Calculation of reactive power service charges under competition of electric power industries

Abstract

This paper proposes a reasonable methodology for computing the service charges for reactive power support and control in an open-access environment. The proposed method consists of two parts: one is to recover the capital costs of installed reactive power facilities, and the other is to recover the operational costs involved in reactive power production. The capital costs are divided into used and unused components, based on capacity usage, and are then recovered by a reactive-power tracing algorithm and a postage stamp rule, respectively. The operational costs are computed using spot prices with an optimal power flow program. Sample studies verify that the proposed method exhibits good results in practice compared with the real-time pricing method only. Moreover, the trend of reactive power charges with capacity variations of capacitor banks would help to determine the size of capacitor banks at the planning stage.

Appendix: Reactive-power tracing algorithm

The electricity tracing method presented in [16] can be applied to reactive power tracing. Reactive-power tracing starts from power flow solutions. Since the method assumes lossless lines, it requires additional fictitious line nodes. Then the balance equation of reactive power outflows at bus i can be expressed as

$$Q_i = \sum\limits_{j \in \Delta _i } {\left| {Q_{ij} } \right| + Qd_i } = \sum\limits_{j \in \Delta _i } {{{\left| {Q_{ij} } \right|} \over {Q_j }}Q_j + Qd_i } $$

(10)

Equation (10) can be rewritten in matrix form as follows

$$ Q_i - \sum\limits_{j \in \Delta _i } {{{\left| {Q_{ij} } \right|} \over {Q_j }}Q_j } = Qd_i \;{\rm or}\;A_d Q = Qd $$

(11)

where an i–j element of the matrix is represented as 1 for i=j, or

$$ - {{\left| {Q_{ji} } \right|} \mathord{\left/ {\vphantom {{\left| {Q_{ji} } \right|} {Q_j }}} \right. \kern-\nulldelimiterspace} {Q_j }}\;{\rm for}\;j \in \Delta _i $$

On multiplying the both sides of (11) by A _d ⁻¹, we get the following equation:

$$Q_i = \sum\limits_{k = 1}^n {\left[ {A_d ^{ - 1} } \right]_{ik} Qd_k } $$

(12)

Using the proportional sharing principle, the reactive power generation at a bus can be calculated as

$$Qg_i = {{Qg_i } \over {Q_i }}\sum\limits_{k = 1}^n {\left[ {A_d ^{ - 1} } \right]_{ik} Qd_k } = \sum\limits_{k = 1}^n {K_{ik} Qd_k } $$

(13)

Equation (13) shows the contribution of the kth reactive power demand to the ith generator and can be used to trace reactive power flows.