C.1 Four-Order Linearized Dynamical Model

In order to design a robust power system controller, it is first necessary to find an appropriate linear mathematical description of the multimachine power system. In the viewpoint of “generator unit i,” the nonlinear state space representation model for such a system with two-axis model has the form

(C.1)

where the states

(C.2)

are defined as deviation from the equilibrium values

(C.3)

The nonlinear model of (C.1) can be presented as follows:

(C.4)

where

(C.5)

(C.6)

and

(C.7)

A detailed description of all symbols and quantities can be found in Ref. [1]. Using the linearization technique and after some manipulation, the nonlinear state (equations C.1) can be expressed in the form of following linear state space model.

(C.8)

where

(C.9)

and

(C.10)

The above parameters are defined as follows:

	Machine rotor angle
	Machine rotor speed
	d-axis internal machine voltage
	q-axis internal machine voltage
	Damping constant
	Inertia constant
	Driving point conductance
	d-axis open-circuit transient time constant
	q-axis open-circuit transient time constant
	d-axis synchronous reactance
	d-axis transient reactance
	q-axis synchronous reactance

The elements of matrix in (C.10) are

(C.11)

(C.12)

(C.13)

(C.14)

(C.15)

where

(C.16)

(C.17)

(C.18)

(C.19)

(C.20)

(C.21)

(C.22)

(C.23)

C.2 Four-Machine Infinite-Bus Power System

Unit No.	, s		, pu	, pu	, pu	, pu	, s	, s	MVA
1	8.05	0.002	1.860	0.440	1.350	1.340	0.733	0.0873	1000
2	7.00	0.002	1.490	0.252	0.822	0.821	1.500	0.1270	600
3	6.00	0.002	1.485	0.509	1.420	1.410	1.550	0.2675	1000
4	8.05	0.002	1.860	0.440	1.350	1.340	0.733	0.0873	900

Line No.	Bus–Bus	, pu	, pu	, pu
1	1–9	0.02700	0.1304	0.0000
2	2–10	0.07000	0.1701	0.0000
3	3–11	0.04400	0.1718	0.0000
4	4–12	0.02700	0.1288	0.0000
5	10–6	0.02700	0.2238	0.0000
6	11–7	0.04000	0.1718	0.0000
7	12–8	0.06130	0.2535	0.0000
8	9–10	0.01101	0.0829	0.0246
9	10–11	0.01101	0.0829	0.0246
10	11–12	0.01468	0.1105	0.0328
11	12–5	0.12480	0.9085	0.1640

1.00	19.21	10.00	6.48	5.71	7.60	−5.20
(s)	(s)	(s)	(s)	(s)	(s)	(s)
0.010	1.560	0.013	0.013	0.200	3.000	10.000

Parameters	Unit 1	Unit 2	Unit 3	Unit 4
(s)	0.08	0.06	0.07	0.07
(s)	0.10	0.10	0.10	0.10
(s)	0.10	0.10	0.10	0.10
(s)	0.40	0.36	0.42	0.42
(s)	10.0	10.0	10.0	10.0
(s)	0.05	0.05	0.05	0.05
(s)	0.08	0.08	0.08	0.08
(s)	0.58	0.58	0.58	0.58
(pu)	0.31	0.31	0.31	0.31
(pu)	0.24	0.24	0.24	0.24
(pu)	0.45	0.45	0.45	0.45
(pu/min)	0.50	0.50	0.50	0.50
(pu/min)	0.20	0.20	0.20	0.20
(pu/min)	1.50	1.50	1.50	1.50
(pu/min)	−0.50	−0.50	−0.50	−0.50
(pu/min)	−0.20	−0.20	−0.20	−0.20
(pu/min)	−0.50	−0.50	−0.50	−0.50

, s		, pu	, s
5.00	10.00	1.00	0.025
(s)	(s)	(s)	(s)
0.056	0.054	0.037	0.53