Current-transformer-saturation-calculator.xlsx

	A	B	C	D	E	F	G	H	I	J	K	L	M	N	O	P	R	S	T	U	V	W	X	Y	Z	AA	AB	AC	AD	AE	AF	AG	AH	AI	AJ	AK	AL	AM	AN	AO	AP	AQ	AR	AS	AT	AU	AV	AW	AX	AY	AZ	BA	BB	BC	BD	BE	BF	BG	BH	BI	BJ	BK	BL	BM	BN	BO	BP	BQ	BR	BS	BT	BU	BV	BW	BX	BY	BZ	CA	CB	CC	CD	CE	CF	CG	CH	CI	CJ	CK	CL	CM	CN	CO	CP	CQ	CR	CS	CT	CU	CV
1		CONTENTS
2	Sheet 1:	CALCULATOR (this sheet)										A document of the
3	Sheet 2:	INSTRUCTIONS					Excel Spread Sheet					IEEE Power Systems Relaying Committee
4	Sheet 4:	BACKGROUND					See IEEE publication C37.110: "IEEE Guide for the Application					Contact: gswift@nxtphase.com
5							of CurrentTransformers Used for Protective Relaying Purposes"					Refer also to "CT SAT Theory (PSRC)".
11	ASSUMPTIONS:		CT core losses and sec'y reactance zero (thru-hole primary).						Frequency: 60 Hz
12			CT primary current is zero for t<0.				CT is 5 amp nominal		Time step = 1/12,000 second.
13
14	INPUT PARAMETERS:				ENTER:							CALCULATED:
15			Inverse of sat. curve slope =	S =	22	---					Rt =	Total burden resistance = Rw + Rb =			4.000	ohms
16			RMS voltage at 10A exc. current =	Vs =	400	volts rms					pf =	Total burden power factor =			0.894	---	CALCULATION OF RP
17			Turns ratio = n2/1=	N =	240	---					Zb =	Total burden impedance =			4.472	ohms
18			Winding resistance =	Rw =	0.000	ohms					Tau1 =	System time constant =			0.032	seconds	S =	22
19			Burden resistance =	Rb =	4.000	ohms					Lamsat =	Peak flux-linkages corresponding to Vs			1.501	Wb-turns	INDEX =	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30	31	32	33	34	35	36	37	38	39	40	41	42	43	44	45	46	47	48	49	50	51	52	53	54	55	56	57	58	59	60	61	62	63	64	65	66	67	68	69	70	71	72	73	74	75	76	77	78	79	80	81
20			Burden reactance =	Xb =	2.000	ohms					w =	Radian freq =			376.99	rad/s	ANGLE =	0	0.0157	0.0314	0.0471	0.0628	0.0785	0.0942	0.1100	0.1257	0.1414	0.1571	0.1728	0.1885	0.2042	0.2199	0.2356	0.2513	0.2670	0.2827	0.2985	0.3142	0.3299	0.3456	0.3613	0.3770	0.3927	0.4084	0.4241	0.4398	0.4555	0.4712	0.4869	0.5027	0.5184	0.5341	0.5498	0.5655	0.5812	0.5969	0.6126	0.6283	0.6440	0.6597	0.6754	0.6912	0.7069	0.7226	0.7383	0.7540	0.7697	0.7854	0.8011	0.8168	0.8325	0.8482	0.8639	0.8796	0.8954	0.9111	0.9268	0.9425	0.9582	0.9739	0.9896	1.0053	1.0210	1.0367	1.0524	1.0681	1.0838	1.0996	1.1153	1.1310	1.1467	1.1624	1.1781	1.1938	1.2095	1.2252	1.2409	1.2566	1.2723
21			System X/R ratio =	XoverR =	12.0	---					RP =	Rms-to-peak ratio =			0.34584		(SINE^S)^2 =	0	0.0000	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0	0.000000000178662653	0.0000000004419399443	0.000000001062033897	0.00000000248227441	0.000000005648775377	0.00000001252788785	0.00000002710304757	0.00000005724623168	0.0000001181441409	0.0000002384185791	0.0000004708001128	0.0000009103090758	0.000001724515451	0.000003202766516	0.000005834486997	0.00001043097062	0.00001831066068	0.00003157484113	0.00005350885198	0.00008915308211	0.0001460974137	0.0002355613896	0.0003738285294	0.0005841047697	0.0008988652912	0.001362738031	0.002035942918	0.002998260627	0.004353441764	0.006233886618	0.008805329289	0.01227115301	0.01687585428	0.02290707371	0.03069553594	0.04061220601	0.05306199255	0.06847342375	0.08728390145	0.109920406	0.1367758741
22			Per unit offset in primary current =	Off =	1.00	-1<Off<1					A =	Coefficient in instantaneous ie
23			Per unit remanence (based on Vs) =	lrem	0.00	---						versus lambda curve: ie = A * l^S :			3.83E-03	---	RP =	0.3458383708
24			Symmetrical primary fault current =	Ip =	12,000	amps rms					dt =	Time step =			0.000083	seconds
25											Lb =	Burden inductance =			0.00531	henries
26
27			Thick lines:	Ideal (blue) and actual (black) secondary current in amps vs time in seconds.
28			Thin lines:	Ideal (blue) and actual (black) secondary current extracted fundamental rms value, using a simple DFT with a one-cycle window.
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43		To determine the effect of saturation on a particular digital relay, one must have "models" for the blocks shown below:
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51
52										Calculation of Mag. Of Fund'l			Calculation of Mag. Of Fund'l		Phase	Phase
53			is =							IDEAL			ACTUAL		IDEAL	ACTUAL
54	step	time	pri cur/N	fl-linkages	exc curr		sec cur	d/dt(is)
55	number	t	i1(t)/N	l(t)	ie(t)	Dl(t)	i2(t)		I1(t)*sin	I1(t)*cos	I1MAG	I2(t)*sin	I2(t)*cos	I2MAG	I1PH	I2PH
56		seconds	amps	Wb-turns	amps	Wb-turns	amps	amps/s
57
58		TIME	IDEAL				ACTUAL
59
60	-200	-0.0167	0.000	0.00010	0.000	-0.00166	0.000	-3750			0			0	0.0	0.0
61	-199	-0.0166	0.000	0.00010	0.000	-0.00128	0.000	-2903			0			0	0.0	0.0
62	-198	-0.0165	0.000	0.00010	0.000	-0.00091	0.000	-2057			0			0	0.0	0.0
63	-197	-0.0164	0.000	0.00010	0.000	-0.00054	0.000	-1212			0			0	0.0	0.0
64	-196	-0.0163	0.000	0.00010	0.000	-0.00016	0.000	-370			0			0	0.0	0.0
65	-195	-0.0163	0.000	0.00010	0.000	0.00021	0.000	469			0			0	0.0	0.0
66	-194	-0.0162	0.000	0.00010	0.000	0.00058	0.000	1304			0			0	0.0	0.0
67	-193	-0.0161	0.000	0.00010	0.000	0.00094	0.000	2133			0			0	0.0	0.0
68	-192	-0.0160	0.000	0.00010	0.000	0.00131	0.000	2957			0			0	0.0	0.0
69	-191	-0.0159	0.000	0.00010	0.000	0.00167	0.000	3774			0			0	0.0	0.0
70	-190	-0.0158	0.000	0.00010	0.000	0.00203	0.000	4584			0			0	0.0	0.0
71	-189	-0.0158	0.000	0.00010	0.000	0.00238	0.000	5386			0			0	0.0	0.0
72	-188	-0.0157	0.000	0.00010	0.000	0.00273	0.000	6179			0			0	0.0	0.0
73	-187	-0.0156	0.000	0.00010	0.000	0.00308	0.000	6962			0			0	0.0	0.0
74	-186	-0.0155	0.000	0.00010	0.000	0.00342	0.000	7735			0			0	0.0	0.0
75	-185	-0.0154	0.000	0.00010	0.000	0.00376	0.000	8497			0			0	0.0	0.0
76	-184	-0.0153	0.000	0.00010	0.000	0.00409	0.000	9246			0			0	0.0	0.0
77	-183	-0.0153	0.000	0.00010	0.000	0.00441	0.000	9983			0			0	0.0	0.0
78	-182	-0.0152	0.000	0.00010	0.000	0.00473	0.000	10706			0			0	0.0	0.0
79	-181	-0.0151	0.000	0.00010	0.000	0.00505	0.000	11416			0			0	0.0	0.0
80	-180	-0.0150	0.000	0.00010	0.000	0.00535	0.000	12110			0			0	0.0	0.0
81	-179	-0.0149	0.000	0.00010	0.000	0.00565	0.000	12789			0			0	0.0	0.0
82	-178	-0.0148	0.000	0.00010	0.000	0.00595	0.000	13452			0			0	0.0	0.0
83	-177	-0.0148	0.000	0.00010	0.000	0.00623	0.000	14098			0			0	0.0	0.0
84	-176	-0.0147	0.000	0.00010	0.000	0.00651	0.000	14727			0			0	0.0	0.0
85	-175	-0.0146	0.000	0.00010	0.000	0.00678	0.000	15337			0			0	0.0	0.0
86	-174	-0.0145	0.000	0.00010	0.000	0.00704	0.000	15929			0			0	0.0	0.0
87	-173	-0.0144	0.000	0.00010	0.000	0.00730	0.000	16502			0			0	0.0	0.0
88	-172	-0.0143	0.000	0.00010	0.000	0.00754	0.000	17055			0			0	0.0	0.0
89	-171	-0.0143	0.000	0.00010	0.000	0.00778	0.000	17588			0			0	0.0	0.0
90	-170	-0.0142	0.000	0.00010	0.000	0.00800	0.000	18099			0			0	0.0	0.0
91	-169	-0.0141	0.000	0.00010	0.000	0.00822	0.000	18590			0			0	0.0	0.0
92	-168	-0.0140	0.000	0.00010	0.000	0.00843	0.000	19059			0			0	0.0	0.0
93	-167	-0.0139	0.000	0.00010	0.000	0.00862	0.000	19505			0			0	0.0	0.0
94	-166	-0.0138	0.000	0.00010	0.000	0.00881	0.000	19929			0			0	0.0	0.0
95	-165	-0.0138	0.000	0.00010	0.000	0.00899	0.000	20330			0			0	0.0	0.0
96	-164	-0.0137	0.000	0.00010	0.000	0.00915	0.000	20707			0			0	0.0	0.0
97	-163	-0.0136	0.000	0.00010	0.000	0.00931	0.000	21061			0			0	0.0	0.0
98	-162	-0.0135	0.000	0.00010	0.000	0.00946	0.000	21390			0			0	0.0	0.0
99	-161	-0.0134	0.000	0.00010	0.000	0.00959	0.000	21695			0			0	0.0	0.0
100	-160	-0.0133	0.000	0.00010	0.000	0.00972	0.000	21975			0			0	0.0	0.0
101	-159	-0.0133	0.000	0.00010	0.000	0.00983	0.000	22230			0			0	0.0	0.0
102	-158	-0.0132	0.000	0.00010	0.000	0.00993	0.000	22460			0			0	0.0	0.0
103	-157	-0.0131	0.000	0.00010	0.000	0.01002	0.000	22665			0			0	0.0	0.0
104	-156	-0.0130	0.000	0.00010	0.000	0.01010	0.000	22843			0			0	0.0	0.0
105	-155	-0.0129	0.000	0.00010	0.000	0.01017	0.000	22996			0			0	0.0	0.0