Richard Pates
Researcher interested in control theory, electrical power systems and mathematics.

# Controlling Power Systems with Renewables — A Modular Approach (Part I)

In this series of posts we will investigate an often overlooked aspect in the challenge of replacing fossil fuel generation with renewables: that of grid stability. We will see that a modular design approach allows the existing technology installed in today’s wind and solar generators to solve this problem in a simple and provable manner.

In this post we will motivate the issue of grid stability, and explain why it needs to be revisited if a large proportion of generation is going to come from renewables. Future posts will describe a modular design approach that can be used to address the arising stability challenges. The content will essentially follow this preprint, which Enrique Mallada and I recently had accepted for a special issue on the control and optimization of energy system networks.

#### What is the problem?

The effects of global climate change are already being seen today. Glaciers are retreating, sea ice is disappearing — last summer Sweden even experienced wildfires inside the Arctic circle. The question is not “should we do something about climate change?”, but “can we do enough in time?”.

Generating electrical power using fossil fuels is a major factor driving the increase in global temperatures. Therefore replacing this with generation from renewable sources is an essential ingredient in preventing climate change. Doing so brings with it a host of engineering challenges. One critical issue, which we will investigate in this article, is how to transmit the power generated from renewable sources to the customer using the existing transmission system.

At the heart of the issue is the fact that it is not sufficient to simply generate enough electrical power — it is essential to generate exactly the right amount of power, and convert it into a form that can be transmitted. In today’s grids this is done using a three-phase transmission system. In this system a network of transmission lines is used to transport power electrically from its source to the customer.

The transmission lines themselves consist of three parallel lines that transmit power via an alternating current (AC). Critically this is done at a fixed voltage and frequency, where the voltage is determined by the rating of the particular transmission line, and the frequency is fixed throughout the network. These quantities must be kept very close to these rated values independently of the amount of power being transmitted (within ~5% for voltages, and ~0.5 Hz for frequency). Failure to do so will invariably lead interruptions in supply, load shedding and potentially blackouts.

When generating power from fossil fuels, these ‘power quality’ aspects are regulated by the synchronous machines used to convert power from the primary source into electrical power. Indeed these methods of generation and transmission are intimately linked, and this is a major reason why we have AC grids to today. However it is not efficient to convert power from renewable sources such as wind and solar into electrical power using synchronous machines. Instead power is normally generated asynchronously, and then converted into an AC current and voltage using power electronics.

While this nicely solves the problem of how to inject power into the grid in a form that can be transmitted, it does not solve the problem of how to regulate the ‘power quality’, as described above. This is a real issue, and most grid operators still rely on the control systems installed in synchronous machines to do this. This places a limit on the proportion of power that can be generated by renewables, and therefore on the extent that fossil fuel generation can be replaced. Ireland for instance is already resorting to wind curtailment whenever wind production exceeds 50% of existing demand in order to preserve grid stability.

#### Why are new approaches needed?

In a nutshell, the engineering problem posed by the above is:

How should the power electronics in asynchronous generators be designed in order to robustly maintain system voltages and frequency in the face of disturbances?

Two `natural solutions’ which would require little additional research or experimentation to implement are:

1. Mimic the control systems and mechanisms used in synchronous machines;
2. Use standard design methods from control theory to design robust controllers.

Unfortunately it seems that neither is possible.

The problem with the first is that is that the control mechanisms used to regulate frequency and voltage in synchronous machines are intimately related to their construction. Take for example the control of frequency. If more power is drawn by the consumers in a power grid, then the mechanically driven rotating masses at the centre of the synchronous machines will slow down (these are driven by steam turbines, powered by the primary fuel sources).

This happens because these large masses store a lot of kinetic energy, and some of this will be given up to make up for the shortfall in supply. While this causes the system frequency to reduce, by measuring the rotation speed of the rotors, this can be locally detected. Consuming more of the primary fuel source in response to this then speeds up the rotors again, which has the effect of increasing the system frequency. By balancing this response appropriately, supply and demand can be matched while maintaining the system frequency close to its rated value.

Since renewable sources typically operate asynchronously, this mechanism simply isn’t available when generating power from wind and solar. As such wind and solar cannot be used to regulate system frequency in the same way as synchronous machines. However the power electronics used in their construction are extremely flexible, and can act on very short timescales. This brings with it many opportunities for performing regulation. However there is no established method to do this, and therefore the challenge is to work out how this can be done.

The science of how to design such systems is called control theory. Control theory provides many general purpose methods for regulating abstract system properties such as stability. In the majority of these, a system model is used to generate a control system that meets various mathematically specified performance and robustness requirements. On the face of it, this looks very promising for our power electronics design problem. All we need to do is produce a model of our power system, and then apply the appropriate general method to produce a controller to robustly regulate system frequency and voltage.

However there is a subtle, but important issue. The problem is that to create a model suitable for applying control theoretic tools requires:

• A mathematical model of the dynamics of the power system;
• Knowledge of the current operating point.

In practice this is very difficult to obtain. This is because the operating point of the power system is continually changing depending on where power is being generated and consumed, and it is often not known how this is happening. This issue is exacerbated by the use of renewables, since their levels of production are highly uncertain and are determined by the weather, rather than the system operator. This makes it very difficult to determine which operating point should be used to design the controllers, and the sheer size of these systems makes it infeasible to check every possible scenario individually (the number of operating scenarios grows combinatorially in the number of system components).

#### Designing controllers using a modular approach

My research on modular design is tailored specifically to overcome the issues discussed above. In subsequent posts we will delve into the details of how to develop a modular control design method for this power electronics design problem.

The objective will be to develop a method that works as follows:

That is, given a component model and robust stability requirement, the method can be used to generate a component control system.

The key property of the method that we will develop is that the control systems that it produces guarantee that the robust stability requirements hold independently of operating point and the topology of the transmission system. It is this feature that distinguishes the modular approach from conventional control techniques, and makes it applicable to the power system setting. We will use this to design control systems for the power electronics used in asynchronous generation. This gives a simple way to design systems that allow renewable sources to robustly maintain system voltages and frequency in the face of disturbances.

The intention is to cover both how to use the method, and also explain where it comes from. This is already quite an ambitious program, and will cover many aspects of control theory and power system modeling. For simplicity we will only consider the problem of frequency regulation. However the same ideas can also be used to address voltage regulation problems, though the details are more involved — I hope to return to this in future articles.

The basic plan of attack is as follows:

• Part II: Introduce the relevant power system modelling concepts;
• Part III: Derive a decentralised stability criterion;
• Part IV: Explain how the stability criterion applies to the power system model;
• Part V: Develop the modular design method, and explain how to use it.

Links will become available as I finish the posts. For those who cannot wait, please see the preprint, which contains all the essential details!

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### 3 Responses

1. June 26, 2019

[…] the second post in the series on the modular control of electrical power systems — please see Part I for an overview and introduction to the problem if you didn’t […]

2. July 7, 2019

[…] is the third post in the series — please see Part I for an overview, and Part II for an introduction to power system modelling if you didn’t […]

3. July 9, 2019

[…] far we have motivated the need for modular design in power systems, developed a modular power system model, and derived a general purpose modular stability criterion. […]