Teoria completa Electric Power Systems

Power Systems

Power systems need energy but also power. About the power we know that there is a constraint regarding the balance conditions. The total power produced has to be the total power required by the load.

This implies that, when we are on a generation pattern includes also the non programmable energy sources, we have a problem about this conditions, because the nonprogrammable renewable energy resources, photovoltic and wind power plants, are a controlled by a strong volatility. The output (the power produced by this unit) depends on the real time conditions of the weather (wind speed, sunny day).

Their power injected in the systems is not constant, more over is not possible to control the power injected, the consequence of this situation is that we have a strong variation of the power injected in the systems in the real time, that depends, of the penetration of this source on the systems.

Also possible to manage this situation? Generally the traditional units, have very flexible, that we can possible to control the output of the units to be used to manage this situations.

The traditional units change in the real time their output to compensate the variation of the power produced by the non-programmable energy sources.

One of the possible solution of this point regards the possibility to integrate the non-programmable renewable enr. source with the storage system.

The st. systems can be help the syst. to control the power injected of this npre in the systems.

Any variation of the power to produce, by the increase of the m power plant can be compensated by the possibility to contact the power injected or recovered by the storage system in the network, because this st syst. can be managed in real time to change the power produced or the power injected on the systems. This systems are able to change very fast, the not only the power, the value of the power, also the sign of the power.

TRANSMISSION NETWORK

In the electric pow. system we have different layers.

1. one layer is from generation systems
2. transmission

is controlled by extreme high value of voltage systems (400 kV - 230 kV); is meshed network and transformers are able to connect this EHV (132 ÷ 150 kV) to the HV systems.

The HV systems is connected to the MV systems.MV systems and LV systems → they formed the distribution network

The interconnection between this different voltage levels is obtained using the transformers.

TS and DS characteristics are very different in many point of view, in particular TS is meshed network...

They have a particular structure: for example, if we have this structure: [diagram]

because, if we have in operation the fault of this line, the load connected to the station of MILANO, the other stations, the load connected to the COLO station is anyway supplied.Without a generator or transformer.The number of the load supplied by each station is very high, and this load is given by the combination of the loads of many customers that are connected to distribution network at this station.

It is important to guarantee the continuity of the service because if one of this station is not supplied by the network, the number of the customers that are disconnected is very high.

About the DV the situation is different.The DV are typically radial systems.[diagram]

The radial systems not guarantee the continuity of the service in case we have a fault,

Function:

_Y = Y_Maxe^j(wt+₀)

in the analytical app.: (t) = Y_Max cos (wt + ₀) with the property that: (t) = Re{_Y}

We can try to use this (for this app.) of the sinusoidal funct. to study the elec. circui.

_Y = Y_Max e^j(wt+₀)

Y = Y_Max e^j₀ e^jwt

In the complex plane:

• Y_Max e^j₀
• In_w e^jωt
• |e^jωt| = 1

Phasor calculations

Y₁(t) = Y₁ ⋅ cos(wt + _0,1) = Re{_Y1}

Y₂(t) = Y₂ ⋅ cos(wt + _0,2) = Re{_Y2}

Sum:

Y₁(t) + Y₂(t) = Re{_Y1 + _Y2} = Re{_Y}(t)

Y = Y₁ ⋅ e^ϕ_0,1 + Y₂ ⋅ e^ϕ_0,2 ⋅ e^jwt

_Y = _Y e^ϕ_,0 e^jwt

Multiplication:

Y₁(t) Y₂(t) = Re{_Y1 ⋅ _Y2} = Re^{Y}

B ⋅ cos β₀ ⋅ Y₁(t) = Re^{B_⋅ e^β₀ ⋅ ₁} = Re^{Y_p}

_p = BY₁ e^β₀ e^jwt

_Yp = _Yp ⋅ e^ϕ_0,p e^jwt

R_T2 = k² R_T1

X_T2 = k² X_T1

R_LOAD,2 = k² R_LOAD,1

X_L2 = k² X_L1

_Z = Z_eqZ̅_T1 = Z̅_T2

A_ntntY

• k = V_m1/V_m2V_r1/V_r2
• R_T4 = R_T2 / Z̅_T2P_cuick V_n2² _AnV_r2² A_ntP_cuick A_r
• X̅_T = √(X̅_Z² + R̅²)

  For the shunt elements:

  • Y̅_t1 = I0_% V_r1² A_nt / 100 V_n1² A_r
  • Y̅_eq = 1 / (V_r1 A_r)

  PASSIVE NETWORK

  Any other active component is not included here, and the interaction between the passive network, the load and the generation units is modeled with an injection. In particular, in this system you can see:

  • 5 Buses, and you can see the other Branches that connect the Buses.

  This Branch can be used to model or a transformer or a line.

  In this Buses you can see it is represented the interconnection with external elements of your network.

  • Choosing a reference node, you can define the potential Ep of each Buses and Ip, the current injected in the node.

  The Ip current are named NODAL CURRENT; the current injected in your Buses, in your node, from the external component, and we assume that this current is positive if it is injected.

  • For example, in the Bus 5 we have a load. You compute the current Ps, Qs injected in the Bus 5 if in the bus there is a load, power Ps is negative, Ps < 0.

  The power go from the network to load. For the Qs, if a Qs < 0 (negative) the load requires REACTIVE POWER, it means that the load is an R-L.

  • If on the Bus we don't have any load or generation units, the current in the Buses is equal to zero Ip = 0.

  E5, E2, E1 represented the value of the voltage with respect to the ground are named NODAL VOLTAGE.

  When we have this graph:

  when we have 5 Buses and 7 Branches, the first step is define the number of each Buses. The same thing for the branch.

  You can define the Branch the goes from the Buses to the Buses. If oriented in this way, I free to choose the direction of each branch.

  This graph is called ORIENTED GRAPH.

  Now we can define different electrical quantity: for example, we can define a vector of the nodal voltage.

  The value of the voltages in each Buses

  This is the vector of the nodal current injected in each Bus.