{s}}+{\mathrm{x}}_{\mathit{\mu }}\right){\mathrm{i}}_{\mathrm{qs}}+{\mathrm{x}}_{\mathit{\mu }}{\mathrm{i}}_{\mathrm{qr}}$(13)

(14) ${\mathrm{v}}_{\mathrm{qs}}=-{\mathrm{r}}_{\mathrm{s}}{\mathrm{i}}_{\mathrm{qs}}-\left(\left({\mathrm{x}}_{\mathrm{s}}+{\mathrm{x}}_{\mathit{\mu }}\right){\mathrm{i}}_{\mathrm{ds}}+{\mathrm{x}}_{\mathit{\mu }}{\mathrm{i}}_{\mathrm{dr}}\right)$(14)

(15) ${\mathrm{v}}_{\mathrm{dr}}=-{\mathrm{r}}_{\mathrm{r}}{\mathrm{i}}_{\mathrm{dr}}+\left(1-{\mathit{\omega }}_{\mathrm{m}}\right)\left(\left({\mathrm{x}}_{\mathrm{s}}+{\mathrm{x}}_{\mathit{\mu }}\right){\mathrm{i}}_{\mathrm{qr}}+{\mathrm{x}}_{\mathit{\mu }}{\mathrm{i}}_{\mathrm{qs}}\right)$(15)

(16) ${\mathrm{v}}_{\mathrm{qr}}=-{\mathrm{r}}_{\mathrm{r}}{\mathrm{i}}_{\mathrm{qr}}-\left(1-{\mathit{\omega }}_{\mathrm{m}}\right)\left(\left({\mathrm{x}}_{\mathrm{s}}+{\mathrm{x}}_{\mathit{\mu }}\right){\mathrm{i}}_{\mathrm{dr}}+{\mathrm{x}}_{\mathit{\mu }}{\mathrm{i}}_{\mathrm{ds}}\right)$(16)

Here, ${\mathrm{v}}_{\mathrm{ds}},{\mathrm{v}}_{\mathrm{dr}}$= d-axis stator voltage and rotor voltage, ${\mathrm{v}}_{\mathrm{qs}},{\mathrm{v}}_{\mathrm{qr}}$= q-axis stator voltage and rotor voltage, ${\mathrm{i}}_{\mathrm{ds}},{\mathrm{i}}_{\mathrm{dr}}$= d-axis stator current and rotor current, ${\mathrm{i}}_{\mathrm{qs}},{\mathrm{i}}_{\mathrm{qr}}$= q-axis stator current and rotor current, ${\mathrm{r}}_{\mathrm{s}},{\mathrm{r}}_{\mathrm{r}}=$ Stator resistance and rotor resistance, ${\mathrm{x}}_{\mathrm{s}},{\mathrm{x}}_{\mathrm{r}}=$ Stator reactance and rotor reactance, ${\mathrm{x}}_{\mathit{\mu }}$, ${\mathit{\omega }}_{\mathrm{m}}$= Mutual reactance and rotor speed.

Neglecting losses it can be assumed that the active power (P) of the rotor is the active power seen by the converter. Regarding reactive power (Q), supplied power into the grid can be found by not considering stator resistance and assuming that the d-axis coincides with the maximum of the stator flux. Therefore, the powers supplied to the grid results in,

(17) $\mathrm{P}={\mathrm{v}}_{\mathrm{ds}}{\mathrm{i}}_{\mathrm{ds}}+{\mathrm{v}}_{\mathrm{qs}}{\mathrm{i}}_{\mathrm{qs}}+{\mathrm{v}}_{\mathrm{dr}}{\mathrm{i}}_{\mathrm{dr}}+{\mathrm{v}}_{\mathrm{qr}}{\mathrm{i}}_{\mathrm{qr}}$(17)

(18) $\mathrm{Q}=\frac{-{\mathrm{x}}_{\mathit{\mu }}\mathrm{v}{\mathrm{i}}_{\mathrm{dr}}}{{\mathrm{x}}_{\mathrm{s}}+{\mathrm{x}}_{\mathit{\mu }}}-\frac{{\mathrm{v}}^2}{{\mathrm{x}}_{\mathit{\mu }}}$(18)

Equation 19(19) ${\mathrm{X}}_{\mathrm{tcr}}\mathit{\hspace{0.17em}}=\mathit{\hspace{0.17em}}{\mathrm{X}}_{\mathrm{c}}[1\mathit{\hspace{0.17em}}-\mathit{\hspace{0.17em}}\frac{\mathrm{K}{\mathrm{x}}^2(\mathit{\sigma }+\sin \mathit{\sigma })}{(\mathrm{K}{\mathrm{x}}^2-1)\mathit{\pi }}\mathit{\hspace{0.17em}}+\mathit{\hspace{0.17em}}\{\frac{4\mathrm{K}{\mathrm{x}}^2\cos 2(\frac{\mathit{\sigma }}{2})}{\mathrm{p}{(\mathrm{K}{\mathrm{x}}^2-1)}^2}\}\mathit{\hspace{0.17em}}({\mathrm{K}}_{\mathrm{x}}\tan ({\mathrm{K}}_{\mathrm{x}}\frac{\mathit{\sigma }}{2})-\tan (\frac{\mathit{\sigma }}{2})],$(19) –Equation 19(19) ${\mathrm{X}}_{\mathrm{tcr}}\mathit{\hspace{0.17em}}=\mathit{\hspace{0.17em}}{\mathrm{X}}_{\mathrm{c}}[1\mathit{\hspace{0.17em}}-\mathit{\hspace{0.17em}}\frac{\mathrm{K}{\mathrm{x}}^2(\mathit{\sigma }+\sin \mathit{\sigma })}{(\mathrm{K}{\mathrm{x}}^2-1)\mathit{\pi }}\mathit{\hspace{0.17em}}+\mathit{\hspace{0.17em}}\{\frac{4\mathrm{K}{\mathrm{x}}^2\cos 2(\frac{\mathit{\sigma }}{2})}{\mathrm{p}{(\mathrm{K}{\mathrm{x}}^2-1)}^2}\}\mathit{\hspace{0.17em}}({\mathrm{K}}_{\mathrm{x}}\tan ({\mathrm{K}}_{\mathrm{x}}\frac{\mathit{\sigma }}{2})-\tan (\frac{\mathit{\sigma }}{2})],$(19) are stated from (Tanbhir Hoq et al., 2018). The block diagram of the DFIG which is available in the NEPLAN software (40) is depicted in Figure 4(a). It shows the speed and pitch angle control of WT which is based on real power and the rotation speed of the rotor shaft of the generator. Controllable pitch blade allow to control the real power output of turbine. Crow bar resistance is also used to provide protection against grid’s voltage and current overshoot.

Figure 4. (a). Block diagram of DFIG modelling (b). PV model for converter.

3.3. PV modelling

A typical structure of grid connected PV is illustrated in Figure 3(b). PV array receives the solar power and convert it to electrical power, it is then transferred through DC-DC converter where it has maximum power point tracking (MPPT) mechanism to have target voltage level. DC-AC inverter controls the output AC voltage, current, transmission angle and real power. PV may regulate terminal voltage but regulation of reactive power can damage the inverter if it goes beyond the rated current. PV can focus only on real power and very limited reactive power. Thus two models of PV are in use, these are known as P-V model and P-Q model (Tamimi et al., 2013). Figure 4(b) illustrates both model of PV. P-Q model does not include voltage control.

4. FACTS devices

4.1. TCSC

TCSC consists of a fixed static capacitor and parallel reactance which is regulated by thyristor. Firing angle (α) of thyristor in between 90° to 180° can manipulate the reactance but they should not produce any resonance where both the inductance and capacitance become identical. Figure 5(a) represents the construction of a TCSC which is connected in series with a transmission line. Inductance is the variable part in TCSC which depends on firing angle of thyristor (α), hence the total reactance becomes function of (α). It can be denoted by the following equation (Rosso et al., 0000).

Figure 5. (a) TCSC; (b) STATCOM.

(19) ${\mathrm{X}}_{\mathrm{tcr}}\mathit{\hspace{0.17em}}=\mathit{\hspace{0.17em}}{\mathrm{X}}_{\mathrm{c}}[1\mathit{\hspace{0.17em}}-\mathit{\hspace{0.17em}}\frac{\mathrm{K}{\mathrm{x}}^2(\mathit{\sigma }+\sin \mathit{\sigma })}{(\mathrm{K}{\mathrm{x}}^2-1)\mathit{\pi }}\mathit{\hspace{0.17em}}+\mathit{\hspace{0.17em}}\{\frac{4\mathrm{K}{\mathrm{x}}^2\cos 2(\frac{\mathit{\sigma }}{2})}{\mathrm{p}{(\mathrm{K}{\mathrm{x}}^2-1)}^2}\}\mathit{\hspace{0.17em}}({\mathrm{K}}_{\mathrm{x}}\tan ({\mathrm{K}}_{\mathrm{x}}\frac{\mathit{\sigma }}{2})-\tan (\frac{\mathit{\sigma }}{2})],$(19)

(Rosso et al., 0000) where, X_tcr= reactance.

X_C, X_L represent the capacitive and inductive reactance respectively at fundamental frequency.

σ = 2(π- α)= opening angle of TCSC controller and K_x=$\sqrt{\frac{{\mathrm{x}}_{\mathrm{c}}}{{\mathrm{x}}_{\mathrm{L}}}}$

4.2. STATCOM

STATCOM is a converter based device which produces output which is always in same phase of the grid so that no real power is exchanged between the converter and the grid. If the converter output voltage is greater than the grid, it supplies reactive power to the grid. If the output voltage of the converter is lower than the grid, converter absorbs reactive power. So, STATCOM can acts like both inductor and capacitor (Hingorani & Gyugyi, 2001). STATCOM does not use any static capacitor so its rating remains same at the event of voltage reduction at grid side. Figure 5(b) shows a STATCOM diagram.

4.3. Damping controller design

Reactance must be larger than resistance by around ten times if the system is expected to be healthy. So if any series compensation is designed for transmission line it must be under 70% (Yang et al., 1998). In BPS, we will use TCSC for series compensation at both the first and second East-West interconnectors which provide 70% series compensation each. To provide shunt compensation, two STATCOMs are set at receiving end of both interconnectors. Both the STATCOMs are 2 p.u or 200 MVAR. Modal analysis technique is carried out of the system with RES penetration to find out the critical Eigenvalue. Now lead-lag controller is adopted to enhance the damping ratio of the critical mode. Typical acceptance damping ratio is 3–5% (Paserba et al., 2001). The design process of phase compensation is shown in (Aboul Ela et al., 1996; Rosso et al., 0000). In Equation 19(19) ${\mathrm{X}}_{\mathrm{tcr}}\mathit{\hspace{0.17em}}=\mathit{\hspace{0.17em}}{\mathrm{X}}_{\mathrm{c}}[1\mathit{\hspace{0.17em}}-\mathit{\hspace{0.17em}}\frac{\mathrm{K}{\mathrm{x}}^2(\mathit{\sigma }+\sin \mathit{\sigma })}{(\mathrm{K}{\mathrm{x}}^2-1)\mathit{\pi }}\mathit{\hspace{0.17em}}+\mathit{\hspace{0.17em}}\{\frac{4\mathrm{K}{\mathrm{x}}^2\cos 2(\frac{\mathit{\sigma }}{2})}{\mathrm{p}{(\mathrm{K}{\mathrm{x}}^2-1)}^2}\}\mathit{\hspace{0.17em}}({\mathrm{K}}_{\mathrm{x}}\tan ({\mathrm{K}}_{\mathrm{x}}\frac{\mathit{\sigma }}{2})-\tan (\frac{\mathit{\sigma }}{2})],$(19) , transfer function of the Damper is given. Figure 6 shows block diagram of a damping controller.

Figure 6. Block diagram of a damping controller.

(20) $\mathrm{H}(\mathrm{s})=\mathrm{K}\ast \frac{\mathrm{S}{\mathrm{T}}_{\mathrm{W}}}{1+\mathrm{S}{\mathrm{T}}_{\mathrm{W}}}\ast \frac{(1+\mathrm{S}{\mathrm{T}}_{\mathrm{lead}})}{{(1+\mathrm{S}{\mathrm{T}}_{\mathrm{lag}})}^{{\mathrm{m}}_{\mathrm{c}}}}=\mathrm{K}{\mathrm{H}}_1(\mathrm{s}),$(20)

(Aboul Ela et al., 1996; Rosso et al., 0000) where,

T_w= Wash out time constant (5–10 sec), T_lead or T_lag= Time constant of lead or lag compensator, K= gain of the function

The lead–lag parameters can be determined using the following equations:

${\phi }_{\mathrm{comp}}=180^0-\arg \left(\mathrm{Ri}\right)$

${\alpha }_{\mathrm{c}}=\frac{\mathrm{Tlead}}{\mathrm{Tlag}}=\frac{\left\{1-\sin \left(\frac{{\mathit{\phi }}_{\mathrm{comp}}}{{\mathrm{m}}_{\mathrm{c}}}\right)\right\}}{\left\{1+\sin \left(\frac{{\mathit{\phi }}_{\mathrm{comp}}}{{\mathrm{m}}_{\mathrm{c}}}\right)\right\}}$

(21) ${\mathrm{T}}_{\mathrm{lag}}=\frac{1}{\mathrm{wi}\surd \alpha \mathrm{c}}$(21)

(Aboul Ela et al., 1996; Rosso et al., 0000) Where, arg(Ri) denotes phase angle of the residue Ri, w_i is the frequency of the mode of oscillation in rad/sec, m_c is the number if compensation stages (usually m_c = 2).

5. Methodology

In Barua & Quamruzzaman (2018a); Barua et al. (2021b), steady-state stability limit of BPS was determined by increasing load gradually. SNB occurs at 198% of loading where the BPS has no FACTS adoption and no RES penetrated into it. Dynamic-state stability occurs at 172% of loading where HB occurs. Authors inserted TCSC and STATCOM to increase both stability limits further. Using TCSC and STATCOM, the steady-state stability limit was increased to 227% and no HB occurs before the steady-state stability limit. In (Barua, Quamruzzaman, et al., 2022), Unified Power Flow Controller was used in first East-West interconnector only instead of TCSC and STATCOM on the same system as (Barua & Quamruzzaman, 2018a; Barua et al., 2021b). It was able to increase steady-state stability limit to 233% and no HB triggers before this point.

In Barua et al. (2021a) & Barua et al. (2021), authors revealed the PV and WT effect on BPS individually based on stability. In Barua, Barua, et al. (2022), both the PV and WT were penetrated in BPS and contingency analysis was carried out. A STATCOM was also used in the most critical bus. But no work was executed to determine the combined effect of PV and WT on BPS stability. In our present work, 55 MW WT and 100 MW PV are penetrated as following: (a) Case 01-BPS is planning to integrate 55 MW WT in Bagerhat grid. So this work considers each WT unit as 5 MW, hence 11 units will be introduced in Bagerhat grid. Near Bagerhat, Khulna grid has 165 MVA Synchronous machines (SM). When WT is penetrated in Bagerhat, equivalent amount of SM will be phased out. To increase the voltage and rotor angle stability beside other stabilities, TCSC and STATCOM are used at both interconnectors. (b) Case 02-Sirajganj bus is taken to inject 100 MW PV. Baghabari is the nearest generating stations of 195 MVA, so equivalent amount of SM will be replaced by PV from this bus. Again to check the impact of remote replacing of SM, 50 MW is dropped out from Khulna grid and 50 MW is dropped out from Baghabari. P-Q type model of PV is chosen in this work. Data of both WT and PV is provided in appendix section. Again, TCSC and STATCOM are considered to increase the stability.(c) Case 03-Finally, with the penetration of both WT and PV in the respective location as above mentioned, the stability study is carried out. Application TCSC and STATCOM at both the interconnectors with properly tuned controller will reveal the stability states of the system. NEPLAN (40) software is used to run all the simulations and to plot corresponding results. Table 1 shows the different penetration level of BPS.

Table 1. Different penetration level of RES

Case	WT (MW)	PV (MW)	Penetration (%)
1	55	0	12.23
2	0	100	22.23
3	55	100	34.43

6. Result and Discussion

6.1. BPS with only WT penetration

As stated in Section 4, steady-state stability of Western grid of BPS is at 198% of loading. Now 11 units of 5 MW DFIG-based WTs are penetrated in Bagerhat bus. At the same time, equivalent amount of 55 MW generating units are phased out from Khulna generating stations. Now CPF analysis is carried out with case 1 as stated in Table 1. At 180% of loading, the SNB occurs as depicted in Figure 7(a). Before SNB, HB triggers at 165% of loading as shown in Figure 7(a) with dotted vertical line. With the application of TCSC and STATCOM at both interconnectors, the SNB is shifted further at 228% as per Figure 7(b). Now to overcome the HB at 165% loading, damping controller is designed for TCSC and STATCOM. With the proper tuned controller, HB can be removed from the SNB region. Hence, using FACTS the steady-state stability and dynamic-state stability are increased. Now to show the positive effect of damping controller of FACTS devices, transient voltage stability and rotor angle stability analysis are carried out at 165% of loading.

Figure 7. (a) Stability limit with case 1; (b) Stability limit is enhanced with case 1 using TCSC and STATCOM.

To check the transient stability of both voltage and rotor angle of Khulna machine unit with case 1, a three-phase short circuit fault is applied at Sirajganj bus for 5 cycles. Figure 8(a) illustrates that rotor angle of Khulna machine is unstable and it becomes oscillatory around 2100° to 2300°. Figure 8(b) shows that the voltage is unstable after the fault. It is oscillatory and keep fluctuating below 4 kV after a oscillatory sag during fault of 5 cycles which applied at 100 sec.

Figure 8. At 165% loading (a) Rotor angle of Khulna machine unit; (b) Voltage of Khulna generating bus.

Now with TCSC and STATCOM having properly tuned controller, the rotor angle stability and voltage stability are further studied. Figure 9(a) shows much improvement in rotor angle of Khulna machine. Before fault the angle was 34.3° and after fault of 5 cycles it settles back just after 6 sec. from the fault commencement. Likewise, the voltage level of Khulna generating bus shows great improvement as compared to Figure 8(b). From Figure 9(b), it can be seen that, against fault the voltage stability is very robust and it settles to stable stage just after 2 sec. of fault occurring time. So, Figures 8(a,b) show the negative impact of using WT in the system. Both Figures 9(a,b), show the improvement in rotor angle stability and voltage stability respectively which is a clear indication of positive impact of using TCSC and STATCOM.

Figure 9. At 165% of loading with TCSC and STATCOM (a) Rotor angle of Khulna machine unit; (b) Voltage of Khulna generating bus.

6.2. BPS with only PV penetration

100 MW of PV is installed in Sirajganj bus. So equivalent amount of generating station will be replaced from Baghabari bus. With this situation, CPF is adopted to find out the steady-state stability limit with case 2. With PV penetration in the BPS system, SNB occurs at 170%. With the modal analysis, the HB is detected at 158% of loading. Figure 10(a) shows the steady-state and dynamic-state stability limit. Using TCSC and STATCOM at both the interconnectors, the steady-state stability limit is shifted to 220%. With the assignment of properly tuned damping controller the HB can be removed. Figure 10(b) represents the improving effect of using TCSC and STATCOM. Now to exhibits the damping controller effect, transient analysis of voltage and rotor angle of both Baghabari machine and Khulna machine are carried out at 150% of loading. It is worth mentioning that, Baghabari machine is replaced with equivalent amount of generating unit as PV in Sirajganj.

Figure 10. (a) Stability limit with case 2; (b) Stability limit is extended with case 2 using TCSC and STATCOM.

Now a three phase short circuit fault for 15 cycles is applied at Shahzadpur bus which is near bus of Sirajganj. Transient voltage phenomenon is depicted in Figure 11(a), where the voltage of Khulna bus goes to 6.5 kV during fault and after fault it settles at 7.5 kV. Baghabari bus voltage is severely affected which voltage goes down to 3.5 kV. Rotor angle of both Khulna and Baghabari machines are plotted in Figure 11(b). Rotor angle of Khulna machine reaches peak of −4.5° from −26.1° then it oscillates for long time to achieve a new operating angle. Baghabari machine also oscillates with peak of −2.5° from −25.7°.

Figure 11. At 150% of loading (a) Voltage of Khulna and Baghabari generating bus; (b) Relative rotor angle of Khulna and Baghabari.

At 150% of loading with the same scenario as mentioned above, TCSC and STATCOM with proper tuned controller are adopted. Now Figure 12(a) shows the Khulna bus voltage has a sag till 7 kV during fault and it reaches to initial operating voltage level just after 2.5 sec. after fault takes place. Baghabari bus voltage also reaches the stable voltage point after 2 sec. of fault. Rotor angle stability is also improved due to TCSC and STATCOM as shown in Figure 12(b). Rotor angle of Khulna machine has less oscillation compared to 11 (b), it reaches the peak of 9.1° to −6.5° and comes back to previous state of 1° just after 5 sec. of fault. Baghabari machine unit also show improvement in rotor angle stability where it has peak of −5.9° to −16.6° and settles at −15° after 5 sec. Baghabari machine is less oscillatory than Khulna machine as TCSC and STATCOM are near to it. So, Figure 12 reveals the positive results of using TCSC and STATCOM with tuned controller.

Figure 12. With TCSC and STATCOM (a) Voltage of Khulna and Baghabari generating bus; (b) Relative rotor angle of Khulna and Baghabari.

6.3. BPS with WT and PV penetration

This section analyzes BPS with case 3. 55 MW of SM is phased out from Khulna grid and 100 MW SM is phased out from Baghabari machine. To check the steady -tate stability of Western grid with case 3, CPF is applied by increasing load gradually. SNB occurs at 160% of loading. Using modal analysis technique the HB is found at 152% of loading, so the point is dynamic-state stability limit. Figure 13(a) illustrates both the limits. To improve steady-state stability limit, TCSC and STATCOM are adopted at both the interconnectors. It extend the stability limit till 230% as per Figure 13(b). Now properly tuned damping controllers of TCSC and STATCOM, help to remove dynamic stability limits beyond steady-state stability limit point.

Figure 13. (a) Stability limit with case 3; (b) Stability limit is extended with case 2 using TCSC and STATCOM.

Without TCSC and STATCOM, transient-state stability is examined of case 3 at 152% loading by applying a short circuit fault at Shahzadpur bus for 15 cycles. Voltage stability of Khulna and Baghabari bus are shown in Figure 14(a) where, Khulna bus has sag of 5 kV during fault and Baghabari bus has 3.3 kV. Figure 14(b), depicts the rotor angle stability of Khulna and Baghabari machines. Khulna machine has a peak to 6.89° and become unstable against fault. Baghabari machine also becomes unstable with a peak of 7.67° against the fault.

Figure 14. At 152% of loading (a) Voltage of Khulna and Baghabari generating bus; (b) Relative rotor angle of Khulna and Baghabari.

Applying TCSC and STATCOM with properly tuned controller both the voltage and rotor angle stability are improved. From Figure 15(a) it can be shown that, Khulna bus voltage has a sag of 6.5 kV during fault periods. After fault it has an overshoot of 10.1 kV and almost immediately settle to initial position. Same improvement is detected at Baghabari bus with a sag of 3.8 kV during fault as the fault zone is nearer to it. Again, it settles to stable voltage level almost immediately with a peak of 10.1 kV. Rotor angle stability can be analyzed from Figure 15(b). Khulna machine’s rotor angle stability improved as it settles to initial operating condition of relative rotor angle of −6.5° just after 5 sec. of fault commencement. Baghabari machine shows improvement as it returns to its relative operating rotor angle of −17.5° after 5.5 sec.

Figure 15. At 152% of loading (a) Voltage of Khulna and Baghabari generating bus; (b) Relative rotor angle of Khulna and Baghabari.

7. Conclusion

The paper performs stability study of Bangladesh power system with wind and solar power penetration at its Western grid at a large scale. The study shows that, with only wind power penetration the steady-state stability limit decreases by 9% and dynamic-state stability reduced by only 2.3%. Voltage and rotor angle transient stability become unstable when subjected to a short circuit fault. With the aid of TCSC and STATCOM, steady-state stability is enhanced by 15% and dynamic-state stability is shifted beyond steady-state stability limit with properly tuned damping controller. Both voltage and rotor angle response reveal the stability improvement of the system at transient scale. Next, with only solar power penetration, the stability study decodes that the steady-state stability is reduced by 14.2% and dynamic stability is reduced by 8.2%. Voltage and rotor angle stability study at transient scale against a fault demonstrates the instability phenomenon. Again, incorporation of TCSC and STATCOM, increases the steady-state stability by 10% and dynamic-state stability is shifted out of steady-state stability region by damping controller. Transient stability of both voltage and rotor angle are enhanced remarkably. Finally with both wind and solar power, stability investigation of BPS is carried out. With this RES penetration steady-state stability of BPS is declined by 19.2%, which is the most from above two cases. Dynamic-state stability faces the reduction of 11.6%. Voltage and rotor angle stability in transient state also displays the instability of the BPS system. Proper damping controller eradicates the stability problem by enhancing the steady-state stability limit by 16.2% and removing the barrier of dynamic stability limit point. Further study of voltage and rotor angle shows the positive effect of using TCSC and STACOM with properly tuned controller.

Some future scopes of this paper can be the study of the Western grid with 100% RES penetration and optimal location of FACTS devices.

7.1. DFIG based WT data

Table

Nominal power (Sn)	5.2 MVA	Moment of inertia (j)	240.62 kgm2
Nominal voltage (Un)	3.3 KV	Pole pairs	2
Stator resistance (Rs)	3.2 m Ω	Wind speed	13 ms^−1
Rotor resistance (Rr)	7.6 m Ω at slip .388	Air density	1.225
Stator leakage inductance (Xs)	.161 H	Blade length	50 meter
Rotor leakage inductance (Xr)	.2 H	Cut in speed	3 ms^−1
Mutual inductance (Lm)	4.9 H	Cut out speed	25 ms^−1

7.2. PV data

Table

No of cell in series	10	Internal series resistance	.007 ohm
No of cell in parallel	125913	Ideality factor	1.3
SC current (Isc)	3.8 A	Temperature coefficient of Isc	.0063
Open circuit voltage (Voc)	21.1 V	Temperature coefficient of Voc	.042
Cell temperature	25° C	Voltage peak to peak	20.9 V
Solar irradiation	1000 w/m^2	Current peak to peak	3.8 A

Table

Nomenclature
Symbol	Abbreviation	Symbol	Abbreviation
BPS	Bangladesh Power System	λ	Loading Parameter
RES	Renewable Energy System	θ	Loading Angle
WT	Wind Turbine	σ	Step Size
PV	Photo Voltaic	J	Jacobian Matrix
FACTS	Flexible AC Transmission System	η	Predicted Value of State Variable
POD	Power Oscillation Damper	Ѱ	Right Eigenvector matrix of matrix J
STATCOM	Static Synchronous Compensator	Ʌ	Diagonal Eigenvalue matrix of matrix J
TCSC	Thyristor Controlled Series Compensator	Ø	Left Eigenvector matrix of matrix J
CPF	Continuation Power Flow	${\mathrm{P}}_{\mathrm{m}}$	Turbine Mechanical Power Output
SM	Synchronous Machine	${\mathrm{C}}_{\mathrm{p}}$	Power Coefficient
SNB	Saddle Node Bifurcation	$\mathit{\rho }$	Air Density
HB	Hopf Bifurcation	$\mathrm{v}$	Wind Speed
RSC	Rotor Side Converter	ωr	Rotor Speed
GSC	Grid Side Converter	ωs	Stator Speed
SCIG	Squirrel Cage Induction Generator	${\mathrm{v}}_{\mathrm{ds}},{\mathrm{v}}_{\mathrm{dr}}$	d-axis stator, rotor voltage
DFIG	Doubly Fed Induction Generator	${\mathrm{v}}_{\mathrm{qs}},{\mathrm{v}}_{\mathrm{qr}}$	q-axis stator, rotor voltage
Tw	Washout Filter Time Constant	Xtcr	TCSC reactance
Tlead	Leading Compensator Time Constant	Kx	Degree of Compensation
Tlag	Lagging Compensator Time Constant	φcomp	Compensation Angle

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Pollen Barua

Pollen Barua received his B.Sc. in E.E.E from University of Science and Technology Chittagong (USTC) in 2012 and M.Sc. in E.E.E from Chittagong University of Engineering and Technology (CUET) in 2018. He served as a deputy manager of Electrical dept. in Western Marine Shipyard Ltd and electrical instructor in Bangladesh Marine Academy. He is currently working as a Head Electrical Instructor in MAS Marine Academy. Also, the author will join Renewable Energy in the Marine Environment (REM+) program in session 2022-2024. His research area includes power system stability and capacity analysis, power system security, renewable energy in marine environment, energy storage system, control system, marine electrical system, etc. The present paper will enable Bangladesh Power System to search for renewable energy penetration very soon as it will also have the security and reliability like conventional. email: [email protected]

Ratul Barua

Pollen Barua received his B.Sc. in E.E.E from University of Science and Technology Chittagong (USTC) in 2012 and M.Sc. in E.E.E from Chittagong University of Engineering and Technology (CUET) in 2018. He served as a deputy manager of Electrical dept. in Western Marine Shipyard Ltd and electrical instructor in Bangladesh Marine Academy. He is currently working as a Head Electrical Instructor in MAS Marine Academy. Also, the author will join Renewable Energy in the Marine Environment (REM+) program in session 2022-2024. His research area includes power system stability and capacity analysis, power system security, renewable energy in marine environment, energy storage system, control system, marine electrical system, etc. The present paper will enable Bangladesh Power System to search for renewable energy penetration very soon as it will also have the security and reliability like conventional. email: [email protected]