robust control based energy storage stabilizers for power ... · energy storage, converter, pwm and...

Robust Control based Energy Storage Stabilizers forPower Systems with Large Scale Renewables

Indla Rajitha Sai PriyamvadaElectrical Engineering Department

Indian Institute of Science

Bangalore,India

[email protected]

Sarasij DasElectrical Engineering Department

Indian Institute of Science

Bangalore,India

[email protected]

Abstract—This paper proposes robust control theory basedstabilizers utilizing Energy Storage System (ESS) to improvethe damping of power systems with high level RenewableEnergy (RE) penetration. The proposed stabilizer can dampthe electromechanical modes as well as the oscillation modesintroduced by Converter Control Based Generators (CCBGs).A new weight-function for complementary-sensitivity functionof system is proposed to improve robustness of the stabilizer.The weight function is developed by utilizing information fromdifferent operating points of the power system so as to improvethe robustness. Controllability and observability indices are usedto evaluate the effective input-output signals and the placementof ESS stabilizer. Detailed dynamic model of ESS representingenergy storage, converter, PWM and filter dynamics is consideredin the design procedure of the stabilizer. The physical limitationsof ESS are considered in the stabilizer design by incorporating anew sensitivity function in to the objective function of H-infinitycontrol. The IEEE-39 bus system is modified to represent 50-70% RE penetration level. Small-signal studies and time-domainsimulations of the modified system are performed to verify theeffectiveness of the proposed ESS stabilizer. Cost benefit analysisand sizing of the stabilizer falls out of the scope of this paper.

Index Terms—Energy storage, renewables, stabilizers.

I. INTRODUCTION

In future, power grids are expected to operate with large

scale penetration of Renewable Energy (RE) sources. The

power electronic interface used for Renewable Energy (RE)

generations ie., Converter Control Based Generators (CCBGs)

results in decrease of overall rotational inertia in a power

system. In addition, control loops of CCBGs introduces two

new categories of oscillation modes into power system [1].

Energy Storage System (ESS) has been identified as a

suitable solution for enhancing reliability and power quality

of the modern power systems. In [2], [3] various technologies

of ESS for power system are presented and compared. ESS

for providing virtual inertia, frequency and voltage stability,

output smoothening, curtailment reduction and power quality

improvement is presented in [2], [3]. ESS based stabilizers

have been proposed for damping electro-mechanical oscilla-

tions [4]–[7] in conventional power systems. Impact of ESS

on transient stability of transmission grids is studied in [8],

[9]. These stabilizers do not address CCBG oscillation modes.

However, use of ESS stabilizer to damp both electrome-

chanical and CCBG oscillation modes under large scale RE

penetration scenario has not been discussed much.

This paper proposes ESS based stabilizers for damping of

small signal oscillations in power systems with large scale

RE penetration. The proposed stabilizer is based on H∞

norm robust control theory. As the CCBG modes may not

have participation from any inertial element of the power

system [1], the conventional damping torque analysis can

not be employed to analyze the system. To overcome this

issue, eigen-value based analysis techniques are employed

for the stabilizer design. As eigen-value based analysis is a

generic approach, it is apt for the analysis of power electronics

dominated power systems. The designed ESS stabilizers can

damp both CCBG and electromechanical oscillation modes.

ESS based approach provides flexibility in placing the stabi-

lizers at effective locations. Controllability and observability

indices are used for choosing the effective locations, input and

output signal set of ESS stabilizer. To the best knowledge of

the authors, in the existing works ESS is represented by the

dynamics of filter assuming the dc link capacitor voltage of

inverter is constant [4]–[6]. But dynamics of Energy Storage

(ES) i.e., behind the dc link, have not been considered in

the design procedure of the stabilizer. In the present study,

complete dynamic model of ESS representing ES, Pulse Width

Modulation (PWM) algorithm, converter and filter dynamics

is considered in the proposed controller design procedure for

ESS stabilizer. To ensure the robustness of the controller to

change in operating point of power systems, H∞ based control

theory is employed. H∞ based control theory has been well

explored in the power system domain for transmission delay

consideration, voltage control [10] and frequency control [11].

In these existing works, conventional high pass filters have

been used as weight functions for complementary sensitivity

function and targeted results were achieved. But for the present

study, it is observed that promising results can not be achieved

using these conventional weight functions. In addition to

changes in plant model at high frequencies of bode plot, which

suggests the use of high pass filter type weight functions,

changes in the model are observed even at lower frequencies.

To overcome this issue, the present study proposes a new

weight function. The changes in linearized plant model, due to

changes in operating point are modeled as the multiplicative978-1-5386-6159-8/18/$31.00 © 2018 IEEE

Proceedings of the National Power Systems Conference (NPSC) - 2018, December 14-16, NIT Tiruchirappalli, India

u+-

yref e Rest of the

power systemESS

yProposed

Controller

u*

ESS Stabilizer

Fig. 1. Block diagram for ESS integration

error in the nominal plant. The modeled error is chosen as

weight function for complementary sensitivity function of

the closed loop system to improve the robustness of the

controller. An additional sensitivity function, to capture the

ESS limits such as ramp rate and bandwidth, is included in

the objective function of control problem. The performance of

proposed ESS stabilizer is verified using a modified IEEE 39

bus system, representing 50-70% RE penetration level. Small

signal studies and time domain simulations are performed to

verify the effectiveness of the proposed stabilizer. Various RE

penetration scenarios are considered to verify the robustness

of the proposed stabilizer and for comparison of the proposed

weight function with conventional high pass filter type weight

function. The capability requirement of ESS for the stabilizer

action is calculated based on time domain simulations. The

proposed stabilizer may use a dedicated ESS or may share

ESS with other applications. Cost benefit analysis and sizing

of the proposed stabilizer falls out of the scope of this paper.

II. PROPOSED ESS BASED STABILIZER

A. Description of power system

To demonstrate the work done in this paper, n-bus power

system is considered with a large-scale penetration of CCBGs.

The power system includes Synchronous Generators (SGs),

Photovoltaic (PV) generators and Wind generators (WGs)

to represent conventional generation and RE generations.

Linearized state space model of any n-bus power system

with SGs, PVs and WGs around an operating point can be

formulated as (1), where AT is the system matrix, X is the

state vector of all components of the power system [12].

˙∆X = AT∆X (1)

Block diagram of power system incorporating ESS is rep-

resented in Fig. 1, block diagram of ESS model is shown

in Fig. 2, with yref , y(s), u∗(s), u(s), e(s) as reference input,

feedback signal, control input to ESS, control input from

ESS to system and error signal respectively. To evaluate the

impact of ESS on power system, (1) is reformulated as (2).

Equation (2) is obtained by expressing voltages at generator

buses, VQDgen, in terms of ∆X and controllable inputs from

ESS, ∆u, and expressing feedback signals from system, ∆y,

in terms of ∆X and ∆u.

˙∆X = AT∆X +BT∆u

∆y = CT∆X +DT∆u(2)

where, AT , BT , CT , DT are system, control, output and feed-

forward matrices respectively representing the power system.

B. Choosing location, controllable input and feedback signal

Real power, reactive power and current injections have been

used as controllable inputs in [13]–[15]. Frequency, magnitude

and phase of voltage at buses, tie line powers have been used

as feedback signals in [13]–[15]. The eigen-values, λi, right

and left eigen-vectors, vi and wi, of AT are related as (3).

AT vi = λivi; wTi AT = wT

i λi (3)

From (2) and (3), Controllability vector, β, of kth eigen-

value corresponding to input vector, u is given by (4a).

Observability vector, γ, of kth eigen-value corresponding to

output vector, y is given by (4b). From (4a), each element of

β i.e., βi represents the controllability of λk by ith input. The

signal with highest controllability is chosen as the effective

input from ESS to the rest of the power system. Similarly,

from (4b), the signal with highest observability is chosen as

the effective feedback signal from power system to ESS. The

location that facilitates the injection of effective input signal

to the system is chosen as the effective location for placement

of ESS stabilizer.

β = BTT vk (4a)

γ = CTwk (4b)

C. ESS dynamic model

The dynamics of ESS are crucial in determining the ef-

fectiveness of the output signal of ESS in following the

reference issued by the controller. The dynamic model of ESS

considered in the present analysis is given in Fig. 2(a). The

presented model is derived considering the PWM algorithm

[16], converter average model [17], filter and ES dynamics.

The circuit equivalent of Battery Energy Storage (BES) [18]

considered in the present study is shown in Fig. 2(b). The

transfer function of the ESS is derived based on Fig. 2. This

model is cascaded with the rest of power system model as

shown in Fig. 1 to achieve at the complete model of the plant.

D. Design of ESS controller using robust control theory

For a plant, G(s), with controller, K(s), and with unity

feedback, sensitivity function required for formulation of ro-

bust stability problem, ie., complementary sensitivity matrix,

T (s), [19] is given in (5). The problem formulation of a

H∞ norm based controller design is given in (6), where,∥

∥.∥

∥

∞is infinite vector norm, WT (s) is weighing function

of T (s). Closed loop system can be stabilized using the

controller K(s), if the infinity norm shown in (6) is less than 1

[19]. Detailed description about fundamental H∞ norm based

control and weight functions can be found in [19].

T (s) = [I +G(s)K(s)]−1G(s)K(s) (5)

minimizeK(s)

∥

∥WTT∥

∥

∞(6)

For the present study, the objective function of the mini-

mization problem is formulated so as to account the system

damping, changes in plant model at different operating points

and physical constraints of ESS. The formulation results in


TABLE IIPARTICIPATION FACTORS OF SGS, PVS AND WGS

Participation Factor States of generators

0.743 Controller state of G11

0.663 Controller state of G11

0.1-0.01Rotor mechanical and AVR states of

G2 and controller states of G11

<0.01 Rest of the system states

TABLE IIIRE PENETRATION LEVEL

Case No. RE contribution SG contribution Description

1 60% 40% Base case

2 70% 30% High RE

3 50% 50% Low RE

4 65% 35% Intermediate

The percentage is with respect to total generation in the system

function for R(s) is considered as derived in (13). The control

problem, (11), considering the derived weight functions and

the plant model at nominal operating point, is solved using

MATLAB. The controller is obtained as (15). The infinite

norm of the objective function (11) is obtained as 0.5025.

WT (s) =0.3462s4 + 16.06s3 + 109s2 + 2841s+ 536

s4 + 27.99s3 + 5231s2 + 7758s+ 1115(14)

K(s) =59.29s3 + 481.6s2 − 125.7s+ 3

s3 + 3.195s2 + 5s+ 7.316(15)

The designed ESS is placed at 39th bus as obtained in previous

steps. The critical modes of the power system at nominal

operating point, with and without the designed ESS stabilizer

are shown in Fig. 6. It is verified from the given figure that the

designed controller ensures that the real part of all the eigen-

values, SG modes as well as CCBG modes, is beyond −0.5

✲�✁

✲✂✁

✲✄✁

✁

✄✁

▼☎✆✝✞✟✠✡☛☞✡✌✍

✶✁✎✏ ✶✁✎✑ ✶✁✵ ✶✁✑ ✶✁✏ ✶✁✸✲✒✁

✁

✒✁

✶✓✁

P✔☎✕ ☛☞✡☛✆✍

❇

❋✖✗✘✙✗✚✛✜ ✢✖✣✤✥✦✧

Fig. 5. Bode plot of weight function, WT (s)

★✩✪✫ ★✩✪✬ ★✩✪✭ ★✩✪✮ ★✩✪✯ ✩

❘✰✱✳✴✷✹✺✰✻✼✽✱✳✾✰✿❀

★✫

★✭

★✯

✩

✯

✭

✫

■❁❂❃❄❅❂❆❈❉❊❄❃●❅❍❏❂❑▲●◆❖

❲✹◗❙❚✾◗ ✷❯❯

❲✹◗❙ ✷❯❯ ❱❚✻◗❳❚✳

Fig. 6. Critical eigen-values of power system with and without ESS

TABLE IVCOMPARISON OF PROPOSED AND CONVENTIONAL WEIGHT FUNCTIONS

Case No. Critical ModeUsing proposedweight function

Using high passweight function

1-0.1387±j4.36 11.3% 11.6%

2-0.1413± j4.363 10.07% -3.28%

3-0.1362± j4.358 13.47% 5.23%

4-0.1362± j4.358 11.3% -5.5%

from origin. As the controller is designed based on eigen-value

analysis, irrespective of a mode being SG mode or CCBG

mode, the controller improves the damping of any eigen-value

with real part greater than −0.5. The percentage damping of

the least damped mode of power system with proposed ESS

stabilizer is obtained as 13.47%.

C. Comparison of robustness of the designed ESS using pro-

posed weight function and conventional high pass filter

To compare the robustness of the designed ESS stabilizer

using proposed filter and high pass filter, various generation

scenarios are considered as shown in TABLE III. SG units

are to be rescheduled to maintain power balance. Load flow

study is performed for each case to ensure generation and

load balance. The controller obtained using conventional high

pass filter type WT (s) is shown in (16). The percentage

damping of the critical mode, in different generation scenarios,

achieved using the proposed and conventional high pass filter

type weight functions are given in TABLE IV. The results

in TABLE IV validates the improved robustness of the ESS

stabilizer.

Khp(s) =93.36s3 + 515.5s2 + 346s+ 61.16

s3 + 3.112s2 + 5.405s+ 1.807(16)

D. Time domain simulations

Results obtained from eigen value analysis are verified

using time domain simulations. Modified IEEE 39 bus system

described above is simulated, with base case as operating

point, using PSCAD software. A L-L-L-G fault is created


✼�✁ ✽ ✽�✁ ✾ ✾�✁ ✶✂

❚✄☎✆ ✝✞✟

✂�✵

✂�✠

✂�✽

✶

✶�✡

❘☛☞☛✌✍✎✏✍✑✒✓✔✕✓✒✖✗

t✘✥✙✚✛✜☛✙☛✢

❲✣✤✦ ✧★★❲✣✤✦✩✪✤ ✧★★

(a)

✫✬✭ ✮ ✮✬✭ ✯ ✯✬✭ ✰✱

✲✳✴✷ ✸✹✺

✭

✭✬✻

✭✬✿

✭✬❀

✭✬✮

❀

❀✬✻

❁❂❃❄❅❆❇❂❈❆❉❊❅❉❊❆❋●❍■❅❏❉❏❑

▲▼◆❖ P◗◗▲▼◆❖❙❯◆ P◗◗

(b)

Fig. 7. Time domain simulations (a) Voltage at 39th bus (b) Real poweroutput of G7

on 9th bus for 2 cycles and the corresponding responses

are given in Fig. 7. It is observed that as a response to the

disturbance, current output from ESS reached 0.4p.u. for 2

cycles and subsequently becomes zero as oscillations die out.

It is calculated that energy spent by the ESS for the stabilizing

action is 2.32kWh which is within the capability limits of

available energy storage units [24].

IV. CONCLUSION

The present paper proposes a stabilizer utilizing ESS to

improve damping of the power system with high RE penetra-

tion levels. Controllability and observability indices are used

for selecting effective control and feedback signals for power

system. A complete dynamic model representing ES, PWM,

converter and filter dynamics is considered while designing

the controller for ESS stabilizer. H∞ norm based robust

control is used to design the ESS stabilizer. A new weight

function for complementary sensitivity function is proposed to

improve the robustness of controller. A new sensitivity matrix

has been considered to incorporate ESS capability limits in

the controller design problem. Small signal studies and time

domain simulations are performed on a modified IEEE 39 bus

system to verify the performance of the proposed stabilizer.

The capability requirement of ESS for stabilizing action is

calculated from time domain simulations.

REFERENCES

[1] J. Quintero, V. Vittal, G. T. Heydt, and H. Zhang, “The impact ofincreased penetration of converter control-based generators on powersystem modes of oscillation,” IEEE Transactions on Power Systems,vol. 29, no. 5, pp. 2248–2256, 2014.

[2] K. Divya and J. Østergaard, “Battery energy storage technology forpower systemsan overview,” Electric Power Systems Research, vol. 79,no. 4, pp. 511–520, 2009.

[3] O. Palizban and K. Kauhaniemi, “Energy storage systems in moderngridsmatrix of technologies and applications,” Journal of Energy Stor-

age, vol. 6, pp. 248–259, 2016.[4] W. Du, H. Wang, S. Cheng, J. Wen, and R. Dunn, “Robustness of

damping control implemented by energy storage systems installed inpower systems,” International Journal of Electrical Power & Energy

Systems, vol. 33, no. 1, pp. 35–42, 2011.[5] J. C. Neely et al., “Damping of inter-area oscillations using energy

storage,” in Power and Energy Society General Meeting (PES), 2013

IEEE. IEEE, 2013, pp. 1–5.[6] W. Du, H. Wang, J. Cao, and L. Xiao, “Robustness of an energy storage

system-based stabiliser to suppress inter-area oscillations in a multi-machine power system,” IET generation, transmission & distribution,vol. 6, no. 4, pp. 339–351, 2012.

[7] L. Shi, K. Y. Lee, and F. Wu, “Robust ess-based stabilizer design fordamping inter-area oscillations in multimachine power systems,” IEEE

Transactions on Power Systems, vol. 31, no. 2, pp. 1395–1406, 2016.[8] A. Farraj, E. Hammad, and D. Kundur, “On the use of energy storage

systems and linear feedback optimal control for transient stability,” IEEE

Transactions on Industrial Informatics, vol. 13, no. 4, pp. 1575–1585,2017.

[9] A. Ortega and F. Milano, “Stochastic transient stability analysis oftransmission systems with inclusion of energy storage devices,” IEEE

Transactions on Power Systems, vol. 33, no. 1, pp. 1077–1079, 2018.[10] T. Hornik and Q.-C. Zhong, “H repetitive voltage control of grid-

connected inverters with a frequency adaptive mechanism,” IET power

electronics, vol. 3, no. 6, pp. 925–935, 2010.[11] V. P. Singh, S. R. Mohanty, N. Kishor, and P. K. Ray, “Robust h-

infinity load frequency control in hybrid distributed generation system,”International journal of electrical power & energy systems, vol. 46, pp.294–305, 2013.

[12] P. Kundur, N. J. Balu, and M. G. Lauby, Power system stability and

control. McGraw-hill New York, 1994, vol. 7.[13] H. Wang, F. Swift, and M. Li, “A unified model for the analysis of

facts devices in damping power system oscillations. ii. multi-machinepower systems,” IEEE Transactions on Power Delivery, vol. 13, no. 4,pp. 1355–1362, 1998.

[14] I. J. Perez-Arriaga, G. C. Verghese, and F. C. Schweppe, “Selectivemodal analysis with applications to electric power systems, part i:Heuristic introduction,” ieee transactions on power apparatus and

systems, no. 9, pp. 3117–3125, 1982.[15] N. Martins and L. T. Lima, “Determination of suitable locations for

power system stabilizers and static var compensators for dampingelectromechanical oscillations in large scale power systems,” IEEE

Transactions on Power Systems, vol. 5, no. 4, pp. 1455–1469, 1990.[16] R. Wu, S. B. Dewan, and G. R. Slemon, “Analysis of an ac-to-dc voltage

source converter using pwm with phase and amplitude control,” IEEE

Transactions on industry Applications, vol. 27, no. 2, pp. 355–364, 1991.[17] R. Wu, S. Dewan, and G. R. Slemon, “A pwm ac-to-dc converter with

fixed switching frequency,” IEEE Transactions on Industry Applications,vol. 26, no. 5, pp. 880–885, 1990.

[18] H. Chan, “A new battery model for use with battery energy storagesystems and electric vehicles power systems,” in Power Engineering

Society Winter Meeting, 2000. IEEE, vol. 1. IEEE, 2000, pp. 470–475.[19] G. C. Goodwin, S. F. Graebe, and M. E. Salgado, “Control system

design,” Upper Saddle River, p. 13, 2001.[20] C. Canizares et al., “Benchmark systems for small signal

stability analysis and control,” http://resourcecenter. ieee-pes.

org/pes/product/technical-reports/PESTR18, no. PES-TR, 2015.[21] A. Ellis, “Pv system models for system planning and interconnection

studies,” Sandia National Laboratories, 2009.[22] K. Clark, N. W. Miller, and R. Walling, “Modeling of ge solar pho-

tovoltaic plants for grid studies,” General Electric International. Inc,

Schenectady, NY, vol. 12345, 2010.[23] N. W. Miller, J. J. Sanchez-Gasca, W. W. Price, and R. W. Delmerico,

“Dynamic modeling of ge 1.5 and 3.6 mw wind turbine-generators forstability simulations,” in Power Engineering Society General Meeting,

2003, IEEE, vol. 3. IEEE, 2003, pp. 1977–1983.[24] A. Castillo and D. F. Gayme, “Grid-scale energy storage applications

in renewable energy integration: A survey,” Energy Conversion and

Management, vol. 87, pp. 885–894, 2014.


robust control based energy storage stabilizers for power ... · energy storage, converter, pwm and...

Documents