AC 50/60 Hz power cables can be divided into two main groups:
✅ single-core cables;
✅ three-core cables.

1️⃣ Single-core cables, when bonding screens on both sides, have closed circuits of screens. The core currents (Ic) by their magnetic field induce AC 50/60 Hz currents in the screens (Is) – they are called circulating. Currents pass through the screens 24 hours a day, 365 days a year, heat up cables, increase power losses in the network and reduce the ampacity of the cable line. However, screen bonding types are known to solve the problem of circulating currents. Thus, the designer must choose one of the three bonding types:
🔹 solid bonding;
🔹 single-point bonding;
🔹 screen cross-bonding.

2️⃣-3️⃣-4️⃣ In practise, three–core cables always have the same solod bonding. This raises the question – don’t the same currents occur in the screens for three-core cables as occur in the screens of single-core cables? Why don’t we use single-point bonding or cross-bonding there? We will try to answer these questions, for which we will sequentially consider 4 different cable designs.

1️⃣ Single-core cables.
The phase screens are separated from each other by dielectric outer sheaths. Therefore, there are contours formed by screens: contour A-B, contour B-C, contour C-A. These contours are permeated by the magnetic field of three cores, and EMF and currents are induced in them.

2️⃣ Three-core cables (with three isolated screens).
Such cables are conventionally shown as cables with screens in the form of sectors, but the shape of the screen does not matter. The main thing is that the three screens do not contact each other, and therefore, in terms of losses, such a three–phase cable does not differ from three single-core cables laid in a closed trefoil. Therefore, we can say that there are currents in the screens of such a three-core cable, and they can create problems mentioned above. However, three-core cables with isolated screens are rarely found in practice, and even if they are, then it would be difficult to do there any other bonding type accept solid bonding.

3️⃣ Three-core cables (with three contacting screens).
Touching the screens means that we eliminate the isolation of the screens from each other. That is, we destroy contour A-B, contour B-C, contour C-A. There are no currents in the screens, and we can safely ground screens on both sides.

4️⃣ Three-core cables (with a single shared screen).
There are no individual screens, and there are no currents in the shared screen due to symmetry. We can safely ground screens on both sides.

CONCLUSIONS
There are currents in the screens in cases 1️⃣ and 2️⃣. That is, it cannot be said that only single-core cables have circulating currents in the screens. The rule is simple – for solidly bonded screens, 50/60 Hz currents arise only when two conditions are met at the same time:
✅ there are three separate screens A,B,C;
✅ these three screens A,B,C do not contact each other.

Once again, circulating currents do not occur because the cables are single-core or three-core. They arise because the screens of phases A, B, and C do not contact each other – that is in cases:
1️⃣ Single-core cables;
2️⃣ Three-core cable with three isolated individual screens.

If we want to have solid bonding, and our cable design applies to cases 1 and 2, then the screen circulating currents exist but can be reduced by the following measures:
➡️ by decreasing the screen cross-section (increasing its active impedance);
➡️ by reducing the distance between the phases (reducing the area of the screen contours).

Of course, the reduction of the screen cross-section must be carried out taking into account the need to ensure that the screens are resistant to short-circuit current.

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AFTERWORD
The book “High Voltage Cable Lines” provides various explanations for why circulating currents appear, what are the most effective measures to reduce such currents and power losses associated with them. This is done in a simpler and more convenient way than in the IEC and CIGRE documents. There are electronic version (PDF) of the book and nice printed version (hard copy). The printed version has become cheaper.