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This document starts with some background and general theory in the aim of giving the user more knowledge when solving load flow. But its chief purpose is to describe how various components are involved in load flow analysis. |
Technical Background
The power-flow problem is the computation of voltage magnitude and phase angle at each bus in a power system under balanced three-phase
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From the single-line diagram of a N-bus power system, an N*N admittance matrix Y can be constructed:
Diagonal elements Yii = sum of admittances connected to bus i;
Off-diagonal elements Yij = - (sum of admittances connected between buses i and j)
Using Y, we can write nodal equations for a power system network:
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I=Y*V |
where:
I: the N vector of source currents injected into each bus;
V: the N vector of bus voltages.
For any specific bus ‘i’, the complex power delivered to it will be:
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\overline{S_i}=P_i + jQ_i = \overline{V_i} \times \overline{I_i}^* |
where:
P: active power
Q: reactive power.
Since
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\overline{V_i}=V_i e^{j \theta_i } |
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\overline{V_j}=V_j e^{j \theta_j } |
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\overline{Y_{ij}}=Y_{ij}e^{j \alpha_{ij} } |
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\overline{S_i}=P_i + jQ_i = V_i e^{j \theta_i } \left[ \sum_{j=1}^{n} Y_{ij}V_j e^{j(\theta_j + \alpha_{ij}) } \right]^* |
where:
| bus voltage magnitude at bus i and j | |||||
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| bus voltage angle at bus i and j | |||||
| the value of the admittance between bus i and j | |||||
| the angle of the admittance between bus i and j |
In other words:
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P_i= \sum_{j=1}^{n} V_i V_j Y_{ij} cos(\theta_i - \theta_j - \alpha_{ij}) |
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Q_i= \sum_{j=1}^{n} V_i V_j Y_{ij} sin(\theta_i - \theta_j - \alpha_{ij}) |
For each node i,
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four variables
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need to be determined in these two equations:
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P_i, Q_i, V_i, \theta_i |
The user must define two variables as inputs for the other two to be solved
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.
The buses are categorized into three types, based on their nature:
PV | P&V are known (find Q and θ) | User needs to define P and V |
PQ | P&Q are known (find V and θ) | User needs to define P and Q |
Swing | There is only one swing bus allowed in the network and it should be a generation bus i.e. a generator, a voltage source. For a swing bus, V and θ are fixed, and P and Q are flexible. It provides a reference angle for all other buses in the network and balances the total real and the reactive power. | User needs to define V and θ |
Usually, generator buses are considered as the Swing bus or PV buses since real power and voltage magnitude levels are controlled to the fixed values. PQ type is also supported for generator buses if necessary.
Load buses are considered
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PQ buses (rated load capacity, fixed P and Q, dynamic voltage).
HYPERSIM load flow calculation is an iterative process based on the Newton-Raphson method. For more precise results, the user may adjust the "Tolerance" parameter. However, reducing tolerance will increase the number of iterations, and may not lead to a converging load flow solution within the maximum iterations.
The load flow calculation allows to initialize the system very close to the calculated operating point, But it is still possible that the system, when simulated, may go through small oscillations and stabilize around the closest stable operating point. This is because:
There are components which are not included in the load flow analysis.
Load flow calculation is performed considering a linear system, thus all non-linear components (saturable transformer, arrester, synchronous machine saturation) may affect the actual operating point.
Load flow calculation is performed at the base frequency with the positive sequence circuit values, any unbalanced load, untransposed line or coupled line may affect the actual operating point.
Configuration of Components
Components' Mask Load Flow Tab
When a component is supported in the load flow calculations, it has a load flow tab, and it often looks like the following:
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In the drop-down menu of Type, the user can select the bus type of the bus, as defined in the table above, where this component is selected.
Two out of the four variables (V, θ, Q, and P) must be specified according to the bus type.
The Q limits are used to define the range of values within which the actual value of Q is restricted. For these limits to be effective, the Use Qmin and Qmax limits
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options must be enabled in Load Flow.
Tips and Tricks for Various Components
Library Component | How Users Define Parameters | |||||
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Network Sources | When a network source has a load flow tab, users can define the parameters as described in 2.1. | |||||
Network Machines | All synchronous machines have a load flow tab. However, the Synchronous machine w/ fault doesn't support load flow function for now even if it has a Load Flow tab. All the synchronous machines except for the cross-compound feature the general Load Flow tab, where users can specify the parameters like the other components. They should be treated as Swing bus or PV bus since they are generators. | |||||
Synchronous machine (cross-compound) | The cross-compound thermal turbine generator has two generating units (primary and secondary), thus the Load Flow tab looks like the following: 
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Network Transformers | Transformers participate in the load flow analysis. Its winding impedance is used to calculate the system admittance matrix, and the winding voltage defines the bus voltage where the transformer is connected. | |||||
Network Lines and Cables | The positive sequence parameters of Constant parameter lines and PI section lines are taken into consideration in the load flow analysis. | |||||
Network Load | A dynamic load is always treated as a PQ bus with P0 active power and Q0 reactive power consumption. It is considered as a constant power load in the load flow analysis, even if np and nq can be configured to represent different types of load in the simulation. A harmonic load is identical to the dynamic load as far as the load flow analysis is concerned. The Arc Furnace is not considered in the load flow analysis. | |||||
Network RLC | The shunt and series R, L, C components contribute to the system admittance matrix. Note that when using Shunt R, L, C components to represent loads, the R, L and C parameters can be defined in the format of P and Q, however, it is a constant impedance in the load flow analysis. The components are not included in the Load summary, they can be found in Shunt impedance summary. The resistance value of the R nonlinear is calculated based on the nonlinear characteristic and the base voltage of the bus it is connected. The PQ load with Load-Flow is similar to the Dynamic Load, The difference is that in the load flow analysis, np and nq are effective. For example, if np = 2 and nq =2, the load is a constant-impedance load; if np = 0, nq = 0, it is a constant-power load. | |||||
Network Tools – Load Flow Equivalent | The load flow equivalent helps where components that are not supported by the load flow algorithm are used. When the PQ values are positive it represents a source. When the PQ values are negative, it represents a load. For example, when importing a model from Simulink or developing a network type UCM that can have an impact on the power flow solution, the user can add a load flow equivalent next to it to input the values to be considered by the load flow algorithm to determine the steady-state solution of the network. The load flow equivalent can also be used to represent an HVDC system as a constant load/source at the connection point to the AC system. The bus type can be PV or PQ depending on the control algorithm of the HVDC system. The DC system won't be initialized but the load flow result on the AC side is correct upon simulation start. The component is only effective in load flow analysis, it cannot be used to represent a part of the network in the simulation. For more details, please refer to Load Flow Equivalent. | |||||
Control Exciters | When Control Exciters are used with the synchronous machines, initial values of Ifd0 and Efd0 can be set automatically, based on load flow calculations, by entering a referenced synchronous machine variable. For instance, if the name of the synchronous machine to which the excitation system is connected is “SM1”, then Ifd0 and Efd0 shall be set respectively as “=SM1.IfdInit” and “=SM1.EfdInit”. The HYPERSIM® simulation option “Set Initial Conditions” must be checked for the automatic initialization to work properly. Please refer to Control Exciters for more details. | |||||
Control Governors | When Control Governors are used with the synchronous machines, the speed reference W0 can be set automatically, based on load flow calculations, by entering a referenced synchronous machine variable. For instance, if the name of the synchronous machine to which the governor/turbine is connected is SM1, then W0 shall be =SM1.wo. The HYPERSIM simulation option Set Initial Conditions must be checked for the automatic initialization to work properly. Please refer to Control Governors for more details. |
References
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