Well, if you feel like you're going off balance, or if you're wanting a result from the meditation, sometimes you will get tense because you're doing it in order to get a result. Sometimes there's a wish to get a feeling, although I don't know if this is the case, in this instance.
Sometimes we are not balancing within the meditation, in that we're focusing too much on one type of person, maybe difficult people, and trying too hard to bring them Compassion. At that time it may be helpful to bring our attention to ourselves, see our own tension and resistance and have compassion for ourselves at that time. It may be helpful to also do a bit of D/D with this person so we are not focusing totally on our situation with them.
Sometimes there may be "project mentality" with the Compassion/Lovingkindness, trying to start with or work too much on one person, or types of people that are causing difficulty. It is easier to begin with people we like or who are neutral, to ease into the meditation before considering difficult people. So if you're getting a lot of tenseness, look at the subjects you're doing and try to begin with easier subjects. Try to also balance the compassion side with the Lovingkindness within the meditation to also recognize the potential for the way out of Dukkha.
Sometimes other issues are coming up in the meditation, that need another type of meditation and another Compassion/Lovingkindness meditation may not be appropriate to do at that time. You write that you did three Compassion Lovingkindness meditations in a row but still feel quite tense. So identify where the tension is coming from - what hindrance. If for instance you are having doubt or under confidence, the meditation that may be more appropriate to do at that time is a confidence inspiring object of meditation - perhaps Sympathetic Joy, or reflection on your good past Kamma. Then it will not be avoiding the Compassion/ Lovingkindness meditation but using wisdom to see what is appropriate for the situation.
For example: Suppose you are going through your life with Compassion/Lovingkindness meditation, and you get to an age where you were very under-confident. If you find that you're still identifying with that person you were, it may be more appropriate to reflect on how you've changed - and the person who we are now is not the same as the person you were then. To strengthen this understanding it could be helpful to do a confidence-inspiring type of meditation in the next period, to more fully illustrate to the mind that you are not the person who you used to be.
So it really depends on what types of Compassion/Lovingkindness meditations you happen to be doing at the time, and seeing what is the appropriate method to balance the mind.