Elsevier

Applied Energy

Volume 270, 15 July 2020, 114984
Applied Energy

Coordinated optimal strategic demand reserve procurement in multi-area power systems

https://doi.org/10.1016/j.apenergy.2020.114984Get rights and content

Highlights

  • Coordinated procurement of optimal strategic reserve in multi-area power systems.

  • Counterbalancing the value of lost load and the strategic reserve procurement cost.

  • Procurement strategy ensures the fulfillment of long-term reliability targets.

  • Methodology harmonizes well with ENTSO-E’s vision for ensuring generation adequacy.

Abstract

With renewable energy sources becoming an ever-increasing share of the generation mix of modern power systems, having the proper amount of reserve becomes of utmost importance to ensure the short-term as well as the long-term adequacy level in the system. This reserve can be in the form of generation assets or it can be provided from assets on the demand side. The contribution that these resources make to the adequacy of the system is referred to as their capacity credit. This paper derives a methodology for calculating the capacity credit of a resource in a multi-area system. Based on that, an approach is developed that quantifies how strategic demand reserve should be distributed between power system areas in a multi-area system in order to reach individual long-term reliability targets in all areas. Lastly, an algorithm is derived that optimizes the coordinated procurement of multi-area strategic demand reserve by counterbalancing the value of lost load against the costs related to maintaining generation adequacy. A combination of an iterative multi-variate gradient approach and a Monte Carlo simulation with an efficient sensitivity analysis allows this to be achieved in a computationally economical way. An illustrative example and numerical simulations of test systems using real data from the Nordic power system demonstrate the effectiveness of the proposed approach.

Introduction

In order to provide electricity to consumers in a reliable manner, electric utilities must be concerned with both the generation adequacy and the security of the bulk power electric system. Generation adequacy deals with the capacity of the system and involves having enough generation and transmission capacity available to meet customer demand for electricity plus reserves for contingencies. Adequacy encapsulates the system’s ability to meet demand in the medium to long term. Adequacy deals with the inherently fluctuating and uncertain balance between supply and demand and the longer time scale of capacity expansion. Traditionally, generation adequacy has been measured in terms of the system’s amount of reserves as well as the corresponding loss of load probability (LOLP). These metrics have served as criteria for planning and investment decisions. The notion of security on the other hand identifies the operational aspects of the system in the short term through practices such as contingency analysis and dynamic stability assessment. The security of the system is ensured by the means of protection devices as well as operation standards and procedures. [1].

A generator’s contribution to the generation adequacy of a power system is more accurately captured by its capacity credit than by its installed capacity. The capacity credit takes into account factors such as forced outages and limited primary energy supply and the latter is especially important for volatile renewable sources that behave quite differently from dispatchable sources. Their installed capacity gives very limited information about their contribution to the generation system adequacy. Approaches to calculate the capacity credit have been around since the 1960s. In [2], Garver generalized the loss-of-load probability mathematics and introduced a graphical method for estimating the effective load carrying capability of a new generating unit. The paper describes the effective capability of a new unit as “the load increase that the system may carry with the designated reliability”. More specifically, this definition regards the capacity credit as the maximum amount that the load in the system, including this generator, can be increased while keeping the reliability of the system at the same level as before when this generator was excluded. There exist several other definitions of capacity credit. See [3], which compares the different properties of four capacity credit definitions and shows that the choice of definition can in fact influence the results.

The IEEE Power and Energy Society Task Force on the Capacity Value of Wind Power describes a preferred method for calculation of the capacity value of wind power in [4]. Relevant issues surrounding the method are discussed in addition to a description of approximate methods and their limitations. In [5], the authors discuss the capacity value of wind power among other topics related to integration of wind power. The paper compares results from eight studies and concludes that the capacity value of wind power has been estimated to be up to 40% of installed wind power in systems where wind power production is high at times when load is high, and down to 5% in systems where the load and the wind power generation are negatively correlated.

Some efforts have been made to estimate the contribution of non-generating resources to power system generation adequacy. The authors of [6] present a study that extends the generation-oriented concept of capacity credit to electric energy storage and demand response. In a similar fashion, the authors of [7] estimate the capacity value of load-shifting devices and conclude that they can provide an adequacy contribution and thus have a capacity value.

One can think of capacity credit and generating reserve as linked concepts. They both deal with generation adequacy. More specifically, the former quantifies the effect of additional generation and/or demand side assets on the reliability of the power system while the latter explores how to ensure generation adequacy by means of additional generation and/or demand side assets. Much effort has been spent studying both the spinning [8] and the non-spinning [9] reserve requirements of power systems in the short-term. The provision of short-term operating reserves from the demand side of the market has also been studied by utilizing for example smart appliances [10], electric vehicles [11] or by aggregating responsive loads into equivalent virtual power plants [12]. See also [13] in which the authors propose to use a deterministic unit commitment (DUC) model with a set of state-of-the-art probabilistic reserve constraints (DUC-PR). The performance of the proposed model is studied numerically when estimating the contribution of operating reserves to system adequacy. The proposed model is shown to estimate the true EENS volume more accurately than the DUC model.

Looking at generation adequacy in the long-term, there are concerns that energy-only markets fail to adequately compensate investments. Capacity is only fully utilized during a small number of critical peak demand hours each year. If prices during those hours are too low, the revenues will not adequately support the efficient generation quantity and the efficient generating capacity mix. This results in underinvestment in capacity, an increase in the number of hours when capacity is fully utilized, more reliance on non-price rationing and a higher probability of a network collapse. This is referred to as the ”missing money” problem [14]. Several capacity mechanisms have been proposed to tackle this problem. According to the European Commission, an important criterion for all potential capacity mechanisms is their compatibility with the regulations that apply to the EU’s internal market for electricity [15]. This means guaranteeing energy supply in a cross-border context, without distorting energy trading with neighboring countries and was stressed in a recent joint declaration signed by twelve central European countries [16]. This paradigm is however not the reality today where different capacity remuneration mechanisms are applied nationally rather than in a coordinated fashion. Currently, the aim is to fulfill a national reliability criterion without relying on neighbouring areas. As published in [17], European target reliability levels in terms of the Loss Of Load Expectation (LOLE) are typically in the range of 3–8 h/year. The report states that setting such reliability targets is a highly sensitive issue that needs to consider economic, technical and political aspects. The reasoning behind these targets is arguably more historical than economically justified and dates back to the times of vertically integrated monopolies. The report argues that these targets should rather be determined by means of counterbalancing the value of lost load (VoLL) against the costs related to maintaining a reliable generation capacity.

Strategic reserve is one capacity mechanism aimed at ensuring generation adequacy [18]. It is built up by making contracts with actors in the electricity market, which state that the contracted assets will be used only after all market-based solutions to the scarcity problem are fully exhausted. TSOs might also enter into contracts with large electricity consumers, but in that case the agreements concern reducing their electricity consumption. Recently, interest from the latter group in providing demand side participation during times of scarcity has been increasing and is an attractive option because of its short lead time. In [19], the authors present an overview of the adequacy challenge in a selection of jurisdictions in Europe as well as in the United States. The overview shows that strategic reserve is the capacity mechanism of choice in nearly half of the studied jurisdictions. Countries that apply strategic reserve include Sweden, Finland, Belgium and Germany who all procure strategic reserve on an annual basis. In a 2016 study, the authors of [20] apply an agent-based simulation model for the German electricity market and showed that an energy-only market extended with a strategic reserve can incentivize investments, and guarantee supply security in a market with a high share of renewable energy. The authors of [21] introduce a new benchmark model of a capacity mechanism in a competitive electricity market and outline a new socially-optimal design of a strategic reserve with a discriminatory capacity payment. See also [22], which analyzes the connection between peak prices, system reliability and required amount of subsidized capacity, i.e., the volume of the strategic reserve.

Currently, some national TSOs within Europe apply proprietary methods to calculate the need for strategic reserve in order to ensure the generation adequacy only within their own isolated control area [19]. However, the procurement of strategic reserve is not coordinated between interconnected power system areas. This is against the pan-European market paradigm of the European Commission that was mentioned above. Moreover, none of the abovementioned references concerning methods for estimating the capacity credit or strategic reserve requirements have treated multi-area systems with a limited transmission capacity between areas. A realistic power system consists of multiple areas and to include such multi-area constraints is therefore of importance.

In response to these methodological deficits, this paper introduces a novel multi-area approach that is able to quantify how strategic reserve that is procured from the demand side of the market (hereafter referred to as Strategic Demand Reserve or SDR) should be distributed between different power system areas in a multi-area system in order to reach certain long-term reliability targets in the individual areas. Moreover, the proposed approach allows system operators to schedule how the SDR should be procured and distributed optimally in a multi-area system while taking the cost associated with ensuring generation adequacy into consideration.1 This methodology harmonizes very well with [17], which states that reliability targets should be determined by means of finding a balance between the value of lost load and the costs of ensuring generation adequacy. The methodology also captures the synergy between the areas by procuring the SDR in a coordinated fashion. In our analysis we have followed the European model for strategic reserve where we consider it to be procured in an annual tender.

A combination of an iterative multi-variate gradient approach and a Monte Carlo simulation with an efficient sensitivity analysis allows this to be achieved. The proposed approach is based on the work carried out in [23], which introduced the concept of multi-area capacity credit. In this paper, the multi-area capacity credit approach is extended and put in the context of strategic demand reserve estimation. The main contributions of the paper are:

  • 1.

    A derivation of the theoretical background behind the concept of multi-area capacity credit along with a procedure to estimate the multi-area capacity credit of a resource in a power system. This includes an efficient method for estimating the sensitivity of reliability indices with respect to changes in demand/SDR using Monte Carlo simulation.

  • 2.

    An algorithm that estimates the amount of multi-area SDR needed in order to reach individual long-term reliability targets in a multi-area system.

  • 3.

    An algorithm that estimates the optimal amount of multi-area SDR needed in order to minimize the combined cost associated with lost load as well as the procurement cost of the SDR.

The rest of the paper is organized as follows. Section 2 describes the multi-area capacity credit approach in general. Section 3 covers how sensitivity analysis can be applied efficiently in a Monte Carlo simulation to determine the sensitivity of reliability indices in a power system to deviations in the demand in the system. Section 4 derives the procedure used to estimate the multi-area capacity credit of a source in a power system. Section 5 derives the algorithm used to estimate the multi-area SDR requirements in order to reach long-term reliability targets of individual areas. Section 6 derives how the procurement of SDR can be carried out in an optimal way while considering its procurement cost as well as the customers’ cost of lost load. Section 7 describes the linearized AC power flow model and the optimization problem that is solved within the Monte Carlo simulation of the proposed approach. Section 8 covers an illustrative example as well as numerical simulations of test systems using real data from the Nordic power system that showcase the performance of the proposed methods for SDR requirement estimation and optimal procurement. Section 9 concludes the paper.

Section snippets

Multi-area capacity credit

When calculating the capacity credit of a source, the standard way [2] is to calculate the LOLP in the system, with and without the source connected to the system. The LOLP value when the source is connected to the system will be lower since additional capacity will increase the reliability of the system. One then increases the demand in the system, which includes the source, until the LOLP value is equal to the one for the system without the source. The amount of demand increase is the

LOLP sensitivity to demand change

Finding an estimate of a reliability index of interest can be expressed as finding the expected value of a given functionE(F)=xXF(x)P(x),where x is the system state vector, X is the set of all possible states, P(x) is the probability of state x and F(x) is a function that measures the performance of the state x. As an example, when estimating the LOLP, the performance function F(x) takes the value of “1” in case load shedding is necessary for state x and a value of “0” in case load shedding

Multi-area capacity credit calculation

Based on the derivations in the previous sections, a procedure for calculating the multi-area capacity credit of a new generating or non-generating source in a power system can by summarized by the following steps:

  • 1.

    Run a Monte Carlo simulation for the power system without the new source connected to the system and store the multi-variate LOLP per area value as LOLP.

  • 2.

    Initialize the iteration counter as k=1. Initialize the multi-area demand increase as the zero vector: Δd1=0. Set tolerance level

Multi-area strategic demand reserve requirement algorithm

The algorithm for calculating the multi-area SDR requirements of a power system borrows from the theory of multi-area capacity credit that was introduced in Section 2. Its goal is to estimate the amount of multi-area SDR that results in a specific long-term reliability target LOLP in all of the individual areas of the power system. However, instead of thinking in terms of the demand increasing, it considers how the system is affected when the SDR is increased. Note that LOLP is a vector and

Optimal procurement of multi-area strategic demand reserve

The aim of this section is to develop an approach to estimate the optimal amount of multi-area SDR that minimizes the cost associated with generation adequacy in the system. Whenever load shedding is necessary in the power system, there is an associated cost that can be captured by the VOLL of the system or the individual areas. In general, increasing the SDR in the system will decrease the amount of expected involuntary load shedding, therefore lowering the cost associated with the lost load.

Linear AC power flow formulation and optimization

The algorithms above are based on Monte Carlo simulation, which is used to calculate the reliability indices of interest as well as their sensitivities. For each sample within the Monte Carlo simulation, a power flow model needs to be solved to determine whether there is a capacity deficit situation in any of the areas. A traditional DC power flow formulation, which is often applied in reliability studies because of its computational efficiency, completely neglects reactive power constraints as

Illustrative example

In order to be able to demonstrate the proposed SDR procurement algorithms graphically, the first simulation is for a simple single area model. The power system is modeled as a single bus, with generation and demand connected directly at the bus. The power system is based on the IEEE-RTS system but a 350 MW coal power plant has been replaced by a 1000 MW wind farm. Further information about the IEEE-RTS system can be found in [31]. The wind power time series for the wind farm is generated using

Conclusion

This paper derived the concept of multi-area capacity credit and based on that developed an algorithm to estimate the strategic demand reserve requirements in a multi-area system. One the one hand, the approach is able to determine the amount of reserve that is required to reach a certain reliability target in each of the individual areas. On the other hand, the approach allows one to determine the optimal amount of strategic demand reserve in order to minimize the combined cost associated with

CRediT authorship contribution statement

Egill Tómasson: Conceptualization, Methodology, Software, Data curation, Writing - original draft, Writing - review & editing, Visualization. Lennart Söder: Conceptualization, Methodology, Supervision, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The authors would like to thank the Swedish TSO, Svenska Kraftnät, for their financial support of the project.

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