Enhancing Oscillation Damping in an Interconnected Power System with Integrated Wind Farms Using Unified Power Flow Controller

Abstract

The well-developed unified power flow controller (UPFC) has demonstrated its capability in providing voltage support and improving power system stability. The objective of this paper is to demonstrate the capability of the UPFC in mitigating oscillations in a wind farm integrated power system by employing eigenvalue analysis and dynamic time-domain simulation approaches. For this purpose, a power oscillation damping controller (PODC) of the UPFC is designed for damping oscillations caused by disturbances in a given interconnected power system, including the change in tie-line power, the changes of wind power outputs, and others. Simulations are carried out for two sample power systems, i.e., a four-machine system and an eight-machine system, for demonstration. Numerous eigenvalue analysis and dynamic time-domain simulation results confirm that the UPFC equipped with the designed PODC can effectively suppress oscillations of power systems under various disturbance scenarios.

1. Introduction

1.1. Motivation

In the past decade, renewable energy generation has developed quickly around the globe. The wind power generation installed capacity is currently ranked the second highest in renewable energy technology, after hydro [1]. By integrating large-scale wind farms, which are mainly doubly-fed induction generators (DFIG) [2], into a power system concerned, wind energy is expected to supply 20% of global electricity by 2030 [3].

In spite of the benefits of wind power generation, if not controlled properly, a high-level penetration of wind power generation could have negative impacts on power system dynamic stability, especially the oscillation damping characteristics. Oscillations are in-built phenomena of a power system, especially an interconnected one. Typically, the oscillation frequency in ≈0.1–2 Hz belongs to electromechanical oscillations, which can be classified as local mode oscillations and interarea mode oscillations [4,5,6]. In an M+N-machine interconnected power system including two independent power systems, i.e., a M-machine independent power system and a N-machine one, there will be M+N-1 electro-mechanical oscillation modes and numerous operating scenarios. Electro-mechanical oscillatory modes and damping may become worse if the power system operating condition changes, especially with the increasing penetration of wind power integration. Therefore, in a wind farm integrated power system, it is important to analyze the oscillation damping characteristics.

1.2. Literature Review

In 2003, the potential impacts of large-scale wind farm integration on power system damping characteristics was first investigated in Reference [7], and later followed by References [8,9]. The research work in References [10,11,12,13] shows that a large-scale wind power integrated power system suffers new challenges with respect to stability. More specifically, damping inter-area oscillation is becoming more difficult under many conditions in an interconnected power system with a large-scale integrated wind power. Therefore, it is necessary to carefully examine the impacts of DFIG on power system inter-area oscillation and find some strategies to enhance oscillation damping characteristics.

The well-known flexible AC transmission system (FACTS) is very effective in controlling power flow [14,15]. FACTS devices can also contribute to voltage stability improvement and oscillation damping enhancement. Because of its flexibility and capability in controlling power system dynamics effectively [16,17], the FACTS device has been employed for voltage support and stability improvement [18], as well as for making the transmission system with a small capacity margin operate more reliably.

In Reference [19], it is shown that with an appropriate controller design, it becomes possible to control the wind turbine under various operating conditions, while reducing the structural oscillations at the same time. In Reference [19], the classic proportional-integral-derivative (PID) controller, input–output pole placement controller and full state feedback controller for wind turbine pitch control are compared. Control of power flow and stability improvement in a power system with offshore wind and seashore wave farms using unified power flow controller (UPFC) are both discussed in Reference [20]. To mitigate sub-synchronous resonances in a power system, a comprehensive analysis on utilizing UPFC in the transmission system has been given [21], and a damping controller was interrogated through extensive time domain simulations so as to attain the best damping performance for oscillations.

In Reference [22], a simultaneous robust coordinated multiple damping controller design strategy for a power system incorporating the power system stabilizer (PSS), static Var compensator, power oscillation damper, and DFIG power oscillation damper is presented. Simulation results show that the proposed DFIG power oscillation damper can coordinate well with other damping controllers for enhancing power network damping performance. Some control strategies of UPFC, such as the widely-used proportional integral (PI) control, fuzzy control [23], robust finite-time control [24], and add-on self-tuning control [25], are applied to enhance the damping characteristics. Meanwhile, an adaptive fractional integral terminal sliding mode power controller of UPFC [26], a feedback controller [27], and a novel DFIG damping controller [28] are developed to maintain the supply and demand balance in a power system with high wind power penetration.

1.3. Contributions

Although the oscillation damping characteristics of wind farm generators have been reported in existing publications, some important issues are still not yet addressed. Impacts of the tie-line power, DFIG output and the UPFC damping controller on the damping oscillation characteristics of an interconnected power system have not yet been thoroughly examined. Given this background, the following issues are addressed in this work:

• A power oscillation damping controller (PODC) is designed and used with UPFC for damping oscillations in an interconnected power system.
• The continuous load fluctuation profile is employed for oscillation characteristics analysis.
• Typical impacting factors such as tie-line power, DFIG output, and load disturbances, as well as the damping controller of UPFC, are considered as part of a small signal stability analysis of an interconnected power system.
• Eigenvalue analysis and dynamic time-domain simulations are carried out to examine the capability of UPFC on improving inter-area oscillation mode and enhancing oscillation damping of an interconnected power system with wind farm integrated.

This paper is organized as follows. Models of UPFC and DFIG are presented in Section 2. Eigenvalue analysis for small signal stability is addressed in Section 3. Oscillation damping characteristics in a wind farm are presented in Section 4 and the PODC controller of UPFC developed in Section 5. Sensitivity studies are presented in Section 6, and a large system application in Section 7. Conclusions are given in Section 8.

2. System Configuration and Models

Figure 1 shows the block scheme of the studied power network with a DFIG, a synchronous generator, and a UPFC integrated together. This scheme is referred to the industry model and is used widely in commercial power system simulations. The currents and voltages are the outputs of the synchronous generator and UPFC.

2.1. Modelling of UPFC

As illustrated in Figure 2, the UPFC contains a static synchronous shunt compensator (VSC1) and a series one (VSC2). VSC1 and VSC2 are coupled together through a DC link capacitor that provides bidirectional power exchanges between them. The parallel converter VSC1 is connected to the power system through a parallel transformer TA, and an adjustable reactive current is injected into the connecting point of the system. It is equivalent to a parallel current source, providing or absorbing reactive power, so as to control the connecting point voltage V_A. VSC2 is connected to the system through the series transformer TB. Different from the parallel side, it can be used to control both active and reactive power on the line by placing an adjustable voltage to the connecting point. Regarding the regulation of UPFC, the series voltage source is used to exchange active and reactive power with the system by using a DC capacitor for transferring active power and simultaneously maintaining the stability of the capacitor voltage. The mathematical model of the UPFC is formulated as Equation (1):

$$\{\begin{array}{l}\left[\begin{array}{l}{V}_{Ad}\\ V_{Aq}\end{array}\right]=\left[\begin{array}{cc}0& -x_A\\ x_A& 0\end{array}\right]\left[\begin{array}{l}{i}_{3d}\\ i_{3q}\end{array}\right]+\frac{1}{2}\left[\begin{array}{cc}{m}_1{V}_{DC}& \cos {\delta }_1\\ m_1{V}_{DC}& \sin {\delta }_1\end{array}\right]\\ \left[\begin{array}{l}{V}_{Bd}\\ V_{Bq}\end{array}\right]=\left[\begin{array}{cc}0& -x_B\\ x_B& 0\end{array}\right]\left[\begin{array}{l}{i}_{2d}\\ i_{2q}\end{array}\right]-\frac{1}{2}\left[\begin{array}{cc}{m}_2{V}_{DC}& \cos {\delta }_2\\ m_2{V}_{DC}& \sin {\delta }_2\end{array}\right]\\ \frac{d{V}_{DC}}{dt}=\frac{3m_1}{4C}\left[\begin{array}{cc}\cos {\delta }_1& \sin {\delta }_1\end{array}\right]\left[\begin{array}{l}{i}_{3d}\\ i_{3q}\end{array}\right]-\frac{3m_2}{4C}\left[\begin{array}{cc}\cos {\delta }_2& \sin {\delta }_2\end{array}\right]\left[\begin{array}{l}{i}_{2d}\\ i_{2q}\end{array}\right]\end{array}$$

(1)

From Figure 2, the electric field energy exchange rate of the DC capacitor can be attained using:

$$C_{DC}{V}_{DC}\frac{d{V}_{DC}}{dt}=\mathrm{Re}\left[{\dot{V}}_C{\dot{I}}_C^{*}-{\dot{V}}_D{\dot{I}}_D^{*}\right]$$

(2)

The current and voltage of the parallel side and series side converters are subject to the following equation constraints:

$$\{\begin{array}{l}\left(r_C+j\omega l_C\right){\dot{I}}_C={\dot{V}}_A-{\dot{V}}_C\\ \left(r_D+j\omega l_D\right){\dot{I}}_D={\dot{V}}_B-{\dot{V}}_D\end{array}$$

(3)

UPFC is a passive component, and the capacitor voltage must be maintained constant in steady state operation:

$$\mathrm{Re}\left[{\dot{V}}_C{\dot{I}}_C^{*}-{\dot{V}}_D{\dot{I}}_D^{*}\right]=0$$

(4)

2.2. Modeling of DFIG

The mechanical power of DFIG can be computed using:

$$\{\begin{array}{l}{P}_m=0.5\rho A^{\prime }{V}^3{C}_p\\ A^{\prime }=\pi R^2\end{array}$$

(5)

where $C_P$ can be attained using:

$$\{\begin{array}{l}{C}_p(\lambda ,\beta )=0.22\left(116/{\lambda }_0-0.4\beta -5\right)e^{-12.5/{\lambda }_0}\\ 1/{{\lambda }_i}^{\prime }=1/(\lambda +0.08\beta )-0.035/({\beta }^3+1)\end{array}$$

(6)

The dynamics of the drive train can be expressed as:

$$\{\begin{array}{l}d{\omega }_r/dt=(T_{sh}-T_e-D_t{\omega }_r)/2H_g\\ d{\theta }_t/dt={\omega }_b({\omega }_t-{\omega }_r)\\ d{\omega }_t/dt=(T_m-T_{sh})/2H_t\end{array}$$

(7)

where T_e, T_sh, and T_m can be expressed as:

$$\{\begin{array}{l}{T}_m=P_m/{\omega }_t=0.5\rho \pi R^2{C}_P{V}^3/{\omega }_t\\ T_{sh}=K_{sh}{\theta }_t+D_{sh}{\omega }_b({\omega }_t-{\omega }_r)\\ T_e=L_m(i_{ds}{i}_{qr}-i_{qs}{i}_{dr})\end{array}$$

(8)

Detailed DFIG models can be found in References [9,29,30]. In the d-q frame, the DFIG can be modeled using:

$$\{\begin{array}{l}\begin{array}{ll}{x}_s\prime /{\omega }_s\times d{i}_{ds}/dt& =-[r_s+(x_s-x_s\prime )/{\omega }_s{T}_0\prime ]i_{ds}+x_s\prime i_{qs}+v_{ds}\\ & -(1-s_r)e_{ds}\prime +e_{qs}\prime /{\omega }_{s}T{\prime }_0-v_{dr}{L}_m/L_r\\ x_s\prime /{\omega }_s\times d{i}_{qs}/dt& =-[r_s+(x_s-x_s\prime )/{\omega }_s{T}_0\prime ]i_{qs}-x_s\prime i_{ds}+v_{qs}\\ & -(1-s_r)e_{qs}\prime -e_{ds}\prime /{\omega }_{s}T{\prime }_0-v_{qr}{L}_m/L_r\end{array}\\ d\mathrm{e}{\prime }_{ds}/dt=s_r{\omega }_s{e}_{qs}\prime -{\omega }_s{v}_{qr}{L}_m/L_r-[e_{ds}\prime +(x_s-x_s\prime )i_{qs}]/T{\prime }_0\\ d\mathrm{e}{\prime }_{qs}/dt=-s_r{\omega }_s{e}_{ds}\prime +{\omega }_s{v}_{dr}{L}_m/L_r-[e_{qs}\prime -(x_s-x_s\prime )i_{ds}]/T{\prime }_0\end{array}$$

(9)

The UPFC and DFIG models presented above are used in the next sections for small signal stability analysis in a power system with wind farms integrated.

3. Fundamentals of Small Signal Stability Analysis

The state space model of a power system can be formulated as a differential and algebraic equation (DAE) set as described by Equation (10), in which the differential equations and algebraic equations of UPFC and DFIG as described in Section 2 are included.

$$\{\begin{array}{l}\dot{\mathit{x}}=f(\mathit{x},\mathit{y})\\ 0=g(\mathit{x},\mathit{y})\end{array}$$

(10)

where, x and y are the vectors of the state variables and the algebraic variables, respectively.

The state space model can be linearized, and then eigenvalues and eigenvectors can be used to evaluate the small signal stability of the power system.

From the Taylor series expansion at a stable operating point (x₀, y₀), DAE can be linearized as

$$\left[\begin{array}{l}\Delta \dot{\mathit{x}}\\ 0\end{array}\right]=\left[\begin{array}{ll}{\nabla }_{x}f& {\nabla }_{y}f\\ {\nabla }_{x}g& {\nabla }_{y}g\end{array}\right]\left[\begin{array}{l}\Delta x\\ \Delta y\end{array}\right]=\left[\begin{array}{ll}{A}_1& B_1\\ C_1& D_1\end{array}\right]\left[\begin{array}{l}\Delta x\\ \Delta y\end{array}\right]$$

(11)

where ∇_xf = ∂f(x,y)/∂x is the gradient of f(x,y); other symbols are defined similarly.

If ∇_xg is nonsingular, Equation (11) can then be expressed as

$$\Delta \dot{\mathit{x}}=[A_1-B_1{(C_1)}^{-1}{D}_1]\Delta x=A\Delta x$$

(12)

where A is the state matrix.

$\lambda =\sigma +j\omega$ is an eigenvalue of A. Any nonzero n-column vector/nonzero n-row vector respecting Equation (13) are called the right/left eigenvector associated with $\lambda$.

$$\{\begin{array}{l}Aw=\lambda w\\ vA=\lambda v\end{array}$$

(13)

where $f=\omega /2\pi$ is the oscillation frequency.

The damping ratio is defined as: $\xi (\%)=-\sigma /\sqrt{{\sigma }^2+{\omega }^2}\times 100\%$. Based on the eigenvalues, the participation factors, which can reflect the relative contribution of each system state variable to a specified system mode, can be obtained with the right eigenvector w and left eigenvector v accordingly. Specifically, p_ij = w_ijv_ji/w^T_jv_j is the participation factor of the i-th state variable to the j-th eigenvalue.

4. Oscillation Damping Analysis of a Power System Using UPFC with Compensated Wind Farms

4.1. Test System

The well-known two-area four-machine interconnected power system, as shown in Figure 3 [4], is widely used for small-signal stability analysis. In this system, G₁–G₄ represent a group of generators that are strongly coupled, and both local and inter-area oscillation modes are observed. Neglecting the magnetic saturation, G₁–G₄ are described by a six-order model equipped with an IEEE (Institute of Electrical and Electronics Engineers) type 1 voltage regulator [4]. G₁ and G₂, and G₃ and G₄, are equipped with fast and slow exciters, respectively. An equivalent wind farm is connected to bus 6 in area 1, representing a wind farm with a capacity of 30 MW or 20 DFIGs with 1.5 MW each. The data of DFIG with respect to the model presented in Section 2, are given in

Table 1. DFIG data.

Parameter	Value	Parameter	Value
Power	30 MW	Rotor Resistance	0.005 p.u.
Frequency	60 Hz	Rotor Reactance	0.156 p.u
Blade Length	75 m	Magnetization Reactance	3.5 p.u.
Stator Resistance	0.00706 p.u	Inertia constant	3 kWs/kVA
Stator Reactance	0.171 p.u	Gear Box Ratio	1/89

. Based on the residue index [31], an UPFC is located in line 8–9.

For the purpose of comparisons, a base scenario was defined as the system without the wind farm and UPFC. In this system, the total installed synchronous generation capacity was 2800 MW.

The active power transmission capability of the tie-line from area 1 to 2 was 400 MW. The electro-mechanical modes, as well as eigenvalues, damping, frequency, and dominant machines, are shown in

Table 2. Electro-mechanical oscillatory modes under different conditions.

		Without UPFC			With UPFC
	No.	λ	ξ (%)	f (Hz)	λ	ξ (%)	f (Hz)	Dominant Machines
Without DFIG	1	−3.0984 ± j8.8672	32.99	1.4949	−3.1008 ± j8.8665	33.01	1.4950	G3, G4
	2	−1.9635 ± j7.5341	25.85	1.2391	−1.9722 ± j7.5289	25.34	1.2387	G1, G2
	3	−0.6609 ± j4.0114	16.26	0.6470	−0.6563 ± j3.9845	16.25	0.6427	G1, G4
With DFIG	1	−3.1005 ± j8.8664	33.01	1.4949	−3.1029 ± j8.8658	33.03	1.4950	G3, G4
	2	−2.0195 ± j7.5357	25.89	1.2417	−2.0267 ± j7.5306	25.99	1.2412	G1, G2
	3	−0.6634 ± j4.0267	16.26	0.6495	−0.6589 ± j4.0005	16.25	0.6453	G1, G4
	4	−0.6092 ± j0.7568	62.71	0.1546	−0.6238 ± j0.7470	64.10	0.1549	ALL

.

The participation factor was used to assess the contributions of G₁–G₄ to an oscillatory mode, as demonstrated in Table 2. It can be seen that λ₁ was characterized by the oscillation of G₃ against G₄ in area 2; λ₂ was characterized by the oscillation of G₁ against G₂ in area 1; λ₃ was characterized by the oscillation of G₁ and G₂, which were located in area 1, against G₃ and G₄, which were located in area 2; while λ₄ was characterized by the oscillation among G₁, G₂, G₃, G₄, and DFIG.

Therefore, λ₁ and λ₂ represented local modes; λ₃ and λ₄ represented interarea oscillation modes. From the results presented in Table 2, it is known that the oscillation damping ratio tended to increase with the installation of UPFC.

4.2. Oscillation Damping Analysis in a Compensated Wind Farm

The oscillation damping circumstances in the power system with the integration of a compensated wind farm is addressed in this subsection to identify appropriate cases for further studies. The Power System Analysis Toolbox (PSAT) [32] and MATLAB/Simulink were employed to carry out simulations for various scenarios. Two main factors for oscillation damping analysis were investigated: (1) the level of the series compensation, and (2) the DFIG output.

The DFIG output was assumed to be 30 MW, while three various compensation levels, i.e., 30%, 50%, and 80%, were examined. A three-phase short-circuit grounding fault located at the tie-line between buses 7 and 8 is served for demonstration. The angle oscillations were obtained for different cases, while the time-domain responses are shown in Figure 4a. It is illustrated that with the increase of the series compensation level, the magnitude of oscillations became smaller.

Three different values, i.e., 10, 50, and 90 MW, were specified for the wind farm output. A fixed 80% series compensation was applied. The angle oscillations were obtained for different cases as shown in Figure 4b, and the time-domain responses show that the magnitude of oscillations became larger with the increase of the DFIG output.

Similar sets of simulations were conducted with different system conditions. It was observed that with the decreasing compensation level and increasing wind power output, the damping behaviors of the system tended to worsen. Hence, oscillation instability may happen under some combinations of a low compensation level and a high wind power output.

5. Power Oscillation Damping Controller of UPFC

A power oscillation damping controller (PODC) is developed based on swing equations to damp oscillations caused by disturbances in a power system.

The input signals of the PODC can be various quantities associated with the tie-line, such as voltage, current, or the power flow on the tie-line. The output of this controller is fed as an input to the shunt side of the UPFC. The configuration of the PODC is displayed in Figure 5 and is very similar to the PSS controller. It consists of two lead and lag components; gain K; time constants T_l, T₂, T₃, and T₄; and the time constant for the washout circuit T_w. The data of the PODC are listed in

Table 3. The data of the PODC.

Parameter	K	Tw	Tl	T2	T3	T4
Value	0.1 p.u.	10 s	0.35 s	0.2 s	0.5 s	0.3 s

.

It was specified that the load on bus 7 fluctuates 5% during the period from 1.0 s to 1.5 s; the active power output from each generator in G₁, G₂, G₃, and G₄ was 700 MW; the power output from the wind farm was 30 MW, and the transmitted power from region 1 to region 2 was 430 MW. Figure 6 shows the power angle response curve of G₄ and the voltage curve at bus 9.

As shown in Figure 6, when the system low frequency oscillation occurs, the oscillation amplitude increased and tended to be stable for a long time without the installation of the PODC; especially in Figure 6b, the voltage curve became jagged due to the numerical oscillation problem. When the PODC was added, the oscillation amplitude decreased, and tended to be stable in short time.

Compared with the results presented in Reference [22], similar conclusions can be drawn that the relative power angle low frequency oscillations can be damped out by equipping a PODC.

6. Sensitivity Analysis

This section presents sensitivity analysis to explore the oscillation damping characteristics of a wind farm integrated power system, under different operating conditions.

6.1. Disturbance of Tie-Line Power Change

To investigate the effects of the UPFC capability on mitigating the intra-area damping oscillation, the damping oscillation modes under different degrees of the tie-line power flow are examined. For this purpose, the outputs of G₁–G₄ were adjusted under various operating conditions and the output power of DFIG was set at 30 MW with a compensation level of 80%.

The tie-line power transmitted from area 1 to 2 can be changed by adjusting the outputs of G₁–G₂ in area 1. The related damping characteristic trends of the intra-area oscillation modes are given in

Table 4. The interarea oscillation modes under different degrees of the tie-line power flow.

No.	Tie-Line Power/MW	Without UPFC			With UPFC, Without PODC			With Both UPFC and PODC
		λ	ξ (%)	f (Hz)	λ	ξ (%)	f (Hz)	λ	ξ (%)	f (Hz)
Interarea mode 1	46	−0.5790 ± j3.9564	14.48	0.6364	−0.6054 ± j4.0426	14.81	0.6506	−1.7012 ± j4.3688	36.28	0.7462
	143	−0.5720 ± j4.0201	14.09	0.6463	−0.5730 ± j4.0296	14.08	0.6478	−1.0519 ± j3.7497	27.01	0.6198
	239	−0.6687 ± j4.0328	16.36	0.6506	−0.6670 ± j4.0394	16.29	0.6516	−1.0583 ± j3.5303	28.72	0.5866
	335	−0.6656 ± j4.0418	16.25	0.6519	−0.6618 ± j4.0417	16.16	0.6518	−1.0247 ± j3.4482	28.49	0.5725
	430	−0.6634 ± j4.0267	16.26	0.6495	−0.6581 ± j4.0144	16.18	0.6474	−1.0090 ± j3.3843	28.57	0.5621
Interarea mode 2	46	−0.4905 ± j0.4320	75.04	0.1040	−0.5010 ± j0.4253	76.24	0.1046	−0.4693 ± j0.4629	71.19	0.1049
	143	−0.5090 ± j0.5055	70.95	0.1142	−0.5173 ± j0.4968	72.13	0.1142	−0.5088 ± j0.5438	68.32	0.1185
	239	−0.6026 ± j0.6578	67.55	0.1420	−0.6105 ± j0.6463	68.67	0.1415	−0.5887 ± j0.6787	65.52	0.1430
	335	−0.6073 ± j0.7070	65.16	0.1483	−0.6153 ± j0.6941	66.34	0.1476	−0.6024 ± j0.7317	63.56	0.1508
	430	−0.6092 ± j0.7568	62.71	0.1546	−0.6178 ± j0.7419	63.99	0.1537	−0.6119 ± j0.7854	61.46	0.1585

.

For the sake of comparisons, the following three cases are investigated:

• Without UPFC: Basic case
• With UPFC, Without PODC: Corresponding to the scenario described in Section 4
• With both UPFC and PODC: Corresponding to the scenario described in Section 5

It is demonstrated, from the results in Table 4, that with the variation of the tie-line power from 46 MW to 430 MW, ξ of the intra-area oscillation mode 2 shown decreased for all three cases, while the oscillation damping ratio for the case with both UPFC and PODC equipped increased.

As shown in Figure 7, the UPFC was indeed effective in mitigating the oscillations. Similar sets of simulations were conducted with different levels of tie-line power, and the similar response curve profiles attained are given in Figure 7.

6.2. Disturbance of Transmission Line Outage

The effect of UPFC in damping oscillations during transmission line outage is investigated in this subsection. In this case, the active power flow in the tie-line was around 430 MW, and the power output from the wind farm was 30 MW. It was assumed that the transmission line between bus 7 and bus 9 was out of service at 1 s. As shown in Figure 8, the results were similar with those in Section 6.1. Figure 8 shows the voltage response curves at bus 7 under different scenarios. As shown, the employment of both UPFC and PODC resulted in better performance in damping oscillations compared with the case with only UPFC, even in worse conditions.

6.3. Oscillation Modes with Different Levels of Wind Penetration

The performance of the UPFC in damping oscillations under different wind penetration levels is addressed in this subsection. As described in Section 6.1, the DFIG output was 30 MW. To maintain the tie-line power from region 1 to region 2 at 400 MW, the power outputs from G₁ and G₂ were adjusted under different levels of wind penetration.

The interarea oscillation modes under different DFIG penetration levels are shown in

Table 5. The interarea oscillation modes under different DFIG outputs.

No.	Wind Power Output/MW	Without UPFC			With UPFC, Without PODC			With Both UPFC and PODC
		λ	ξ (%)	f (Hz)	λ	ξ (%)	f (Hz)	Λ	ξ (%)	f (Hz)
Interarea mode 1	0	−0.6609 ± j4.0114	16.26	0.6470	−0.6563 ± j3.9845	16.25	0.6427	−0.9429 ± j3.4921	26.07	0.5757
	10	−0.6605 ± j4.0293	16.18	0.6498	−0.6560 ± j4.0031	16.17	0.6456	−0.9358 ± j3.5055	25.79	0.5775
	30	−0.6634 ± j4.0267	16.26	0.6495	−0.6589 ± j4.0005	16.25	0.6453	−0.9350 ± j3.5047	25.78	0.5773
	70	−0.6700 ± j4.0228	16.43	0.6491	−0.6654 ± j3.9969	16.42	0.6449	−0.9328 ± j3.5044	25.72	0.5772
Interarea mode 2	0	−0.5455 ± j0.5501	70.41	0.1233	−0.5602 ± j0.5390	72.06	0.1237	−0.5406 ± j0.5398	70.76	0.1216
	10	−0.6120 ± j0.7220	64.66	0.1506	−0.6273 ± j0.7155	65.92	0.1515	−0.6231 ± j0.7446	64.18	0.1545
	30	−0.6092 ± j0.7568	62.71	0.1546	−0.6238 ± j0.7470	64.10	0.1549	−0.6198 ± j0.7815	62.14	0.1588
	70	−0.5967 ± j0.8511	57.41	0.1654	−0.6106 ± j0.8378	58.90	0.1650	−0.6089 ± j0.8868	56.60	0.1712

. The examined wind power output level was from 0 to 70 MW and the oscillation damping characteristics are then investigated. From Table 5, it was known that with the increase of the output power of DFIG, f of the intra-area oscillation mode 1 tends to decrease, ξ decreases initially and then increases, while f and ξ of the intra-area oscillation mode 2 tend to increase under different system conditions with the UPFC equipped. The results indicate that the employment of the UPFC can make interarea oscillation eigenvalues fall into the region with a larger stability margin.

6.4. System Robustness Analysis

In order to systematically examine the UPFC performance on enhancing power system robustness, suppose at t_f = 1.0 s, a three-phase short-circuit grounding fault occurred on bus 8, and was cleared at t_c = 1.2 s.

The following three cases are investigated:

• Case 1: Both the UPFC and PODC were not equipped. The power output of the wind farm was 30 MW, and the tie-line power from region 1 to region 2 was 430 MW;
• Case 2: The UPFC was equipped and the PODC was not. The power output of the wind farm and the tie-line power from region 1 to region 2 were the same with those in Case 1;
• Case 3: Both the UPFC and PODC were equipped. The power output of the wind farm was 50 MW, and the tie-line power from region 1 to region 2 was 449 MW.

The curves of ${\delta }_{G1}$ and P₄ are shown in Figure 9. The superior performance in mitigating oscillations using the UPFC is demonstrated, compared with the case without the UPFC equipped. The oscillations were damped in 12 s after the fault was cleared for the case with the UPFC equipped, and in about 20 s for the case without the UPFC equipped. Moreover, the capability of the UPFC in mitigating oscillations was further enhanced by the coordinated use of the PODC and UPFC. In other words, oscillations were more significantly mitigated by the combined use of the UPFC and PODC, and in this case the oscillations were damped in 7 s. This clearly demonstrated the efficiency of the joint employment of the UPFC and PODC for damping oscillations in wind farm integrated power systems.

6.5. Variations of Load and Wind Power Output

In this subsection, the same cases as those in Section 6.1 are investigated, i.e., (1) without UPFC; (2) with UPFC, without PODC; and (3) with both UPFC and PODC. The basic power output of the wind farm was 90 MW, and the transmission power from region 1 to region 2 was about 520 MW.

The load on bus 7 was subject to variations. The wind power output was assumed to fluctuate by 5% at 30 s, while the load at bus 7 declined by 5% at t = 1 s and t = 30 s, and increased by 10% at t = 15 s and t = 45 s. Variations of the load at bus 7 and wind power output are shown in Figure 10.

Figure 11 depicts the power angle curves of G₁, δ_G1, and voltage curves at bus 10 for the three cases. As shown in Figure 11a, δ_G1 was continuously variable with time due to variations of the load at bus 7 and the wind power output, and presented an insignificant increase, while the voltage at bus 10 decreased from 0.988 to 0.968 p.u., as shown in Figure 11b.

It can be clearly observed from these responses that the power angle and voltage fluctuations due to variations of the load at bus 7 tended to be stable after several oscillation periods in the case without the UPFC equipped, while the fluctuations were effectively suppressed with the UPFC equipped, especially in the case with the PODC equipped as well.

7. Applications in a Larger Sample Power System

To investigate the applicability and scalability of the UPFC and PODC, a larger power system with 2 areas, 8 generators, and 24 nodes [9] was employed. Each generator is represented by a sixth-order model. Area 1 included G₆–G₈, while area 2 included G₁–G₅. The regional tie-lines included two channels, i.e., the single-branch circuit 6–7 and the double-branch circuit 4–10 and 4–11. There were four interarea oscillation modes caused by oscillations of generators located in area 1 against those in area 2. In general, the load in the single-circuit channel was heavier than that in the double-circuit channel. Therefore, the single-circuit channel 6–7 was considered to be equipped with a UPFC. An equivalent DFIG wind unit was connected to bus 2 in area 1, then there was one more interarea oscillation mode related to the DFIG with an oscillation frequency around 0.6 Hz.

The following case studies are carried out:

• Case 1. Without UPFC. This represents the basic case. The total active power output of the wind farm was around 50 MW, and the tie-line power from region 1 to 2 through the tie-line 6–7 was 265 MW;
• Case 2. With UPFC, Without PODC. This case corresponded to the one in Section 4, and the other operating conditions were the same as Case 1;
• Case 3. Withboth UPFCand PODC. This case corresponded to the one in Section 5, and the other operating conditions were the same as Case 1.

The electro-mechanical oscillation modes in these three cases are given in

Table 6. Interarea oscillation modes in three cases.

No.	Without UPFC			With UPFC, Without PODC			With Both UPFC and PODC			Dominant Generators
	λ	ξ (%)	f (Hz)	Λ	ξ (%)	f (Hz)	λ	ξ (%)	f (Hz)
1	−0.9215 ± j10.6661	8.61	1.7038	−0.9289 ± j10.6302	8.71	1.6983	−0.9490 ± j10.6779	8.85	1.7061	G1, G7
2	−0.53111 ± j9.2646	5.72	1.4769	−0.5421 ± j9.2667	5.84	1.4774	−0.4303 ± j8.8692	4.85	1.4132	G1, G2, G7
3	−0.6954 ± j7.5278	9.20	1.2032	−0.7014 ± j7.5461	9.25	1.2062	−0.7366 ± j7.5910	9.66	1.2137	G5, G6
4	−0.4685 ± j6.4509	7.24	1.0294	−0.4792 ± j6.4622	7.40	1.0313	−0.5226 ± j6.5064	8.01	1.0389	G1, G5, G6
5	−0.00354 ± j3.7425	0.0946	0.5956	−0.00201 ± j3.5011	0.0574	0.5572	−0.0412 ± j 3.5926	1.15	0.5718	G1, G5, DFIG

. It is known that in these three cases, f and ξ in modes 1–4 do not change significantly. ξ₁ and ξ₄ tend to increase, while ξ₂ and ξ₃ tend to decrease. Regarding the interarea mode 5, f tends to decrease while ξ tends to increase; this is consistent with the analysis in Section 6. Similar to previous case study results, the combined use of UPFC and PODC significantly improves the oscillation damping characteristics of this wind farm integrated power system.

Suppose that a three-phase grounding short-circuit fault occurred at t_f = 1.0 s on the line between buses 8 and 11, and was cleared at t_c = 1.2 s. Figure 12 presents the active power output curves of G8, and the joint capability of the UPFC and PODC in suppressing oscillations is obvious.

8. Conclusions

In this work, the oscillation damping characteristics of a wind farm integrated power system with UPFC equipped was investigated. The distribution of the system eigenvalues was extended after wind farms were integrated into a given power system. This made the problem of suppressing inter-area oscillations more challenging. In this work, the d-q axis equivalent model was employed for DFIG, and the damping controller for the shunt converter of the UPFC was designed. The effectiveness of the proposed UPFC was evaluated using an eigenvalue analysis and time-domain simulation approach for various scenarios. Extensive simulation studies on a 2-area 4-machine 13-node power system and a 2-area 8-machine 24-node power system demonstrated the effects of UPFC, as well as the joint employment of UPFC and PODC, in suppressing oscillations in wind farm integrated power systems. Moreover, it was shown by the simulation results that the joint employment of UPFC and PODC could attain significantly better effects than the sole employment of UPFC in suppressing oscillations.