Distribution Networks and DER

The decision being supported

Can this feeder host more rooftop PV; where will the low-voltage network need reinforcement as heat pumps and EV charging arrive; what is a flexibility contract with local resources worth compared with copper; how should a DSO’s connection queue be prioritised; what does an aggregator’s portfolio actually deliver at a grid node.

Distribution has become the frontier of grid modelling, because that is where most new connections land and where the least data exists.

Why transmission methods do not transfer

Four assumptions from module 4 fail here.

High X/R. Distribution lines and LV cables have R comparable to or larger than X. The decoupling of P–θ and Q–V collapses, so active power injections move voltage directly — which is exactly why rooftop PV causes over-voltage at the end of a feeder rather than merely loading it. The DC power flow is not merely inaccurate here; it is inapplicable, since with X → 0 it has nothing to work with.

Balance. LV networks are single-phase-connected at the customer level and are genuinely unbalanced. Positive-sequence analysis discards the neutral current and the phase-to-phase voltage spread, both of which are often the binding issue. Unbalanced three-phase (or four-wire) modelling is required for credible LV work.¹

Meshing. MV and LV networks are usually built meshed but operated radially, with normally-open points. Radial topology makes some methods much easier — backward/forward sweep power flow, and exactness results for certain convex relaxations of AC-OPF hold on radial networks — but it also means the operative topology is a switching decision, and reconfiguration is a control action.²

Observability. Transmission is densely instrumented; distribution frequently is not. Many LV feeders have measurement only at the substation, with customer smart-meter data at 15-minute or hourly resolution, delayed, and privacy-restricted. Models must be built and validated with far less data than transmission practice assumes.

Formulation

For a radial feeder, the DistFlow (branch flow) model is the standard formulation, expressing flows and squared voltage magnitudes recursively along the feeder.³ Its relaxed form (dropping or conically relaxing the quadratic term) yields a second-order cone program that is provably exact under conditions typically satisfied on real radial distribution networks — one of the few places in power systems where a convex relaxation of AC-OPF is both tractable and rigorous.⁴

For unbalanced analysis, the standard approach is a three- or four-wire model solved by:

• Backward/forward sweep — exploits radial structure, robust, simple, the default in distribution tools.
• Current-injection Newton — better for meshed or heavily DER-populated networks.

Line models must include mutual coupling between phases (Carson’s equations, reduced with Kron’s method), and the neutral/earthing arrangement must be represented explicitly if neutral-point shift matters — which it does for LV voltage-quality questions.⁵

Hosting capacity

Hosting capacity is the maximum DER that can be connected without violating a defined criterion. The definition is the whole exercise:

Criteria: steady-state over- and under-voltage (EN 50160 limits of ±10% of nominal on LV in Europe), thermal loading of lines and transformers, voltage unbalance, protection coordination and reverse-flow issues, and power-quality limits.⁶

Method: the naive approach scales a uniform DER injection until the first violation. This yields a single number that is almost always misleading, because the answer depends heavily on where on the feeder the DER connects and on coincidence between generation and load. Stochastic hosting capacity — Monte Carlo over DER siting, sizing, and time series — produces a distribution and is the defensible form.⁷

Sensitivities that dominate the result: the assumed inverter reactive-power behaviour (a fixed power factor or a Q(V) droop can double hosting capacity relative to unity power factor), the load coincidence assumption, the tap-changer setting at the MV/LV transformer, and the choice of assessment time steps. State each one; a hosting capacity figure without them is not a result.

Flexibility as an alternative to reinforcement

The economic question underneath most DSO modelling is whether contracted flexibility — demand response, storage, curtailable connections — can defer or replace network investment.

A defensible comparison needs:

• The counterfactual reinforcement, costed properly and with its lead time.
• The flexibility requirement over time, as an hours-per-year and MW-per-hour profile, not an annual energy figure. Constraints are often binding for very few hours, which is what makes flexibility attractive; it also means the value is concentrated and fragile.
• Deliverability at the right node. Aggregated flexibility contracted at a portfolio level may not be located where the constraint is. This is the single most common defect in flexibility business cases.
• Rebound and payback. Deferred EV charging returns later, sometimes creating a sharper peak than the one avoided.

Flexible (“non-firm”) connection agreements are the regulatory instrument that makes this concrete, and they shift the modelling question from “can this connect?” to “how many hours per year will this be curtailed, and is that acceptable to the connectee?” — a question that requires time-series analysis rather than a worst-case snapshot.⁸

The TSO–DSO interface

As DER volumes grow, resources connected at distribution participate in system-level markets, and the two operators’ models must meet. The modelling artefact is a flexibility region (or aggregated feasible set) at the interface node: the set of (P, Q) exchanges the distribution network can support given its internal constraints. Computing it exactly is hard; approximations by sampling or projection are the practical approach, and it is an active research area with several competing coordination schemes.⁹

The related operational problem is prequalification: verifying that a distribution-connected resource bidding into a TSO market can actually deliver without violating a DSO constraint. This requires the DSO to run a network check on market bids, which in turn requires a distribution model of quality that many DSOs do not yet have.

Data and tooling

Data sources: DSO published network data where mandated (varies widely by country), smart-meter aggregates, SimBench and IEEE test feeders for benchmarking, and OpenStreetMap plus building/cadastral data for synthetic LV network generation.¹⁰

Tools: pandapower (balanced and unbalanced, good Python ergonomics, German synthetic networks included), OpenDSS (the reference open-source unbalanced distribution simulator, quasi-static time series built in), PowerFactory and CYME commercially, and PyPSA where the question is more economic than electrical.¹¹

Failure modes

• Using a balanced positive-sequence model for an LV voltage question. It will pass cases that a real feeder fails.
• Snapshot analysis for a time-dependent problem. Peak load and peak generation are different hours; both matter, and so do the hours in between when storage state matters.
• Assuming a synthetic network’s parameters are the real feeder’s. Conclusions must be stated at the population level (“typical German suburban feeders can host X”), not the asset level.
• Ignoring inverter control settings. They are a first-order determinant of the answer and are set by grid codes that change.

Summary

Distribution modelling requires abandoning the high-X/R, balanced, positive-sequence assumptions that make transmission analysis tractable. Radial structure buys back some tractability, including exact convex relaxations. Hosting capacity must be stochastic and its assumptions stated, and flexibility business cases live or die on nodal deliverability rather than on aggregate megawatts.

References