We now state the assumptions that are made in this chapter and also in Chapter2.
A1 Distribution system losses are assumed to be negligible.
A2 The communication network is ubiquitous, broadband, reliable, and has a low latency. The end-to-end communication delay is on the order of a few milliseconds.
A3 MCC nodes can detect overloads, reverse flows, and over-voltage and under-voltage incidents sufficiently quickly so that any transient problem is within system toler-ances and the protection system will not be invoked.
A4 Line and transformer overloads cannot be inferred from local measurements per-formed at end-nodes. Therefore, congestion must be explicitly signalled to the end-nodes.
A5 Active end-nodes are tamper-resistant and under control of the electric utility. Thus, any control signal sent to them is assured of a cooperative response.
A6 Active end-nodes can instantly adjust their power production or consumption to the level desired by operators. This impacts the loading of lines and transformers that supply these end-nodes almost immediately as power flows in the grid at the speed of light.
A7 EV batteries can be charged at any rate that does not exceed the maximum charge power supported by their charger, independent of their SOC. This variable rate charging has negligible impact on the lifetime of batteries.
A8 EVs are not capable of delivering power back to the grid as is the case in V2G.
A9 Battery storage systems and smart EV chargers do not consume reactive power and operate at unity power factor.
A10 Smart inverters can synthesize reactive power. We assume that their real and reactive power outputs can be jointly controlled on a fast timescale.
3.4 Chapter Summary
Real-time control can reliably and economically address congestion, voltage, and reverse flow problems that might occur due to the integration of residential PV systems, storage technologies, EV chargers, and other elastic loads. We presented an approximate linear branch flow model for radial distribution systems that neglects losses. Branch flow equa-tions given by this model can be incorporated in the formulation of convex optimal control problems. We developed a time-slotted model for active end-nodes that are common in today’s distribution networks. We concluded this chapter by summarizing the assumptions that we have made in modelling loads and active end-nodes.
Chapter 4
Congestion Management in Distribution
Networks
In this chapter, we consider a radial distribution system that supplies homes and EV chargers. We explore the real-time power allocation to smart EV chargers to satisfy efficiency and fairness criteria and avoid congestion in the distribution network. Inspired by Internet congestion control mechanisms, we design a distributed feedback control mechanism for smart chargers using measurements of the congestion state of feeders and transformers. Our approach deals with line and transformer overloads but does not address voltage problems, since the underlying model ignores reactive power flows and resistive losses. We tackle these problems in Chapter5.
4.1 Introduction
Uncontrolled charging of EVs can congest lines and transformers and cause voltage swings in the distribution system at moderate to high penetration levels [58,80]. Even at low penetration levels, uncontrolled charging may lead to congestion in certain neighbour-hoods, due to a non-homogeneous distribution of EVs in the distribution network [25].
Unrelieved congestion can overheat transformer windings and accelerate degradation of line and transformer insulation, leading to premature equipment failure. Although distri-bution system congestion can be relieved by upgrading system components piecemeal, this approach is both expensive and time-consuming. A more promising alternative is for the utility company to directly control smart EV chargers so that system components are rarely overloaded. This is the motivation for our work in this chapter.
The real-time computation of the charging rate for smart chargers achieves higher utilization than prediction-based scheduling approaches by continuously adapting the charge power of smart EV chargers to the measured available capacity of the network. In this approach, enabled by the widespread adoption of measurement and communication technologies in future distribution systems, information about the congestion state of lines and transformers is sent from measurement nodes to smart chargers in the form of feedback. This allows the chargers to independently adjust their charge power, using a higher rate when there is available capacity and reducing it when the distribution network becomes congested. Note that during demand peaks, the available capacity of the network may not allow chargers to charge connected EVs at their maximum rate1. Therefore, it is desirable to continuously allocate the available capacity in a fair manner among EV chargers. Computing the charge power for EV chargers, given the available network
1In fact, this is a best-effort service. Hence, in the rare event that the grid is overly congested some EVs might not be fully charged by their deadlines.
capacity, can be viewed as an optimization problem whose solution is an allocation that simultaneously satisfies efficiency and fairness criteria.
Drawing on the design of congestion control protocols in packet-switched net-works [85], we formulate a nonlinear convex optimization problem for a snapshot of the system to obtain an allocation of charge powers which is both proportionally fair [50], and scale-invariant Pareto optimal [105]. We propose a TCP-inspired iterative distributed algorithm for solving the optimization problem and for computing the optimal control using dual decomposition [70] and the projected subgradient method [18]. More specifi-cally, we decompose the dual optimization problem into several subproblems, each solved independently by a charger to adjust its charge power. These subproblems are coordinated by a master problem through congestion prices [50], which are computed based on the congestion state of distribution lines and transformers and communicated to EV chargers periodically. Hence, unlike TCP endpoints that infer congestion, the degree of congestion is explicitly signalled to the chargers.
We first consider a quasi-static setting, where household demands and the number of active chargers are fixed during a time slot, and then extend our study to a dynamic setting, where household demands and the number of active chargers change over time.
We validate, using power flow analysis on a standard test distribution system, that our control algorithm does not violate operational limits of the distribution network and rapidly converges from large disturbances to a stable operating point in both static and dynamic settings. We investigate the sensitivity of our control algorithm to EV arrivals and departures, EV penetration levels, the rated capacity of EV chargers, and the choice of control parameters and setpoints.
This work draws on the seminal work of Low and Lapsley on flow control [59]. The authors proved and evaluated, using extensive simulations, that a distributed price-based iterative algorithm that takes a control action in every iteration converges as long as changes are sufficiently small in every iteration. Hence, our proposed control is also stable under some conditions. We analyze the convergence speed of the control algorithm in the worst case, provide engineering insights into the dynamic operation of the real-time distributed control algorithm, and discuss different design choices for control parameters to meet utility performance requirements.
time
uncontrolled load
capacity sum of controlled and uncontrolled loads
controlled load
Figure 4.1: Available network capacity changes on a slower timescale than the timescale of control for active end-nodes.