Feasibility Analysis on FESS Damping for Power System Oscillation

Application of Flywheel Energy Storage System (FESS) to damp multi-mode oscillations is investigated in multi-machine power systems. The feasibility of damping multi-mode oscillations with FESS is proved by application of Damping Torque Analysis (DTA). Making use of the characteristic of the independent of the active and reactive power control loops of the FESS, the method of the single FESS to damp multi-mode oscillations is proposed by superposing stabilizers on each control loop, which damp different oscillation mode respectively. The control loop and feedback signal are selected for each mode base on control theory, and the parameters of FESS-based stabilizers are tuned by Particle swarm optimization (PSO). Finally, with a four-machine power system case investigated, the eigenvalue and non-linear simulation results show that single FESS has ability of damping power system multi-mode oscillations.


I. INTRODUCTION
In the recent years, researchers all over the world have done a lot of work on using FESS to improve the stability of power system consisting of doubly-fed induction motors (DFIM) [1], [2]. However, there are few research papers on applying FESS to damp multi-mode oscillation in multi-machine system. The usual solution is to configure stabilizers in multi-machine system according to each oscillation mode respectively [3]. However, there is a problem called "eigenvalue deviation" because the stabilizers would affect each other [4]. To address it, some researchers put forward optimization algorithm to tune the parameters of the stabilizers [5], [6].
FESS has two independent loops to control active power and reactive power respectively. Because both of its loops can be configured with stabilizers, FESS device has the ability to Manuscript  damp multi-mode oscillation in power systems.
This paper mainly describes the theory on damping power system multi-mode oscillation using FESS. Firstly, damping torque analysis is applied to prove that FESS has the ability to damp the multi-mode oscillation. Then, control loops and feedback signals are chosen based on control theory, and particle swarm optimization (PSO) is used to tune the parameters of the stabilizers. Finally, a four-machine power system case was investigated to testify the validity of the proposed method.

II. LINEARIZED MODEL OF THE MULTI-MACHINE SYSTEM
WITH FESS Compared with other energy storage technology, FESS, composed by doubly fed induction motor (DFIM), is paid more attentions owing to its advantage in economy and practice [2], [7], [8]. As energy is stored in its rotating rotor, FESS can exchange energy with the system via DFIM by adjusting the speed of the flywheel (  FESS can be described as a third-order dynamic model. Generally, Stator flux orientation is chosen as its excitation control strategy because it can accomplish the decoupling control of active and reactive power. Meanwhile the reactive power can be replaced by voltage control.
When FESS is used to damp low frequency oscillation, stabilizers can be configured for its active power and voltage control loops. The schematic diagram is shown in Fig. 2. where: Ks is the gain of stabilizer; KPX and KIX are respectively proportional integral factors. It is assumed that FESS damping controllers are configured in active power and voltage control loops respectively and the output signals are Vsp and Vsu.
Combine the network algebraic equations and with linearized model of FESS, the linear equation of whole system can be written as 0 23 31 32 33 where ∆δ is the deviation in generator power angle; ∆ω is the deviation in generator speed; ∆Z is the state variables of generator (except power angle and speed), including state variables of FESS devices (except stabilizer). B JP and B Ju are respectively the transfer functions from the input signals (∆V sp and∆V su ), to the state variables.
The output signal that is the feedback signal can be expressed in the following equation where C is the transfer function from the state variables to y.
where ∆y p and ∆y u , are respectively the deviations in active power and voltage damping controllers' input signals, which can be achieved from (2).
(1)-(3) are the linearized model of the multi-machine system with FESS.

III. FEASIBILITY ANALYSIS ABOUT MULTI-MODE OSCILLATION DAMPING WITH FESS
FESS has two independent loops, controlling active power and reactive power respectively. Both loops can be configured with damping controllers independently.
According to (1) and Fig. 3, total influence to the mode λ i of two additional stabilizers can be calculated as follows [9] ( ) where: S ij is the sensitivity coefficient, defined as mode λ i partial derivative of T Dij , which is the damping torque of electro-mechanical oscillations in the j-th generator. H pj ∠φ pj and H uj ∠ φ uj are the forward channel from the damping controllers to electro-mechanical oscillations in the j-th generator.
From (4), it is obvious that the damping controllers supply damping torque to N generators with through N channels firstly and then N generators distribute the damping torque to each mode in the system via sensitivity coefficient. It shows how these two damping controllers restrain the multi-mode oscillation, and prove the feasibility that FESS can suppress the multi-mode oscillation.

IV. TUNING PARAMETERS OF FESS DAMPING CONTROLLERS
For damping multi-mode oscillation in the power systems, it is necessary to select appropriate FESS control loops, feedback signals, and parameters tuning of the damping controllers based on control-ability and observe-ability. Furthermore, owing to its high efficiency and the ability to find the optimal global solution, PSO algorithm is adopted to tune the parameters [10].
According to the control theory, the performance index b iK of mode λ i can be written as (5) , where W i T is the left eigenvector of system state matrix A corresponding to mode i. B K is the column vector in (1) where B Jp and B Ju are, controlling ∆V sp and∆V su , respectively.
The observe-ability index c iK of mode λ i , can be written as follows where V i is the right eigenvector of system state matrix A corresponding to mode i. From (5) and (6), control loops and feedback signals can be selected according to the performance indicators of controllability and observe-ability, respectively.
From (4), it is obvious that two damping controllers influence each other when they are used to restrain multi-mode oscillation. Therefore, PSO algorithm is adopted to tune the parameter of the damping controllers in FESS.
The structure of the controller is shown in Fig. 2. The time constants of measuring sector and DC block sector, marked as T 5 and T 6 , are given. Lead and lag sectors have the same time constants, that is to say, T 1 = T 3 , T 2 = T 4 . Hench each controller has three unknown parameters, time constant T 1 , T 2 and gain Ks. Then there are totally six unknown parameters. The objective function is maximizing the minimum of damping ratios of two weak damping modes, marked as ξ 1 , ξ 2 . So it can be written as: ( ) where K α is the gain of two controllers; T α is the time constant of the lead and lag links in the controllers.
(7) is a typical optimization problem with constraints, which can be dealt by PSO to achieve coordinated tuning.

V. CASE STUDY
A four-machines power system was investigated in this paper [11], shown in Fig. 4, assuming FESS connected at node 7. According to the eigenvalue, there are three weak damping modes: 1) Regional mode, λ 1 =0.05259±j3.9484, the damping ratio is -0.013 (unstable).
3) Part mode between generator G3 and G4, λ 3 = -0.3070±j6.1364, the damping ratio is 0.050 (weak damping mode). Since FESS is set in node 7, which is far from generator G3 and G4, the effect towards mode 3 will be not so well. Therefore, FESS is used to restrain λ 1 and λ 2 .
According to (5), the controllability indices of FESS active and reactive power control loops towards λ 1 and λ 2 can be calculated and summarized in Table I. The results in Table I show that: 1) FESS can control regional mode λ 1 effectively, while it is not very ideal to control part mode λ 2 .
2) Both indices show that active power control loop performs better than voltage control loop. According to (6), the observe-ability indices of FESS to regional mode λ 1 and part mode λ 2 can be calculated and shown in Table II.
From Table II, oscillation power P 78 of line 7-8 is suitable to be taken as the feedback signal to restrain regional mode λ 1 , and the integral of the power difference between line 5-7 and line 2-7 (∫(P 57 -P 27 )) is suitable to be taken as the feedback signal to restrain part mode λ 2 . Taking maximum of the minimum damping ratios of λ 1 and λ 2 as the objective function, stabilizer's parameters can be achieved based on PSO algorithm, which is shown in Table  III. Applying such parameters into operation control, the eigenvalues of λ 1 and λ 2 can be recalculated as Table IV shows. It is obvious that oscillation of λ 1 and λ 2 are restrained.  Considering there was a three-phase short-circuit fault occurred at bus 8 which lasts 0.1s, simulation results shown in Fig. 5 also verify the validity of the proposed stabilizers.

VI. CONCLUSIONS
It has been proved in this paper that FESS can restrain multi-mode oscillation in power system based on the analysis of damping torque.
Optimization algorithm can be utilized for parameters tuning for the design of FESS stabilizer.