Confusion with TRIAC firing and zero crossing point
Overview

The details of zero-cross and phase-angle control have been discussed by others. A step back may help in understanding the decision process.


Using triacs to adjust AC power is a form of PWM (pulse-width modulation) of an AC power source. 
It is subject to the constraint that, once turned on, the triac will continue to conduct to the end of the half-cycle.
Using phase angle control we can get sub half-cycle control of the power. The power control is infinitely adjustable.
Using zero-cross on/off control we can only get cycle by cycle control. If we were to use this with a duty cycle time period of 10 cycles then we can only adjust power in 10% steps. (Yes, half-cycles steps are possible too.)


If the physical response to application of power is slow (a thermal load, for example) we can use on-off control over a long period. This is similar to switching a relay on and off to control a heater but with the advantage that with zero-cross control we greatly reduce EMI (electro-magnetic interference) and avoid radio and TV interference as well as greatly reducing the risk of interference with our control circuit.

Choosing a control strategy



Figure 1. SSR type decision tree.

Figure 1 shows the decision process for control type.


If rapid response is to be catered for then phase angle control is required using a triac or non-zero-cross SSR.


Phase-angle control



Figure 2. Full phase angle control waveforms.

On-off / full-wave duty-cycle control


If a slower response is adequate then on-off control will be adequate. If a readymade SSR with built-in zero-cross control is used then no additional circuitry is required. If not, then the controller should monitor the voltage and switch the triac at close to zero-cross.




Figure 3. Proportional on-off time control. Note that step size is one half-cycle minimum. This can make the response seem coarse if the repeat time is short.

The original question


  What I'm having trouble to understand is that, if one injects firings to the TRIAC very close to the zero crossing points, how then it is achieved the full control of the power delivered to the load?
  I mean if the firing is always in the neighborhood of the zero crossing point how can one reduce the average power to lets say %50 or %60 ?


As shown in Figure 3. Here the effective output power is about 25%.

SSRs



Figure 4. A typical industrial grade SSR by Crydom. These are available in zero-cross and non-zero-cross versions. (I've chosen the wrong picture: this one has an AC control input. A DC input type would be more normal.

With a ready-made SSR with built-in zero-cross detection the control circuit doesn't need to be aware of the mains waveform. It sends out the trigger command and the SSR looks after referencing it to the mains.

If the control circuit has to manage the zero-cross timing as well then a mains reference signal is required for synchronisation. This can be awkward (as evidenced by the many questions on the topic on this site) as it involves mains and the control board.

The internal operation of the SSR zero-cross devices is rather interesting. I explain operation in answer to Using AC current to trigger Triac.

Examples


Lamp dimmer: To avoid flicker phase control is used.
Motor speed control: To avoid chattering / jerking phase control is used.
Heater, domestic cooker hob: Thermal response of hob and pan is slow. On-off control with cycle time of 20 s is adequate.
Hot water heating: thermal response is slow (minutes). On-off control is adequate.


Please ask for clarification, if required.