Whether you train using a tool like a power meter or a heart rate monitor, you have to keep one thing in mind: don't get too obsessed about the absolute accuracy of the numbers you use to gauge your efforts.
Our specific fitness fluctuates every day based on different variables such as rest, life stress, daily nutrition, time of the day for the session, accumulated fatigue, etc. thus trying to monitor your training levels to an exact watt or beat per minute can be a futile exercise. Instead of obsessing about precise numbers what is very important is for you is to proactive at developing your perceive exertion in combination with your heart rat and/or power.
What I mean is by this? First of all remember, training levels are man made as an attempt to make our training more efficient and your body doesn’t really know between your level 2 and your level 3, it juts 'feels' like you are doing more or less work. Certainly a series of physiological processes take place and some will be maximized training at 'x' or 'y' zone. Still, the training adaptations inter layer with each other and different adaptations will take place just at a greater/lesser degree.
The point is if you are doing a session at ‘x’ % of your Critical Power (CP) or your Maximum Lactate Steady State Heart Rate (MLSS-HR), whether you are 3 watts higher or 2 beats per minute lower won’t make impact your session as much as long as you are pushing based on what your body can take at a given point in time (also this is a reason I giggle when I hear coaches/athletes limiting training to certain 'zones'). Remember that your CP or MLSS HR are estimates of where your fitness was at a given point in time when you tested.
That estimate will allow you have an idea of your capabilities (fitness), but, since our fitness changes slightly everyday, then using your perceived exertion to adjust the effort level becomes something very important. In other words, instead of obsession whether you are to the decimal watt/bpm of your training level, instead, let the way your body 'feels' on that particular training session dictate the effort level and use your HR/Watts as a way to monitor where are you roughly when compared to your training levels.
To illustrated this point let’s assume your CP is 250 watts or MLSS HR170 bpm and you have a 3x10 minutes sets at CP or MLSS HR; based on how your fitness fluctuates and how your body is feeling on that particular day different things could happen:
1. You’ve done a great job resting, eating, recovering, managing your swim/run, etc. and during the session you manage to average a bit more of your usual training level (i.e 252w or 172bpm) even though perceived exertion wise, it feels like you are just pushing at your usual CP/MLSS HR. In other words, at the higher intensity level, the effort level was 'easier' for your body.
2. You’ve done an 'ok' job resting, eating, recovering, managing your swim/run, etc. and during the session you average exactly your 250 watts or 170 bpm. It means on that day based the intensity level matched your effort level (perceived exertion)
3. You’ve done a poor job resting, eating, recovering, managing your swim/run, etc. and during the session you can complete it all but at a lower intensity (i.e. 245w or 168bpm) yet the effort level was harder of the actual intensity. In other words, though your power/HR was lower than usual, it still felt that it was as hard as when you average your actual CP or MLSS HR
4. You’ve done a terrible job resting, eating, recovering, managing your swim/run, etc. and during the session since the very first set, it 'feels' very hard though you are at or below CP or MLSS HR. Each set feels harder and eventually you are forced to stop the session. Given your body's stage on that day, effort level ‘feels’ much harder of what the intensity level really is.The best thing to do is either resume training at an effort level that 'feels' right though intensity might be lower or rest/recover to take another shot in coming days.
In the long run as long if you re-test/adjust your training levels periodically, for most workouts your power/HR will follow a pattern and fall within your levels. But also, given the different variables affecting your daily fitness, focusing only on your training levels to dictate a session can be misleading. Using your perceive exertion AND power/HR effectively will also help you avoid going too hard in early sets or portions of a session.
The take away is that you need to learn listening to body, when you accomplish this, your perceive exertion will be like training with a built in power meter/pace/heart rate monitor all in one! This will allow you to deal with the different variables we have to deal every day and let you adjust to the right intensity based on how your body 'feels' on a given day. This will become very helpful when you train AND more so for racing.
HR/Power are tools to helps us make better training decisions, quantify load and even predict performance, still, both have limitations and we should use those to complement our training, not to dictate it. When you learn how to use your perceive exertion properly, it will tell you all you need to know about your body on that particular moment!