Case study 4 – Bialek coefficients

This section presents a case study regarding the model proposed in section 3.5. It considers the simulation of a joint market with an AC OPF and a new methodology based on Bialek topological factors for solving of network constraints and congestion caused by all AS scheduling.

4.5.1. Outline

The case study is divided into two scenarios. One of the scenarios considers the join market simulation using an AC OPF for simulating the characteristics of the network.

G1

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114 October 2013

The second scenario is based on the previous scenario with the inclusion of the methodology developed using the method of Bialek topological factors. The scenarios presented in this chapter use a transmission network with 7 buses illustrated in Figure 4.9.

The characteristics related to resistance, inductance and thermal limit of each branch used in the network are presented in Table 4.18.

Table 4.18 – 7-buses features. network, where Qt is the quantity of power and Pe is the bid price.

Table 4.19 – Generators input data.

Resources Energy Regulation Down Regulation Up Spinning Reserve Non-Spinning

Reserve Maximum

Table 4.20 presents the energy and Ancillary services requirements for each load on the network. The requirements of ancillary services (Regulation Up, Spinning and Non-Spinning Reserve) for Loads 1 and 2 were set to 10 MW, in order to provide situations of opposites power flow caused by the dispatches of all services for increased generation.

Thus, it is possible to highlight the main advantages and disadvantages of the models used in each scenario of this case study.

Table 4.20 – Energy and AS requirements.

Loads Energy Regulation

Down Regulation Up Spinning

Reserve Non-Spinning

4.5.2. Results

4.5.2.1. Scenario 1 – Baseline case

This subsection shows the simulation results of the energy and ancillary services joint market using an AC OPF (baseline case).

Table 4.21 shows the results relating to each service dispatch obtained in the market. The solution proposed is only possible if all services are been dispatched at the same time.

In fact, the dispatch of all services has a hierarchy in which the energy service is the first to be dispatched. In this way, one must ensure that the dispatch of energy service is feasible. In the results presented, it seems that energy dispatch alone is not feasible. For the generator G2 was awarded a dispatch of about 149.70 MW; however, the branches which connect Bus 2 (where generator G2 is coupled) to other buses is limited to 50 MVA in each branch. The load coupled to Bus 2 has a consumption of 30 MW. In seems that there is congestion on the branches (149.70-50-50-30=19.70), making the energy dispatch infeasible.

Table 4.21 – Energy and AS dispatch in scenario 1 of joint market model considering Bialek coefficients.

Generator Energy Regulation

Down Regulation Up Spinning

Reserve Non-Spinning Reserve

Qt (MW) Qt (MW) Qt (MW) Qt (MW) Qt (MW)

1 41.05 27.7 0 0 0

2 149.70 0 0 0 0

3 86.25 0 42.82 38.89 38.89

In this way, the energy dispatch only becomes feasible when it is considered the power flow resulting from the energy, Regulation Up, Spinning and Non-Spinning dispatches. This happens because the Load related to Bus 2 has a considerable requirement for Regulation Up, Spinning and Non-Spinning services, and the requirements of these services are supplied by the generation unit G3. This implies that for each ancillary service the generation unit G3 causes a opposite power flow regarding the energy dispatch power flow, which decreases mathematically the power flow that flows in branches between Bus 2 and Bus 3. Moreover, with a simultaneous market simulation, the optimization process allows the combination of the services dispatch, so that the simultaneous dispatch of all services does not violate the thermal limits of the branches. However, when analyzing the dispatch independently, it seems that the energy dispatch is unfeasible.

In the context of independent analysis of the energy dispatch, Table 4.22 represents the power flow of energy service imposed on network. Thus, it is possible to verify that the particular energy dispatch is infeasible, since it violates the thermal limits of the branch 2-4 and the branch 2-7.

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116 October 2013

Table 4.22 – Power flow of energy service and joint market, in scenario 1 of joint market model considering Bialek coefficients.

Bus i Bus j Power flow for energy service Overall power flow Line Capacity (MVA) Active (MW) Apparent (MVA) Active (MW) Apparent (MVA)

1 5 21.05 22.42 -8.95 11.51 40

Therefore, one can conclude that the simultaneous dispatch of all services traded in the market may not be feasible in the power systems operation.

4.5.2.2. Scenario 2 – Base case with Bialek factors

The scenario described in this subsection considers the energy and ancillary services joint market simulation according to the methodology developed in section 3.5. Through this method it is possible to ensure the dispatch feasibility for each service, and the results presented in this subsection related to the desired simulation. The simulation is performed according to the hierarchical structure of the services considered in the market.

Table 4.23 shows the simulation results of the joint market which include the innovative methodology. The solution presented reports that each dispatch is feasible.

Through Table 4.23 it is possible to verify that the power flow of the energy dispatch obtained through the developed methodology follows the same direction of power flow from the energy dispatch shown in the previous scenario. However, it seems that through this new methodology, the joint or individual services dispatches are feasible.

Table 4.23 – Energy and AS dispatch in scenario 2 of joint market model considering Bialek coefficients.

Generator Energy Regulation

Down Regulation Up Spinning

Reserve Non-Spinning

In this scenario and following the reasoning of the previous observation, generator G2 was awarded a dispatch of 129.41 MW for energy service as it can be seen in Table 4.23. In this way, considering the characteristics of the network, the generator G2 does not cause congestion in the network. Generator G2 obtained an energy dispatch of 129.41 MW, about 30 MW of its generation was used to supply the load L2. This generator contributed approximately 49.81 MW for branch 2-4 with thermal limit of 50 MVA and also

approximately 49.60 MW for branch 2-7 with a thermal limit of 50 MVA. Thus, it is clear that the obtained dispatch for energy service is feasible. However, the feasibility of the presented solution is very close to the maximum limit allowed by the network features, as it can be seen in Table 4.24, which presents the values of the power flow resulting from the market simulation. Table 4.24 shows the power flow in network regarding the energy dispatch and to all services, simultaneously. In this way, it seems that in some branches of the network, the power flow has reached the maximum limit of the power allowed to flow on the branch. Branch 4-5 is exploited to its limits due to generator G1 allocated on Bus1, that is a generation unit cheaper for energy service compared to other generators, as well as the thermal limits of the branch that are more restricted than in other branches.

Table 4.24 – Power flow considering Bialek topological factors.

Bus i Bus j Power flow for energy service Overall power flow Line Capacity (MVA) Active (MW) Apparent (MVA) Active (MW) Apparent (MVA)

1 5 29.08 30.23 -0.91 3.14 40 developed methodology. The case study is divided into two distinct scenarios.

The first scenario describes a joint market simulation based on the use of an AC OPF, in which it is verified the infeasibility of the solutions presented by the method, due to all services considered in the power flow.

The second scenario presents the simulation results of the market based on the developed methodology which considers the use of an AC OPF and the Bialek topological factors, in order to ensure a feasible dispatch for each service on the market. In this way, the sequential dispatch of energy, Regulation Up, Spinning and Non-Spinning reserve are feasible regardless of the hierarchical structure of the services.

The main advantage of the method developed compared to the methodology in the first scenario is the guarantee of obtaining feasible solutions, regardless of the services considered in the market.

The main disadvantages are related to the execution time of the market clearing price process, for which in first scenario there is a execution time of around 3 seconds, while in the second scenario, the execution time of simulation is about 9 seconds. This

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disadvantage tends to prevail more when increasing the complexity of the problem, when considering more complex constraints in the market simulation.

Another disadvantage concerns to the operation costs. The first scenario has an operational cost of around 7626 (m.u.), while the second scenario involves operation costs of around 8014.75 (m.u.). This implies an increase of 5% in operation costs.

In networks with greater amount of resources, it is assumed that the market clearing price is considerably more preponderant, thus yielding different operation costs which are considerably significant to the ISO.