SEC_TO_TIME and TIME_TO_SEC is constrained to the range of the TIME data type (-838:59:59 to 838:59:59). This MySQL function overtakes this limit.

BIG_SEC_TO_TIME.sql

DROP FUNCTION IF EXISTS BIG_SEC_TO_TIME;
DELIMITER $$
CREATE FUNCTION BIG_SEC_TO_TIME(SECS BIGINT)
RETURNS TEXT
READS SQL DATA
DETERMINISTIC
BEGIN
	DECLARE HEURES TEXT;
	DECLARE MINUTES CHAR(5);
	DECLARE SECONDES CHAR(5);

	IF (SECS IS NULL) THEN RETURN NULL; END IF;

	SET HEURES = FLOOR(SECS / 3600);

	SET MINUTES = FLOOR((SECS - (HEURES*3600)) / 60);

	SET SECONDES = MOD(SECS, 60);

	IF MINUTES < 10 THEN SET MINUTES = CONCAT( "0", MINUTES); END IF;
	IF SECONDES < 10 THEN SET SECONDES = CONCAT( "0", SECONDES); END IF;

	RETURN CONCAT(HEURES, ":", MINUTES, ":", SECONDES);
END;
$$
DELIMITER ;

BIG_TIME_TO_SEC.sql

DROP FUNCTION IF EXISTS BIG_TIME_TO_SEC;
DELIMITER $$
CREATE FUNCTION BIG_TIME_TO_SEC(TIME TEXT)
	RETURNS BIGINT
 	DETERMINISTIC
 	READS SQL DATA
BEGIN
	DECLARE HEURES TEXT;
	DECLARE MINUTES CHAR(5);
	DECLARE SECONDES CHAR(5);

	IF (TIME IS NULL) THEN RETURN NULL; END IF;

	SET HEURES = SUBSTRING_INDEX(TIME, ":", 1);

	SET MINUTES = SUBSTRING(TIME FROM -5 FOR 2);

	SET SECONDES = SUBSTRING(TIME FROM -2 FOR 2);

	RETURN CAST(HEURES AS  UNSIGNED INTEGER)*3600 + CAST(MINUTES AS  UNSIGNED INTEGER)*60 + CAST(SECONDES AS  UNSIGNED INTEGER);
END;
$$
DELIMITER ;

Thank you for these functions!!!