Algae is so prevalent in the aquatic hobby that many aquarists have given up trying to eradicate it and have just accepted it as part of normal tank life. We assure you it is perfectly achievable to have planted aquariums free from visible algae - especially filamentous green algae.
It takes a combination of factors to get a tank to that stage; algae will exploit any angle of weakness in a setup - in this sense it also acts as a signal as to what is being done wrong or right.
Algae interactions in a planted aquarium are complex and is best explained with an analogy. Similar to the weeds of the terrestrial world, algae is opportunistic and will bloom when the opportunity arises. Higher order plants out-compete weeds for space & light. In a dense forest, undergrowth yield to taller trees that block out the light by forming a dense canopy. Treefall gaps in crowded jungles give a chance for the undergrowth to spawn; for young trees to race to fill the canopy gap.
In aquatic ecosystems, our aquarium plants are the equivalent of large trees in the jungle, occupying most the liveable space - and many aquatic plants can grow emersed as well, gaining access to surface oxygen and shading the water beneath. Algae is at a disadvantage in such a position and has evolved to bloom opportunistically only when it detects that a gap has opened up in the system.
While they appear still and unmoving on the outside, there is complex biochemistry on going inside the plant as the plant generates carbohydrates, sugars and other metabolites from photosynthesis. Plants are leaky organisms and aquatic plants eject a portion of excess metabolites directly through their leaf surfaces and margins. Algae feed off these waste organics. When plants are under stress, for example, when adapting to a new environment, which requires a significant amount of re-programming of proteins and enzymes, the excretion of waste proteins and metabolites is increased.
An example of this is when you transfer a plant from an environment with high CO2 levels to an environment with low CO2 levels; the plant will need to channel more energy to CO2 capturing functions to compensate for the lower CO2 levels in the environment. The plant will activate more proteins associated with CO2 capture while also discarding enzymes and proteins responsible for growth functions. Older waste protein/DNA material is ejected directly on the leaf surface, as the plant re-configures its internal machinery to make best use of what is available in the current environment.
This is why plants that are newly introduced to a tank from a source with different growth conditions are often hit by algae, especially on the older leaves. Algae directly feeds off these waste organic material. These waste organic material include ammonia and other nitrogenous waste.
Ammonia and nitrogenous waste are common triggers for algae. Other sources in a tank a include heavy usage of ammonia/urea based fertilizer in the water column, waste from livestock or decaying plants. Consequently, having good filtration and a biologically matured tank where organic waste material and ammonia is broken down quickly helps reduce trigger factors. Light is merely an accelerator - reducing light does reduce the rate at which algae spawns but it is seldom the root trigger by itself for algae.
On the flip side, when plants are healthy, they generate defensive antimicrobial chemicals and enzymes to ward off pathogens and algae. Healthy plants, with enough excess energy to generate defensive chemicals, are very algae resistant. If a plant is nutrient deprived, or lack adequate access to CO2, they tend to be weaker and less robust, and have less energy to generate these defensive chemicals, which makes them more vulnerable to algae.
In a planted tank, unhealthy plants are prime algae triggers. So the first step to any algae issue is to pay attention to plant growth parameters - Nutrients, CO2, flow and make sure that each plant is getting what it needs to have healthy growth.
From an evolutionary point of view, attaching to a damaged plant that is not growing well maximizes survival potential for algae. A healthy growing plant will shade and crowd out the surrounding areas while a dying plant will not. Algae are finely attuned to bloom when plants are weak.
In a aquarium filled densely with healthy, robust plants, algae will find it hard to find a foothold.
An aquarium with a large percentage of its area planted is a more algae resistant environment than a sparsely planted tank. A similar situation is that a densely planted grass field is more resistant towards weeds as the weeds will find it difficult to anchor. An aquarium that is full of healthy, growing plants, with each plant defending their leaves with anti-pathogen chemicals, and threatening to shade surrounding areas with new growth, is a very hostile environment for algae.
The more sensitive / picky a plant is, the higher the chance that it will suffer from stress and trigger algae. A tank growing easier, larger, robust plants will be much easier to keep algae free compared to a tank growing higher demand, delicate, smaller plants. Slower growing plants also tend to be more vulnerable as a whole compared to faster growing plants, which adapt more quickly to changes in the tank environment. A holistic approach to light, CO2, fertilization is necessary to grow plants well consistently - this website has pages on the requirements for individual plants and how to tune each variable.
Plant husbandry plays a big role in the overall upkeep of the tank. All leaves age and deteriorate with time. Plants tend to channel more energy and resources into defending new growth, while leaving older leaves behind. This is especially so if the plant is short on growth resources. This means that a growing tank will always face some level of decaying older leaves and old growth. This can lead to over-crowding, and decaying older growth often attract algae. Old growth thus need to be cleared periodically. This is done by cutting off and discarding older leaves, especially those that have already attracted algae to attach. To rejuvenate growth on stem plants, it is necessary to periodically uproot the entire plant, cut off and replant the robust, fresh top portion of the plant, and remove and discard the older bottom rooted portion. To read on how to keep a tank algae free through removing old growth, read this article on solving algae issues without algicides.
Lobelia cardinalis adapting after being freshly transplanted. The plant defends the newer leaves from algae, while older leaves are discarded and attacked by algae. Trim away older leaves that are affected by algae to make space for new leaves to form.
Regularly replanting the fresh tops of stem plants, while discarding the older, less robust bottoms, rejuvenates plants and keep them algae free.
Other traces of organic waste persist in the water column and organic debris also accumulate on the substrate layer over time. These will also trigger algae if not cleared periodically. Water changing the 2hr Way aims at removing organic debris and algae spores that settle on the substrate layer of the tank. Doing this method greatly reduces algae spawning rate in the tank.
Read more on the fine details here.