• Nie Znaleziono Wyników

UMBRELLA project - Deliverable D 7.4 “Workshop results on solutions for maximising power transits”

N/A
N/A
Protected

Academic year: 2021

Share "UMBRELLA project - Deliverable D 7.4 “Workshop results on solutions for maximising power transits”"

Copied!
101
0
0

Pełen tekst

(1)

SEVENTH FRAMEWORK PROGRAMME

THEME [ENERGY.2011.7.3-1]

[Innovative tools for the future coordinated and stable

operation of the pan-European electricity transmission

system]

Project Deliverable

Deliverable D 7.4

“Workshop results on solutions

for maximising power transits”

Project acronym: UMBRELLA

Project full title:

Toolbox for Common Forecasting, Risk

assessment, and Operational Optimisation

in

Grid

Security

Cooperations

of

Transmission System Operators (TSOs)

Grant agreement no.:

282775-2

(2)

Research Project UMBRELLA

Page 2

Contents

1 INTRODUCTION ... 3

2 ORGANIZATION AND STRUCTURE OF THE WORKSHOPS ... 4

2.1 Workshop on Optimized Solutions ... 4

2.2 Workshop on System State Modelling and Toolbox Design ... 5

3 SUMMARY OF THE WORKSHOP PRESENTATIONS ... 7

3.1 Workshop on Optimized Solutions ... 7

3.1.1 WP3.1 Presentation and discussion ... 7

3.1.2 WP3.2 Presentation and discussion ... 7

3.1.3 WP3.3 Presentation and discussion ... 8

3.1.4 WP4 Presentation and discussion ... 8

3.2 Workshop on System State Modelling and Toolbox Design ... 9

3.2.1 Overview ... 9

3.2.2 WP2: Modelling uncertainties relevant for the operation of the European transmission grid ... 9

3.2.3 WP3: Optimization algorithms for transmission system operation... 10

3.2.4 WP4: Risk-based Security Assessment incorporation Forecast Uncertainty and Cascading events ... 11

3.2.5 Toolbox Requirements based on TSO Demands and Testing Environment ... 11

(3)

Research Project UMBRELLA

Page 3

1

Introduction

UMBRELLA is developing an innovative toolbox to support the decentralised grid security approach of TSOs, giving the opportunity to increase cooperation when facing the increased complexity in system's operation. A decentralised network security analysis with everyone "on board" looking at the same results and evaluating solutions in a coordinated and optimised way, increases the efficiency of the network operation. Furthermore, umbrella methodologies gives a step forward in the evaluation of uncertainties and their impact in different operational timeframes, the introduction of risk-based assessment and optimisation of remedial actions. This toolbox to be used in different operational timeframes includes:

 Modelling and simulation of uncertainties due to market activities, renewable energy sources on different time scales (RES forecast) and outages

 Optimisation algorithms of remedial actions in reaction to simulated risks on different time scales according to total costs and transmission capacities

 Development of risk based assessment concepts for anticipated system states with and without corrective actions

In the present deliverable, the results of the workshop ‘UMBRELLA Workshop on Optimized Solutions’ and ‘UMBRELLA Workshop on System State Modelling and Toolbox Design’ are summarized. The workshops were both hosted at ENTSO-E’s premises on October 22, 2013 and October 23rd, 2014 with a total number of 15 and 33registered participants respectively, including experts from industry, academia and regulatory bodies. This deliverable is structured in the following way: Chapter 1 introduces the framework for an introduction of the UMBRELLA project, Chapter 2 presents the organization and structure of both workshops, Chapter 3 presents summaries of the workshop presentations and in the Appendix the presentation slides of the workshop of October 23rd 2014 are

displayed. The slides of the workshop of October 22nd 2013 are not included since an

updated version is also published within the previous Deliverable 7.3.

The presentations and related documents are available for download at www.e-UMBRELLA.eu, as approved by all presenters.

(4)

Research Project UMBRELLA

Page 4

2

Organization and structure of the workshops

First the agenda and structure of the workshop on Optimized Solutions of October 22nd

2013 will be discussed. Secondly the workshop on System State Modelling and Toolbox Design of October 23rd 2014 will be discussed.

2.1

Workshop on Optimized Solutions

The first workshop was held at ENTSO-E’s premises in Brussels on October 22nd, 2013.

Most of the stakeholders were invited by email.

The agenda of the workshop consisted of the following parts:

10:00 Workshop opening

10:15 Overview of WP3(Optimization algorithms) 10:30 Presentation Task 3.1

Proactive EOPF for anticipated Critical System States

12:00 Lunch Break

13:00 Presentation Task 3.2

Short Term and Real Time EOPF

14:30 Lunch Break

14:45 Presentation Task 3.3

Advanced methods for uncertainty accounting in (enhanced) optimal

power flow

15:15 General Discussion 15:45 Coffee Break

16:00 Presentation WP4 (Risk based assessment) 17:00 Workshop Closing

(5)

Research Project UMBRELLA

Page 5

2.2

Workshop on System State Modelling and Toolbox Design

The last workshop was held at ENTSO-E’s premises in Brussels on October 23rd , 2014.

Most of the stakeholders were invited by email. Moreover, the consortium published a newsletter in the middle of August 2014. This newsletter contained information about the workshop and about the way to subscribe.

The agenda of the workshop consisted of the following parts: 10:00 Workshop opening

10:30 Introduction

Welcome speech by ENTSO-E

Introduction to the UMBRELLA Project (work packages 1 & 7)

11:00 Part A: Results on optimized solutions for maximizing power transits, system state modeling and toolbox functionalities

Forecasting (work package 2):

Modeling uncertainties relevant for the operation of the European transmission grid

Optimization (work package 3):

Optimization algorithms for transmission system operation

12:30 Lunch

13:30 Part A Continued

Riskbased assessment concepts (work package 4):

Riskbased Security Assessment Incorporating Cascading Events and Forecast Uncertainty

14:15 Coffee Break

14:30 Part B: Prototyping and toolbox design

Synthesis and prototyping (work package 5)

Demonstration and testing (work package 6)

16:15 Conclusion and summary 17:00 End of workshop

(6)

Research Project UMBRELLA

Page 6

Figure 1: UMBRELLA Workshop October 23rd 2014

(7)

Research Project UMBRELLA

Page 7

3

Summary of the workshop presentations

The content of both workshops will be discussed. Again, first the workshop on Optimized Solutions of October 22nd 2013 and second the workshop on System State Modelling and

Toolbox Design of October 23rd 2014 will be discussed.

3.1

Workshop on Optimized Solutions

3.1.1

WP3.1 Presentation and discussion

The presentation on Work Package (WP) 3.1 includes a short description of the requirements on the optimization algorithms aligned in a meeting in Aachen in January 2013, an explanation of the developed optimization algorithms and some exemplary results.

The availability and activation time of remedial measures is discussed, since it is an important part of the prototype parameterization. The optimization algorithm itself is capable to deal with the corrective application of remedials, if they are available on a short term. Operational practice allows a limited number of topology switching measures. This requirement is met by the step-by-step selection of topology modifications starting from an initial network state and selecting only one modification at a time. The properties of the chosen heuristic are discussed in terms of optimality. Further enhancement of the optimization tool, especially in terms of power plant startups, will be made in WP 3.3.

3.1.2

WP3.2 Presentation and discussion

An overview of the used methods is given for Short Term and Real Time EOPF: modelling of measures (dispatch, HVDC lines, shunt elements, transformers with adjustable taps), handling N-1 security and Topology optimization.

There has been some discussion on the estimation of contingency situation. The estimated overloads caused by different line-failures are put in the objective function in a linear or quadratic way, since different lines may have different importance with regard to failure. Therefore the presented model includes the possibility to weigh the lines according to their importance. The idea of putting overloads as a penalty into the objective function relates to the work being done in WP4.3.

WP3.1 and WP3.2 have in common that they are both using topology-optimization, but different methods are used. The method presented by WP3.1 is a heuristic approach intended to reduce overloadings before starting the optimization process. The heuristic is used to effectively limit the search space, but suggested topology modifications are used only, if they lead to improvement. The method presented by WP3.2 serves to reduce costs and congestions after a feasible solution is found. The different topology-optimization

(8)

Research Project UMBRELLA

Page 8

methods are not confined to the two respective work package parts. The two work package parts give the possibility to compare, for small instances, the obtained solutions to optimal solution found by brute force, say using MINLP.

Finally, some work on extending Matpower to automatically optimize transformer tap position is presented. For variable transformers, there is currently no extension for Matpower. It would be a very useful addition for the broader community. The extension will be made available when it’s ready.

3.1.3

WP3.3 Presentation and discussion

The presentation contains the requirements of WP3.3 according to the description of work and the basic concept on how those requirements could be considered in the implementation. In addition, possible probabilistic criteria as alternative for conventional (N-1)-criterion are presented. This could be the TSO experience or an input of WP4.

The advantages of considering uncertainties are discussed. TSOs see the calculation of startup necessities for power plants as key benefit. It is difficult for TSOs to define a maximum risk level for each line due to regulatory reasons. The probabilistic criterion should be an outcome of WP4.

3.1.4

WP4 Presentation and discussion

WP4 presented some ideas on how to model severity (i.e. as technical violations or overall system risk). One severity function model currently being developed within WP4is reflecting risks (e.g. cascading) or costs (e.g. of remedial measures) that are not explicitly accounted for in the OPF. The physical implications of this severity function and how it used as an interface between the other work packages.

Finally, better estimates of probability of outages (i.e. sensitivity to errors in the estimation) and available data were discussed.

(9)

Research Project UMBRELLA

Page 9

3.2

Workshop on System State Modelling and Toolbox Design

3.2.1

Overview

UMBRELLA is developing an innovative toolbox to support the decentralised grid security approach of TSOs, giving the opportunity to increase cooperation when facing the increased complexity in system’s operation. A decentralised network security analysis with everyone “on board” looking at the same results and evaluating solutions in a coordinated and optimised way, increases the efficiency of the network operation. Furthermore, umbrella methodologies gives a step forward in the evaluation of uncertainties and their impact in different operational time-frames, the introduction of risk-based assessment and optimisation of remedial actions. This toolbox to be used in different operational time-frames includes: Modelling and simulation of uncertainties due to market activities, renewable energy sources on different time scales (RES forecast) and outages [Work Package (WP) 2]. Optimisation algorithms of remedial actions in reaction to simulated risks on different time scales according to total costs and transmission capacities [WP3]. Development of risk based assessment concepts for anticipated system states with and without corrective actions [WP4]. To perform the presented work, Umbrella has the following project structure: All this will be integrated into one toolbox [WP5]. Finally, the functionality of this toolbox will be tested and demonstrated [WP6].

3.2.2

WP2: Modelling uncertainties relevant for the operation of the

European transmission grid

WP2 is concerned with the assessment and description of uncertainties that influence the grid operation notably. Thereby, the uncertainties are described in a way that allows for a straightforward integration of the additional information into the TSO’s operational planning. Therefore, so-called system state parameters, which characterise crucial information about the whole system in a feasible way for operational processes, have to be derived and subsequently forecasted.

The forecast uncertainties of renewable energy infeed and load are modelled at each grid node with non-parametric kernel density approaches. The spatial interdependence of each factor is described with a copula. The uncertainty of short-term trading is modelled by a merit order model, which takes the aforementioned uncertainties as input. This allows for running a Monte-Carlo simulation that returns the distributions of load and infeed at each grid node. With subsequent load-flow calculations, the distributions of system state parameters (line loading, voltage etc.) can be computed. By filtering critical systems states and their respective forecast conditions, the relationship can be used to forecast critical system states.

The methods for describing the uncertainties have been fully developed and tested. Currently, the developed methods for forecasting critical system states are tested.

(10)

Research Project UMBRELLA

Page 10

3.2.3

WP3: Optimization algorithms for transmission system operation

The aim of the UMBRELLA Project is to assist transmission grid operators to ensure secure transmission grid operation. Therefore, optimization algorithms have been developed, which are capable of determining remedial measures to maintain system security at minimal costs. In order to provide system operators with adequate action recommendations, it is of special significance, that these algorithms take into account all available remedial measures as well as all relevant contingencies. In particular, relatively new technologies with great influence on power flows like HVDC connections operated in parallel to the asynchronous grid and phase shifting transformers are considered among conventional measures like topology modifications and redispatch.

The new options in transmission grid operation resulting from an increased controllability of load flow control devices in contingency situations are optimized as corrective remedial measures and provide significantly increased flexibility to transmission system operators in stressed grid situations. However, uncertainties resulting from error-prone feed-ins of renewable energy sources can lead to deviations from anticipated system states.

A reasonable way to deal with this issue is to postpone activation decisions of remedial actions as long as possible and react if critical deviations from anticipated system states actually occur. Therefore, a short term optimization algorithm has been developed, which takes into account measures available on a very short term as well as real-time constraints. Nevertheless, it is crucial for system security to avoid unmanageable system situations. To deal with this issue, probabilistic optimization algorithms have been developed, which are capable of directly incorporating uncertainties within the operational planning process. This way, especially optimal power plant start-up decisions, which have to be performed up to 24h before the actual operation, can be taken.

Figure 3: General overview of Work Package 3

Network model including load/feed-in

Network related remedials

Redispatch potential

© SD 2013

Network use cases

0:302:30 4:30 6:308:3010:3012:3014:3016:3018:3020:3022:300:30 D D+ 1 Contingency simulation Estimation of relevant contingencies Results Contingency list Outage A Branch i: Node j: Outage B Branch k: Outage …

Optimization of transmission system operation

Possible switching states Continuous optimization Topology optimization Remedial measure utilization Umbrella Optimization Tool

Secure network state Uncertainties

(11)

Research Project UMBRELLA

Page 11

3.2.4

WP4: Risk-based Security Assessment incorporation Forecast

Uncertainty and Cascading events

The topic of WP4 is risk-based security assessment, which encompasses both the probability and the severity of events. Since the beginning of the UMBRELLA project, we have developed and tested different models for power system operational risk and different representations of uncertainty related to fluctuating in-feeds from RES. The result is a set of methods which can be used for a risk-based security assessment, including both risk-based, probabilistic optimal power flow (OPF) formulations and methods for probabilistic evaluation of the risk from cascading events.

The last deliverable of Workpackage 4 is “D4.3 Methods for optimization of power transits” and has two parts. First, the previously developed risk-based methods have been extended to handle state-of-the-art technological means such as HVDC and PSTs. This allows for an assessment how HVDC and PSTs can be used to reduce risk and handle uncertainty, thus allowing for an optimization of the power transfer capacities. Second, the developed methods are used to assess how different market designs and cooperation rules influence the risk in system operation.

3.2.5

Toolbox Requirements based on TSO Demands and Testing

Environment

3.2.5.1 WP5: Synthesis and Prototyping

The review of the concepts developed for forecasting, optimization and risk-based security assessment is completed and led to the selection of those functionalities and modules which will be included in the toolbox design and the development of the toolbox prototype. The synthesis of the selected modules with the expectations and requirements formulated by TSOs is finished as well.

Figure 4: General overview of Work Package 5

Prototype

Development

Toolbox

Synthesis

Usage

Concept

Visualisation

Concept

Toolbox Design

(12)

Research Project UMBRELLA

Page 12

The conclusion of this work forms the basis for the developing of a toolbox design and of the toolbox prototype which will be used for demonstration purposes and tested by TSOs. First steps on the development of the usage and visualization concepts have been carried out. The work on both concepts started with an analysis of the scientific state-of-the-art and the approaches currently applied by TSOs. Based on the results of the analysis, the two concepts will be developed as part of the toolbox design and integrated in the prototype. The feedback provided from the testing of the prototype will show if these concepts fulfill the requirements by TSOs in terms of the integration of the toolbox in the existing processes and of the plain interpretation of the results obtained by operating the toolbox.

The discussion on the setup of the toolbox prototype concluded in a centralized approach i.e. the toolbox prototype will be installed on a central server.

Figure 5: Schematic overview of centralized toolbox

The TSOs executing the demonstration and testing will have access to the central server and be able to run the toolbox prototype. The major advantages of such an approach is the fact that a bidirectional communication is required between the central server and the users/testers of the toolbox prototype only and no data exchange between the different TSOs is required. Furthermore the implementation of experimental software in secured TSO-IT-systems is minimized. Nevertheless a decentralized use of the toolbox is possible by using an appropriate IT-framework.

3.2.5.2 WP6: Demonstration and testing

Since the last newsletter two major steps have been taken forward within the demonstration and testing part of the project.

Toolbox-Prototype

(13)

Research Project UMBRELLA

Page 13

Step one was the finalization of the “testbook”. Three test cases have been chosen which are each described with a general synopsis by all TSO. Furthermore, every case features detailed descriptions by each TSO concerned, comprising the encountered grid situation, the countermeasures taken and the expectation of the TSO regarding the toolbox results. The test case “Cold snap February 2012” has also been harmonized with the FP7-project iTesla. The other test cases cover more aspects - e.g. high wind infeed in the northern part of Germany and different seasonal current limits on lines.

Figure 6: Average minimum temperatures in February 2012 & 2013 to illustrate the cold snap period graphically. (source: www.wetteronline.de)

Step two was the first testing workshop. Due to the mixed approach of a physical meeting with the possibility to participate via web conference, all involved TSOs could participate in the test. Although, in this stage of the prototype only the deterministic functions of the toolbox are available, the optimization possibilities and the short computation time were really impressive. Further guided online test sessions and two physical meetings shall be held to roll out the additional functions of the toolbox. Within these sessions, users will get more acquainted with the toolbox and feedback for the improvement of the toolbox prototype will be collected.

Acknowledgement

The UMBRELLA consortium would like to thank ENTSO-E for hosting both workshops and the organizational work for the very good cooperation.

(14)

Research Project UMBRELLA

Page 14

(15)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 11

The Umbrella project

Workshop on System State Modelling

hop on S

and

System State Mod

on S

d Toolbox Design,

23rd

and

and

d

d oolbox De

To

To

oolbox Desig

d of October 2014, Brussels (

n,

n

esig

esig

s (

(

(

s (

(

(

entso

so

so-

o

o

o

o

o

o

o

o

o

o

o

o

--

-

-e

e

e premises)

Agenda - Morning

10:00 Welcome with coffee

10:30 Introduction

a) Welcome speech by ENTSO-E

b) Description of the UMBRELLA project (Work Packages 1&7)

11:00 Part A: Results on optimised solutions for maximising power

transits, system state modelling and toolbox functionalities

a) Forecasting (Work Package 2)

Modelling uncertainties relevant for the operation of the European transmission grid

b) Optimization (Work Package 3)

Optimization Algorithms for Transmission System Operation

(16)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 3

Agenda - Afternoon

13:30 Continuation of Part A

a) Risk-based Assessment Concepts (Work Package 4)

Risk-based Security Assessment Incorporating Cascading Events and Forecast Uncertainty

14:15 Coffee break

14:30 PART B: Prototyping and Toolbox Design

a) Synthesis and prototyping (Work Package 5)

b) Demonstration and Testing (Work Package 6)

16:15 Conclusion and summary

17:00 End of workshop

Helmut He He He He He He He He He

He ut Paeschke (TenneT ke (TenneTeT TSO O GmbH), Wulf Engl (Englgl-glglgl----Energie on behalf alf TenneT TSO GmbHmbHH), Laura TSO TSO Gm eT eT TS ura ura Ramírez Gm rez

rez-bH), Wulf Engl (Englglglglgl----Energie on behalEnEn alf TennTe bH GmbH Gm z z z z z z z z z z z z z z z z

z----Elizondo (Delft University of Technology)

Workshop on System State Modelling and Toolbox Design

Project Overview

(17)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 5

Agenda

I.

Welcome

II.

Workshop Agenda & Introduction to the Panel

III. Motivation of the UMBRELLA Project

IV. Project Objectives

V.

Project structure and Participants

VI. Demonstrator and KPIs

VII. Dissemination

Conferences, Workshops, Newsletter

o

Uncertainties in transmission network operation due to increase of

o

intermittent renewable energy sources (RES) and

o

volumes of market-based cross border flows and related physical flows

o

Maximization of transportation possibilities

o

New interconnections and devices for load flow control

o

Zonal structure of the European

energy market with legal responsibilities

of TSOs imposes increasingly complex

requirements to the TSOs’ cooperation

concerning quality and accuracy

à Development of coordinated grid security tools

taking into account all technological measures

for flexible power system operation

Motivation of the UMBRELLA Project

(18)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 7

Agenda

I.

Welcome

II.

Workshop Agenda & Introduction to the Panel

III. Motivation of the UMBRELLA Project

IV. Project Objectives

V.

Project structure and Participants

VI. Demonstrator and KPIs

VII. Dissemination

Conferences, Workshops, Newsletter

“Toolbox for Common Forecasting, Risk Assessment, and

Operational Optimisation in Grid Security Cooperations of TSOs”

Develop an innovative toolbox to support the decentralised grid

security approach of TSOs

This toolbox shall include:

§ Simulation of uncertainties (WP 2 Forecast) due to market activities

and renewables on different time scales

§ Optimisation (WP 3) of corrective actions in reaction to simulated risks

on different time scales according to total costs and transmission

capacities

§ Development of risk based assessment concepts (WP 4) for

anticipated system states with and without corrective actions (WP 4)

Demonstrate the enhancement of existing and running procedures

by utilisation of the developed toolbox (WP 5 & WP 6)

Provide a scientifically sound basis to support common TSO

decisions

(19)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 9

Agenda

I.

Welcome

II.

Workshop Agenda & Introduction to the Panel

III. Motivation of the UMBRELLA Project

IV. Project Objectives

V.

Project structure and Participants

VI. Demonstrator and KPIs

VII. Dissemination

Conferences, Workshops, Newsletter

(20)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 11

Project structure

Risksksk--based Risksksk basedbaba Assessment Optimization

Forecasting Synthesis andSynthesis and

Prototyping

PM

M

Project Management (WP1)

PMB

PMB

Project

Project

Management

Manage

Board

WP2

WP3

WP4

WP5

Demonstration Demonstration and Testing

WP6

Dissemination

WP7

Project Consortium

U Duisburgburgg--Essen RWTH Aachen ETH Zurich Amprion TransnetBW TU Delft TenneT TSO Germany

PMT

T

Project Management Team

Project Mana

P

(PM, WG

Mana

G

G

-agement T

na

ana

G

G--

Leaders)

Participating TSOs: TenneTeTTSO Participat Pa O GmbH, ating TSOs icipat bH, bH, Amprion Os: TSOs n

nGmbHbHbHbH, , ČEPSPSPS, , a.sa.sa.ss.., Tenn Elektro Tenn tro tro -eT eT TSO TSO nneT Tenn o o--Slovenija O ija ija, GmbH Gm Gm Gm a a, d.o.o bH o.o o.o, Amprion Am n Gm Am bH bH, Am o o o, TransnetBW GmbH Gm BW BW BW, bH bH, bH bH GmbH BW BW, BW PSE

ČEPSPSPS, a.a.a.sa.ss

, ČEČEČE

E

E Operator

s., or orS.A.,

Elektrtroo SlovSl

swissgrid ov Slov d d dag ovenij ov ag ag ag ag, a a, d.o.d.d. ij ija enij ag ag, TenneT , Tr o. o.oo eT eTTSO ansnet Tran Tr Tr O O O B.V. ansnet V. V., etBWBWBW, BW PSPS et snet V. V., Austrian Operator Op PSE PSE Op an an anPower or or erator wer wer Grid A., or A.S.A. id idAG

Participating Universities and research institutes:

Participating Universities Delft University of es and resea sities of of Technology esea gy gy, rch institutes earc esea gy gy, gyETH Zurich, Delft University o Graz University of Technology Te ty o of of ofTechnology logy gy gy, ETH Zurich, ET ET gy gy gy gy gy gy gy, gy gy gy gy gy gy gy logygy gy gy, gy RWTH Aachen, az University of University of TechnoloTe y ofof ty tyDuisburg nolo rg rg -logygygygygygygygygygygygygygy, logy nolo rg rg--Essen , RW sen sen, RWTH Aac RWTH RW RW RW n n, FGH TH Aac H H e.V he ache Aac e.V e.V e.V e.V.

Agenda

I.

Welcome

II.

Workshop Agenda & Introduction to the Panel

III. Motivation of the UMBRELLA Project

IV. Project Objectives

V.

Project structure and Participants

VI. Demonstrator and KPIs

VII. Dissemination

(21)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 13

The five innovation clusters of TSOs

Cluster Name Functional

Objective Full names of Functional Objectives

C1 Grid architecture

T1 Definition of scenarios for pan-European network expansion T2 Planning methodology for future pan-European transmission system

T14 Towards increasing public acceptance of transmission infrastructure

C2 Power technologies

T3 Demonstration of power technology to increase network flexibility and operation means T4 Demonstration of novel network architectures

T5 Interfaces for large-scale demonstration of renewable integration

C3 Network operation

T6 Innovative tools and methods to observe and control the pan-European network T7 Innovative tools and methods for coordinated operation with stability margin evaluation T8 Improved training tools and methods to ensure better coordination at theregional and pan- European levels

T9 Innovative tools and approaches for pan-European network reliability assessment

C4 Market designs

T10 Advanced pan-European market tools for ancillary services and balancing, including active demand management

T11 Advanced tools for capacity allocation and congestion management

T12 Tools and market mechanisms for ensuring system adequacy and efficiency in electric systems integrating very large amounts of RES generation

C5 Asset management

T15 Developing approaches to determine and to maximize the lifetime of critical power components for existing and future networks

T16 Development and validation of tools which optimize asset maintenance at the system level, based on quantitative cost/benefit analysis

T17 Demonstrations of new asset management approaches at EU level

Source: Methodological Guide on EEGI KPIs

Demonstrator and KPIs

Source: Methodological Guide on EEGI KPIs

Project KPIs

Overarching KPIs

Progress of EEGI activities to overarching goal

Specific KPIs

Link with Clusters and Functional Objectives. Measure impact of group of R&I activities Defined on a project by project basis Pr ov

EEGI

Roadmap

Cluster of

Projects

ect Is De proj

Projects

o

A KPI should be reasonable, understandable, meaningful

o

The overall number of KPIs for a project should be reasonable

o

A KPI usually is calculated by comparing the “business as usual (BAU)”

case versus the “research and innovation (R&I)” case

(22)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 15

Agenda

I.

Welcome

II.

Workshop Agenda & Introduction to the Panel

III. Motivation of the UMBRELLA Project

IV. Project Objectives

V.

Project structure and Participants

VI. Demonstrator and KPIs

VII. Dissemination

Conferences, Workshops, Newsletter

Second Newsletter (2014/1)

(23)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 17

Posters

Conferences

o

CIGRÉ 2014 @ Paris, France

o

Innogrid2020+ @ Brussels, Belgium

o

Energycon @Dubrovnik, Croatia

o

EU Energy week, @ Brussels, Belgium

EEGI Grid+ Event

(24)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 19

Thank you very much for your attention!

www.e-umbrella.eu

This research work has been carried out within the scope of the project UMBRELLA, supported under the 7th Framework Programme of the European Union, grant agreement 282775.

Questions?

Comments?

Dr. ir. L.M. Ramirez Elizondo

Assistant Professor DC Systems & Storage

TU Delft Mekelweg 4 2628 CD Delft Telephone: +31 15 27 81848 Mailto: L.M.RamirezElizondo@tudelft.nl Website: www.ewi.tudelft.nl/en/the-faculty/departments/electrical-sustainable-energy/ Dr. Wulf A. Engl

Consulting, Interim and Project management

Engineering consultant Engl-Energie Thingstr. 24 D-82041 Oberhaching Telephone: +49 (89) 905470 - 90 Telefax: +49 (89) 905470 - 88 Mailto: info@engl-energie.de wulf.engl@tennet.eu Website: www.engl-energie.de

(25)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 11

Christoph Weber (University of Duisburg-Essen)

Workshop on System State Modelling and Toolbox Design

Forecasting

23rd of October 2014, Brussels

Agenda “Forecasting” (WP 2)

I.

Background and overview

II.

Challenges

III.

Scientific Approach

IV. Results

V.

Outlook

VI. Conclusions

(26)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 3

WP 2: Background and Overview

Main objective:

Developing a set of methods describing the key uncertainties

relevant for operating the transmission grid

Considered uncertainties:

Feed-ins from renewable energy sources

Load

Intraday trading

Power plant outages

WP 2: Operational planning today

DACF: TSOs create point forecasts of certain system parameters

(load, infeeds, …)

෠ܺ

Snapshots: Measurements of system parameters

ܺ

differ from the

forecasts à forecast error:

ܧ

෠ܺ

ܺ

ݐ

ܺ

ͳ

Ͳ

ʹ

͵

Ͷ

ͷ

෠ܺ

ܺ

ܧ

෠ܺ

ܺ

ହ Point forecast: Measurement: Forecast error:

(27)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 5

WP 2: Forecast error

Possible deviations from the point forecast can be used for

operational planning

Deviations are described by the random variable

ܧ

What is the probability of a certain deviation? à WP2

ݐ

ܺ

െͶ

െͷ

െ͵

െʹ

െͳ

Ͳ

ܺ

=

෠ܺ

െ ܧ

ଵ௑ Probability of the forecast error?

ͳ

WP 2: Forecast error

WP2 does not make nor improve any point forecasts

WP2 develops methods that describe the deviation from the point forecast

and their probability à focus on forecast error/ forecast uncertainty

How to describe forecast uncertainty à probability density function (pdf)

ݐ

ܺ

െͶ

െͷ

െ͵

െʹ

െͳ

Ͳ

݂

ܺ

ൌ ݂

෠ܺ

െ ܧ

ଵ௑

Focus on:

݂ ܧ

ͳ

(28)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 7

WP 2: Time dependence

Uncertainty increases with an increasing time horizon à each

look-ahead time step should have its own forecast error pdf

݂

ܧ

ǡ ݂

ܧ

, ….,

݂

ܧ

ݐ

ܺ

െͶ

െͷ

െ͵

െʹ

െͳ

Ͳ

ͳ

ʹ

͵

WP 2: Forecast condition

Different forecast conditions (

point forecast

෠ܺ

) lead to different forecast

error pdf

à pdf must be conditional on the point forecast à conditional

pdf (cpdf)

݂

ܧ

ȁ

෠ܺ

ǡ ݂

ܧ

ȁ

෠ܺ

, ….,

݂

ܧ

ȁ

෠ܺ

ݐ

ܺ

െͶ

െͷ

െ͵

െʹ

െͳ

Ͳ

ͳ

ʹ

͵

(29)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 9

WP 2: Spatial interdependence

Point forecasts and uncertainty forecasts are only usable at a grid

node level à cpdf for each grid node ݊ ൌ ͳǡ ǥ ǡ ܰ: ݂

ሺܧ

݂

ܧ

ȁ ෠ܺ

ǡ ݂

ܧ

ȁ ෠ܺ

, ….,

݂

ܧ

ȁ ෠ܺ

݂

ܧ

ȁ ෠ܺ

ǡ ݂

ܧ

ȁ ෠ܺ

, ….,

݂

ܧ

ȁ ෠ܺ

݂

ܧ

ȁ ෠ܺ

ǡ ݂

ܧ

ȁ ෠ܺ

, ….,

݂

ܧ

ȁ ෠ܺ

Forecast errors at different grid nodes are correlated

E.g.: if the forecast error at

݊ ൌ ͳ is high, the forecast error at ݊ ൌ

ʹ is also high

Linear correlation coefficients are limited to linear relationships à

use of copulas

WP 2: Copulas

A copula defines the functional relationship between a joint

distribution function,

ܨሺݔ

ǡ ǥ ǡ ݔ

ሻ, and its marginals ܨ ݔ

ǡ ǥ ǡ ܨሺݔ

ܨ ݔ

ǡ ǥ ǡ ݔ

ൌ ܥሺܨ ݔ

ǡ ǥ ǡ ܨሺݔ

ሻሻ or as a density function

f

ݔ

ǡ ǥ ǡ ݔ

ൌ ܿሺ݂ ݔ

ǡ ǥ ǡ ݂ሺݔ

ሻሻ

Thus, this allows to separate the modelling of the marginal

distributions and the relationship between them

(30)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 11

WP 2: Main benefits for

operational planning

Likely contingencies could be overlooked if a point forecast is used merely

– However, e.g. power plants need a certain startup timeà Optimization necessary

(WP3)

HILP events might lead to cascading events

– However, risk assessment necessary (WP 4)

ݐ

ܺ

െͶ

െͷ

െ͵

െʹ

െͳ

Ͳ

ͳ

ʹ

͵

Redispatch

necessary?

High impact, low probability (HILP) event?

Agenda

I.

Background and overview

II.

Challenges

III.

Scientific Approach

IV. Results

V.

Outlook

VI. Conclusions

(31)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 13

WP 2: Challenges

Main challenge:

Most of the processes are more or less easy to predict individually

However, TSOs can only observe an aggregation of them

Solution:

(1) Disaggregation and individual simulation

(2) Incorporation of interdependences

(3) Reaggregation

Transmission grid Distribution grid Observable Non-observable

WP 2: Challenges

(1) Disaggregation and individual simulation of :

RES infeed

Residual load and underlying

conventional generation

Power plant outages

(2) Incorporation of interdependences

RES infeed

Intraday market uncertainty

(3) Reaggregation to system parameters

than can be used in operational planning:

ܲ

௟௢௔ௗ

(

includes RES infeed

,

residual load

)

ܲ

௜௡௙௘௘ௗ

(includes intraday market, power plant outages)

aint

t

y

Transmission grid

Distribution grid

Observable Non-observable

(32)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 15

Agenda

I.

Background and overview

II.

Challenges

III.

Scientific Approach

IV. Results

V.

Outlook

VI. Conclusions

WP 2: Uncertainty in renewable power

forecasts

Objective

Identify appropriate possibilities for describing these uncertainties in

a way that grid operators may make use of the information most

efficiently

Methodology

Estimation of forecast uncertainty for each grid node

– Conditional probability density function (cpdf) of the forecast error

conditional on the deterministic forecast

– Different estimation for each grid node and look-ahead time using

non-parametric approaches (Nadaraya-Watson estimator)

Modelling of spatial interdependences

– Copula models (foregoing goodness-of-fit tests)

Simulation of forecast uncertainty

(33)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 17

WP 2: Uncertainty in load forecasts

Objective

Identification of suitable descriptions of the associated uncertainties

in view of providing a consistent overall system state description

Methodology

Estimation of forecast uncertainty for each grid node

– Different estimation for each grid node and look-ahead time using

non-parametric approaches (kernel density estimation)

1. If underlying RES infeeds: residual load is model

2. If “pure” load node: vertical grid load (same as in DACF) is modelled

Modelling of spatial interdependences

– Copula models (foregoing goodness-of-fit tests)

Simulation of forecast uncertainty

– cpdf + point forecast + copula à Monte-Carlo-Simulation

WP 2: Uncertainty in power plant outages

Objective

• Identification of suitable descriptions of the associated

uncertainties in view of providing a consistent overall system

state description

Methodology

• Time to fail is modelled for each power plant type using an

exponential distribution

• Time to repairs is not modelled, because it is assumed that

power plant operators notify TSOs in advance

(34)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 19

WP 2: Uncertainty in short-term trading

Objective

• Detailed analysis of intraday renominations and a subsequent

proposal for statistical description

Methodology

• Merit order model: running power plants will be active in the

intraday market depending on their marginal costs

• Uncertainties on the load side can be used to anticipate

intraday trades

• Remaining uncertainties (fuel costs, irrational behaviour,

provision of spinning reserves) are represented by a sampled

merit order

WP 2: Uncertainty in short-term trading

Price

Quantity E(PRES)

E(Load) Input: Uncertainty

of RES and load

Output: Change in power

production at each grid node and, thus, change of trades

(35)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 21

WP 2: Deriving forecast

distributions for the system state

Objective

Development of methods to derive information about future system

states and their occurrence probability based on previously

discussed forecast distributions

Provide information about the system state to system dispatch

Methodology

Based upon the modelled uncertainties a Monte-Carlo-Simulation is

run

– Requires the reaggregation of uncertainties to vertical grid load and

infeed at each node

For each Monte-Carlo run a load flow calculation is carried out

System state parameters (voltage, line loading etc.) can be

computed

WP 2: Deriving forecast

distributions for the system state

Load flow Calculations

Load flow Calculations

Load flow Calculations

Load flow Calculations

Distributions of load and RES infeed

Incorporation of specifics, in particular related to

intraday trading

Load flow Calculations

Distributions of system states

P and Q (load)

Pump storages

Cross-border flows

Monte-Carlo-Simulation

Distributions of intraday trades

(36)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 23

WP 2: Deriving forecast

distributions for the system state

Objective

Quantify the probability of occurrence for specific combinations of

uncertain events that cause critical system states in real-time

Methodology

Running a full Monte-Carlo-Simulation is too time-consuming in

real-time

Thus different approaches, that link certain forecast conditions with

the occurrence of critical system states, are currently tested:

– Artificial intelligence approaches

– Selective approach

A continuous improvement and training with new data will be

handled offline

WP 2: Deriving forecast

distributions for the system state

Load flow Calculations

Load flow Calculations

Load flow Calculations

Load flow Calculations

Distributions of load and RES infeed

Incorporation of specifics, in particular related to

intraday trading

Load flow Calculations

Distributions for system states

P and Q (load)

Pump storages

Cross-border flows

Monte-Carlo-Simulation

Distributions of intraday trades

P and Q (load+injection)

Forecast conditions

Level of expected wind infeedHour of the day

Forecast of

critical

system

states

(37)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 25

Agenda

I.

Background and overview

II.

Challenges

III.

Scientific Approach

IV. Results

V.

Outlook

VI. Conclusions

Ͳ

Deviation from

the point forecast More wind infeed

that expected

Less wind infeed that expected

(38)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 27

Simulation of wind power uncertainty

Ͳ

Deviation from the point forecast

Rather strong interdependence à

deviations into one direction occur often

simultaneously

Simulation of solar power uncertainty

Ͳ

Deviation from the point forecast

Local weather effects (e.g. clouds) have an higher

impact à weaker interdependence

(39)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 29

Simulation of solar power uncertainty

Ͳ

Deviation from the point forecast

(40)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 33

Agenda

I.

Background and overview

II.

Challenges

III.

Scientific Approach

IV. Results

V.

Outlook

VI. Conclusions

Outlook

• System is currently implemented for 9 TSOs

• Further testing with data from 2012

• Integration of the forecasting module into the

Umbrella toolbox

(41)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 35

Functional Link

Probabilistic Forecasting

Critical System States

Optimisation Framework

System States with Remedial Measures

Security Margins for Circuit Capacities Risk Assessment of Cascading Events Uncertainty of Circuit Flows Severity Function

External input data

External input data External input data

External input data

Critical System States

Optimisation Framework

System States with Remedial Measures

Security Margins for Circuit Capacities Risk Assessment of Cascading Events Uncertainty of Circuit Flows Severity Function

External input data External input data

External input data External input data External input data

External input data

WP2

Agenda

I.

Background and overview

II.

Challenges

III.

Scientific Approach

IV. Results

V.

Outlook

(42)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 37

WP 2: Conclusions

• The Umbrella toolbox goes beyond today’s practice by

regarding the uncertainty of factors relevant for

operational planning such as wind infeed or intraday

trades

• In order to assess their uncertainty, nowadays’

processes have to be disaggregated, modelled

individually and finally reaggregated while regarding

relevant interdependences

• By using additional information (such as spatial

correlations, forecast conditions and time dependences)

for describing the uncertainties, the state space is limited

what allows for a computation within a practical period of

time

Thank you very much for your attention!

Questions?

Comments?

www.e-umbrella.eu

This research work has been carried out within the scope of the project UMBRELLA, supported under the 7th Framework Programme of the European Union, grant agreement 282775.

(43)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 11

Jonas Eickmann, Tobias van Leeuwen, Andreas Moormann

Institute for Power Systems and Power Economics, RWTH Aachen University

Workshop on System State Modelling and Toolbox Design

Optimization

23rd of October 2014, Brussels

Agenda

“Optimization” (WP 3)

I.

Background and Overview

II.

Challenges

III.

Scientific Approach

IV. Results

(44)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 3

o

Growing complexity and importance of transmission system operation

è

Development of expert system to provide optimized guidance

(n-0)-secure

Overall Objective

Objective

o

Reaching a (n-1)-secure grid state

Selected Approach

è

Development of an Optimization Framework

to support TSO in operational planning and

grid operation

o

Considering all available remedial

measures

o

Accounting for uncertainties in operational

planning process to provide sufficient

security margins and controllability

o

Reacting to deviations with real-time

applicability

(n-1)-secure

(45)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 5

Probabilistic load -flow

Critical System States

Optimization Framework

System States with Remedial Measures

Security Margins for Circuit Capacities Risk Assessment of Cascading Events Uncertainty of Circuit Flows Severity Function

External input data

External input data External input data

External input data

Probabilistic load -flow

Critical System States

Security Margins for Circuit Capacities Risk Assessment of Cascading Events Uncertainty of Circuit Flows Severity Function np

External input data External input data

np

External input data External input data

np

External input data External input data

Overview Umbrella Project

WP3

Agenda

I.

Background and Overview

II.

Challenges

III.

Scientific Approach

IV. Results

(46)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 7

Challenges

System Size

o

Large number of elements in European transmission grid

o

Cross border flows couple neighbouring transmission networks

(n-1)-Criterion

o

Transmission grid operation needs to cope with contingencies

o

Optimization problem size grows linear with number of relevant outages

Discrete Decisions

o

Several remedial actions require binary variables

o

Topology modifications have strong interdependency with other measures

Uncertainties

o

Future system state development in planning stage unknown

o

Accounting for a range of possible upcoming states required

Agenda

I.

Background and Overview

II.

Challenges

III.

Scientific Approach

IV. Results

(47)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 10

Optimization for operational planning

Optimization Algorithms

Network model including load/feed-in

Network related remedials

Redispatch potential

Network state Network state

© SD 2013

Network use cases

0:30 2:30 4:30 6:30 8:3010:3012:3014:3016:3018:3020:3022:30 0:30 D D+ 1 Contingency simulation Estimation of relevant contingencies Results Contingency list Outage A Branch i: ܲ௜஺ǡ ܳ௜஺ Node j: ܷ௝஺ǡ ȣ௝஺ Outage B Branch k: ܲ௞஻ǡ ܳ௞஻ Outage …

Optimization of transmission system operation Possible switching states Continuous optimization Topology optimization Remedial measure utilization Umbrella Optimization Framework

Secure network state

Optimization for real time application

System State MoSSystem State Mo

Uncertainty

dellinin and Toing aning aninin Mode Modede nty accounting Tool ng in of O of Design 23rdof Desi De box x De olbobo in in optimization Uncertainties Uncertainties

Risk based security assessmentReal time restrictions

Optimization Objectives

o

Selection of appropriate objective function key for representation of

Security Considerations

o

Minimization of constraint violations

o

Minimization of Risk

Economic Effects

o

Minimization of redispatch costs

o

Minimization of grid losses

Regulatory Considerations

o

Minimization of redispatch volume / market impact

è

Multi objective optimization with appropriate weighting of different

objectives required

(48)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 12

Remedial Actions

Topology Modification

Switching lines on/off

Adjustment of busbar configuration

Transformer Tap Changing

Longitudinal & quadrature

Shunt Elements

Capacitors & reactors

HVDC Connections

Market based & TSO operated

Point-to-point & radial structures

Redispatch

Conventional generation units (incl. startups)

Curtailment of RES

Load shedding

Key Features

Decoupling of topology optimization and continuous optimization

o

Optimization problem tractable for large scale power systems

Deterministic optimization

o

Consideration of temporary admissible transmission loading (TATL)

after the outage (curative measures)

o

Real-time applicability

Probabilistic optimization

o

Minimization of probability of constraint violations and risk

o

Accounting for short term controllability while determining power plant

startups

Time coupling optimization of subsequent use cases

(49)

UMBRELLA Workshop on System State Modelling and Toolbox Design, 23rdof October 2014, Brussels 14

Umbrella Optimization Framework

è

Flexible adjustment for different time horizons and requirements possible

Je d er N N F iso li ert Je d er N N F iso li ert

Network use cases

0:30 2:30 4:30 6:30 8:30 10:30 12:30 14:30 16:30 18:30 20:30 22:30 0:30

D D+1

Topologieschaltmaßnahmen TopologieschaltmaßnahmenRobust Switching States

time-coupling, continuous relaxed, mixed-integer optimization Contingency simulation Load flow Solve problem time-co continuous Build problem Results

Load Flow Losses Remedials Costs

N e tw or k u se cases

Selection of topologyof topology ൎ scenarios scenarios scenarios

• (n-1)-constraints

• Voltages

• Currents

Topology Optimization (1/2)

o

Estimation of relevant congestions

o

For case without outage

o

For all contingencies

o

Heuristic preselection of relevant

topological measures (TM)

o

Congestion based selection of

relevant TM based on fast load flow

approximation

o

Normal operation

o

Contingency situations

o

Full continuous optimization

procedure for remaining measures

to estimate best topology

modification in current state

108 103 102 10 1 Initialization Identification of congestions Heuristic selection Substations Topological measures

Congestion driven selection Load flow approximation

(n-0) case (n-1) cases

Redispatch driven selection Continuous optimization

Cytaty

Powiązane dokumenty

Ja n M arcin Szancer nie tylko w tym w ypadku wzorował się na wcześniej pow stałych tekstach plastycznych; również w innych jego pracach w yraźnie widoczny

Depending on the learning methods, which may be more or less prone to the curse of dimensionality (and therefore, to overfitting), it may be wise to envision a feature selection

powieść o niemieckim faszyzmie. Jest to informacja istotna, uświadamia bowiem czytelnikowi, że powieść rodziła się wówczas, gdy straszliwy system siał

Inne państwa osiągające wysokie saldo dodatnie w bilansie handlo­ wym (jak np. USA od 1958 r.) nie są w stanie zrównoważyć bilansu płatniczego. Większość państw

pamiętnika Zofii Lenartowiczowej, zawiera- jącego bulwersujące (zwłaszcza dla bezpośrednio zain- teresowanych) szczegóły dotyczące Adama Mickiewicza i jego najbliższych, otóż

Problem protestantów w Rzeczpospolitej XVI wieku jest jednym z najistot­ niejszych zagadnień naszej historii tego okresu.. Gwałtowny rozwój reformacji wy­ warł ogromny

Praw o natury tak rozumiane nie ma swej podstawy wyłącznej w istotnych cechach człowieka, nie jest czymś w yrastającym z natury jednostek — jest ono świadomym

To prawda, że poznanie takie jest czysto teoretyczne i nie przydatne do przetwarzania świata, ale prawdą jest też, iż to poznanie jest szczególnie cenne,