Simulation Process

In order to reduce computational requirements, power flow calculations are performed consecu-tively for independent parts of the network; the smallest being a ring, tree, or direct connection between a consumer and a substation, the largest being composed of multiple interconnected rings or trees spanning over multiple areas or even voltage levels. As a decomposition of a meshed network may go in hand with violating Kirchhoff’s circuit laws, a meshed network is always treated as one single independent part. The upper boundary for the size of an independent part is only limited by the available computational resources. On an average work station, several thousand buses and branches can typically be processed at once in a time frame of a few minutes. To optimally use existing resources, either the size of an independent part can be adapted or calculating power flows for the independent parts can be done in parallel. In the following description of the simulation process an independent part is assumed to be an area as introduced in Section 2.2.

Increase voltage / Simulate power flows for all branches, start with the lowest

voltage level specified in the input data flows assigned to all buses and power lines of the PNM Buses connected via

branches on all voltage levels of a PNM

Step 3

Voltage Level Combination Redefine PV buses of the current voltage level becoming

PQ buses of the next higher voltage level

Figure 2.3: Regular power flow simulation process for an entire PNM with multiple voltage levels.

The process, illustrated in Figure 2.3, starts at the lowest voltage level by simulating power flows on every branch as described in Section 2.3.2.1 (Step 1). The results are then validated according to the feasibility criteria introduced in Section 2.2.1 as explained in Section 2.3.2.2 (Step 2). The outputs generated for a single voltage layer are then taken as inputs for the next level as described in Section 2.3.2.3 (Step 3). Voltage levels may alternatively be combined without installing voltage regulating devices as described in Section 2.3.2.4. The outcome of the entire simulation process consists of active and reactive power values on both ends of each branch and the power losses in every branch. Additionally, the voltage for each bus is determined.

2.3.2.1 Step 1: Power Flow Simulation

The simulation is initialized by defining all consumers or substations acting as consumers to be PQ buses, all power stations or substations acting as producers to be PV buses, and one of

the PV buses as the slack bus. PQ buses are initialized by their active and reactive power demand, P_D,i and Q_D,i, respectively, PV buses by their active power supply P_S,i and their voltageVi = 1.0 pu, and the slack bus by its voltageVi = 1.0 pu according to Table 2.1.

The power flow simulation starts by determining the active and reactive power on both ends of each branchj and the voltageV_i at every busiusing the power flow model described in Section 2.3.1. The power difference between both ends of a branch is thus the active and reactive power loss,P_L,j andQ_L,j. Applying Kirchhoff’s current law, the power supply of each PV bus can be determined by the sum of power flows on all directly connected branches with outgoing power flows. The total active and reactive power the PV buses have to supply are then calculated as

Finding a feasible solution to the power flow problem is a necessary yet not sufficient condition for the validity of the power flows in the context of this simulation process. While a feasible solution guarantees adherence to Kirchoff’s laws, Conditions (2.1) to (2.3) have additionally to be met. If at any PQ bus the voltage violates Condition (2.2), the initial voltage at the PV buses is increased using a binary search until either the condition is met or the maximum threshold for the value is reached. In the latter case or if at any bus Condition (2.1) or at any branch Condition (2.3) cannot be held, this particular part of the network is considered overloaded. This overload may only happen when the power demand at any PQ bus is higher than the one used to originally plan the PNM. This can occur in the presence of additional loads which were not considered for the planning of the PNM. In Section 4.3, an example for this case can be found where the impact of PEV charging is investigated for a PNM which was initially not designed to accommodate PEVs. In a real-world setting, this overload would require load reducing measures by thepower system operator as, for instance, implemented through congestion pricing or more complex schemes such as demand response mechanisms.

As a primary target, the framework identifies times and locations of grid congestion and voltage drops. The simulation therefore assumes that an appropriate load reducing measure is taken in an overloaded part of the grid by decreasing the power demand at the PQ buses.

As a default setting which treats all consumers equally, the power demand for PQ buses is curtailed proportionally to their power demand compared to other PQ buses. Load curtailments are documented both temporally and spatially to allow analyzing them after conducting a power flow study. More sophisticated measures such as smart loads or distributed battery energy storage participating in demand response schemes or peak shaving may alternatively be implemented by the user.

2.3.2.3 Step 3: Voltage Level Combination

After calculating power flows in all branches within one voltage layer, the process continues at the next higher level. For this purpose, substations which on the lower voltage level are defined as PV buses are on the current level defined as PQ buses. The same substation therefore serves as a generator on a lower voltage level while it acts as a load on a higher level. PDand Q_D at each of these PQ buses are set to the values ofP_S andQ_S of its corresponding PV bus.

This shifting of power between the two windings of a substation is done upwards for all voltage levels. It is assumed that voltage regulators, such ason-load tap changers orseries regulators, are installed at each PV bus justifying initialization values ofVi= 1.0 pu for each voltage level.

In case the power demand of any substation acting as a consumer has been decreased due to a violation of any of the Conditions (2.1) to (2.3), the demand of all PQ buses directly or indirectly affected by this decrease also has to be curtailed. This process is illustrated in Figure 2.4. This example includes 2 PV buses and 9 PQ buses which are connected in a ring topology over two voltage levels. For the sake of simplicity, power losses are neglected in this example. In the regular upward simulation process shown in Figure 2.4a, the power supply of substations acting as producers is determined by the power demand of connected consumers (blue: 200 kW each, green: 10 kW each). In the example, this results in Substation A supplying 60 kW and Substation B supplying 660 kW. As the demand exceeds the maximum rating of 600 kW of Substation B, this setting is considered infeasible. This network is therefore simulated again by setting the supply of Substation B to its maximum rating of 600 kW.

The simulation proceeds downwards to determine the maximum possible power demand of the directly connected PQ buses as shown in Figure 2.4b. According to the description in Section 2.3.2.2 the demand of each blue colored consumer is reduced proportionally to its power demand compared to other PQ buses of the same independent part by around 9 % from 200 kW to 181.8 kW. At the same time the demand of Substation A is decreased by the same

Demand/

Figure 2.4: Result of (a) the regular upward simulation process determining each PV bus’ power supply and (b) its downward counterpart determining each PQ bus’ maximum power demand in case of a PV bus’ overload. The horizontal line divides the network into two different voltage levels.

percentage from 60 kW to 54.5 kW. As Substation A can now only consume 54.5 kW, all green consumers together are not allowed to consume more than this value. This requires curtailing the total power demand of each green colored PQ bus from 10 kW to 9.1 kW.

2.3.2.4 Alternative for Step 3: Voltage Level Combination without Regulating Devices When the installation of voltage regulators at each substation of the PNM is not possible or desired for whatever reason, the voltage level combination step described in the previous Section 2.3.2.3 has to be changed to an iterative process to produce valid results. The first step, the upward simulation, remains identical. Since the installation of regulating devices is omitted, the initialization of each PV bus’ voltage withV_i= 1.0 pu is only preliminary. The backward simulation process now becomes mandatory to determine the specific voltage at each bus for every voltage level. Additionally to the process described in Section 2.3.2.3,the voltage at each substation’s lower voltage winding is set to the voltage of its higher voltage part. This way, the voltage at each consumer is determined only by the voltage drops on the branches being directly or indirectly connected to a power plant without the interference of any regulating device artificially increasing the voltage. If at any consumer at any voltage level Constraint (2.2) is violated, the initialization value of the connected PV bus’ voltage is increased by either a fixed value, e.g., V = 0.01 pu, or the value can be determined by a binary search. With the increased voltage initialization value another iteration of the process is started until Constraint (2.2) is valid for all consumers.