“There was grid stability in the past, we still have it mainly now, and of course we’ll have it in the future”.

That statement is heard often enough.

“As the generator and load buses become more ‘dynamic’, we’ll adapt the grids organically—we’ll do whatever needs to be done to keep the system stable as there is always some engineering solution we can resort to” — another frequent expression of sanguinity as renewables make more and more inroads into the national grids.

*By Phil Kreveld, CT Lab, Stellenbosch, South Africa*, for Transmission & Distribution Magazine Australia.

A planned approach to forecasts taking into account the future variability of loads and generators and their effects on grid stability, makes for lower cost engineering solutions, as compared to holding off and ‘taking action when needed’. Standing in the way of a thoroughly analytical approach to grid stability is the lack of overarching, comprehensive dynamic data, which is now essential as national grids approach 50% and higher of non- dispatchable generation and substation loads are increasingly subject to large power flow changes because of behind-the-meter solar.

The organic approach (waiting for problems to appear) is scaring off investors in solar and wind and seeing others unloading their shareholdings; take for example, the solar farms in north western Victoria and across the border in NSW, having to reduce their output because of voltage oscillation in weak links, or marginal loss factors that are imposed instead of measured in real time and that have left many investments in jeopardy.

Demonstrating the need for overall, multi-node, synchronised measurements in national grids is not easy in the current climate of disparate ownerships of electrical transmission and distribution assets because what is needed is a national objective for assuring grid stability as the basis for such a monitoring and control platform. In practice this has been, to date, basically a disincentive to anything other than a ‘wait and see’ approach. It need not be so.

**The Two-Bus Example For The Basis Of Stability**

Iterative power flow calculations, when many loads and generators are subject to fast power changes, domestic inverter stability subject to frequency jumps and the behaviour of voltage regulation equipment is multi factorial, etc., are practically impossible to perform or rely on.

The start for most control solutions is the measurement of all available data and this is certainly so for complex grids.

To focus the mind, consider the simplest of grids, the two- busbar system with only reactance, X. The solution for power flow is simple, making discussion easier than when considering multi-bus systems, but by extension indicates the importance of gathering voltage, power, reactive power, sequence components, harmonics, etc in extensive grids.

A little bit of trigonometry (see Figure 1) on the vector diagram reveals the power and reactive power at bus 2. Note: VS is the sending voltage, VR is the receiving voltage, and δ is the angle by which the sending voltage leads the receiving voltage.

The above equations are sufficient to provide the limits of voltage stability in terms of power and reactive power at bus 2.

Normalising the terms in the above equations, by letting v = V_{R}/V_{S}, p = P.X/V_{S2} and q = QX/V_{S2}. Then:

Squaring both equations yields:

Substituting for v.cos б, equals q + v^{2}.

Adding and rearranging the terms:

Solving this as a quadratic equation for v^{2}, and then taking the square root, yields:

The above equation, using normalised parameters permits evaluation of voltage stability at the load bus using real value roots.

Figure 2 is a graphical presentation of solutions for v in terms of normalised power, p, and reactive power q. The central line connecting the individual maxima for v, clearly indicates the stable solutions, in the positive territory above the meridian line. Below is the unstable region.

*The voltage stability curves are for a two-bus system. The vertical axis shows the normalised load bus voltage v (V _{R}/V_{S}) as a function of normalised load p (XP/V_{S2}) and normalised reactive load q (XQ/VS^{2}).*

**Transitioning To Multi-Bus Systems**

Of course, the very simple example is not equal to describing the complexities of a multi-bus network with thousands of nodes.

To fully describe three-bus system stability boundaries, in terms of power, P, reactive power Q, voltage V, and voltage angle θ four partial derivatives are required:

The Jacobean matrix for appears below for a three-bus system, and this would simply be sub-cell of a multi-bus network (n x n matrix of huge size). Solutions via Newton-Raphson, or Gauss-Seidel iterations would follow.

We can safely leave the complexities of Jacobean matrices aside, and for that matter standard, linearised computer programs for power flow because the rapid changes with time due to weather variability demand a totally different approach—one that inputs very short, time-variant, rapid fluctuations of power, reactive power, and in the case of distribution networks, also harmonics due to the vast number of inverters.

**Distribution Networks Feed Instability Forward**

Currently voltage control in distribution networks is the main concern but as the penetration of solar inverters steadily increases problems with inverter synchronisation will appear due to harmonics and also changes in substation voltage angles.

Inverter synchronisation is an important topic in its own right and will be a subject in a follow-on article. In short, rapid changes in power flow will feed up the line into transmission unless substations are required to maintain a high level of stability.

Let’s make use of the simple two-bus link example, and think through the effects in the upstream sub-transmission and transmission networks.

At the low voltage distribution level, voltage angle differentials are negligibly small, but they become appreciable at the medium voltage feeder level, where the simple two-bus example applies.

The fact is that bus 1 is an nth node and its P δ, and Q δ depend also on upstream power, reactive power, and voltage angle dynamics.

With rapid changes in power and reactive power, the only effective form of control of a network with a large penetration of renewables is via multi-nodal monitoring of voltage and current synchrophasors, power, reactive power, sequence components and power quality parameters such as harmonics, short-term and long- term flicker in distribution networks.

In an ideal world we could stipulate that at the connection point to transmission, substations should present as near-constant, or slowly varying loads.

‘Slow varying’ substation load is something from the past. As already stated, distribution instability is, therefore ‘exported’ to transmission networks, and from there interacts with many non-dispatchable generators. Without monitoring and control at the HV level, major system instabilities could arise.

The occurrence of voltage collapse in transmission links by the time we have 50% penetration of non-dispatchable renewables is not some farfetched idea. Therefore, the necessity of monitoring nodes for voltage, real power, reactive power, and voltage and current phase angles in real-time becomes crystal clear.

**Voltage Angle Stability For Proper Synchronisation Of Inverters**

Synchronisation is a crucial aspect in grid-tied systems, including single-phase photovoltaic inverters, and can affect the overall performance of the system.

A chief concern in synchronisation is the presence of harmonics and upstream voltage angle instability. Synchronisation schemes, such as the multi-harmonic decoupling phase-locked loop present a fast response to grid disturbances and high accuracy under harmonic distortions. However, it not inured from frequency disturbance.

Distribution grids cannot consider themselves isolated from upstream events.

A USA study of the effects of wind power as measured by synchrophasors in a 120-volt distribution network, at the University of Texas, Austin, observed voltage angle fluctuation at 120-volt power outlets.

Allen, Alicia & Santoso, Surya & Grady, W.M.. (2010). Voltage phase angle variation in relation to wind power. 1 – 7. 10.1109/PES.2010.5590001.

At one level, this is an academic curiosity, but it is a demonstration of how far transmission events reach as well.

**The Near-Future Distribution Gri**d

The monitoring VECTO 3 power quality/SCADA units are GPS time-stamp synchronised to within ~100 nanoseconds of real-time. Providing grid-wide, synchronised voltage, current, power, reactive power, sequence components, synchrophasors, harmonics, flicker, etc.

There is no practical limit to the number of nodes that can be monitored, given the monitoring design is correctly specified and implemented.

Edge-computing capability in power monitors permits local control, for example OLTC-line drop compensators, SVCs, breaker switched capacitors, series compensators, power flow controllers, etc.

The VECTO 3 monitors also connect to a Big Data system (VECTO Grid OS) which provides granular operational data, power quality data, maintenance scheduling with push notifications, permitting real-time and near real-time monitoring and control.

Communication, for example via IEEE2030.5 with inverters permits complete management of power quality.

A very important aspect of monitoring is the use of instrument transformers suitable for a range of frequencies and predictable responses (3rd order polynomial phase angle and 4th order polynomial for ratios) together with the monitors which have exceedingly low transverse vector errors and are capable of resolving phasors to milliradians of accuracy.

*The blue bar indicates a significant RMS voltage drop in the W phase (green trace) at transformer TX1, indicated on the centre map, and to further clarify its location, on the distribution line diagram (on the righthand side). The voltage scatters* plot for TX1 is shown on the left-hand side. The actual voltage waveforms are also shown, clearly indicating the W phase voltage drop. All measurements are synchronised via GPS and time-stamped* so that data and actual real-time measurement can be correlated accurately without any further data clean-up.*

In gathering information from engineers in distribution networks, it is apparent that local solutions are actively being worked on. However, rather than focussing on the complete problem, partial solutions, none GPS-synchronising based and therefore ultimately unsuitable for network stability control, are sought on the basis of minimum cost as opposed to true cost-effectiveness.

At some point, forcing engineers to develop solutions with such a siloed approach is going to have unintended and potentially dire and costly consequences. Grid-wide, time synchronised monitoring will empower power engineers with the data they require to develop robust, cost-effective solutions that will ensure future grid-resilience.