Medium Transmission lines representation

Medium transmission lines are represented in two ways 

1) nominal - T Representation

2) nominal - π Representation

Nominal - T Representation

In this representation the shunt admittance is placed in the middle and the series impedance is divided into two equal parts and these parts are placed on either side of the shunt admittance. The nominal-T representation is shown in Fig below.

               Nominal-T representation

In this figure

Vs ,Is             - Sending end voltage & current

Vr,Ir         - Receving end voltage & current

Z/2          - half of the lumped series impedance of the line

Y             -lumped shunt admittance of the line

VM          -mid point voltage

Then the application of KCL at the midpoint results in

(1)

Rearranging the above equation can be written as

(2)

Now the receiving end current is given by

(3)

Substituting the value of V_M from (2) in (3) and rearranging we get

(4)

Furthermore the sending end current is

(5)

Then substituting the value of V_M from (2) in (5) and solving

(6)

Then the ABCD parameters of the T-network are

	(7)
	(8)
	(9)

Load flow Solution of IEEE-30 Bus by NR method

IEEE-30 BUS

NUMBER OF LINES                              =          41

NUMBER OF BUSES                             =          30

NUMBER OF GENERATOR BUSES    =          5

TOLERANCE VALUE                            =          0.0001

                                                                LINE DATA

SB	EB	R (p.u)	X (p.u)	Ys	Tap
1	2	0.0192	0.0575	0.0264	1
1	27	0.0452	0.1852	0.0204	1
2	5	0.0472	0.1983	0.0209	1
2	11	0.057	0.1737	0.0184	1
2	13	0.0581	0.1763	0.0187	1
3	13	0.012	0.042	0.0045	1
3	28	0.0636	0.2	0.0214	1
4	7	0	0.208	0	1
5	12	0.046	0.116	0.0102	1
6	9	0	0.14	0	1
7	8	0	0.11	0	1
8	17	0.0324	0.0845	0	1
8	20	0.0936	0.209	0	1
8	21	0.0348	0.0749	0	1
8	22	0.0727	0.1499	0	1
9	14	0.1231	0.2559	0	1
9	15	0.0662	0.1304	0	1
9	16	0.0945	0.1987	0	1
10	25	0.1093	0.2087	0	1
10	29	0.2198	0.4153	0	1
10	30	0.3202	0.6027	0	1
11	13	0.0119	0.0414	0.0045	1
11	27	0.0132	0.0379	0.0042	1
12	13	0.0267	0.082	0.0085	1
13	28	0.0169	0.0599	0.0065	1
14	15	0.221	0.1997	0	1
15	18	0.107	0.2185	0	1
15	23	0.1	0.202	0	1
16	17	0.0824	0.1932	0	1
18	19	0.0639	0.1292	0	1
19	20	0.034	0.068	0	1
21	22	0.0116	0.0236	0	1
22	24	0.115	0.179	0	1
23	24	0.132	0.27	0	1
24	25	0.1885	0.3292	0	1
25	26	0.2544	0.38	0	1
29	30	0.2399	0.4533	0	1
13	7	0	0.208	0	0.978
13	8	0	0.556	0	0.969
11	9	0	0.256	0	0.962
28	10	0	0.396	0	0.968

                                                               SHUNT DATA
NUMBER OF SHUNTS =2

B.No.   ADMITTANCE

  10            0.19
  24             0.043  

                                                                              BUS DATA

Bus No.	Type	Generation		Load		Voltage	Q min.	Q max.	V min.	V max.
		Real	Reactive	Real	Reactive
1	3	0	0	0	0	1.06	0	0	0.9	1.1
2	1	0.4	0	0.217	0.127	1.045	-0.4	0.5	0.9	1.1
3	1	0.2	0	0	0.3	1.01	-0.1	0.4	0.9	1.1
4	1	0	0	0.3	0	1.082	-0.06	0.24	0.9	1.1
5	1	0	0	0.942	0.19	1.01	-0.4	0.4	0.9	1.1
6	1	0	0	0	0	1.071	-0.06	0.24	0.9	1.1
7	2	0	0	0	0	1	0	0	0.9	1.1
8	2	0	0	0.058	0.02	1	0	0	0.9	1.1
9	2	0	0	0.112	0.075	1	0	0	0.9	1.1
10	2	0	0	0	0	1	0	0	0.9	1.1
11	2	0	0	0.076	0.016	1	0	0	0.9	1.1
12	2	0	0	0.228	0.109	1	0	0	0.9	1.1
13	2	0	0	0	0	1	0	0	0.9	1.1
14	2	0	0	0.062	0.016	1	0	0	0.9	1.1
15	2	0	0	0.082	0.025	1	0	0	0.9	1.1
16	2	0	0	0.035	0.018	1	0	0	0.9	1.1
17	2	0	0	0.09	0.058	1	0	0	0.9	1.1
18	2	0	0	0.032	0.009	1	0	0	0.9	1.1
19	2	0	0	0.095	0.034	1	0	0	0.9	1.1
20	2	0	0	0.022	0.007	1	0	0	0.9	1.1
21	2	0	0	0.175	0.112	1	0	0	0.9	1.1
22	2	0	0	0	0	1	0	0	0.9	1.1
23	2	0	0	0.032	0.016	1	0	0	0.9	1.1
24	2	0	0	0.087	0.067	1	0	0	0.9	1.1
25	2	0	0	0	0	1	0	0	0.9	1.1
26	2	0	0	0.035	0.023	1	0	0	0.9	1.1
27	2	0	0	0.024	0	1	0	0	0.9	1.1
28	2	0	0	0	0	1	0	0	0.9	1.1
29	2	0	0	0.024	0.009	1	0	0	0.9	1.1
30	2	0	0	0.106	0.019	1	0	0	0.9	1.1

                                                             POWER FLOW SOLUTION

B.No	Type	Generation		Load demand		Bus voltages Solved
		Real	React	Real	React	Volt Mag		Ang (Deg)
1	3	2.3873	-0.1765	0	0	1.06	0
2	1	0.4	0.5204	0.217	0.127	1.045	-5.0361
3	1	0.2	0.1917	0	0.3	1.01	-9.8046
4	1	0	0.2271	0.3	0	1.082	-18.3703
5	1	0	0.3574	0.942	0.19	1.01	-13.5302
6	1	0	0.1931	0	0	1.071	-15.0062
7	2	0	0	0	0	1.0399	-15.1913
8	2	0	0	0.058	0.02	1.0244	-16.1105
9	2	0	0	0.112	0.075	1.0458	-15.0062
10	2	0	0	0	0	1.0792	-15.5341
11	2	0	0	0.076	0.016	1.0151	-8.7828
12	2	0	0	0.228	0.109	1.0026	-12.0551
13	2	0	0	0	0	1.0105	-10.1343
14	2	0	0	0.062	0.016	1.0311	-15.9467
15	2	0	0	0.082	0.025	1.0267	-16.0779
16	2	0	0	0.035	0.018	1.0293	-15.7442
17	2	0	0	0.09	0.058	1.0204	-16.2135
18	2	0	0	0.032	0.009	1.0135	-16.8029
19	2	0	0	0.095	0.034	1.0089	-17.0388
20	2	0	0	0.022	0.007	1.0119	-16.8652
21	2	0	0	0.175	0.112	1.0154	-16.5169
22	2	0	0	0	0	1.0171	-16.4866
23	2	0	0	0.032	0.016	1.0206	-16.5169
24	2	0	0	0.087	0.067	1.021	-16.7487
25	2	0	0	0	0	1.0518	-16.1605
26	2	0	0	0.035	0.023	1.0348	-16.5526
27	2	0	0	0.024	0	1.0239	-7.2915
28	2	0	0	0	0	1.0121	-10.7532
29	2	0	0	0.024	0.009	1.0605	-16.6376
30	2	0	0	0.106	0.019	1.0497	-17.427

Total loss from line flows         =          0.1533418 +j 0.3293267

Total shunt loss                         =          0.00000000 -j 0.2661092

Slack bus power                        =          2.3873 -j 0.1765

Total Generation                       =          2.98734 +j 1.313224

Total Load                                 =          2.834 + j 1.25

System loss                               =          0.15334 + j 0.06322