Jaka Strumbelj. The Influence of PSTs on the Power Flow in the Power Grid Under Consideration of Uncertainty. Semester Thesis

Transcription

1 eeh power systems laboratory Jaka Strumbelj The Influence of PSTs on the Power Flow in the Power Grid Under Consideration of Uncertainty Semester Thesis Department: EEH Power Systems Laboratory, ETH Zürich Examiner: Prof. Dr. Göran Andersson, ETH Zürich Supervisor: Msc. ETH Line Roald, ETH Zürich Zürich, June 203

2 ABSTRACT Abstract Growth of consumption and new types of distributed production, such as wind and photo voltaic, are changing the traditional power flows in the power system and increase uncertainty. Transmission system operators are searching for different ways of cooping with this dilemmas. In this work the influence of phase shifting transformers, as a mean of power flow control, on the dispatch costs without and with consideration of uncertainty and N- security is studied. Based on a case study on a small test system, it is shown, that phase shifting transformers help reducing costs of security and uncertainty.

3 INHALTSVERZEICHNIS 2 Inhaltsverzeichnis Introduction 3 2 Literature Overview 5 3 Phase Shifting Transformers in Power Grid 7 3. PSTs in Continental Europe Problem Definition 9 5 DC Power Flow 0 5. OPF Security constrained OPF Wind In-feed Modeling Probabilistic OPF Probabilistic Security Constrained OPF Including PSTs in OPF equations Preventive control Corrective control Case 8 6. Evaluation Criteria Test System Wind In-feed Results Total costs of generation Costs of Security Costs of Uncertainty Corrective control Conclusions 25 9 Future Outlook 25 Literatur 26

4 INTRODUCTION 3 Introduction European countries power grids are connected in an interconnected power grid under coordination of European Network of Transmission System Operators for Electricity (ENTSO-E). The system consists of thousands of buses, lines, generators and loads. Due to its size, the system is very reliable and resistant to load and generation variation, as well as component outages. It is operated to fulfill the N- criterion at all times. Interconnecting lines between two countries are subject to net transfer capacity (NTC), which limits the maximum value of load flow between the countries. The values is determined by transmission system operators (TSOs) under coordination of ENTSO-E in such way, that at all times the N- criterion is fulfilled on countries boarders []. The NTC is a subject of auctions and each TSO strives to optimize the power flows to achieve profit by fulfilling the contracts. Higher load and maintaining the power system integrity are the reasons, why the power flow control has become interesting and necessary. It helps TSOs maintaining the integrity of the grid and fulfilling N- criterion, while allowing to dispatch production in such a way that total costs of the system are lower even under consideration of uncertainty. The uncertainty is a consequence of a big increase in the renewable energy sources (RES) power in-feed. These sources are mainly wind and photo voltaic. Opposed to the traditional power sources, wind and solar power is weather dependent. This creates an uncertainty of power in-feed prediction and has an impact on system reliability. Power flows throughout the system can be controlled with different technologies, for example with phase shifting transformers (PSTa), which influence the phase shift between beginning and the end of the line or with thyristor controlled series capacitances (TCSCa), which influence the reactance of the line. In this thesis we are studying how PSTs can be used to help reduce costs of integration of RES production in the power system, the influence of PSTs on the total costs of generation and their influence on fulfilling the N- security criterion in the system. An optimal power flow (OPF) formulation accounting for the RES uncertainty and the influence of PSTs was developed based on method developed [2]. To demonstrate the usefulness of developed method, a case study is shown. For simplicity all test are made on a smaller test system already used before for cost analysis [3]. Analysis will be made with four types of linear optimal power flow methods, both deterministic and probabilistic. The deterministic methods assume all variables, like load and generation, to be know, i.e. assume perfect power in-feed forecast in case of RES. In contrast the probabilistic methods take into account the uncertainty of RES in-feed and consider probability distribution for the forecast deviations. To evaluate the influence of PSTs different cost types

5 INTRODUCTION 4 will be compared and conclusions drawn from that comparison.

6 2 LITERATURE OVERVIEW 5 2 Literature Overview The working principles and possible uses of PSTs are already long known. But the fabrication of PSTs is very complicated, expensive and requires a lot of high technology, so PSTs started coming in use only a few decades ago. There are studies describing the influence of PSTs on a part of the grid, like [4], where phase shifter distribution factors (PSDFs) are described and derived to show the influence of PSTs on line flows. The authors show, that the contribution of PSTs to the control of power flow depends on the number of PSTs in relation to the number of interconnecting lines. In [5], the improvement of security of power transfer by use of PST is examined. The PST is used to increase the active power load flow through the higher voltage line and thus reduce the load on heavily loaded lower voltage lines. They analyze both steady states and transient condition and conclude, that installing a PST in that particular location improves the security of power transfer. In 2008 J. Verboomen discussed use of PSTs in in the optimization of transmission system [6]. He mainly focused on the PSTs in and around Belgium. Similar, but more generic study on the use of PSTs in the grid is made in [7]. The author examines the relationship between PST settings, load flow, and generation on an Institute of Electrical and Electronics Engineers (IEEE) 4/20 grid model. A probabilistic load flow formulation to include power system uncertainty was first proposed in [8]. The author describes the method for power flow calculation taking into account the uncertainty of node data (generation or load), based on the assumption of normally distributed random variables. This method is the adopted by [9], where they consider the uncertainty of wind in-feed, load and generation availability. They also consider the dependencies between random variables and optimize the problem to achieve minimal computation requirements. In [2] probabilistic security constrained optimal power flow method is derived, combining probabilistic optimal power flow and security constrained power flow method. The work performed in this thesis is based on the formulations from this article, with the extension to include PSTs and their influence. PSTs and their use in former Union for Coordination of Transmission of Electricity (UCTE) region is described in REALISEGRID Deliverable D.2.2 [0]. The PST arrangements are grouped based on their geographic position. For each country the information on reasons why PSTs were installed in that particular locations are given. More information can also be found in REALISEGRID Deliverables D.4. and D.4.2. The authors of [] discuss on the problem of optimally locating PSTs in the grid. They base their method on the optimal power flow program and concentrate on the identification of binding inequality constraints. At the end they optimize

7 2 LITERATURE OVERVIEW 6 the screening method to reduce the computation requirements. They state that this method should be used carefully and that it might not always give accurate possible locations.

8 3 PHASE SHIFTING TRANSFORMERS IN POWER GRID 7 3 Phase Shifting Transformers in Power Grid Phase shifting transformers (PSTs) are a special kind of transformers which enable to control the voltage phase shift between source and load side. If PST is installed in a line, one can change the voltage angles on both ends of the line within certain range. This way one is able to control the active power flow through the line, as it mainly depends of angle difference at the begging and at the end of the line. Abbildung : Principal schematics of PST [7] Simplified schematics of PST is shown in Figure. Unlike normal transformers, PSTs usually do not provide galvanic separation of network parts, because their primary (source) side and secondary (load) side are directly connected through the inducta. Besides the phase shift, some PSTs can provide amplitude transformation as well, but this is very rare due to size and higher costs. 3. PSTs in Continental Europe In Regional Group (RG) Continental Europe of ENTSO-E PSTs are mainly used to control the power flows of interconnecting lines between countries. This way transmission system operators (TSOs) help to meet the assigned NTC values and fulfilling the contracts. One of the exceptions is Austria, where PSTs are installed in lines inside the country. In Austria they experience a permanent bottlenecks between North and South part of transmission grid due to low transmission capacity of existing lines and delays in construction of new lines with higher possible loading. With PSTs on all three lines the Austrian TSO is able to control

9 3 PHASE SHIFTING TRANSFORMERS IN POWER GRID 8 the power flow between North and South part of the power grid. Detailed information on this can be found in [0]. All PSTs in RG Continental Europe, their position and some technical data are reported in REALISEGRID D.2.2 report [0]. In the table below installed PSTs in interconnecting lines until 202 or which are to be installed in the near future, are listed by countries they connect. Countries Line Voltage level BE - NL Zandvliet - Geertruidenberg 400 kv CZ - PL Nosovice - Wielopole 400 kv FR - ES Prangers - Biescas 220 kv DE - NL Diele - Meeden 400 kv Gronau - Hengelo 400 kv DE - PL Hagenwender - Mikulowa 400 kv Vierraden - Krajnik 220 kv La Praz - Venaus 400 kv FR - IT Trinite Victor - Camporoso 220 kv Albertville - Rondissone 400 kv IT - SI Padriciano - Divaca 220 kv Redipuglia - Divaca 400 kv Tabelle : List of PSTs in UCTE region

10 4 PROBLEM DEFINITION 9 4 Problem Definition The aim of this paper is to demonstrate the influence of PSTs on the total costs of generation, cost of security and costs of uncertainty. For this purpose four DC optimal power flow formulations will be derived, extended to include PSTs and used: Standard optimal power flow (OPF) Probabilistic optimal power flow (popf) Security constrained optimal power flow (SCOPF) Probabilistic security constrained optimal power flow (pscopf) It is expected that PSTs will help to reduce total costs of generation, especially when considering security criterion. As power system is designed to serve loads, costs will be analyzed with respect to load variation. A relation between load variation, costs of security and system integrity will be studied. We would like to show, that PSTs can help to maintain system integrity at higher loads and lower the costs of security at the same time.

11 5 DC POWER FLOW 0 5 DC Power Flow The DC optimal power flow (DC OPF) calculation is based on a linear power flow calculation method. It can be used when the condition X R > 2 () is satisfied [2]. The method assumes lossless line (neglects resistance R and transconductance G) and voltage of p.u. at both ends of the line. The sinusoidal function of angle difference is linearized: sin (Θ j Θ i ) = (Θ j Θ i ) (2) Accuracy of the DC method is lower compared to AC power flow methods due of the three simplifications made: neglection of line resistance, substitution of sin of the bus angle difference with linear bus angle difference in radians and setting voltages to p.u. at both ends of the line. Wide discussion on the accuracy of DC OPF can be found in [2]. They state, that with already stated assumption and the criteria given in (), the accuracy of DC OPF always lies within the 5% with respect to the AC power flow methods and the angles differ for less than ±2. In [3] accuracy of DC method with included power flow controlling devices, especially PSTs, is discussed. They claim that the accuracy of DC method still lies within the 5% range, when power flow controlling devices are modeled, but that special care should be taken when drawing conclusions from the obtained results. When angle difference gets higher, the substitution made in (2) can deviate significantly. This introduces higher error in the method. The deviation is shown in Figure 2. It was decided, that such deviation is still acceptable considering the objectives of this thesis. 5. OPF The DC OPF method in this thesis was employed through the linear programing function in MATLAB. The linear programing function finds a minimum of given function for a set of variables considering the equality constraints, inequality constraints and lower and upper boundaries for variables. It is formally formulated as: N gen min j= C j P Gj (3) where C j is a vector of generation costs for each generator, P Gj is the vector of power generated by each generator and N g en the number of generators.

12 5 DC POWER FLOW Abbildung 2: Absolute difference between sin and linear approximation of angle The variables are subject to constraints given bellow: P Gi + P Wi + n P ij = P Li (4) j= P W = P forecast W (5) P min,i P gen,i P max,i (6) P ij P max,ij (7) Θ slack = 0 (8) First constraint (4) states that the sum of conventional generation P Gi, wind generation P Wi and line power flows P ij must be equal to load P Li. With (5) the wind in-feed P W is set to have the forecasted value P forecast W. Constraint (6) limits the lowest and maximum conventional generation production. Constraint (7) states that the line flow P ij must not exceed the maximum allowed P max,ij. Finally slack bus angle is set to zero by constraint (8). In standard OPF formulation the line flow P ij in constraint (7) is defined as: P ij = (Θ j Θ i ) (9) X ij where X ij is the line reactance, Θ i the voltage angle on bus i and Θ j the voltage angle on bus j.

13 5 DC POWER FLOW Security constrained OPF To formulate the security constrained OPF, introduction of linear sensitivity factors is required [2]: Line Outage Distribution Factors (LODF) Generalized Generation Distribution Factors (GGDF) weighting matrix d LODFs describe the influence of line outage on the power flow in other lines. GGDFs are similar to LODFs and they describe how deviation from generation schedule influences the power flows in lines. LODFs and GGDFs are dependent of system topology only. The mathematical definition can be found in [2]. The weighting matrix d defines how the generation changes due to deviation from generation schedule. In security constrained optimal power flow (SCOPF) the N- criterion is taken into account. This means, that we assume that any system component, be it line or generator, can fail at any time without having an impact on system integrity. With the use of LODF and GGDF a constraint for power flow trough the line is obtained: X ij (Θ j Θ i ) + LODF ij,mn X mn (Θ n Θ m ) γ P max ij (0) X ij (Θ j Θ i ) + GGDF ij,k P G,k γ P max ij () Equation (0) defines the power flow on line ij after the outage of line mn and () power flow on line ij after outage of generation unit P G,g. The factor γ is added in the equations, which allows higher emergency line flows then the steady state limit. With weighting matrix d generation constraints are formed: P G,g + d k,g P G,k δ P max G,g (2) where d k,g describes what fraction of power of generator k will be compensated by generator g. The total generating power of generator g must not exceed the emergency generation limit defined by additional available reserve in case of emergency δ and P max G,g. 5.3 Wind In-feed Modeling The wind in-feed modeling was modeled the same way as in [2]. There, it is proposed to the model in-feed as a sum of forecasted value and forecast error for each wind farm: P W,w = P forecast W,w + P error W,w (3)

14 5 DC POWER FLOW 3 The forecast error is represented as a Gaussian random variable with zero mean and standard deviation σ w, which depends on the total installed wind capacity at given bus. 5.4 Probabilistic OPF In probabilistic optimal power flow (popf) Gaussian uncertainty of wind in-feed is taken into account. This way a deterministic constraint is enforced with a certain probability. Introduced uncertainty constricts line and generation limits. Exact derivation of probabilistic constraints can be found in [2], here only finally obtained constraints will be given. The line constraint for the line flow under normal operation is given by: (Θ j Θ i ) Pij max Φ ( ɛ) X ij N W w= GGDF 2 ij,w σ2 W,w (4) where Φ is the inverse of normal distribution function, ɛ the constraint violation probability and σ the normal distribution of wind in-feed error. The same is applied to generation constraints: P G,g PG,g max Φ ( ɛ) N W d 2 g,wσw,w 2 (5) where d g,w gives the part of the wind farm outage power compensated by conventional generator and σ W,w the uncertainty. If probabilistic constraints given with equations (4) and (5) are compared with deterministic constraints (7) and (6) it can be seen that the introduction of uncertainty σ W,w and the violation probability ɛ leads to tighter constraints. w= 5.5 Probabilistic Security Constrained OPF Probabilistic security constrained optimal power flow (pscopf) combines chosen security criterion and the uncertainty due to wind in-feed error. Again only final constraint formulations will be given. Their exact derivation can be found in [2]. Line constraint for line ij after the outage of line mn is given as: (Θ j Θ i ) + LODF ij,mn (Θ n Θ m ) γ Pij max X ij X mn Φ ( ɛ) N W (GGDFij,w 2 + LODF ij,mn 2 GGDF ij,mn 2 )σ2 W,w (6) w=

15 5 DC POWER FLOW 4 When formulating line constraints considering generator outage, a distinction between outage of wind farm, which reduces the uncertainty and an outage of conventional generator must be made. For outage of conventional generator k the constraint is: (Θ j Θ i ) + GGDF ij,k P G,k γ Pij max X ij Φ ( ɛ) N W (GGDFij,w 2 + GGDF ij,k 2 d2 k )σ2 W,w (7) w= and for an outage of a wind farm v: (Θ j Θ i ) + GGDF ij,v P forecast W,v X ij γ Pij max Φ ( ɛ) N W w= GGDF 2 ij,w σ2 W,v (8) Combining equations (2) and (5) and distinguishing between wind farm and conventional generator outage, generation constraints are formed: P G,g + d k,g P G,k δ PG,g max Φ ( ɛ) N W (d 2 g,w + d 2 k,g d2 k,w )σ2 W,w (9) for an outage of a conventional generator k and for an outage of a wind farm v: P G,g + d v,g P forecast W,v δ PG,g max Φ ( ɛ) N W d 2 g,wσw,w 2 (20) It can again be seen that introducing uncertainty with probabilistic constraint decreases the line and generation limits in comparison to the deterministic constraints. w= 5.6 Including PSTs in OPF equations PSTs influence the line flow by changing the angle between both ends of the line. In DC power flow line flow equation, (9), the influence of PST is modeled as the additional angle α ij : w= P ij = X ij (Θ j Θ i + α ij ) (2) The PST angle α ij in this thesis is assumed to be continuous, which is not true in reality, where PSTs have discrete tap position changes.

16 5 DC POWER FLOW 5 There are two ways PST power flow control can be used in the network: Preventive control Corrective control 5.6. Preventive control Preventive control of power flow with the use of PSTs means that PSTs are employed to optimize the power flow in such way that the system integrity is maintained when an outage occurs. The possibility of changing the PST settings is not considered in this type of control. Because the basic power flow equation changed from (9) to (2) all subsequent line flow equations must be reformulated. Line limit is changed from (9) to (2). Security constrained power flow limits in case of line outage are changed from (0) to: X ij (Θ j Θ i + α ij ) + LODF ij,mn X mn (Θ n Θ m + α mn ) γ P max ij (22) In case there is no PST in line ij or mn the corresponding angle α is set to zero. For generator outage constraint () is formulated as: X ij (Θ j Θ i + α ij ) + GGDF ij,k P G,k γ P max ij (23) Probabilistic line constraint is reformulated from (4) to: (Θ j Θ i + α ij ) Pij max Φ ( ɛ) N W GGDFij,w 2 X σ2 W,w (24) ij Probabilistic security constrained OPF line flow constraints are reformulated to: (Θ j Θ i + α ij ) + LODF ij,mn (Θ n Θ m + α mn ) γ Pij max X ij X mn Φ ( ɛ) N W (GGDFij,w 2 + LODF ij,mn 2 GGDF ij,mn 2 )σ2 W,w (25) for line outage; w= (Θ j Θ i + α ij ) + GGDF ij,k P G,k γ Pij max X ij Φ ( ɛ) N W (GGDFij,w 2 + GGDF ij,k 2 d2 k )σ2 W,w (26) w= w=

17 5 DC POWER FLOW 6 for conventional generator k outage and for an outage of a wind farm v: (Θ j Θ i + α ij ) + GGDF ij,v P forecast W,v X ij γ Pij max Φ ( ɛ) N W w= GGDF 2 ij,w σ2 W,v (27) All constraints regarding generators remain unchanged. Additional constraint regarding phase shifter angles is added to the optimization problem formulation as: α min α ij α max (28) Corrective control Corrective control optimization assumes a change of PST angle can be made in case of line outage. After optimization one obtains PST angle (α) and changes of those angles in case of line outages ( α). This introduces more flexibility to control power flows in the system, which makes the integrity of the system is easier to maintain. Corrective control can only be considered for SCOPF and pscopf methods. Because of the simplicity, a situation with only one PST in the network is considered for corrective control. Corrective control is introduced with the help of linear sensitivity factors phase shifter distribution factors (PSDF). They indicate how power flow in lines is influenced by change of PST angle. The derivation of PSDFs is described in [6]. They depend only on system configuration and are calculated differently for line with PST and ones without: P SDF ij,ij = X ij ( + X ij (2C ij C ii C jj )) (29) P SDF ij,mn = X ij X mn (C mj C mi + C ni C nj ) (30) where X ij and X mn are the reactances of lines and C ij is the value in the X bus matrix at position ij. In reality first an outage of line occurs and then the PST setting are changed. But from mathematical point of view it does not make a difference whether the outage occurs or PST settings are changed first. This is due to use of linear sensitivity factors. To derive the corrective control constraints it is assumed that PST settings are changed first and then security criterion is applied, although in reality the PST settings are changed in response to the outage. If PST is positioned in line ij, line power flow for corrective control is formulated with the help of PSDFs as: P ij = P α 0 ij + P SDF ij,ij α ij (3)

18 5 DC POWER FLOW 7 where P ij is the power flow after application of corrective control, P α 0 ij is the power flow in the line obtained with equation (2) and the last term describes the change of power flow due to change of PST settings. In second step the security criterion is applied: P ij = P α 0 ij + P SDF ij,ij α ij + LODF mn,ij (P α 0 mn + P SDF ij,mn α) (32) Equation (32) can be rearranged to group α in one term: P ij = P α 0 ij + LODF mn,ij P α 0 mn+ (P SDF ij,ij α ij + LODF mn,ij P SDF ij,mn α) (33) In final step P α 0 ij is replaced with equation (2) and P α 0 mn with equation (9). Thus the final formulation of line constraint is obtained: X ij (Θ j Θ i + α ij ) + LODF ij,mn X mn (Θ n Θ m )+ (P SDF ij,mn + P SDF ij,mn LODF ij,mn ) α P max ij (34) The term (P SDF ij,mn + P SDF ij,mn LODF ij,mn ) α introduces additional flexibility of corrective control compared to preventive. The line power flow after outage can be corrected by changing the angle α ij for α. This way generation can be dispatched in a more efficient way.

19 6 CASE 8 6 Case 6. Evaluation Criteria To evaluate the influence of PST three cost types were compared [2]: total costs of generation (TCG) cost of security (CoS) cost of uncertainty (CoU) Total costs of generation represent the costs of dispatched generators. CoS is defined as difference in total costs of generation obtained by OPF and SCOPF methods. They indicate how much more it costs to dispatch the generation in such a way that N- security criterion is met. CoU is the difference between deterministic SCOPF and probabilistic SCOPF method. CoU give the additional costs which arise when dispatching generation under consideration of uncertainty. 6.2 Test System Abbildung 3: 0-bus test system [3] Analysis was carried out on the system described in [3]. The test systems consists of 0 buses and 4 lines and is shown in Figure 3. There is load

20 6 CASE 9 connected to all buses, except bus 8. Generators are connected to 5 buses and wind farms are connected to buses and 3. As a base case, analysis of costs without PSTs was made with all four optimal power flow methods. Line flow analysis is also given in [3]. Based on this analysis, lines in which PSTs could be used were chosen. It was decided to put PST in line (between buses 6 and 7), to achieve better utilization of line 2 (between buses 7 and 8). Another two PSTs were installed in line 7 (2-9) and (-3). With this arrangement one is able to control power flows through the majority of lines in the test system. PST were added to the system one by one, first in line, then in line 7 and finally in line. Each time system was analyzed with all four optimal power flow methods. 6.3 Wind In-feed Wind farms are connected to buses and 3. Their characteristics are given in Table 2. Bus PW installed [MW ] P forecast W [MW ] Tabelle 2: Wind farms characteristics Wind in-feed uncertainty was modeled as Gaussian distribution standard deviation from the forecasted value. Standard deviation of 7, 5% of the installed wind in-feed capacity was chosen. This is the same value as in [2] and is based on analysis made in [4].

21 7 RESULTS 20 7 Results 7. Total costs of generation Total costs of generation were one of the main criteria, because they indicate the price of electricity on the market. Obtained costs of generation are shown Abbildung 4: Total generation costs with respect to the number of PST in the grid in the graph in Figure 4, where plots of TCG for all four methods are made with respect to the number of PSTs in the network. As 00% the TCG value obtained by standard OPF analysis with no PSTs in the network was taken. All other costs were then normalized with this value. It can be seen that the TCG obtained by OPF and popf do not vary in dependence of the number of installed PSTs. This is because there is not any line in the system which is 00% loaded in the base case. If any line would be loaded to the limit, installing PST in a way it would help to decrease the load flow on that particular line, would decrease the TCG obtained by OPF as well. With more PSTs strategically installed in the network, the total generation costs obtained with SCOPF and pscopf are decreasing towards the TCG obtained with OPF. Based on this it, could be concluded that more installed PSTs also mean

22 7 RESULTS 2 lower TCG irrespective of their arrangement. It can be seen from Figure 4 that with each additional installed PST the decrease in TCG is lower. In this case a lot of consideration was made where to install PSTs to obtain the presented results. 7.2 Costs of Security Costs of security (CoS) are defined as difference between the total costs of generation obtained with SCOPF and OPF. The decrease of CoS is shown Abbildung 5: Costs of security with respect to the number of PST in the grid in Figure 5. CoS are normalized in the same way as TCG. As already seen from Figure 4, CoS decrease with more PSTs in the network. CoS analysis was also made with respect to the load. This way it was possible to determine long term effects of PSTs and how they help handle the increasing load. For each load level base case was OPF with no PSTs. All costs were later normalized to this costs. One can see from the Figure 6, that again CoS decrease with more PSTs in the network. There is also another profit. When the load is increasing above p.u. the test system without PSTs is not N- secure anymore. By adding PSTs in the netwrok, the N- criterion can be meet above the base load as well. This finding is very important, as

23 7 RESULTS 22 Abbildung 6: Costs of security with respect to the number of PST in the grid and load it shows, that installing a PST can have a comparable effect on security as constructing a new line. In the future, when the load will be increasing, this way the integrity of the network could be easier to maintain. 7.3 Costs of Uncertainty Costs of uncertainty (CoU) depend of the amount of wind in-feed, its uncertainty and the constraint violation probability. CoU are defined as difference between the probabilistic and deterministic SCOPF. CoU were analyzed with respect to the load as well. CoU with respect to the load are plotted in Figure 7. Again, for each load level the base case was OPF with no PSTs. Based on that graph no final conclusions can be made about the influence of PST as the obtained results are very scattered and have no distinct pattern. It can only be said, that PSTs have an influence on CoU. In Figure 8 costs of uncertainty with respect to the constraint violation probability is plotted for different number of PSTs. It can be seen, that with higher constraint violation probability the CoU decrease. CoU always decrease when one or more PSTs are installed compared to the base case.

24 7 RESULTS 23 Abbildung 7: Costs of uncertainty with respect to the number of PST in the grid 7.4 Corrective control It was predicted that with corrective control total costs of generation as well as costs of security can further be decreased. Only one PST was considered in this case and α was limited to 0%. In Figure 9 TCG for preventive and corrective control are compared. It can be seen, that in OPF case there is no difference. This goes to the same reason as in Section 7.. In SCOPF analysis the decrease of TCG was about 2%. This is because action can be taken in case of line outage. This enables cheaper dispatch of generation.

25 7 RESULTS 24 Abbildung 8: Costs of uncertainty with respect to the number of PST in the grid and constraint violation probability Abbildung 9: Comparison of total costs of generation for preventive and corrective control

26 8 CONCLUSIONS 25 8 Conclusions It was shown, that PSTs help reducing total costs of generation if properly positioned in the network. Their main contribution lies in reducing the costs of security, but it was seen that with more and more PSTs installed, the contribution of each additional PST to cost reduction becomes smaller. PSTs help reducing the costs of uncertainty. But in this case more PSTs does not mean further reductions of costs of uncertainty. The contribution of PSTs in this case largely depends on their position in the system. In addition PSTs enable grid operators to handle increasing load and fulfill the N- criterion easier. This is very important point for future network development, when grid would have to strengthened to still fulfill the security criteria. PSTs could be a good alternative to building new lines, at least from technological point of view. Ease of construction may as well be in favor of PSTs. Installing a PST can be much easier and faster from administrative point of view, as construction is conducted in small area and less permissions from landlords are required. 9 Future Outlook In this thesis effects of PSTs were investigated on a small test system to show the main relations. To some extent the conclusions made here may be applied to the real power grid. The thesis gives a firm starting point to analyze bigger systems, such as complete European Power Grid (ENTSO-E Grid). The data obtained from such analysis can later be used to coordinate the development of Power Grid to ensure it will fulfill the desired criteria. The PST effects regarding costs of uncertainty should further be investigated, especially in relation to load variation. The relation was not clearly found in this work but it is thought that there is a different cost saving potential for different loads in comparison to base case.

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