Exhibit 4.21

Summary of the Share Purchase Agreement between Transmissora Aliança de Energia Elétrica S.A., Abengoa Concessões Brasil Holding S.A., and Abengoa Participações Holding S.A.

On June 2, 2011, Transmissora Aliança de Energia Elétrica S.A. (“Taesa”) signed a Share Purchase Agreement (the “Newco Share Purchase Agreement”) with Abengoa Concessões Brasil Holding S.A. (“Abengoa Concessões”), to acquire control of 50% of the holding then owned by Abengoa Concessões in:

STE — Sul Transmissora de Energia S.A. (“STE”),

ATE Transmissora de Energia S.A. (“ATE”),

ATE II Transmissora de Energia S.A. (“ATE II”), and

ATE III Transmissora de Energia S.A. (“ATE III”)

— when referred to jointly, the “Subsidiaries”.

For the acquisition to be concluded, Abengoa Concessões transferred 100% of the shares it held in the subsidiaries to Abengoa Participações Holding S.A. (“Abengoa Participações”), less one share in each of the Subsidiaries, to be held by Abengoa Concessões, and one share in each of the Subsidiaries to be transferred by Abengoa Concessões to Taesa at completion of the transaction. Taesa will then acquire 50% of the shares of Abengoa Participações, less two shares which will be held by Abengoa Concessões and Taesa, respectively. On the closing date of the transaction, Abengoa Concessões will transfer to Taesa one share in each Subsidiary.

The acquisition price is R$ 763.15 million, for the 50% equity holding in the Subsidiaries.

The acquisition price will be adjusted by the variation in the Selic rate (the rate calculated by the Special Settlement and Custody System — Sistema Especial de Liquidação e Custódia, or Selic) for December 30, 2010, up to the business day immediately prior to the closing date of the transaction, and reduced, as applicable, by 50% of any dividends or Interest on Equity paid by the Subsidiaries during this period. The acquisition price will also be updated in accordance with any increase or reduction of capital during that period.

In the event of the Newco Share Purchase Agreement being rescinded, the infringing party will be subject to a penalty equivalent to 10% of the acquisition price.

The Newco Share Purchase Agreement contains warranties, guarantees and obligations by Taesa and Abengoa Concessões. The closing of the transaction is subject to certain conditions, which include:

·transfer to Abengoa Concessões of all the shares in ATE and ATE III that are currently held by Compañía Española de Financiación del Desarollo (Cofides);

·transfer of all the shares held by Abengoa Concessões in the Subsidiaries to Abengoa Participações;

·approval by the competent bodies, including the National Electricity Agency (Agência Nacional de Energia Elétrica, or Aneel);

·and any consents from financing banks of the Subsidiaries, when necessary.

The acquisition will also be subject for approval by Economic Defense Administrative Council (Conselho Administrativo de Defesa Econômica, or Cade), within the period and in the manner specified in the relevant legislation.