# Defining Transmission System Operators’ Investment Shares for Phase-Shifting Transformers Used for Coordinated Redispatch

^{*}

## Abstract

**:**

## 1. Introduction

- redispatch, which takes into account an exact grid location of generating units used for remedial actions,
- countertrading, which refers to the zonal shift of net position of the whole zone, achieved by multiple units without considering their specific locations.

#### 1.1. Phase Shifting Transformer as an Investment

#### 1.2. Cost Sharing of Coordinated and Optimised Redispatch

## 2. Method for Defining Investment Shares

#### 2.1. Calculation of Cost Sharing Key

- (a)
- identification of overloaded network elements—to determine the congested elements that are subject to further remedial actions,
- (b)
- flow decomposition—to identify the influence of each zone on every network element under consideration and divided into flow types,
- (c)
- transformation—to convert the set of (decomposed) flow components into zonal shares for cost-covering associated with each network element under consideration,
- (d)
- remedial Action Optimisation—to select both a set of measures that provide a secure operating point, and assess the overall cost of subsequent actions,
- (e)
- mapping—to estimate the aforementioned costs per network element,
- (f)
- multiplication—to combine the results of transformation and mapping, reaching zonal shares in overall redispatch and countertrading costs.

#### 2.1.1. Identification of Overloaded Network Elements

- (i)
- determining the set of cross-border relevant network elements, which consist of all cross border lines and other branches satisfying a sensitivity threshold determined by zone-to-zone PTDFs,
- (ii)
- finding contingency states via the analysis of Line Outage Distribution Factors [13],
- (iii)
- computing power flow for all contingency states.

#### 2.1.2. Flow Decomposition

- (i)
- Obtain two models of the power system by dividing each operating point of generation and load located in the grid into two components (Figure 2)—first for internal use of each zone (b) and second, for market exchange with other zones (c). Model (b), called ‘self-balanced’, is characterised by zero net position of each zone, while model (c) (‘model with exchanges’) for each zone, consists either from generation only (for exporting zones) or from pure demand (for importing zones).
- (ii)
- Utilise a self-balanced model in order to obtain internal & loop flows produced by each zone.
- (iii)
- Use a model with exchanges to determine the distinction between import/export flows and transit flows (along with zonal assignment of causers).

#### 2.1.3. Transformation

#### 2.1.4. Remedial Action Optimisation

#### 2.1.5. Mapping

#### 2.1.6. Multiplication

#### 2.2. Investment Shares

## 3. Results

#### 3.1. Input Data

#### 3.2. Investment Share Outcomes

#### 3.2.1. Congestion Identification

#### 3.2.2. Flow Decomposition and Transformation

#### 3.2.3. Proposal for New Investments

- (a)
- alternative scenario $DA$: PST on DE-AT border,
- (b)
- alternative scenario $PC$: PST on PL-CZ border.

#### 3.2.4. Remedial Action Optimisation

#### 3.2.5. Costs, Savings and Investment Shares

## 4. Discussion

#### 4.1. Savings for Different Scenarios

#### 4.2. Utility of the Costs’ Partition

## 5. Conclusions and Future Steps

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CBA | Cost Benefit Analysis |

CCR | Capacity Calculation Region |

CNE | Critical Network Element |

CNEC | Critical Network Element with Contingency |

CS | Cost Sharing |

DC | Direct Current |

ENS | Energy Not Served |

HHI | Herfindahl-Hirschman Index |

IN | internal flow |

IE | import/export flow |

LF | loop flow |

MILP | Mixed-Integer Linear Programming |

PSS | Power System State |

PST | Phase Shifting Transformer |

PTDF | Power Transfer Distribution Factors |

RA | Remedial Action |

RAO | Remedial Acion Optimization |

RES | Renewable Energy Sources |

TR | transit Flow |

TSO | Transmission System Operator |

## Appendix A. The Algorithm for Defining Zonal Fractional Shares for a Given CNEC

**Table A1.**Algorithmic description of the final step of transformation. The procedure is aimed at finding values of ${\rho}_{p}$ and using them to determine ${\tau}_{\ell ,z}$ (line 11).

Pseudo-Code | Meaning | ||
---|---|---|---|

1. | ${x}_{\ell}\leftarrow ({f}_{\ell}-{F}_{\ell}^{max})$ | 1. | ${x}_{\ell}$ denotes the volume of remaining overload, |

2. | $p\leftarrow 0$ | 2. | p stands for consecutive number of prioritised flow type, |

3. | $\forall {p}^{\prime}:{\rho}_{{p}^{\prime}}\leftarrow 0$ | 3. | for each flow type, $\rho $ factor is initialised with zero, it represents a fraction of flow type ${p}^{\prime}$ that is penalised for overload. |

4. | while (${x}_{\ell}>0$) | 4. | As long as remaining overload is a positive number: |

5. | $\phantom{\rule{1.em}{0ex}}p\leftarrow p+1$ | 5. | increment p, |

6. | $\phantom{\rule{1.em}{0ex}}{x}_{\ell}\leftarrow ({x}_{\ell}-{\sum}_{z}{\widehat{f}}_{\ell ,z}^{p})$ | 6. | subtract from ${x}_{\ell}$ all the flows of type categorised as p, |

7. | $\phantom{\rule{1.em}{0ex}}{\rho}_{p}\leftarrow 1$ | 7. | assign 1 to relevant $\rho $ factor, |

8. | $\phantom{\rule{1.em}{0ex}}{p}^{*}\leftarrow p$ | 8. | assign p (the recent priority number) to variable ${p}^{*}$; |

9. | end | 9. | the loop terminates if ${x}_{\ell}\le 0$. |

10. | ${\rho}_{{p}^{*}}\leftarrow \left(1+\frac{{x}_{\ell}}{{\sum}_{z}{\widehat{f}}_{\ell ,z}^{{p}^{*}}}\right)$ | 10. | The recent $\rho $ is proportional to the fraction of ${p}^{*}$-type flow causing overload (${x}_{\ell}$ is now negative and $0\le {\rho}_{{p}^{*}}\le 1$). |

11. | ${\tau}_{\ell ,z}\leftarrow \frac{{\sum}_{p}{\widehat{f}}_{\ell ,z}^{p}\xb7{\rho}_{p}}{{f}_{\ell}-{F}_{\ell}^{max}}$ | 11. | Zonal share ${\tau}_{\ell ,z}$ is a normalised sum of these netted flows, which exceed the thermal limit ${F}_{\ell}^{max}$. |

## Appendix B. Assumptions on Redispatch Costs

## Appendix C. Numerical Values of Zonal Costs, Savings and Shares

Zonal Costs and Savings [EUR] | Investment Share [%] | ||||||
---|---|---|---|---|---|---|---|

$\mathit{R}$ | $\mathit{DA}$ | $\mathit{PC}$ | $\mathit{DA}$ | $\mathit{PC}$ | |||

$\mathit{z}$ | ${\mathit{C}}_{\mathit{z}}^{\mathit{R}}$ | ${\mathit{C}}_{\mathit{z}}^{\mathit{DA}}$ | ${\mathit{K}}_{\mathit{z}}^{\mathit{R}\to \mathit{DA}}$ | ${\mathit{C}}_{\mathit{z}}^{\mathit{PC}}$ | ${\mathit{K}}_{\mathit{z}}^{\mathit{R}\to \mathit{PC}}$ | ${\mathit{v}}_{\mathit{z}}^{\mathit{R}\to \mathit{DA}}$ | ${\mathit{v}}_{\mathit{z}}^{\mathit{R}\to \mathit{PC}}$ |

AT | 1485 | 41 | 1443 | 871 | 613 | 11.8 | 19.3 |

CZ | 1460 | 36 | 1423 | 1091 | 369 | 10.7 | 11.6 |

DE | 5861 | 187 | 5674 | 4682 | 1179 | 46.6 | 37.2 |

HR | 125 | 0 | 125 | 76 | 49 | 1.0 | 1.5 |

HU | 904 | 14 | 890 | 566 | 338 | 7.3 | 10.7 |

NL | 102 | 5 | 97 | 100 | 2 | 0.8 | 0.1 |

PL | 1725 | 77 | 1648 | 1389 | 336 | 13.5 | 10.6 |

RO | 57 | 1 | 56 | 34 | 23 | 0.5 | 0.7 |

SI | 154 | 0 | 154 | 95 | 59 | 1.3 | 1.9 |

SK | 270 | 21 | 249 | 195 | 75 | 2.0 | 2.4 |

UA | 438 | 11 | 427 | 308 | 129 | 3.5 | 4.1 |

SUM | 12,579 | 394 | 12,185 | 9407 | 3172 | 100.0 | 100.0 |

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**Figure 3.**Example of transformation: netted flow components of type 1, and in part type 2, are considered responsible for exceeding the flow limit. In this case, flow type 2 is considered the last one responsible for causing the overload, and transformation algorithm (defined in Table A1) terminates while reaching the following set of $\rho $-coefficients: ${\rho}_{1}=1$; ${\rho}_{2}=0.3$; ${\rho}_{3}={\rho}_{4}={\rho}_{5}=0$.

**Figure 5.**Zonal fractional shares averaged over all congested network elements with the highest overload.

**Figure 6.**Zonal costs (R) and savings due to investments on German-Austrian (R→DA) or Polish-Czech (R→PC) border.

Scenarios | Reference (R) | New PST: DE-AT ($\mathit{DA}$) | New PST: PL-CZ ($\mathit{PC}$) |
---|---|---|---|

cost of redispatch [EUR] | 12,579 | 394 | 9407 |

savings compared to R [EUR] | - | 12,185 | 3172 |

Index | R→DA | R→PC |
---|---|---|

${h}^{\mathsf{\Delta}PSS}$ | 0.2879 | 0.2967 |

${h}_{norm}^{\mathsf{\Delta}PSS}$ | 0.2166 | 0.2266 |

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## Share and Cite

**MDPI and ACS Style**

Kłos, M.; Urresti-Padrón, E.; Krzyk, P.; Jaworski, W.; Jakubek, M.
Defining Transmission System Operators’ Investment Shares for Phase-Shifting Transformers Used for Coordinated Redispatch. *Energies* **2020**, *13*, 4019.
https://doi.org/10.3390/en13154019

**AMA Style**

Kłos M, Urresti-Padrón E, Krzyk P, Jaworski W, Jakubek M.
Defining Transmission System Operators’ Investment Shares for Phase-Shifting Transformers Used for Coordinated Redispatch. *Energies*. 2020; 13(15):4019.
https://doi.org/10.3390/en13154019

**Chicago/Turabian Style**

Kłos, Michał, Endika Urresti-Padrón, Przemysław Krzyk, Wojciech Jaworski, and Marcin Jakubek.
2020. "Defining Transmission System Operators’ Investment Shares for Phase-Shifting Transformers Used for Coordinated Redispatch" *Energies* 13, no. 15: 4019.
https://doi.org/10.3390/en13154019